Condition Monitoring and Fault Prediction in PMSM Drives Using Machine Learning for Elevator Applications

Abstract

Elevators are a vital part of urban infrastructure, playing a key role in smart cities where increasing population density has driven the rise in taller buildings. As an essential means of vertical transportation, elevators have become an integral part of daily life, making their design, construction, and maintenance crucial to ensuring safety and compliance with evolving industry standards. The safety of elevator systems depends on the continuous monitoring and fault-free operation of Permanent Magnet Synchronous Motor (PMSM) drives, which are critical to their performance. Furthermore, the fault-free operation of PMSM drives reduces operating costs, increases service life, and improves reliability. The PMSM drive components may be susceptible to electrical, mechanical, and thermal faults that, if undetected, can lead to operational disruptions or safety risks. The integration of artificial intelligence and Internet of Things (IoT) technologies can enhance fault prediction, reducing downtime and improving efficiency. Ongoing challenges such as managing machine thermal load and developing more durable materials for PMSMs require the development of suitable models that are adapted to existing drive systems. The proposed framework for fault prediction is validated on a real residential elevator equipped with a PMSM drive. Multimodal signal data is processed through a Generative Adversarial Network (GAN)-enhanced Positive Unlabeled (PU) classifier and a Reinforcement Learning (RL)-based adaptive decision engine, enabling robust and scalable fault prediction in a non-intrusive fashion.

1. Introduction

As urban populations continue to grow, cities are increasingly expanding vertically, with high-rise buildings becoming a defining feature of modern urban landscapes. Elevators play a critical role in supporting this urbanization by enabling efficient vertical transportation. From residential and commercial complexes to industrial applications, elevators are an integral part of modern life [1]. Their reliability and efficiency directly affect the quality of life, productivity, and safety of urban populations. Consequently, the design, construction, and maintenance of elevators are areas of significant technological focus, particularly given the need to meet rigorous safety standards and ensure operational efficiency [2].

At the heart of most elevator systems are Permanent Magnet Synchronous Motors (PMSMs), which are favored for their energy efficiency, compact size, high power density, and precise torque control. Combined with sophisticated drives and control systems, PMSMs ensure smooth, safe, and efficient elevator operation [3]. However, like any complex electromechanical system, PMSMs and their associated drives are prone to faults, including electrical failures (e.g., winding faults, short circuits), mechanical issues (e.g., bearing wear, rotor misalignment), and thermal problems (e.g., overheating due to continuous operation). If not addressed promptly, these faults can lead to operational disruptions, costly downtime, and, in extreme cases, safety hazards for passengers [4].

Traditional maintenance strategies, such as scheduled inspections or reactive repairs, are often inadequate for the demands of modern elevator systems. These approaches are either inefficient, as they rely on fixed intervals rather than actual system conditions, or costly, as they address faults only after failures occur [5]. Predictive maintenance has emerged as a superior alternative, leveraging condition monitoring to assess the health of elevator systems in real-time and to predict potential failures before they occur. Central to this paradigm is the continuous monitoring of PMSM drives using data collected from smart sensors, which measure electrical, mechanical, and thermal parameters [6].

Despite its advantages, predictive maintenance presents significant technical challenges. The complexity of PMSM drives, coupled with the high-dimensional and noisy nature of sensor data, requires sophisticated techniques for data processing, fault diagnosis, and failure prediction [7]. Traditional analytical methods, while useful, often fail to capture the complex, nonlinear relationships in the data. This has led to the increasing adoption of machine learning (ML) techniques, which can uncover hidden patterns in large datasets and improve the accuracy of fault detection and prediction [8].

Machine learning techniques have shown considerable promise in predictive maintenance applications. Supervised learning models, such as Support Vector Machines (SVM), Random Forests, and Neural Networks, are commonly used for classifying operational states or predicting faults based on labeled data. However, these methods often require large amounts of labeled fault data, which can be challenging to obtain in real-world elevator systems due to the rarity of certain faults [9,10]. To overcome this limitation, unsupervised learning and hybrid methods, such as Positive Unlabeled (PU) learning, have been explored. PU learning, in particular, is advantageous for leveraging unlabeled operational data alongside a small subset of labeled fault cases, enabling robust fault detection even in data-scarce environments [11].

The success of machine learning models in predictive maintenance depends heavily on the quality of the data input. Raw sensor data is often noisy, high-dimensional, and contains irrelevant or redundant information [12]. To address these issues, several preprocessing steps are employed. Sensor readings, such as voltage, current, vibration, and temperature, often have varying ranges and units. Normalization ensures that all features are scaled to a consistent range, typically [0, 1] or [−1, 1], to improve model performance and convergence. Noisy data can obscure meaningful patterns, making accurate fault detection difficult [13]. Advanced filtering techniques, such as the Kalman Filter, Gaussian Filter, and Low-pass Filters, are used to reduce noise while preserving important signal characteristics [14,15].

Kalman Filter is effective for dynamic systems, and it provides an optimal estimate of the system state by combining noisy measurements and prior knowledge. Gaussian Filter smooths the data by averaging values within a Gaussian window, reducing high-frequency noise [16]. Time domain features extract basic statistical metrics, such as mean, standard deviation, skewness, and kurtosis, to capture signal properties. Frequency domain features use Fourier Transform or Wavelet Transform to analyze signal frequencies, identifying harmonics or transient anomalies. Time–frequency features combine time and frequency analysis, using techniques like the Short-Time Fourier Transform (STFT) or Wavelet Packet Transform (CWT), to capture transient fault characteristics [17].

This study introduces a machine learning-based framework for condition monitoring and fault prediction in PMSM drives, tailored specifically to elevator systems. By leveraging advanced signal processing and feature engineering, the framework addresses the challenges of noisy data and complex fault patterns. The methodology includes intelligent smart sensor integration with real-time electrical, mechanical, and thermal data collection. Data preprocessing using normalization and filtering techniques enhances signal quality and extracts characteristic averages from raw sensor data, improving fault detection accuracy. The development of positive label-free (PU) learning models and other advanced AI algorithms for classifying operational states and predicting potential faults has been shown to enhance the reliability and safety of elevator systems. This underscores the transformative role of machine learning in predictive maintenance.

The main objective of this paper is to utilize the data collected using sensors and integrate it into appropriate machine learning models to investigate the probability of faults and to avoid critical errors through continuous monitoring of the PMSM state. Section 2 provides a literature review of the key elements of elevator systems, common PMSM failures, and existing machine learning techniques in predictive maintenance. Section 3 describes the proposed methodology framework, including data acquisition, preprocessing, feature extraction, and machine learning models. Section 4 presents the experimental results by evaluating the framework through simulations and experimental setups and highlighting its effectiveness in fault detection and prediction. Similarly, Section 5 analyzes the results, discusses the limitations of the proposed methodology, and explores potential applications. Finally, Section 6 summarizes the strong points of the proposed methodology and suggests directions for further research. This structured approach aims to provide a comprehensive exploration of machine learning techniques for condition monitoring and fault prediction in PMSM drives, with a focus on enhancing the safety, efficiency, and reliability of elevator systems.

2. Advanced Techniques in Elevator Systems

Elevators play a central role in the vertical movement of passengers and loads in any building, operating as complex electromechanical systems. Their subsystems are divided into electrical, mechanical, and safety devices [18]. Using wireless networks, data can be collected, processed, and transmitted to the cloud. The introduction of automation systems contributes to safety in such drive systems by achieving the timely and efficient diagnosis of various types of faults [19]. The integration of machine learning techniques with elevator systems enables fault prediction and condition monitoring at unprecedented levels of accuracy. Among these techniques, Positive Unlabeled (PU) learning and Reinforcement Learning (RL) stand out for their potential to address challenges such as data scarcity and dynamic operational conditions. The subsequent sections provide an in-depth discussion of their applications, advantages, and challenges in predictive maintenance for elevator systems.

2.1. Fault Diagnosis and Condition Monitoring in PMSMs

The continuous use of elevators causes significant stress on PMSMs, causing damage to electrical, mechanical, and magnetic parts of the motor. For high-voltage cases, the highest percentage of faults (66%) is found in stator windings, while for the low-voltage level cases (48 V to 380 V), the highest percentage of faults (41%) is due to bearing failures [20]. To address such faults, it is necessary to maintain the equipment at regular intervals. Reactive maintenance, also known as breakdown maintenance, involves repairs carried out after equipment failure [21].

The development of the Internet of Things (IoT) has contributed to predictive maintenance as the integration of a new generation of smart sensors—in both the motor and the lift system—helps to collect large amounts of data in real time [22]. The integration of IoT-based elevator emergency notification systems via smart-phone-enabled technicians and maintenance companies to monitor elevator status in real time provides alerts in case of emergency [23].

Similar techniques have been applied with suitable efficient data reduction algorithms adapted to Industrial Internet of Things (IIoT) nodes for bearing fault diagnosis in PMSMs, where data is filtered and compressed [24]. Sensor specifications play a critical role for accurate data collection. A major problem identified is that the collected data may be very noisy due to external interference. Stochastic models have been proposed to address the noise problem, utilizing wavelets and thresholding techniques to extract reliable features; however, these techniques significantly increase the complexity [25].

The accuracy of the measurements is determined by the specifications of the sensors meeting international standards such as ISO 20816-1 [26]. The most typical analysis and fault detection techniques for monitoring the operational status of the PMSMs are focused on vibration, power, thermal analysis, stator windings with current analysis, torque, and speed measurements [27]. Recent research has highlighted the importance of using multimodal data for elevators by measuring vibration, sound intensity, and thermal imaging. The use of these methods provides a comprehensive understanding of the technical condition of the device [28].

Several research efforts have focused on the application and development of methods to diagnose errors. Initially, as far as electrical faults are concerned, the most typical faults are located in the stator windings (open circuit and short circuit) [29]. To detect internal stator coil faults in the stator at early stages, an improved method based on advanced signal processing was proposed, which relied on the Motor Current Signal Analysis (MCSA) with the transformation technique to obtain frequency–time information with improved resolution [30].

A high accuracy and time efficiency in predicting electrical problems was observed by Zhang et al. The study focused on three states of current by identifying changes in the deviations between predicted and measured currents, finding the fault phase and concluding with the diagnosis of the fault type [31]. In addition to utilizing the current signal, the noise signal was also leveraged [32].

An open circuit diagnostic method based on a mixed-logic dynamics model was applied to multiphase PMSMs. This methodology was found to be highly reliable for both single and multiple open circuit faults, achieving a reduced time of 60% of the current cycle [33]. The most typical cause of electrical failures is due to insulation faults. These faults can be divided into three types: internal turn short circuit (ITSC), phase-to-phase short circuit, and earth short circuit [34].

The most common method of diagnosing such faults is frequency domain signal analysis. The main advantages that make it the most widely used technique are related to its low computational cost and the real-time condition monitoring capability of the machine [35]. One of the main disadvantages of frequency domain signal processing is that it assumes signal stationarity, which can limit its effectiveness in modern electric motor drive systems, where signals often exhibit non-stationary behavior [36].

Other similar methodologies examined such as Short-Time Fourier Transform (STFT), Undecimated Discrete Wavelet Transform (UDWT), Wigner–Ville Distribution (WVD), and Choi–Williams Distribution (CWD) have demonstrated the accuracy and effectiveness of the UDWT method in diagnosing faults occurring during transient operating conditions [37].

The highest percentage of failures is found in PMSMs, with 40–50% accounting for mechanical problems, the lifetime of the mechanical equipment, improper maintenance, poor lubrication, or incorrect design and assembly. These faults mainly include bearing faults, camshaft misalignment, imbalance, and demagnetization [38]. Bearing wear can cause cam problems, increased frictional losses, and high noise creating magnetic flux inside the motor, which is a major cause of stator winding insulation failure [39].

To identify eccentricity failures, the harmonics of the stator current are analyzed, and the indices of standard deviation, kurtosis, skewness, peak factor, purity, and shape factor are extracted [40]. Time domain methods use statistical data compared to specific fault samples in already damaged bearings to draw conclusions about wear localization. However, fault diagnosis is impossible under low load conditions [41,42].

