Efficiency-Centered Fault Diagnosis of In-Service Induction Motors for Digital Twin Applications: A Case Study on Broken Rotor Bars

Abstract

The uninterrupted operation of induction motors is crucial for industries, ensuring reliability and continuous functionality. To achieve this, we propose an innovative approach that utilizes an efficiency model-based digital shadow system for in situ failure detection and diagnosis (FDD) in induction motors (IMs). The shadow model accurately estimates IM losses and efficiency across various operational conditions. Our proposed method utilizes efficiency as the primary indicator for fault detection, while losses serve as condition indicators for fault diagnosis based on real-time motor parameters and loss sources. We introduce a bond graph as a fault diagnosis network, linking loss sources, motor parameters, and faults. This interconnected approach is the key aspect of our proposed diagnostic method and aims to be used in fault diagnosis as a general method. A case study of a broken rotor bar is used to validate the proposed method using a dataset of five motors. Among these, one motor operates without failure, while the remaining four exhibit broken rotor faults categorized as 1, 2, 3, and 4. The proposed method achieves 99.99% precision in identifying one to four defective rotor bars in IMs. Comparative analysis demonstrates good performance compared to vibration-based FDD approaches. Moreover, our methodology is computationally efficient and aligned with Industry 4.0 requirements.

1. Introduction

The current worldwide electrical energy consumption is predominantly attributed to the industrial sector, which comprises around 42% of the total electrical energy produced [1]. The energy demand is increasing in the industrial sector and the share of energy produced from renewable resources is not sufficient to meet the needs of the industry. Some of the cost-effective measures that target energy efficiency are important in the achievement of industrial energy goals. Electric motors are the largest consumer of industrial energy, and they consume 70% of the total energy used in industries; induction motors consume about 55% of the industrial electrical energy. This places them in the best position to benefit from energy conservation measures, hence the goal of improving industrial energy efficiency. Many studies repeatedly stress the importance of maintenance as one of the key approaches to achieving energy conservation, which in turn optimizes the performance of machines [2,3,4]. The advent of the fourth industrial revolution has greatly revolutionize the way the maintenance is conducted [5]. The traditional maintenance methods are improved, and some of them has been replaced by methodologies that use AI algorithms or signal processing. Condition-based maintenance (CBM), predictive maintenance (PdM), and perspective maintenance (PsM) have emerged as the main strategies in the context of the maintenance practices in the context of the fourth industrial revolution, also known as Industry 4.0.

CBM involves the estimation of remaining useful life (RUL) to proactively prevent unforeseen failures and plan maintenance actions in advance. This approach enables the reduction in downtime and the minimization of maintenance costs [6]. The concept of RUL involves the prediction of failure through the analysis of previous machine operating data or the extraction of direct data using model-based, data-driven, or hybrid methods. RUL aims to determine the time remaining before failure occurs [7,8]. The majority of references in the literature discuss the utilization of artificial intelligence in the RUL approach [9]. Preventive maintenance (PM) is executed via Prognostic Health Management (PHM), which entails the monitoring of the machine’s health status using sensors that assess various metrics across its components. Subsequently, a prognostic algorithm is employed to simulate and forecast the machine’s state of health. Correlation models, optimization algorithms, and Bayesian approaches are the primary strategies employed in Prognostics and Health Management (PHM), with Bayesian methods being particularly appealing [10]. Prognostics pertains to the estimation of the remaining useful life of a machine, specifically in the context of failure detection and diagnosis.

The process of fault detection and diagnosis starts by detecting an abnormality in a machine, which is followed by the determination of the cause of this abnormality. This procedure addresses the inquiry regarding the fault that is accountable for the occurrence of this abnormality. In the field of FDD, the life cycle of a machine is categorized into three distinct stages, namely normal operation, early fault, and failure. The early detection and diagnosis of defects in IMs throughout the manufacturing process is very important. This allows for timely maintenance, ensuring their continuous operation and significantly minimizing the likelihood of unexpected shutdowns. Several methods have been proposed for the identification and diagnosis of faults in IMs as a result of the contributions made by several researchers in this sector. In their study, Liu and Bazzi (2017) categorized FDD techniques for squirrel cage motors into four distinct groups, differentiating between established and emerging methods [11]. A previous study devised a methodology for detecting and diagnosing faults in rolling element bearings at an early stage. This approach relied on the utilization of the wavelet transform technique applied to vibration signals [12]. The authors of reference [13] presented a classifier that utilizes the Transformer architecture in their article. The classifier demonstrates proficiency in classifying different types and levels of well-known problems and the capacity to detect previously unidentified faults. The researchers transformed raw vibration data into time–frequency spectrograms, which were then employed as the input for the classifier to perform fault categorization.

The quest to enhance fault detection in induction motors continues to be a significant area of research. However, there exists a noticeable gap in the literature concerning the application of Digital Twins for fault detection in induction motors and electrical motors in general. While the Digital Twin development considered multiphysics analysis, the fault detection topic is predominantly examined from a Finite Element Analysis (FEA) perspective [14,15,16,17]. An overview of recent research papers is given on induction motor fault detection in general, including Digital Twin-based detection. In [18], the authors present a novel methodology for detecting broken rotor bar faults in AC induction motors using a cascaded flux linkage and stator current observer. The objective is to enhance fault detection sensitivity and accuracy by introducing the fault diagnosis and amplifying (FDnA) system, which combines flux linkage and current observer signals. The mentioned method achieves over 20% fault detection sensitivity, outperforming traditional methods such as Motor Current Signature Analysis (MCSA), the stator current observer, and flux linkage observer. Simulation results demonstrate that the FDnA system exhibits higher fault detection sensitivity and reliability compared to existing fault detection techniques. In [19], the authors focus on fault diagnosis of induction machines for rotor cage damage using Motor Current Signature Analysis (MCSA) for industrial applications. The objective is to detect rotor cage faults early to prevent sudden breakdowns and improve machine reliability. The methodology involves implementing MCSA to analyze current signatures and identify rotor cage faults. The achieved results show a significant enhancement in machine performance, with efficiency increasing from 69.14% to 88.83% and the machine’s lifespan extending from two to fifty-nine months. In [20], the authors present a novel approach for broken rotor bar (BRB) fault diagnosis in induction motors using the third-order energy operator (TOEO). The objective is to accurately detect BRB faults by effectively suppressing spectral leakage and enhancing fault features. The methodology involves applying TOEO to demodulate current signals and highlight energy and impact components associated with BRB faults. Experimental tests on line-fed and inverter-fed induction motors demonstrate the effectiveness of the TOEO approach, with quantitative results showing improved fault identification compared to other demodulation techniques such as Teager–Kaiser energy operator (TKEO) and normalized frequency domain energy operator (FDEO).

Our methodology introduces the concept of an efficiency model-based digital shadow for condition monitoring in induction motor fault detection and diagnosis. This strategy involves the development of both healthy and faulty motor digital shadows, utilizing a hybrid approach that combines real-time operational data with advanced simulation techniques. This dual-model system not only enhances the accuracy of condition monitoring but also provides a more nuanced understanding of the motor’s performance across different states of health. This study presents an innovative approach for the detection and diagnosis of faults in induction motors, aimed primarily at facilitating predictive maintenance. The proposed method employs a digital shadow based on an efficiency model to monitor losses and efficiency in real-time, serving as condition indicators.

The present paper is structured in the following manner. Following the introductory portion, Section 2 presents our research background, including fault detection techniques, the contribution, and the novelty of the proposed study. In Section 3, we introduce the proposed technique, which utilizes IM losses and efficiency as condition indicators for default detection and diagnosis through the application of Digital Twin (DT) technology. Section 4 provides an account of the outcomes and subsequent analysis according to the proposed methodology. In this study, we conduct a comparative analysis between our proposed method and existing approaches that utilize vibration signals for broken rotor bar fault detection and diagnosis. Our findings demonstrate that our method outperforms these existing methods in terms of performance while also exhibiting a reduced computing cost. Lastly, in Section 5, we present our concluding remarks and discuss potential avenues for future research.