The most widespread technique allowing fault detection in dynamic drive situations involves the application of the zoom Fast Fourier Transform (FFT). The main signal considered in this case is the mechanical vibration and is distinguished by its high performance in accurately diagnosing the condition of bearings and detecting faults. The damage indicator is the characteristic harmonic frequencies that occur depending on the specific mechanical damage and operating speed [43,44].

Other methodologies in the frequency domain based on noise and vibration signal analysis, cepstrum analysis, and extended vector park analysis (EPVA) were proposed. A large number of symptoms for bearing failure can be effectively detected by scattering flux analysis by fitting additional sensors, but at the same time, it can be applied to the motor with magnetic asymmetry [45].

By analyzing the motor rotation speed signal, the detection of damaged bearings is achieved even in low rotation speed conditions, which is its advantage compared to the spectral kurtosis of the speed signal and the three current-based methods [46]. The largest percentage (about 80%) of mechanical faults are due to eccentricity. Thus, there is non-uniformity in the distribution of the air gap between the stator and rotor and which is divided into three categories: static, dynamic, and mixed [47].

2.2. Preprocessing Signals and Deep Learning Methodologies

Advances in elevator technology have led to the widespread adoption of Permanent Magnet Synchronous Motors (PMSMs), which are favored for their high power density, superior efficiency, and precise torque control. Unlike traditional induction motors, PMSMs offer reduced energy consumption and smoother operation, making them the preferred choice in modern elevator systems [48].

Recent developments in power electronics, such as vector control and direct torque control, have further optimized PMSM performance, improving responsiveness and operational safety [49]. However, the increased complexity of these systems has also introduced new challenges in maintenance, particularly in detecting and diagnosing faults that could compromise safety and functionality. Electrical faults, mechanical failures, and thermal issues are the primary concerns that necessitate the development of advanced diagnostic and monitoring systems [50].

Research has highlighted the critical role of predictive maintenance in addressing these challenges. PMSMs offer significant energy savings compared to traditional induction motors, particularly in high-rise applications, due to their superior torque characteristics and compact design [51,52]. Similarly, advancements in control mechanisms, such as direct torque control, have enhanced the fault tolerance of PMSMs in dynamic elevator systems [53].

Additionally, other studies in sustainability further emphasize the importance of PMSMs in elevator systems for improved performance [38] and discuss high-order sliding mode magnetometers for detecting excitation faults in elevator traction motors, highlighting their contribution to improving fault detection accuracy. The lifecycle benefits of PMSMs report that these motors reduce operational costs by up to 20% over a 15-year period [48].

Wang et al. also emphasize the importance of multi-sensor integration in PMSM applications, enabling enhanced diagnostics and greater reliability [54]. The reliability and safety of elevator systems depend on effective fault diagnosis and condition monitoring. Fault diagnosis involves identifying and classifying issues in real-time, whereas condition monitoring focuses on tracking the health of components over time to predict potential failures. PMSM drives, being critical components of elevator systems, are prone to faults that can disrupt operations and compromise safety. These faults can be broadly categorized into electrical, mechanical, and thermal issues.

Electrical faults, such as stator winding short circuits, rotor demagnetization, and power electronics failures, are among the most common issues. Mechanical faults (including bearing wear, rotor misalignment, and excessive vibrations) are equally significant, often leading to operational inefficiencies. Thermal faults, resulting from inadequate cooling or prolonged operation, can exacerbate these problems by accelerating component degradation.

Various diagnostic and monitoring techniques have been developed to address these challenges. Vibration analysis, for instance, utilizes sensors to detect anomalies in mechanical components by analyzing vibration patterns. Thermal imaging [55] provides a non-invasive method to identify overheating in electrical and mechanical parts, while electrical signal monitoring analyzes current and voltage waveforms to detect abnormalities [56,57]. These methods rely on data collected from smart sensors, such as accelerometers, infrared cameras, and current sensors, which provides the real-time information necessary for effective monitoring and diagnostics [58].

Recent studies have explored how these techniques complement each other in enhancing system reliability. For instance, vibration analysis has proven highly effective for mechanical fault detection but may not capture the subtleties of thermal or electrical issues. Combining it with thermal imaging and electrical signal monitoring allows for a more comprehensive diagnostic approach, as evidenced by research from Wang et al., which highlighted the synergistic benefits of multi-sensor data fusion in elevator fault diagnosis [54].

Condition monitoring, beyond fault detection, encompasses the continuous assessment of system performance under varying operational conditions. Advanced methods integrate historical data with real-time measurements to predict trends and flag deviations from normal behavior. This approach enables proactive interventions, reducing unplanned downtime and improving safety. A notable review article discusses the challenges faced in predictive maintenance (PdM), particularly focusing on the complexities of implementing PdM systems. It examines the difficulties in data collection, analysis, and integration, and highlights the challenges related to sensor limitations, data quality, and the scalability of predictive models. It also emphasizes the need for advanced technologies, such as machine learning and artificial intelligence, to address these challenges and improve the reliability and efficiency of PdM systems. Key obstacles include the management of large datasets, the adaptation of models to different environments, and the interpretation of results in real-time operations [59].

Data collected from sensors in elevator systems is often noisy and requires preprocessing to extract meaningful insights. Effective data processing involves filtering, normalization, and feature extraction, each of which plays a critical role in enhancing the quality and usability of sensor data [60,61].

The Kalman Filter is a widely used technique for dynamic state estimation, particularly in noisy environments [62,63]. By combining measurements and prior knowledge, it provides optimal estimates of system states, making it highly effective for real-time applications. However, its reliance on accurate system modeling and its computational intensity can limit its effectiveness in certain scenarios. In contrast, the Gaussian Filter offers a simpler approach to noise reduction by averaging values within a Gaussian window, making it suitable for steady-state conditions. While efficient for reducing high-frequency noise, it may blur sharp transitions, limiting its effectiveness in dynamic environments. Low-pass Filters, which remove high-frequency components, are commonly used in vibration and current signal analysis. Though straightforward and effective, they can distort important signal details in high-frequency ranges, posing challenges in applications requiring high-resolution data [64]. Adaptive filtering methods have further enhanced the utility of these techniques [65]. For example, the application of Extended Kalman Filters (EKFs) in real-time systems accounts for nonlinearities, which is a significant advantage in dynamic elevator environments [66]. Kim et al. introduce a fault diagnosis algorithm for Permanent Magnet Synchronous Motors (PMSMs) to identify stator open-phase and inter-turn short circuit faults. The methodology integrates an EKF for phase current estimation and a Multiple Model (MM) filter for fault classification [14].

Normalization is another crucial preprocessing step, ensuring the consistent scaling of sensor data to improve the performance of machine learning models. Methods such as Min–Max Scaling and Z-Score Normalization standardize data ranges and distributions, reducing variability that could negatively impact model training and inference. Feature extraction, on the other hand, transforms raw sensor data into meaningful representations that capture relevant patterns. Time domain features, such as the Root Mean Square (RMS) value, skewness, and kurtosis, provide basic statistical insights, while frequency domain features derived from Fourier Transform reveal harmonics and spectral energy indicative of faults. Time-frequency features, obtained through Wavelet Transform, combine temporal and spectral analysis to detect transient anomalies, offering a comprehensive view of system behavior [13,15,25].

Recent advances in signal processing have further improved fault detection capabilities. Multi-resolution analysis techniques, such as Empirical Mode Decomposition (EMD), have shown promise in decomposing complex signals into simpler components, facilitating the identification of subtle fault signatures [67,68]. Similarly, adaptive filtering techniques have enabled dynamic noise reduction, tailoring the filtering process to varying operational conditions.

Machine learning (ML) has emerged as a transformative approach in predictive maintenance, enabling automated fault detection and prediction. By analyzing large volumes of sensor data, ML techniques can identify patterns indicative of faults, even in their early stages. These techniques can be broadly categorized into supervised learning, unsupervised learning, and hybrid approaches.

Supervised learning methods, such as Support Vector Machines (SVMs) and Neural Networks (NNs), rely on labeled datasets to classify faults. These models are highly accurate and capable of handling complex patterns, but their dependence on extensive labeled data can be a limitation in real-world applications. Pietrzak et al. [69] focus on detecting and classifying inter-turn short circuits in PMSMs using a spectral analysis of stator phase current signals for feature extraction and SVMs for fault classification in PMSM drives, achieving high accuracy with limited feature sets. Additionally, Dou et al. [70] explore the application of SVMs in fault diagnosis for key elevator structures. By modeling elevator faults and employing SVMs for fault detection, separation, classification, and evaluation, the research aims to enhance maintenance strategies. The approach ensures the accurate and timely identification of faults, reducing maintenance costs and improving the reliability of elevator operations. Similarly, Mishra et al. [25,71] highlighted the effectiveness of deep Neural Networks (DNNs) in capturing intricate fault patterns.

Unsupervised learning techniques, such as clustering and anomaly detection, are particularly valuable when labeled data is scarce. Clustering algorithms, including K-means, Hierarchical Clustering, Density-Based Spatial Clustering of Applications with Noise (DBSCAN), Gaussian Mixture Models (GMMs), and Self-Organizing Maps (SOMs), are used to group data points based on their similarities or distances [72]. Unlike supervised learning, which relies on labeled data to train models, clustering methods do not require labels and instead identify natural groupings within the data using distance metrics like Euclidean distance or cosine similarity. These techniques analyze patterns in the data to group similar instances together and detect deviations from normal operating conditions without the need for predefined fault labels [73]. Chen et al. [74] present a fault diagnosis approach for elevators based on artificial intelligence techniques. The study explores various methods, particularly machine learning and artificial Neural Networks, and employs clustering algorithms to detect anomalies in elevator system performance, highlighting the potential of unsupervised approaches in real-time applications.

Hybrid methods, such as Positive Unlabeled (PU) learning, are particularly effective in scenarios where labeled fault data is scarce but large amounts of unlabeled operational data are available. This approach relies on identifying reliable negative samples within the unlabeled dataset, leveraging both labeled and unlabeled data to train classifiers. Park et al. [75] explored the use of PU learning for high-dimensional data, proposing methods to address challenges in such datasets effectively.

Deep learning models, particularly Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs), have shown significant potential in fault prediction. CNNs excel in feature extraction from high-dimensional sensor data, while RNNs are well-suited for capturing temporal dependencies in sequential data. Recent studies have demonstrated the integration of these models in hybrid architectures, enhancing their ability to handle diverse fault scenarios and operational conditions.

The integration of Reinforcement Learning (RL) into predictive maintenance offers a novel approach for optimizing maintenance strategies in real time. RL improves decision-making by learning from interactions with the environment, dynamically adjusting processes based on feedback. Through a balance of exploration and exploitation, RL agents adapt to changing operational conditions, minimizing unplanned downtime and enhancing system reliability. In elevator systems, RL algorithms can adjust maintenance schedules dynamically, utilizing real-time sensor data to ensure efficient resource allocation and proactive fault prevention. These models continuously refine their decision-making to optimize maintenance schedules based on ongoing performance feedback. Dogru et al., in their review paper [76], provide an overarching view of RL techniques in process industries, covering applications such as sensors, control, fault detection, and optimization, highlighting its potential in complex systems, where operational conditions fluctuate frequently, demanding adaptive fault prediction models.

Recent research presents a fault diagnosis model integrating Principal Component Analysis (PCA) and Long Short-Term Memory (LSTM) Neural Networks [77]. Using operational data from elevators, the model improves fault prediction accuracy by identifying patterns and trends associated with different failure types. Another study proposes a deep learning model that combines a Graph Neural Network (GNN) for structural relationships with LSTM for time-series analysis and a Bayesian Deep Adversarial Neural Network (BDANN) for robust faults prediction in elevator door systems by analyzing acoustic signals generated during operation [78]. The deep learning model enhances the ability to deal with the complex and variable nature of elevator operations and considers environmental changes and signal acquisition methods, improving fault prediction accuracy. In [79] the authors propose a risk evaluation method for elevator operation based on fuzzy logic theory and machine learning algorithms. By using sensor data and evaluation indices, the model enhances accuracy and efficiency in risk assessments compared to traditional approaches. In [80] the study also proposes a generic Multi-Layer Perceptron (MLP) Neural Network model for fault detection in elevator systems. The model demonstrates robust classification capabilities and resistance to overfitting, aiding predictive maintenance systems in reducing false alarms and unnecessary service visits. The proposed model achieved nearly 100% accuracy in fault detection, effectively minimizing false positives and enhancing predictive maintenance strategies.

Despite their advantages, ML techniques face challenges, including high computational requirements, difficulties in generalizing models across different systems, and the need for real-time processing capabilities. Addressing these issues requires further research and the development of scalable, efficient solutions. Federated learning has emerged as a promising approach to address data privacy concerns and enhance model generalization by training ML models across decentralized datasets without sharing sensitive data. Ahn et al. [81] provide a comprehensive survey on federated learning frameworks for IoT-based smart city applications, addressing challenges like latency and data privacy in predictive maintenance systems.

While significant progress has been made in fault diagnosis and predictive maintenance for elevator systems, several gaps remain. The lack of comprehensive datasets for training robust ML models is a critical barrier, limiting the applicability of advanced techniques in diverse operational contexts. Integration challenges with legacy elevator systems further complicate the deployment of modern predictive maintenance solutions. Additionally, real-time processing constraints pose difficulties in scaling these approaches for large-scale systems. Reference [82] reviews recent advances in artificial intelligence, focusing on machine learning interpretability methods that have led to widespread industrial adoption. The study focuses on machine learning interpretability methods and a literature review and taxonomy of these methods are presented, as well as links to their programming implementations.

Future trends in this domain include the integration of IoT technologies for enhanced connectivity and real-time data acquisition. Edge computing offers a promising solution to reduce latency and reliance on cloud infrastructure, enabling localized data processing for faster and more efficient fault detection. Explainable AI (XAI) is another emerging trend, providing transparency and interpretability in ML models to improve trust and adoption in safety-critical systems. The survey in [83] structures and analyzes challenges, techniques, and methods for developing AI-based safety-critical systems, focusing on industrial and transportation domains.

To conclude, recent advancements in machine learning and IoT technologies have significantly enhanced fault detection and predictive maintenance capabilities in building systems, including more safe elevator operations, reduced downtime and maintenance costs, and energy saving. Studies such as the one by Hodavand et al. [84] emphasize the integration of digital twin technology with machine learning, enabling real-time monitoring and fault diagnosis to improve infrastructure reliability and safety. The study in [85] explores the use of artificial intelligence in smart elevators to enhance time and energy management, emphasizing the benefits of AI integration in elevator systems. The study in [86] examines how machine learning models can optimize elevator energy consumption by predicting usage patterns in real-time, contributing to energy-efficient building operations. Nelson et al. [87] highlight the transformative potential of machine learning across smart building operations, focusing on fault detection methodologies tailored to subsystems like Heat Ventilation and Air Conditioning (HVAC) and elevator systems. Reference [88] involves implementing a deep learning algorithm for fault detection and prediction in elevator systems, showcasing the effectiveness of deep learning in maintenance prediction. A systematic review in [89] delves into predictive maintenance techniques in Industry 4.0, showcasing the adaptability of sensor-based monitoring and failure prediction methods to diverse operational contexts. Its relevance to elevator systems lies in the techniques discussed for sensor-based monitoring and failure prediction. Finally, Alanne et al. [90] explore machine learning applications for sustainable building systems, underlining the growing role of these technologies in ensuring the efficient and fault-free functioning of elevators as part of broader smart infrastructure initiatives. These advancements highlight the potential of combining cutting-edge technologies to overcome current limitations and lay a foundation for developing robust methodologies to address the unique challenges of condition monitoring and fault prediction in PMSM-driven elevator systems. Additionally, collaborative research initiatives and open data repositories can play a crucial role in addressing data scarcity, fostering innovation, and accelerating the adoption of advanced predictive maintenance strategies.

Compared to existing diagnostic solutions that rely on static classifiers or unimodal signal sources (e.g., vibration or current only), the proposed method integrates GAN-augmented PU learning and Reinforcement Learning (RL) within a multimodal framework. This architecture allows for real-time adaptability under real-world uncertainties, including varying load conditions and movement profiles typical of elevator systems.

Recent work by Xu et al. [91] proposed a reduced-order interval observer for simultaneous fault diagnosis in inverter-fed induction motor (IM) drives. Their method effectively detects both open-switch and current sensor faults with high precision. However, it assumes full model observability and requires direct access to the inverter’s switching logic conditions, which are not feasible in the context of commercial elevator systems, where such access is restricted by safety regulations and manufacturer-imposed limitations. In contrast, the proposed method in this paper operates in a non-intrusive manner, without accessing or modifying the motor, inverter, or controller. It leverages only externally measurable signals, such as current and vibration, to infer fault states. This makes it suitable for practical deployment in warranty-protected elevator systems.

Based on the literature, while several machine learning approaches address isolated faults in PMSM-based systems, few utilize multimodal data from real elevators operating in residential, commercial, or industrial buildings. Moreover, the integration of PU learning and RL remains underexplored in elevator fault prediction. These gaps in fault prediction for elevator systems motivate the comprehensive, real-world-validated framework proposed in this study.

3. Proposed Methodology

In the field of diagnostics, the quality of data plays a crucial role in the accuracy and reliability of the methodologies. Signals collected by sensors often contain noise resulting from many factors. Thus, the use of appropriate filters to remove noise helps to improve the quality of the signals, ensuring that the input data to diagnostic algorithms is clean, smooth, and informative. By reducing noise and preserving the basic characteristics of the signals, key features important for detecting potential anomalies are extracted. This chapter focuses on the proposed predictive maintenance methodology which was deployed on a fully operational elevator system installed in a residential apartment building. Unlike a laboratory-scale testbench, this installation reflects the real conditions of elevator operation, with unpredictable loading profiles, variable trip frequencies, and natural signal disturbances. The proposed methodology includes the description of the elevator installation for data collection through smart sensors, preprocessing of the signals using appropriate and effective filters, and the extraction of significant indicators by studying the signal in the time and frequency domain. In this installation, data collection is performed using a network of non-intrusive smart sensors compliant with international standards. The entire signal acquisition and preprocessing pipeline operates in real-time, ensuring minimal latency and accurate temporal correlation across sensor modalities. This infrastructure supports a non-intrusive diagnostic process, fully compatible with the manufacturer’s warranty and safety restrictions, as no access to the inverter firmware or motor internals is required.

3.1. Real Elevator Installation and Sensor Deployment in a Residential Apartment Building

The accuracy of data collection is determined by the selection of suitable smart sensors and the placement of the sensors based on international regulations. The placement of the accelerometer was carried out based on the new ISO 20816-3 standard [92], while the energy sensor contributed to the recording of critical energy quantities such as current, voltage, and Total Harmonic Distortion (THD). The elevator system used in this study consists of a gearless traction elevator designed for six passengers (450 kg) and nine stops, equipped with a three-phase, surface-mounted PMSM rated at 5.1 kW and operating at 160 rpm under normal service conditions. It is a multi-pole (12), low-nominal-frequency (16 Hz), and high-torque (350 Nm) motor with a 36-slot stator and distributed two-layer winding. The nominal specifications of the elevator and motor are presented in

Table 1. Nominal parameters of the elevator system.

Quantity	Value	Units
Total Weight Chamber (P)	495	kg
Nominal Load (Q)	450	kg
Counterweight (G)	720	kg
Rated Speed (U)	1	m/s
Diameter of the Friction Pulley (D)	240	mm
Force Power (F)	225	kg

and

Table 2. Nominal characteristics and design parameters of the PMSM.

Parameters	Value	Units
$\mathrm{Output} \mathrm{Power} \left({\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}\right)$	5.1	kW
$\mathrm{Input} \mathrm{Power} \left({\mathrm{P}}_{\mathrm{i}\mathrm{n}}\right)$	6.0	kW
$\mathrm{Nominal} \mathrm{Current} \left({\mathrm{I}}_{\mathrm{n}}\right)$	10	A
$\mathrm{Nominal} \mathrm{Torque} ({\mathrm{T}}_{\mathrm{n}}$)	350	Nm
Nominal Speed (n)	160	Rpm
$\mathrm{Nominal} \mathrm{Voltage} \left({\mathrm{V}}_{\mathrm{n}}\right)$	380	Volt
Number of Poles (p)	12	-
Frequency (f)	16	Hz
Efficiency (a)	85	%
Power Factor (cosφ)	0.95	-
Moment of Inertia (J)	0.35	$\mathrm{kg}·{\mathrm{m}}^2$
Stator Outer Diameter	${\mathrm{D}}_{\mathrm{o}}$	220 mm
Stator Inner Diameter	${\mathrm{D}}_{\mathrm{s}}$	126 mm
Rotor Outer Diameter	${\mathrm{D}}_{\mathrm{r}}$	124 mm
Rotor Inner Diameter	${\mathrm{D}}_{\mathrm{i}\mathrm{r}}$	100 mm
Axial Length	L	350 mm
Shaft Diameter	${\mathrm{D}}_{\mathrm{s}\mathrm{h}\mathrm{a}\mathrm{f}\mathrm{t}}$	60 mm
Airgap Length	${\mathrm{L}}_{\mathrm{g}}$	1 mm
Slot Opening Width	${\mathrm{b}}_{\mathrm{s}\mathrm{o}}$	3 mm
Slot Width at the Base	${\mathrm{b}}_{\mathrm{s}1}$	8.6 mm
Slot Width at the Top	${\mathrm{b}}_{\mathrm{s}2}$	12.5 mm
Stator Tooth Shoe Height	${\mathrm{H}}_{\mathrm{s}\mathrm{o}}$	1.5 mm
Stator Curvature Height	${\mathrm{H}}_{\mathrm{s}1}$	2.5 mm
Slot Total Height	${\mathrm{H}}_{\mathrm{s}2}$	18 mm
Magnet Thickness	${\mathrm{l}}_{\mathrm{m}}$	4.5 mm

. The motor’s constructional features are shown in Table 2 to complement the nominal electrical and geometrical characteristics. Data was sampled at 5 kHz and at 10 kHz using a Hioki PW3390 (Hioki E.E. Corporation, Ueda, Japan) and transmitted via Ethernet and wireless interfaces. Fault observations were captured under real load transitions.

Figure 1 presents an overview of the residential apartment elevator installation, and the main subsystems involved in the implementation of the proposed methodology. It includes a combination of photographs depicting the automation control panel, the inverter, the PMSM installed inside the elevator shaft, and the positions of the deployed sensors. The complete data acquisition, local storage, and transmission system are also shown, highlighting the integration of the energy analyzer, the communication interfaces, and the electrical infrastructure. All components are non-invasively installed on the existing elevator system, preserving operational safety and manufacturer compliance.

• Gearless Interior Permanent Magnet (IPM).
• Automation Panel Elevator System.
• Control board.
• Raspberry pi compute module 4G.
• Variable Voltage Variable Frequency (VVVF) inverter.
• Vibration sensor.
• Power quality analyzer Hioki PW3390.
• Data collector.
• Magnetic field current transformers.
• Device for sending the data to the cloud.
• Automatic switch.
• Three-phase circuit breaker.
• Ethernet cable from data collector to raspberry pi module 4G.
• Uninterruptible power supply (UPS).
• Mean Well Enterpises HDR 30-24 power supply (Mean Well Electronics Co., Guangzhou, China).
• Rail socket for connecting the device that will send the data to the cloud.

Figure 2a presents the cross-section view (one-quarter section) of the PMSM, highlighting the arrangement of stator teeth, windings, and permanent magnets. It is a surface-mounted permanent magnet motor, utilizing NdFe-B magnets with a remanent flux density of 1.23 T, to ensure strong magnetic performance and reliability over long periods of operation. Figure 2b represents a simplified layout of stator winding in the PMSM, showing the potential location of a short circuit fault in phase A.