2. Research Background

2.1. Induction Motor Faults Detection

An induction motor is an electromechanical device that converts electrical energy into mechanical energy by creating an electromagnetic field in a revolving element called the rotor. The rotor is mechanically linked to a load by a shaft and undergoes rotational motion as a result of the electromagnetic field’s interaction with the stator. The stator, being the immobile component of the motor, encompasses windings responsible for generating the electromagnetic field. Induction motors systems are extensively utilized in diverse industry sectors owing to their strong resilience, simplicity, and effectiveness.

However, as illustrated in Figure 1, induction motors (IMs) are vulnerable to various faults that can significantly affect their overall performance, reliability, and safety. The two primary types of faults found in induction motors (IMs) are mechanical faults, which account for 45–55% of the faults, and electrical faults, which make up 35–40% of the faults [21].

The identification and diagnosis of faults is a crucial component of maintenance practices and has garnered significant attention in academic study across diverse fields. Throughout the years, a wide array of methodologies has been developed to identify and diagnose fault in induction motors. These techniques are commonly classified into four distinct classes, namely frequency domain, time domain, time–frequency domain, and AI-based methods. However, for the sake of simplicity, it is possible to integrate the first three methods under the category of fault frequency-based approaches. Hence, these techniques can be categorized into two main groups: artificial intelligence-based fault diagnosis (AI-FD) and fault frequency-based techniques (FF-FD) [11,22]. The integration of multiple methodologies in research has resulted in the development of a novel category referred to as hybrid fault detection and diagnostic methods. This hybrid methodology capitalizes on the respective advantages of AI-FD and FF-FD techniques to augment the precision and dependability of fault identification in induction motors.

Fault frequency-based (FF-based) approaches, which are commonly referred to as classical methods, cover a diverse array of methodologies for processing sensor signals. The aforementioned methodologies employ a range of indications, including but not limited to vibration, current, acoustic, sound, torque, speed, and thermal imaging, to identify and assess malfunctions in induction motors. Vibration-based and current-based approaches are the prevailing techniques employed for FDD in electric motors and generators. These methods are used due to their ability to accurately depict the dynamic behavior of the devices [23]. Nevertheless, the task of detecting faults by analyzing these signals is somewhat challenging due to the presence of high noise interference [24]. To address the problem of noise interference in fault detection, several sophisticated signal processing systems have been created. The methodologies encompassed in this category consist of sparse decomposition (SD), stochastic resonance, local mean decomposition, and ensemble empirical mode decomposition (EEMD). These technologies improve the precision of defect detection by efficiently eliminating signal noise. Furthermore, the successful execution of these methods necessitates the utilization of specific equipment and experience [22].

FDD are important aspects of maintenance that have drawn a lot of scholarly interest. Different approaches have been developed to detect faults in induction motors; these techniques are generally categorized into four categories: frequency domain, time domain, time–frequency domain, and AI-based methods. The first three may be combined into two primary categories, artificial intelligence-based fault diagnosis (AI-FD) and fault frequency-based techniques (FF-FD), for simplicity’s sake. These are based on fault frequency [11,22]. The emergence of hybrid approaches that combine FF-FD and AI-FD has improved the accuracy and reliability of fault diagnosis.

In order to identify faults in induction motors, fault frequency-based (FF-based) approaches, sometimes referred to as classical techniques, examine sensor data such as vibration, current, sound, torque, speed, and thermal imaging. Although noise interference is a barrier, approaches based on vibration and current are particularly successful in capturing the dynamic behavior of motors [23]. Advanced signal processing methods such as local mean decomposition, stochastic resonance, sparse decomposition (SD), and ensemble empirical mode decomposition (EEMD) have been developed to counteract noise. By lowering signal noise, these techniques increase the accuracy of defect identification; yet, they call for certain tools and knowledge [22].