3.2. Data Processing and Transmission

The next step of our proposed methodology is the preprocessing of the collected data based on the experimental setup. In the preprocessing phase the combination of two filters—the Gaussian and Extended Kalman Filter (EKF)—was used due to their significant advantages. The Gaussian Filter is used to remove noise at high frequencies, smoothing the signal by preserving the basic characteristics of the signal and enhancing feature extraction such as RMS and FFT. The Gaussian Filter’s impulse response is given by:

$$\mathrm{g}(\mathrm{x})={\displaystyle \frac{1}{\sqrt{2\mathrm{\pi }{\mathrm{\sigma }}^2}}}\mathrm{e}\mathrm{x}\mathrm{p}(-{\displaystyle \frac{{\mathrm{x}}^2}{2{\mathrm{\sigma }}^2}})$$

(1)

where σ is the standard deviation.

The filtered signal ${\mathrm{s}}^{\prime }$(t) is calculated as the convolution of the collected data from the measurements (signal s(t)) with the Gaussian Filter impulse response g(t):

$${\mathrm{s}}^{\prime }(t)=\mathrm{s}(\mathrm{t}) \ast \mathrm{g}(\mathrm{t})={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\mathrm{s}\left(\mathrm{t}-\mathrm{\tau }\right)·\mathrm{g}\left(\mathrm{\tau }\right)\mathrm{d}\mathrm{\tau }$$

(2)

Discrete signals are calculated as follows:

$${\mathrm{s}}^{\prime }[\mathrm{k}]=\sum _{\mathrm{n}=-\mathrm{N}}^{\mathrm{N}}\mathrm{s}\left[\mathrm{k}-\mathrm{n}\right]·\mathrm{g}[\mathrm{n}]$$

(3)

where N is the length of the filter’s impulse response.

The Extended Kalman Filter (EKF) is suitable for nonlinear systems when the model’s objective is the accuracy of results. The EKF can linearize the system’s nonlinearities through the Jacobian matrix (current, voltage, and acceleration) in order to study the dynamic behavior of the system. The system’s state is described by the expression:

$${\mathrm{x}}_{\mathrm{k}}=\mathrm{f}({\mathrm{x}}_{\mathrm{k}-1},{\mathrm{u}}_{\mathrm{k}-1})+{\mathrm{\omega }}_{\mathrm{k}-1}$$

(4)

where ${\mathrm{x}}_{\mathrm{k}}$ is the system state at time step k, ${\mathrm{u}}_{\mathrm{k}}={\mathrm{s}}_{\mathrm{k}}^{\prime }$ is the system input, and ${\mathrm{\omega }}_{\mathrm{k}}$ is the process noise.

The measurement equation:

$${\mathrm{z}}_{\mathrm{k}}=\mathrm{h}\left({\mathrm{x}}_{\mathrm{k}}\right)+{\mathrm{\upsilon }}_{\mathrm{k}}$$

(5)

where ${\mathrm{z}}_{\mathrm{k}}$ is the measurement vector at time step k, $\mathrm{h}$(${\mathrm{x}}_{\mathrm{k}})$ is the nonlinear function that describes how the state is mapped to the measurements, and ${\mathrm{\upsilon }}_{\mathrm{k}}$ is the measurement noise.

The State Prediction is defined as follows:

$${\widehat{\mathrm{x}}}_{\mathrm{k}|\mathrm{k}-1}=\mathrm{f}({\widehat{\mathrm{x}}}_{\mathrm{k}-1|\mathrm{k}-1}, {\mathrm{\upsilon }}_{\mathrm{k}-1})$$

(6)

$${\mathrm{P}}_{\mathrm{k}|\mathrm{k}-1}={\mathrm{A}}_{\mathrm{k}}{\mathrm{P}}_{\mathrm{k}-1|\mathrm{k}-1}{\mathrm{A}}_{\mathrm{k}}^{\mathrm{T}}+Q$$

(7)

where ${\mathrm{A}}_{\mathrm{k}}$ is the Jacobian matrix in dynamic operation and Q is the process noise configuration.

Gaussian Filtering was applied with a standard deviation of σ = 0.75, which was empirically selected to optimize the trade-off between noise suppression and the preservation of essential signal features. The Gaussian Filter was used to smooth the raw vibration and current signals, reducing high-frequency measurement noise without distorting the underlying waveform shape. Subsequently, the EKF was applied to estimate the system’s dynamic state evolution and further refine the filtered signal trajectories. EKF tuning was performed offline using representative datasets from both healthy and faulty operating conditions, configuring the process noise covariance matrix Q = diag(0.01, 0.01, 0.005) and the measurement noise covariance matrix R = diag(0.05).

The combined use of Gaussian Filtering and EKF showed superior performance over classic filtering techniques such as median filtering and Low-pass Butterworth Filters. Specifically, the proposed approach improved the F1-score by 3–7%, as it preserved transient characteristics and anomalies critical for accurate fault detection, while minimizing both high-frequency noise and smoothing-induced distortion. This improvement is attributed to the method’s ability to suppress irrelevant noise while preserving transient events and diagnostic anomalies. By retaining key fault-related signal features, the proposed two-stage filtering approach enhances the robustness and reliability of downstream fault classification models.

The next step involves the application of Short-Time Fourier Transform (STFT), which is one of the most important tools for analyzing the time-frequency characteristics of signals. STFT provides a way to examine the variation in a signal’s spectrum in time, making it suitable for detecting dynamic phenomena and transient faults. The ability to monitor the signal spectrum in real time offers accurate and efficient monitoring of the frequency sidebands. The STFT of a signal x(t) is defined as:

$$\mathrm{{\rm X}} (\mathrm{\tau }, \mathrm{f})=\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}\mathrm{x}\left(\mathrm{t}\right)\mathrm{\omega }(\mathrm{t}-\mathrm{\tau }){\mathrm{e}}^{-\mathrm{j}2\mathrm{\pi }\mathrm{f}\mathrm{t}} \mathrm{d}\mathrm{t}$$

(8)

where Χ (τ, f) is the short-time–frequency spectrum, x(t) is the signal of analysis, $\mathrm{\omega }\left(\mathrm{\tau }\right)$ is the window function which defines the local time interval, f is the frequency, and t is the time.

The analysis of the indicators provides quantitative information on the overall operation of the engine and is vital for fault detection. These are indicators in frequency bands as well as statistical indicators. The total energy and mean frequency of a signal in a specific frequency band from ${\mathrm{f}}_1$ to ${\mathrm{f}}_2$ is calculated as:

$$\mathrm{E}(\mathrm{t},{\mathrm{f}}_1,{\mathrm{f}}_2)=\underset{{\mathrm{f}}_2}{\overset{{\mathrm{f}}_1}{\int }}{\left|\mathrm{X}\right(\mathrm{t},\mathrm{f}\left)\right|}^2\mathrm{d}\mathrm{f}$$

(9)

$${\mathrm{F}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}(\mathrm{t})={\displaystyle \frac{ \sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{f}}_{\mathrm{i}}·\mathrm{P}\left({\mathrm{f}}_{\mathrm{i}}\right)}{{\int }_0^{\mathrm{\infty }}\mathrm{P}\left({\mathrm{f}}_{\mathrm{i}}\right)}}$$

(10)

where ${\mathrm{f}}_{\mathrm{i}}$ is the frequency of i-th sample in the frequency spectrum, $\mathrm{P}\left({\mathrm{f}}_{\mathrm{i}}\right)$ is the power spectral density or the magnitude of the spectral component at frequency fi, and N is the total number of samples (frequencies) in the spectrum.

Crest factor measures the maximum peak energy relative to the average energy:

$$\mathrm{CF}(\mathrm{t})={\displaystyle \frac{{\mathrm{m}\mathrm{a}\mathrm{x}}_{\mathrm{f}}\left|\mathrm{X}\right(\mathrm{t},\mathrm{f}\left)\right|}{\sqrt{\frac{1}{\mathrm{F}}{\int }_0^{\mathrm{F}}{\left|\mathrm{X}\right(\mathrm{t},\mathrm{f}\left)\right|}^2\mathrm{d}\mathrm{f}}}}$$

(11)

Another critical indicator for the detection of transient damage and vibration characteristics is kurtosis:

$$\mathrm{{\rm K}}={\displaystyle \frac{\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}({\mathrm{x}}_{\mathrm{i}}-\mathrm{\mu }{)}^4}{(\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}({\mathrm{x}}_{\mathrm{i}}-\mathrm{\mu }{)}^2{)}^2}}$$

(12)

where ${\mathrm{x}}_{\mathrm{i}}$ are the signal values, $\mathrm{\mu }$ is the average signal value, and N is the number of samples.

Skewness is an indicator that measures the asymmetry of the distribution of data around the mean value. Indications of asymmetry can reveal mechanical faults, such as rotor imbalance or magnetic asymmetries:

$$\mathrm{S}={\displaystyle \frac{\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}({\mathrm{x}}_{\mathrm{i}}-\mathrm{\mu }{)}^3}{(\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}({\mathrm{x}}_{\mathrm{i}}-\mathrm{\mu }{)}^2{)}^{3/2}}}$$

(13)

Entropy measures the complexity or randomness of the signal.

$${\mathrm{E}}_{\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}}=-\sum _{\mathrm{x}\in \mathrm{X}}\mathrm{p}\left({\mathrm{x}}_{\mathrm{i}}\right)\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{p}\left({\mathrm{x}}_{\mathrm{i}}\right)$$

(14)

where $\mathrm{p}\left({\mathrm{x}}_{\mathrm{i}}\right)$ is the probability of ${\mathrm{x}}_{\mathrm{i}}$.

Principal Component Analysis (PCA) reduces dimensionality by projecting data onto components that capture the maximum variance value. Mutual Information (MI) quantifies the dependency between two variables, identifying features most relevant to the target output. Min–Max and Z-Score Normalization are techniques which ensure that features are on the same scale to a fixed range, typically [0, 1] or [$-$1, 1]. This process is critical for preventing the dominance of features with larger ranges over others in model training.

Before the data feature matrix is extracted, the dataset must be balanced to avoid either undersampling or oversampling. Data balancing is an important process in machine learning problems where there is an imbalance in the categories of the dataset. This occurs when one category (e.g., positive or negative) is much less frequent than the other, which can affect the performance of the model. The appropriate combination of techniques such as the Synthetic Minority Oversampling Technique (SMOT) or Adaptive Synthetic Sampling (ADASYN) for the minority and Tomek Links or Cluster-Based Undersampling for the majority achieves balance without overfitting or loss of information.

The final processed dataset is a feature vector table where each sample must have a label. The label is y = 1 for fault-positive samples only, while the largest percentage of the vector samples is undefined and contains both normal (healthy) and faulty states, making it difficult to train a supervised classifier directly. The integration of PU machine learning aims to train the model to identify undefined signals and classify them accordingly as positive or negative.

3.3. Model Training and Fault Classification

The setup of the problem has two sets: a set of positively labeled samples P and a set of unlabeled samples U, which may contain both positive and negative instances. The goal is to train an initial classifier f(Z) that predicts whether a new sample z is positive or negative.

The use of encoder–decoder architectures in PU learning is a powerful tool that enhances the extraction of meaningful representations from complex, high-dimensional data, such as spectrogram patterns derived from STFT.

The encoder maps the input high-dimensional data X into a low-dimensional latent space Z.

$$\mathrm{Z} = \mathrm{Encoder}(\mathrm{X}; {\mathrm{\theta }}_{\mathrm{e}})$$

(15)

where

X$\in \mathbb{R}$^n×d is the n samples and d features input data;

Z$\in \mathbb{R}$^n×k is the latent representation, where k < d;

θ_e represents the trainable parameters of the encoder.

The encoder compresses the information in X by learning important patterns or features.

The decoder reconstructs the input X from the latent representation Z.

$$\widehat{\mathrm{X}} = \mathrm{Decoder}(\mathrm{Z}; {\mathrm{\theta }}_{\mathrm{d}})$$

(16)

where

$\widehat{\mathrm{X}}$ is the reconstructed version of the original input;

θ_d represents the trainable parameters of the decoder.

To ensure that Z retains the essential features of X, the reconstruction loss, typically the Mean Squared Error (MSE), is minimized.

$${\mathcal{L}}_{\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}={\displaystyle \frac{1}{n}}\sum _{i=1}^n{‖{\mathrm{X}}_i-{\widehat{\mathrm{X}}}_i‖}^2$$

(17)

The latent space representation Z from the encoder is passed to the PU classifier to estimate the probability of a sample being positive p(y=1|Z).

This probability can be expressed as:

$$\mathrm{p}\left(\mathrm{y}=1|\mathrm{Z}\right)=\mathrm{p}\left(\mathrm{y}=1|\mathrm{Z},\mathrm{s}=1\right)\mathrm{p}\left(\mathrm{s}=1|\mathrm{Z}\right)$$

(18)

where

s represents whether a sample is labeled (s = 1) or unlabeled (s = 0);

$\mathrm{p}\left(\mathrm{s}=1|\mathrm{Z}\right)$ is the propensity score, indicating the likelihood of a sample being labeled given its features.

By modeling $\mathrm{p}\left(\mathrm{s}=1|\mathrm{Z}\right)$ and using the labeled data, the classifier f(Z) can infer the true class probabilities.

$$\mathrm{f}\left(\mathrm{Z}\right)=\mathrm{\psi }(\mathrm{W}·\mathrm{Z}+\mathrm{b})$$

(19)

where

W and b are the weights and biases of the PU classifier;

ψ is the activation function.

The Rectified Linear Unit (ReLU) activation function is used in encoder–decoder architectures due to its simplicity and effectiveness in addressing the vanishing gradient problem and in introducing nonlinearity and sparsity. It is defined as:

$$\mathrm{R}\mathrm{e}\mathrm{L}\mathrm{U}\left(\mathrm{x}\right)=\max (0,\mathrm{x})$$

(20)

ReLU is applied to the hidden layers in both the encoder and decoder to activate the meaningful features only:

$${\mathrm{h}}_{\mathrm{i}}=\mathrm{R}\mathrm{e}\mathrm{L}\mathrm{U}({\mathrm{W}}_{\mathrm{i}}·{\mathrm{h}}_{\mathrm{i}-1}+{\mathrm{b}}_{\mathrm{i}})$$

(21)

The expected risk R(f) for the classifier f(Z) is defined as:

$$\mathrm{R}\left(\mathrm{f}\right)=1{𝔼}_{(\mathrm{Z},\mathrm{y})}\left[\mathrm{l}(\mathrm{f}\left(\mathrm{Z}\right),\mathrm{y})\right]$$

(22)

where $\mathrm{l}\left(\mathrm{f}\left(\mathrm{Z}\right),\mathrm{y}\right)$ is the binary cross-entropy loss function.

Since y is not directly available for unlabeled samples, the risk is decomposed as:

$$\mathrm{R}\left(\mathrm{f}\right)={\mathrm{\pi }}_{\mathrm{p}}{\mathrm{R}}_{\mathrm{p}}\left(\mathrm{f}\right)+(1-{\mathrm{\pi }}_{\mathrm{p}}){\mathrm{R}}_{\mathrm{n}}\left(\mathrm{f}\right)$$

(23)

where

${\pi }_p$ is the estimated proportion of positive samples in the unlabeled dataset U;

$R_p\left(f\right)=$𝔼_Z~P$\left[l(f\left(\mathrm{Z}\right),1)\right]$ is the risk for positive samples;

${ R}_n\left(f\right)=$𝔼_Z~U$\left[l(f\left(\mathrm{Z}\right),0)\right]$ is the risk for negative samples;

Approximated using the unlabeled data.

So the decomposed risk estimation is:

$$\mathrm{R}\left(\mathrm{f}\right)={\mathrm{\pi }}_{\mathrm{p}}{𝔼}_{\mathrm{Z}~\mathrm{P}}\left[\mathrm{l}(\mathrm{f}\left(\mathrm{Z}\right),1)\right]+{𝔼}_{\mathrm{Z}~\mathrm{U}}\left[\mathrm{l}(\mathrm{f}\left(\mathrm{Z}\right),0)\right]-{\mathrm{\pi }}_{\mathrm{p}}{𝔼}_{\mathrm{Z}~\mathrm{U}}\left[\mathrm{l}(\mathrm{f}\left(\mathrm{Z}\right),0)\right]$$

(24)

And the total loss function combines the risk and reconstruction losses

$${\mathrm{L}}_{\mathrm{total}} =L_{\mathit{reconstruction}} + \lambda L_{\mathit{PU}}$$

(25)

where L_PU is derived from the risk estimation and λ is a regularization parameter to balance reconstruction and classification.

The encoder–decoder is trained to minimize the L_{reconstruction} ensuring that Z captures meaningful features. The classifier is trained with Z as the input to the PU classifier to minimize the L_PU using the decomposed risk function. Optimization is achieved by fine tuning both components to minimize the total loss function. The model performs an initial estimation and classification of fault diagnosis and anomaly detection at the output, where the data exhibits nonlinear and high-dimensional features even with limited labeled data.

Reinforcement Learning (RL) is used to refine the model’s decision-making process and to optimize its performance before applying data augmentation. By integrating RL after PU learning, the system learns to make optimal decisions based on feedback from its environment, improving its ability to classify or predict outcomes effectively.

In the RL framework, the model operates in an environment characterized by the state (s_t), the actions (a_t), the reward (r_t), and the policy (π(α|s)). The goal is to learn a policy π(α|s) that maximizes the cumulative reward over time.

The state includes all the information, such as the latent representation derived from the PU learning output, the load information (L_t) of the elevator, and the direction indicator (D_t) of ascent or descent.

$${\mathrm{s}}_{\mathrm{t}}=\{\mathrm{Z},p\left(y=1|\mathrm{Z}, \right),{\mathrm{L}}_{\mathrm{t}}, {\mathrm{D}}_{\mathrm{t}}, {\mathrm{L}}_{\mathrm{PU}}$$

(26)

where

L_t is the normalized load as percentage of the elevator’s maximum capacity;

D_t is the indicator of the movement direction modeled as a binary variable.

$${\mathrm{L}}_{\mathrm{t}}={\displaystyle \frac{\mathrm{C}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t} \mathrm{L}\mathrm{o}\mathrm{a}\mathrm{d}}{\mathrm{M}\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{m} \mathrm{C}\mathrm{a}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}}}\in \left[0,1\right]$$

(27)

$${\mathrm{D}}_{\mathrm{t}}=\left\{ \begin{array}{c}1, \\ 0, \end{array}\right.\begin{array}{c}\mathrm{f}\mathrm{o}\mathrm{r} \mathrm{a}\mathrm{s}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\\ \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{d}\mathrm{e}\mathrm{s}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\end{array}$$

(28)

Actions (a_t) are decisions made by the RL agent, including modifying decision thresholds according to normalized load and movement conditions, prioritizing fault diagnosis, and addressing increased loads or changes in operating conditions.

$${\mathrm{a}}_{\mathrm{t}}=\{\mathrm{T}\mathrm{h}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{d} \mathrm{A}\mathrm{d}\mathrm{j}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}, \mathrm{E}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r} \mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{P}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}\}$$

(29)

The reward (r_t) is designed to encourage behavior that improves classification accuracy, reduces misclassification, or enhances robustness and optimization while considering load and direction conditions.

$${\mathrm{r}}_{\mathrm{t}}=a·\mathrm{A}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{y}\left({\mathrm{L}}_{\mathrm{t}},{\mathrm{D}}_{\mathrm{t}}\right)-b·\mathrm{M}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left({\mathrm{L}}_{\mathrm{t}},{\mathrm{D}}_{\mathrm{t}}\right)-c·\mathrm{E}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y} \mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}({\mathrm{L}}_{\mathrm{t}},{\mathrm{D}}_{\mathrm{t}})$$

(30)

where a, b, and c are weighting factors.

The policy π(α|s) is modeled using a Neural Network with parameters θ_π

$$\mathrm{\pi }\left(\mathrm{\alpha }\right|\mathrm{s}); {\mathrm{\theta }}_{\mathrm{\pi }}=\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{m}\mathrm{a}\mathrm{x}({\mathrm{W}}_{\mathrm{\pi }}·\mathrm{s}+{\mathrm{b}}_{\mathrm{\pi }})$$

(31)

where ${\mathrm{W}}_{\pi }$ and ${\mathrm{b}}_{\pi }$ are trainable weights and biases while softmax ensures the output is a valid probability distribution over actions.

The objective in RL is to maximize the expected cumulative reward ${\mathrm{G}}_{\mathrm{t}}$.

$${\mathrm{G}}_{\mathrm{t}}=\sum _{\mathrm{k}=0}^{\mathrm{\infty }}{\gamma }^{\mathrm{k}}{\mathrm{r}}_{\mathrm{t}+\mathrm{k}}$$

(32)

where $\gamma \in \left[0, 1\right)$ is the discount factor, prioritizing immediate rewards over distant ones.

The policy is optimized to maximize the expected reward J(${\mathrm{\theta }}_{\mathrm{\pi }}$) using the gradient method.

$$\mathrm{J}({\mathrm{\theta }}_{\mathrm{\pi }})={𝔼}_{\mathrm{\pi }} \left[{\mathrm{G}}_{\mathrm{t}}\right].$$

(33)

$${\nabla }_{{\mathrm{\theta }}_{\mathrm{\pi }}}\mathrm{J}\left({\mathrm{\theta }}_{\mathrm{\pi }}\right)={𝔼}_{\mathrm{\pi }} \left[{\mathsf{\nabla }}_{{\mathrm{\theta }}_{\mathrm{\pi }}}\log \mathrm{\pi }\left(\mathrm{\alpha }|\mathrm{s};{\mathrm{\theta }}_{\mathrm{\pi }}\right){\mathrm{G}}_{\mathrm{t}}\right]$$

(34)

The value function ${\mathrm{V}}^{\mathrm{\pi }}\left(\mathrm{s}\right)$ estimates the expected return starting from the state s under the policy π.

$${\mathrm{V}}^{\mathrm{\pi }}\left(\mathrm{s}\right)={𝔼}_{\mathrm{\pi }} \left[{\mathrm{G}}_{\mathrm{t}}|{\mathrm{s}}_{\mathrm{t}}=\mathrm{s}\right].$$

(35)

The advantage function ${\mathrm{A}}^{\mathrm{\pi }}\left(\mathrm{s},\mathrm{a}\right)$ quantifies the benefit of taking action a in state s, compared to the average performance.

$${\mathrm{A}}^{\mathrm{\pi }}\left(\mathrm{s},\mathrm{a}\right)={\mathrm{\Omega }}^{\mathrm{\pi }}\left(\mathrm{s},\mathrm{a}\right)-{\mathrm{V}}^{\mathrm{\pi }}\left(\mathrm{s}\right)$$

(36)

where ${\mathrm{\Omega }}^{\mathrm{\pi }}\left(\mathrm{s},\mathrm{a}\right)$ is the action-value function

$${\mathrm{\Omega }}^{\mathrm{\pi }}\left(\mathrm{s},\mathrm{a}\right)={𝔼}_{\mathrm{\pi }} \left[{\mathrm{G}}_{\mathrm{t}}|{\mathrm{s}}_{\mathrm{t}}=\mathrm{s},{\mathrm{a}}_{\mathrm{t}}=\mathrm{a}\right]$$

(37)

The training process begins with the initialization of the policy network $\mathrm{\pi }\left(\mathrm{\alpha }\right|\mathrm{s};{\theta }_{\pi })$, which is set with random weights. The state $\mathrm{s}$_t is defined using the encoder–decoder’s latent space Z derived from PU learning. During exploration, actions a_t are sampled from the policy π(α|s; θπ) to interact with the environment and collect rewards r_t. The policy is updated by computing the gradient of the policy objective using the policy gradient theorem:

$${\nabla }_{{\mathrm{\theta }}_{\mathrm{\pi }}}\mathrm{J}({\mathrm{\theta }}_{\mathrm{\pi }})={𝔼}_{\mathrm{\pi }} \left[{\mathrm{A}}^{\mathrm{\pi }}\left(\mathrm{s},\mathrm{a}\right){\mathsf{\nabla }}_{{\mathrm{\theta }}_{\mathrm{\pi }}}\log \mathrm{\pi }\left(\mathrm{\alpha }|\mathrm{s};{\mathrm{\theta }}_{\mathrm{\pi }}\right)\right]$$

(38)

Additionally, a value network $(\mathrm{s};{\theta }_{\upsilon })$ is trained to approximate the value function ${\mathrm{V}}^{\mathrm{\pi }}\left(\mathrm{s}\right)$ by minimizing the loss function L_value.

$$L_{\mathrm{value}}={𝔼}_{\mathrm{\pi }} \left[({\mathrm{G}}_{\mathrm{t}}-{\mathrm{V}(\mathrm{s};{\theta }_{\upsilon }))}^2 \right]$$

(39)

Optimization is carried out by performing gradient ascent to update ${\theta }_{\pi }$ for the policy network and gradient descent performed on L_value to update parameters ${\theta }_{\upsilon }$ for the value network.

Data augmentation using Generative Adversarial Networks (GANs) involves two main components: a generator and a discriminator. The generator creates synthetic data, while the discriminator evaluates the authenticity of the data by distinguishing between real and synthetic samples.

The generator takes random noise z~ℕ(0, 1) sampled from the latent space as the input and maps the data space X_aug producing synthetic samples $\mathbf{x}\prime =\mathrm{G}(\mathbf{z};{\theta }_G)$. The generator’s objective is to create realistic data that can fool the discriminator. The discriminator receives both real data x and synthetic data x′ as the input. It outputs a probability $D(\mathbf{x};{\theta }_D)$ or $D(\mathbf{x}\prime ;{\theta }_D)$ indicating whether the data is real $D\left(\mathbf{x}\right)\to 1$ or synthetic $D(\mathbf{x}\prime )\to 0$.

So, the generator and discriminator have competing objectives. The discriminator aims to maximize the GAN loss function L_D by correctly classifying real and synthetic data, while the generator aims to minimize L_G by producing data that maximizes the discriminator’s classification probability.

$${\mathit{L}}_D=-{\mathbf{E}}_{\mathbf{x}~\mathrm{pdata}} \left[\log D\left(\mathbf{x}\right)\right]-{\mathbf{E}}_{\mathbf{z}~\mathrm{pz}} \left[\log (1-D\left(\mathrm{G}\right(\mathbf{z}\left)\right))\right]$$

(40)

$${\mathit{L}}_G=-{\mathbf{E}}_{\mathbf{z}~\mathrm{pz}} \left[\log D\left(\mathrm{G}\right(\mathbf{z}\left)\right)\right]$$

(41)

The training loop for GANs involves iterative updates to the generator and discriminator to achieve adversarial optimization. In each iteration, the discriminator is updated by maximizing its ability to distinguish between real and synthetic data, adjusting its parameters ${\theta }_D$ using the gradient ascent rule with a learning rate ${\eta }_D$. Conversely, the generator is updated by minimizing the likelihood of the discriminator correctly identifying synthetic samples, adjusting its parameters ${\theta }_G$ using the gradient descent rule with a learning rate ${\eta }_G$. This adversarial optimization alternates updates between ${\theta }_D$ and ${\theta }_G$ to maintain balance, ensuring neither the generator nor the discriminator becomes too dominant.

$${\theta }_D\leftarrow {\theta }_D+{\eta }_D{\mathsf{\nabla }}_{{\theta }_D}{\mathit{L}}_D$$

(42)

$${\mathrm{\theta }}_{\mathrm{G}}\leftarrow {\mathrm{\theta }}_{\mathrm{G}}-{\eta }_G{\mathsf{\nabla }}_{{\theta }_G}{\mathit{L}}_G$$

(43)

This dynamic interaction drives the generator to produce increasingly realistic synthetic data while challenging the discriminator to refine its classification performance. GAN training reaches convergence when the discriminator’s output approximates $D\left(\mathbf{x}\right)=D(\mathbf{x}\prime )=0.5$ for all samples.

The augmented dataset is represented as (X_aug, Y_aug), where X_aug = {x₁, x₂, …, x_n}; each x_i is a feature vector, and Y_aug = {y₁, y₂, …, y_n} contains the corresponding labels. The dataset is split into training and validation subsets, (X_train, Y_train) and (X_val, Y_val), and is used to train multiple predictive models, including Random Forest (RF), Support Vector Machine (SVM), and Deep Neural Networks (DNNs).

A Random Forest consists of T decision trees ${\left\{h_t\right(\mathbf{x};{\theta }_t\left)\right\}}_{t=1}^T$ trained on different bootstrap samples of the training data. For an input x_i, each tree h_t outputs a class label ŷ_t.

The final prediction is obtained by majority voting:

$$\mathrm{ŷ}=\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\left\{h_t\left(\mathbf{x};{\theta }_t\right):t=1,\dots ,T\right\}$$

(44)

The object of training is for each tree to minimize the entropy for the splitting nodes:

$$\mathrm{I}=\sum _c{p}_c(1-p_c)$$

(45)

where p_c is the proportion of class c in the split.

The class c represents one of the possible categories or labels in the classification problem. Specifically, c refers to a distinct class within the set of all possible classes in the dataset. Entropy quantifies the impurity of the node, measuring how mixed the classes are. A lower entropy indicates a purer split, meaning the samples in the node predominantly belong to a single class.

SVM aims to find a hyperplane ${\mathbf{w}}^{\mathrm{T}}\mathbf{x}+b=0$ that separates the classes with the maximum margin. The optimization problem is formulated as:

$$\underset{\mathrm{w},\mathrm{b}}{\min }{\displaystyle \frac{1}{2}}{‖\mathbf{w}‖}^2+C\sum _{\mathrm{i}=1}^{\mathrm{n}}\mathrm{m}\mathrm{a}\mathrm{x}\left(0,1-{\mathrm{y}}_{\mathrm{i}}\left({\mathbf{w}}^{\mathrm{T}}{\mathbf{x}}_{\mathrm{i}}+b\right)\right)$$

(46)

where $C$ is a regularization parameter.

For nonlinear separable data, a Kernel function $K({\mathbf{x}}_{\mathrm{m}},{\mathbf{x}}_{\mathrm{n}})$ maps the data to a higher-dimensional space, enabling separation in the transformed space:

$$\mathrm{K}\left({\mathbf{x}}_{\mathrm{m}},{\mathbf{x}}_{\mathrm{n}}\right)=\mathrm{\phi }{\left({\mathbf{x}}_{\mathrm{m}}\right)}^{\mathrm{T}}\mathrm{\phi }\left({\mathbf{x}}_{\mathrm{n}}\right)$$

(47)

For a new input x_, the decision function is:

$$\mathrm{f}\left(\mathbf{x}\right)=\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\left(\sum _{\mathrm{m}=1}^{\mathrm{n}}{\lambda }_{\mathrm{m}}{\mathrm{y}}_{\mathrm{m}}K\left({\mathbf{x}}_{\mathrm{m}},\mathbf{x}\right)+b\right)$$

(48)

where ${\lambda }_{\mathrm{m}}$ are the support vector coefficients.

A DNN consists of L layers, including input, hidden, and output layers.

The output of each layer l is computed as:

$${\mathit{a}}^{\left(l\right)}=\mathrm{R}\mathrm{e}\mathrm{L}\mathrm{U}({\mathbf{W}}^{\left(l\right)}{\mathit{a}}^{(l-1)}+{\mathit{b}}^{\left(\mathrm{l}\right)})$$

(49)

where ${\mathbf{W}}^{\left(l\right)}$ and ${\mathit{b}}^{\left(l\right)}$ are the weight matrix and bias vector, and ReLU is the activation function $\mathrm{R}\mathrm{e}\mathrm{L}\mathrm{U}\left(z\right)=\mathrm{m}\mathrm{a}\mathrm{x}(0,z)$.

For classification, the final layer applies a softmax activation:

$${\mathrm{ŷ}}_{\mathrm{i}}={\displaystyle \frac{exp\left({\mathrm{z}}_{\mathrm{i}}\right)}{\sum _{\mathrm{j}=1}^{\mathrm{k}}exp\left({\mathrm{z}}_{\mathrm{i}}\right)}}$$

(50)

where ${\mathrm{z}}_{\mathrm{i}}$ is the raw output for class i.

The cross-entropy loss is minimized to train the network:

$$L=-{\displaystyle \frac{1}{\mathrm{n}}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\sum _{\mathrm{j}=1}^{\mathrm{k}}{\mathrm{y}}_{\mathrm{i}\mathrm{j}}\log {\mathrm{ŷ}}_{\mathrm{i}\mathrm{j}}$$

(51)

where $y_{ij}$ is the true label and ${ŷ}_{ij}$ is the predicted probability.

The DNN parameters $\left\{\mathbf{W},\mathit{b}\right\}$ are updated for optimization using Adaptive Movement Estimation (Adam), which is suitable for various machine learning problems, including large-scale and sparse datasets.

The integration of PU learning, GANs, and RL forms a collaborative mechanism to handle practical elevator conditions. PU learning enables classification from positive and unlabeled data, GANs generate synthetic rare-fault examples, and RL dynamically adjusts thresholds based on load and direction. Feature extraction techniques include RMS, THD, kurtosis, FFT, harmonic amplitudes, crest factor, and skewness. The fault types identified include winding asymmetries, load imbalance, and mild mechanical misalignment.

3.4. Model Evaluation and Database Update

Randomly sampled data is preprocessed to ensure consistency and compatibility with each trained model. The preprocessed test data is evaluated against the trained model to produce predictions compared to the true labels. These predictions are analyzed using multiple metrics to determine the model’s performance.

$$\mathrm{A}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{y}={\displaystyle \frac{\mathrm{T}\mathrm{P}+\mathrm{T}\mathrm{N}}{\mathrm{T}\mathrm{P}+\mathrm{T}\mathrm{N}+\mathrm{F}\mathrm{P}+\mathrm{F}\mathrm{N}}}$$

(52)

$$\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}={\displaystyle \frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{P}}}$$

(53)

$$\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}={\displaystyle \frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{N}}}$$

(54)

$$\mathrm{F}1=2·{\displaystyle \frac{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}·\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}+\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}}$$

(55)

where TP, TN are true positive and negative and FP, FN are false positive and negative.

The F1-score is a performance metric for classification models that represents the harmonic mean of Precision and Recall. It is particularly useful in cases of imbalanced datasets, where accuracy alone may not provide an accurate assessment of the model’s effectiveness. The F1-score balances false positives and false negatives, ensuring a trade-off between Precision (the proportion of true positive predictions among all predicted positives) and Recall (the proportion of true positive predictions among all actual positives). A high F1-score indicates a well-performing model in terms of both Precision and Recall.

The Receiver Operating Characteristic Area Under Curve (ROC-AUC) score evaluates the model’s ability to distinguish between classes:

$$\mathrm{A}\mathrm{U}\mathrm{C}={\int }_0^{1}TPR\left(FPR\right)\mathrm{d}\left(FPR\right)$$

(56)

where $TPR={\displaystyle \frac{TP}{TP+FN}}$ is the true positive rate and $FPR={\displaystyle \frac{FP}{FP+TN}}$ is the false positive rate.

For graphical analysis, visual tools are used, such as the confusion matrix, ROC curve, Precision–Recall curve, and heatmaps, to enhance interpretability and provide insights into the model’s performance:

The Pareto front is used for multi-objective optimization, balancing multiple performance metrics (e.g., Precision vs. Recall). A set of solutions $\{o_1, o_2, \dots , o_n\}$ represents candidate optimal solutions in the multi-objective optimization process. A solution o_i is Pareto-optimal if no other solution exists that improves one objective function without degrading another.

Mathematically, this is defined as:

$$\forall o_j,\hspace{1em}\mathrm{i}\mathrm{f} f_k\left(o_j\right)\ge f_k\left(o_i\right)\hspace{1em}\mathrm{f}\mathrm{o}\mathrm{r} \mathrm{a}\mathrm{l}\mathrm{l} \mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{a} k, \mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n} f_k\left(o_j\right)=f_k\left(o_i\right) \forall k$$

(57)

The scatter plots of performance metrics are used to identify the Pareto front.

Using the computed metrics and visual analysis, predictions of malfunctions are made. The insights from graphical analysis, metrics, and Pareto optimization are integrated into a decision-support system. Predicted errors or anomalies are stored in a knowledge base for further evaluation or feedback.

Figure 3 presents a detailed flowchart of the proposed methodology, which consists of the following stages: data acquisition (from the elevator system), signal preprocessing (Gaussian Filtering, EKF), data transmission, data processing, feature extraction, data balancing and pattern analysis, PU learning, Reinforcement Learning (RL), data augmentation (GAN-based), model training (RF, SVM, DNN), model evaluation, alarm generation, and database update.

The flowchart illustrates a comprehensive methodology for monitoring, analyzing, and maintaining an elevator system using advanced machine learning techniques and data-driven processes. The data begins with sensors attached to the elevator system, capturing raw signals such as vibrations, current, and temperature. These signals undergo preprocessing using Gaussian and Extended Kalman Filters to remove noise and enhance quality before being saved locally. The preprocessed data is transmitted via secure protocols such as MQTT, HTTPS, and TLS, ensuring encrypted and reliable communication. The data packets are formatted with timestamps and sensor IDs, enabling traceability and efficient cloud monitoring for storage and accessibility.

Once transmitted, the data undergoes further processing, integrating historical and real-time information from the database. Feature extraction techniques such as RMS, THD, STFT, and statistical measures like kurtosis and skewness are applied to derive meaningful patterns. Balancing the data ensures that all conditions, including elevator movement during ascent and descent, are adequately represented, and patterns are analyzed to form representative sample vectors for further learning stages.

The methodology includes generating alarms to monitor system conditions in real-time. Thresholds are predefined based on system specifications and operational requirements. Alerts are categorized into normal, marginal, and critical levels, and dispatched to relevant personnel through an automated system. Alerts are archived for future reference, creating a condition monitoring log that supports effective decision-making and rapid responses to potential malfunctions.

Finally, the database is continually updated through secure connections, allowing new data to be inserted while maintaining existing records. Labels are improved through iterative learning, and historical data is archived for long-term analysis. The updated database facilitates the generation of detailed reports, supports decision-making processes, and integrates preventive maintenance scheduling based on statistical insights. This ensures a robust and adaptive framework for the monitoring, analysis, and maintenance of the elevator system, enhancing its operational efficiency and safety.

This system operates independently of the elevator’s control panel, functioning as a non-intrusive monitoring and diagnostic tool. It does not interfere with the elevator’s operational processes or its built-in safety mechanisms, ensuring compliance with all regulatory standards and preserving the integrity of the elevator’s original design. By collecting and analyzing data from external sensors, the system provides valuable insights without altering the core functionality or safety features of the elevator.

The proposed system presents numerous advantages. First, it reduces maintenance costs by enabling predictive and condition-based maintenance strategies. By identifying potential issues before they escalate, unnecessary repairs are minimized, and service schedules can be optimized. The second advantage is the minimization of downtime by proactively addressing faults, ensuring the elevator remains operational and reducing inconvenience for users. The third advantage is that the system enhances the overall safety and reliability of the elevator by continuously monitoring critical parameters and generating real-time alerts when thresholds are exceeded. Additionally, it extends the lifespan of the equipment by ensuring timely interventions and preventing excessive wear and tear.

The proposed system introduces several innovations. It leverages advanced machine learning techniques, including PU learning, Reinforcement Learning, and GAN-based data augmentation, to improve fault detection and classification accuracy. The use of encrypted communication protocols ensures secure data transmission, while the integration of cloud monitoring provides scalability and remote access to data. Furthermore, the system’s ability to adapt to various operating conditions, such as different load profiles during elevator ascent and descent, showcases its robustness and versatility. By incorporating a knowledge base for error analysis and decision support, the system also facilitates informed decision-making, enhancing maintenance efficiency and reducing human error. These innovative features make the system a cutting-edge solution for modern elevator monitoring and diagnostics.

4. Results

This section presents the results of the proposed methodology with an emphasis on the accuracy and reliability of the analysis. Thus, Python code was used for the algorithm development and the graphs captured the two functional states of the machine, providing strong evidence for the effectiveness of the approach. The software stack for the analysis is shown in

Table 3. Implemented framework.

Software	Version	Objective
Python	3.10.11	Main Programming Language
Numpy	1.23.5	Array Computations
Pandas	1.5.2	Data Analysis
Matplotlib	3.6.2	Graph Visualization
Scipy	1.9.3	Signal Processing
Scikit-learn	1.2.2	Preprocessing and Classification
PyKalman	0.9.5	Kalman Filtering
TensorFlow/Keras	2.12.0	Deep Learning

.

4.1. Experimental Current Signals

At state (Section 3.3 of this article), the collection of appropriate data through smart energy and vibration sensors is presented in Figure 4a,b, where the current waveforms during the upward and downward movements of the chamber for different testing loads are shown. In addition, Figure 5a,b show the measured current waveform of the faulty motor with the occurrence of the short circuiting of the winding.

Based on the results of the measurements and the comparative investigation of the current waveforms, we conclude that the elevator could be put in safe mode and serve loads of only 0 to 5 persons during ascent and 2 to 6 persons during descent. However, since it is called upon to perform simultaneous movements in both directions, it follows that under short circuit conditions, the motor could serve loads of 2 to 5 persons, i.e., 150 kg to 375 kg, respectively, in both directions of movement, corresponding to an active force on the motor shaft of 150 kg, i.e., approximately half of the rated force.

4.2. Preprocessing Data

4.2.1. Signal Filtering and Normalization

The use of the inverter and the influence of external factors in the network causes distortions in the various current signals. The healthy signals show pure periodicity. At high loads (300 kg, 415 kg) a small amount of noise is present, which causes fluctuations in the system’s operation. Gaussian and Extended Kalman Filters (EKFs) were used to reduce the noise and capture the dynamic characteristics of the system (see Figure 6 and Figure 7).

Thus, we observe a significant smoothing of the signal using a Gaussian Filter, especially for low loads, while correspondingly, the noise is significantly reduced at high loads, ensuring a smoother representation of the data. Similarly, with EKT, the dynamic and natural behavior of the signal as well as the points with strong fluctuations are preserved, showing accuracy in the machine’s changing operational situations. As far as higher loads are concerned, it accurately reproduces current variations without eliminating peaks.

Figure 8a,b and Figure 9a,b present the current waveforms using Gaussian Filter and EKF, respectively. The Gaussian Filter smooths out the signal and reduces noise, but does not react well to fast signal changes, as it smooths out the rapidly changing spikes. The use of EKF offers accuracy in monitoring the dynamic state of the machine and helps to isolate fault-related features by facilitating the diagnostic process.

4.2.2. Harmonic Analysis

In the case of mechanical faults, one of the most popular and traditional techniques, with a high accuracy and low cost, is Fast Fourier Transform (FFT). FFT transforms the vibration signal from the time domain to the frequency domain, as illustrated in Figure 10a,b and Figure 11a,b for the healthy and faulty state in the motor.

Comparing the two signals in the time domain, we observe that in the healthy state, the signal is relatively smooth and limited to small amplitude values, while in the faulty signal, the amplitude of the signal is higher and there are strong fluctuations, as large peaks are observed, indicating strong anomalies. Similarly, in the frequency domain in the healthy state, the FFT has higher energy at low frequencies, while at higher frequencies, the amplitude decreases very quickly with no significant high frequency components observed, indicating the absence of errors. The faulty waveforms show enhanced components at the low frequency elements, indicating the occurrence of an eccentricity error while higher frequencies are associated with bearing wear.

The ability of STFT to perform frequency domain analysis to monitor signal frequency is a critical factor for dynamic fault diagnosis problems. Figure 12a,b, Figure 13a,b, Figure 14a,b, and Figure 15a,b illustrate the spectrum of the STFT signals for various chamber motion loads.

Table 4. Main characteristics from healthy current signal analysis.

Parameters	Kurtosis	Skewness	${\mathbf{F}}_{\mathbf{m}\mathbf{e}\mathbf{a}\mathbf{n}}$	CF	Entropy
Upward 0 kg	−1.178693	−0.079805	174.641483	2.092751	22.513715
Downward 0 kg	−1.449820	−0.022865	128.423439	1.698632	8.598839
Upward 150 kg	−1.368116	−0.038797	143.970040	1.842108	16.954872
Downward 150 kg	−1.474748	−0.009041	121.203588	1.714493	9.874350
Upward 300 kg	−1.378286	−0.028730	136.443628	1.738689	10.857418
Downward 300 kg	−1.202166	−0.068855	163.865171	1.949762	17.181473
Upward 415 kg	−1.440483	−0.022311	127.162694	1.694734	8.427130
Downward 415 kg	−1.043277	0.032834	185.328061	2.140981	22.979208

and

Table 5. Main characteristics from faulty current signal analysis for different switching frequencies.

Parameters	Kurtosis	Skewness	${\mathbf{F}}_{\mathbf{m}\mathbf{e}\mathbf{a}\mathbf{n}}$	CF	Entropy
${\mathrm{f}}_1$ = 5 kHz	−0.518260	0.037931	169.027522	3.721357	5.707496
${\mathrm{f}}_2$ = 12 kHz	−0.768821	−0.071542	152.274270	2.929318	11.589026

present the main characteristics of the signals and are important factors in determining the operating condition of the machine. The same method is used to analyze the faulty current signal, as shown in Figure 16a,b for switching frequencies of 5 kHz and 12 kHz.

Based on the harmonic analysis of the PMSM sound, we observe a smooth spectral distribution over the whole range of the tested loads. In all cases a smooth distribution of spectral energy at low frequencies (0–100 Hz) with strong peaks of a constant intensity are observed. At 0 kg and 150 kg the fundamental frequency remains dominant while at 300 kg and 415 kg the higher frequencies are slightly more pronounced due to increased mechanical noise.

In the motor with a shorted winding, the spectral energy distribution is observed over a wider frequency range. The higher frequencies are particularly pronounced, indicating the presence of noise and vibration, showing parasitic harmonics at low frequencies. The above conclusions can be easily understood by extracting the characteristics of the signals in the comparative study in Table 4 and Table 5. The healthy motor has a flatter distribution, as shown by more negative kurtosis, while the faulty motor shows sharper peaks. The skewness in both cases is close to zero, indicating relative symmetry in the signal, while the healthy machine shows better distributed peaks, such as in the crest factor. Similarly, in the case of a healthy PMSM, a larger ${\mathrm{F}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}$ occurs during the descent, while the shorted one shows a decrease in the average frequency due to spectral energy dispersion. The entropy is significantly higher in the case of a healthy motor due to the complexity of dynamic operations, while the short circuit machine presents lower spectral complexity.

Figure 17a,b show the vibration signal collected during motor operation in the chamber. The healthy signal is characterized by normal spectral energy distribution at low frequencies without strong vibrations, and stable operation with no evidence of mechanical and electromagnetic faults. In the faulty signal we observe intense energy bands at elevated frequencies, showing an instability in time with fluctuations in dynamic operation.

Based on the data in

Table 6. Vibration signal characteristics for each operation.

Parameters	Kurtosis	Skewness	${\mathbf{F}}_{\mathbf{m}\mathbf{e}\mathbf{a}\mathbf{n}}$	CF	Entropy
Healthy	−0.088098	0.038074	206.423823	3.735503	−23,915.8115
Faulty	61.059997	7.037883	180.372562	8.565845	−17,575.1876

, the main cause may be a mechanical malfunction due to eccentricity, bearing wear, and misalignment of the system. However, these failures can also be caused by electrical anomalies in the motor stator windings and unwanted vibrations due to uneven torque generation.

4.2.3. Pattern Feature Extraction

The pattern feature extraction process is a critical stage after signal preprocessing. This process provides important information for certain key features regarding load conditions and elevator motion (mean value, skewness, kurtosis, Principal Component Analysis (PCA)). The analysis of these features allows for pattern discrimination and combined with data normalization and balancing ensures that the model obtains uniformly distributed data.

Figure 18 compares the distribution of the original (Figure 18a) and normalized features where we observe that normalization balances the data in a single range [0, 1] (Figure 18b). This ensures that all features have comparable values, thus improving the performance of machine learning algorithms before the model training process begins.

Skewness is a statistical measure that describes the degree of skewness of a distribution around the mean. In our application it is a critical factor as it may indicate changes in the operating profile of the lifting system. According to Figure 19, clear differences between the signals are observed as the healthy signals are more dispersed, indicating that the skewness in the normal system may be within normal limits while the faulty signals are clustered around specific skewness values, suggesting a pattern of deviation from normal operation.

In order to better capture and monitor the effect of each indicator on our system, we created the correlation table in Figure 20 which shows the relationship between different attributes, with a color scale indicating the strength of the correlation. We distinguish a very high positive correlation (0.98) between standard deviation and energy, where energy consumption can be predicted from signal variation. Similar characteristics of strong correlation appear between the kurtosis and crest factor (0.91), which are particularly important indicators in suggesting elevator faults, indicating abrupt changes in motor voltage and current. Negative values, especially in variables such as mean and entropy, indicate that a higher mean value leads to less uncertainty in the signal.

The PU and Reinforcement Learning methods are used in order to achieve correct data classification when we only have positive samples and unclassified data, and to optimize the operation of an agent that makes experience-based decisions. In this way they create a self-improving system for prediction and anomaly detection, even if there is limited labeled data. Figure 21 shows the confusion matrix that captures how well the model classifies faulty and healthy samples, with labels 0 and 1, respectively. The model seems to perform well, because true positives (TPs) and true negatives (TNs) are high, while correspondingly, false positives (FPs) and false negatives (FNs) are low, but errors in prediction are shown.

The confusion matrix reveals false negatives during descent under heavy load, indicating the partial masking of fault symptoms. To mitigate this, synthetic signals generated by GANs were used to enhance boundary cases, and PU learning improved classifier robustness under data imbalance. This reduced false negatives by 12% over baseline classifiers.

We used Reinforcement Learning with appropriate adaptation of the reward function to achieve the correction of the wrong predictions with a high accuracy, reaching 90.91%. Figure 22 shows the 2D representation of the original data and its classification into labels (blue = healthy (1), red = faulty (0)). The points of the two classes are relatively separated, which means that PU learning has been able to recognize the structure of the data; however, outliers and points where the two classes overlap are observed, which affects the training process.

The data augmentation technique is a solution to enhance the less representative classes in various deep learning models. By creating synthetic data, the dataset is enriched, allowing the models to learn better. Generative Adversarial Networks (GANs) create realistic data samples, improving the ability of models to better generalize to real data; this helps mitigate sample size and often prevents overfitting. This realistically fits synthetic samples and allows the model to better detect anomalies and unusual situations [93].

An examination of the comparative distribution of important features for the successful implementation of the method is shown in Figure 23. The synthetic data follows the original data (shown in Figure 24) to a significant degree, highlighting the statistical sequence between the data. Most features follow the distribution of the real ones, thereby helping to train a more generalizable model. Similarly, in mean and std_dev there is more overlap between the real and synthetic data, indicating better generalization. In addition, the existence of peaks in the synthetic data indicates overpopulation at specific values where the GAN preferred some values over others, while the data does not exhibit the same natural stochasticity as the original data.

4.2.4. Model Training Algorithms

Recent advances in machine learning (ML) have enabled the adoption of combinatorial approaches that incorporate different algorithms, such as Deep Neural Networks (DNNs), Support Vector Machines (SVMs), and Random Forests (RFs), to improve accuracy and generalization in fault analysis. The hybrid model we propose focuses on the advantages of several algorithms for fault classification.

Table 7. Calculated key features of machine learning algorithms.

Algorithms	Accuracy	Precision	Recall	F1-Score	ROC-AUC
Random Forest	99.50%	99.60%	99.40%	99.50%	99.50%
DNN	90.40%	92.24%	90.40%	91.31%	91.40%
SVM	89.50%	84.96%	96%	90.14%	89.50%
Ensemble	98.10%	100%	96.20%	98.06%	98.10%

shows the calculated key feature parameters for each algorithm considered, which are crucial for evaluating the performance of each model.

The Receiver Operating Characteristic (ROC) and Precision–Recall curves in Figure 25 evaluate the performance of the classifiers. In Figure 25a the curves of the Random Forest and Ensemble models show a perfect ability to discriminate between classes. Similarly, the SVM and DNN, although showing worse performance, are found to be highly efficient. The steep slope of the RF and Ensemble curves demonstrates the ability of these models to identify positive cases. In Figure 25b, the excellent flat line with the RF and Ensemble models means that there are zero false positives, with the model not classifying false negative as positives. The SVM and DNN have a more gradual drop in Recall, showing that they lose some positive cases as coverage increases, while the steep drop towards the end of the curve shows the inability of the models to maintain high accuracy when Recall increases too much, as is the case with DNN.

The histogram in Figure 26 shows the performance of four different classification algorithms (Random Forest, DNN, SVM, and Ensemble) based on five different evaluation metrics. According to the results, SVM has the lowest performance, especially on parameters such as accuracy and Recall, but has absolute Precision, indicating that it is probably overly conservative, avoiding errors but missing several important cases. The Random Forest and Ensemble models show the best accuracy and are characterized by high reliability and balance, making them an excellent choice for classification. Finally, the DNN shows a slightly lower Recall than RF, which means that it may miss some positive cases.

The diagram below in Figure 27 illustrates the confusion matrices for the four different algorithms, showing the total samples that were correctly classified and how many were incorrectly classified. The RF and Ensemble models are characterized as the most accurate classifiers, with 5 and 14 total errors, respectively. SVM shows 74 FNs, failing particularly to identify class 2, which affects its Recall.

The multi-criteria optimization of the two key parameters of accuracy and Precision for the different algorithms tested is described in Figure 28. Random Forest presents the best performance for both metrics, constituting the optimal solution for malfunctions occurring at accuracy values in the range of 80–90%. The Ensemble presents the second-best performance, indicating a high accuracy and a Precision reaching approximately 99%, with very few malfunctions, indicating that the model has a very low failure rate. SVM maintains high accuracy, but its Precision gradually drops, with accuracy values in the range of 90–99%, indicating that it fails at a certain accuracy threshold. DNN shows an even larger drop in Precision compared to accuracy, which may indicate that the model has difficulty in correctly predicting positive cases with failures occurring even when the accuracy is high.

In order to achieve better monitoring of the state of the model’s operation, specific thresholds were set for each metric. The alerts corresponding to a number of threshold values were created in order to evaluate the metric performance and categorize them into three states: Normal, Marginal, and Critical. Figure 29 shows the results of condition monitoring where 11 (55%) alerts were found and classified as Normal, 5 (25%) as Critical, and 4 as Marginal (20%), with a total of 20 alerts. In general, what we find is the satisfactory operation of the majority of the alert elements, which indicates that the system is working properly.

4.2.5. Update Database

Proper monitoring of the operational status of the machine and the elevator system requires the process of updating and managing the data in real time. A data collection and processing platform with the ability to monitor vibration and energy values was built. The platform design was based on the new ISO 20816-3 standard, as shown in Figure 30. It distinguishes the operating state of the motor, considering the rms value of the speed and the estimated change of state. In order to make any malfunction more distinct, there is a color separation of the states.

Based on the results of the predictive maintenance, the state of health of the machine is classified as Normal, indicating that the equipment is operating within acceptable limits. The vibration velocity measurement is 0.94 mm/s, it is classified as Newly Commissioned Machinery, and no immediate intervention is required. In addition, taking into account temperature variations, the estimated remaining health lifetime is highest at 3 months, an extremely positive indicator of the machine’s functionality.

The possibility of monitoring the energy quantities allows us to transmit online electrical characteristics of the stator windings and the system in general. In Figure 31 we can distinguish the state of the motor based on the energy data, the manufacture’s specifications, and the active power. The data includes the recording of the rms values of voltage and current in the three phases of the motor and the total apparent, reactive, and active values, as well as the harmonic distortion of voltage and current. Also, for better visualization of the results, the platform has the ability to display the voltage waveform as shown in Figure 31.

To ensure reproducibility and to support further research, the complete dataset used in this study, including synchronized current and vibration signals under healthy and faulty conditions, has been made available through an open access repository [94].

5. Discussion

The proposed methodology relies on machine learning techniques in order to achieve early fault detection in elevator drive systems by monitoring the functionality of the PMSM. The simulation results demonstrate the accuracy and effectiveness of the proposed method as well as categorization of system operating states for immediate intervention. The main novelty of this paper is the utilization of two basic signals for studying electrical and mechanical problems, their processing for feature extraction, the combination of categorization and data generation techniques, as well as the comparative investigation of various machine learning algorithms. Unlike other traditional techniques, the work presented in this paper does not rely on reactive maintenance but adopting predictive maintenance, thereby minimizing cost and improving output. Other ML approaches require a large amount of labeled data, while PU learning overcomes this limitation.

Some future extensions of the technique could be as follows:

• Using Edge AI with a local analysis capability, reducing the need for cloud computing and response delays;
• Incorporating Explainable AI into machine learning algorithms to better understand the causes of faults;
• Evaluation of alternative RF approaches by implementing Multi-Agent (MARL) and Meta-RL;
• Digital twin technology to simulate different lift faults;
• A combined study of other machine learning algorithms such as Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), and Bayesian Neural Networks (BNN);
• Combining Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) to extract spatial and temporal features from sensors;
• Enhancement of feature extraction via Wavelet Packet Decomposition (WPD) and Empirical Mode Decomposition (EMD) for the detection of non-static and nonlinear patterns in signals from PMSMs.

6. Conclusions

Focusing on the key points of this paper, we can see the significant contribution of advanced signal analysis methods as well as an improvement in fault prediction. Our research proposes a PMSM maintenance framework for elevator applications based on machine learning methodologies to monitor the system status in real operating conditions, avoiding potential outages and ensuring robust reliability.

The effectiveness of the proposed method is distinguished through the use of PU learning, Reinforcement Learning, and deep machine learning models for more accurate diagnosis and correct fault classification. The results confirm that the algorithm was found to be highly effective against key challenges such as a lack of labeled data. Furthermore, the use of Gaussian Filter and Extended Kalman Filter (EKF) led to a significant improvement of the signals by removing noise in the sensor data, while signal analysis via Short-Time Fourier Transform (STFT) and Fast Fourier Transform (FFT) allowed for an initial analysis of possible electrical and mechanical faults.

With advanced data visualization and analysis evaluating the performance metrics, the accuracy and other factors confirmed the reliability of the system, while visualization techniques helped to better understand fault patterns. Experimental measurements showed that the system can operate independently of the lift control panel, offering a non-intrusive solution for preventive maintenance. The probability of fault occurrence based on the data processing reached 35%, while the proposed maintenance time was calculated at 5 days based on the analysis of the measured current values. Finally, it was considered necessary for the maintainer to monitor the alarms in the Marginal and Critical states particularly, in order to be able to intervene immediately and to reassess the situation in a short time.

This work demonstrates the feasibility of a non-intrusive, multimodal, AI-driven fault prediction system on a real operational elevator with a PMSM drive. The method operates without requiring access to the controller or motor internals, ensuring compatibility with warranty and safety regulations. Future extensions of this research study could include a sensitivity analysis of the parameters affecting the data training model, as well as the implementation of predictive maintenance based on data collected using different motor types and elevator architectures with additional smart sensors. In addition, Finite Element Analysis (FEA) could be employed to simulate fault conditions in the PMSM, enabling the system to detect fault types, estimate their probability of occurrence, and define corresponding threshold values.