The use of AI approaches for fault detection and identification in induction motors has gained traction due to the shortcomings of conventional methods. AI-based techniques are becoming more and more common in the detection of motor faults because they provide a number of benefits, including enhanced fault prediction through historical data analysis and flexibility to different operating situations [25].

The process of utilizing AI to analyze massive datasets, extract characteristics, and categorize defects using machine learning (ML) algorithms is known as intelligent fault diagnosis (IFD), or AI-based fault detection. Neural networks (NN), K-Nearest Neighbors (KNN), Support Vector machines (SVM), and the Adaptive Neuro-Fuzzy Inference System (ANFIS) are some of the modern machine learning techniques used in fault detection and diagnosis (FDD) [17,21]. Fault identification and diagnosis are further improved by AI approaches such as Bayesian classifiers, Fuzzy Logic (FL), Genetic Algorithms (GA), Hidden Markov Models, Deep Learning (DL), and Support Vector machines (SVMs). Every AI-based technique has some advantages. ANFIS is good at managing uncertainty, NNs are good at identifying intricate patterns, and KNN is a straightforward but reliable method for regression and classification [26]. The particular motor system, the type of probable problems, and the data at hand all influence the approach selection. As a result, AI techniques are being used more and more for enhancing the identification and evaluation of motor faults.

Hybrid methodologies for failure diagnosis and detection in IMs combine AI with fault frequency-based techniques. By utilizing the advantages of both systems, these techniques improve accuracy, durability, and dependability. Generally, they entail the analysis of sensor inputs using the Fast Fourier Transform (FFT) for feature extraction, and then AI-based fault categorization into distinct categories, such as broken rotor bars or bearing problems. The hybrid approach improves noise reduction, feature selection, and defect prediction while addressing the drawbacks of each methodology, such as resource needs in AI systems and noise sensitivity in FF-based approaches.

2.2. Novelty and Significance of Our Work

In the light of previous analysis, a variety of monitoring strategies have been employed with considerable success in managing the health of induction motors. Notably, vibration-based and thermal-image-based monitoring strategies have yielded positive outcomes. Additionally, Motor Current Signature Analysis, or MCSA-based methods, are increasingly favored for their exceptional online monitoring capabilities and their broad scope in detecting various faults [27]. Despite these advancements, challenges persist, particularly in environments with significant noise interference and variable operating conditions, which can impact the optimal efficiency of health monitoring systems. Consequently, the industry necessitates health monitoring techniques that are not only accurate but also efficient in terms of computational resources. These techniques must guarantee consistent and reliable performance, even in sub-optimal conditions. The Digital Twin concept emerges as the optimal strategy to swiftly attain such high performance standards [28]. By creating a virtual replica of the physical motor, Digital Twins enable real-time monitoring and analysis, facilitating immediate adjustments and preemptive maintenance actions, thereby ensuring the motor’s health and operational longevity with minimal computational overhead.

For Digital Twin-based fault detection, the research carried out in [15] presents a novel methodology for optimal sensor placement in fault detection for permanent magnet synchronous motors (PMSMs) using a Digital Twin-assisted framework. The objective is to enhance the reliability and fault detection capabilities of PMSMs by using finite element simulation models to train a classifier for fault detection and optimizing sensor placement using a genetic algorithm. The study achieved a fault detection accuracy of at least 90% for every state. The study detailed in [16] showcases promising results that suggest the feasibility of constructing Digital Twins for induction motors with faults. This innovative approach allows for the verification of standard characteristics and failure signatures by employing both time and frequency domain analyses. Such a method provides a comprehensive understanding of the motor’s behavior under fault conditions, paving the way for more effective monitoring and maintenance strategies.

This research introduces a new approach that integrates the electrical equivalent circuit and ANFIS-based techniques, as outlined in reference [29], to assess losses and efficiency. These metrics serve as health indicators to aid in identifying the key features for detecting broken rotor bar (BRB) issues. The effectiveness of the proposed methodology enables the utilization of a condition-based algorithm for the identification and categorization of problems in BRBs. The validity of the method is established by conducting experiments and comparing its performance to that of state-of-the-art procedures.

The term “Digital Twin” (DT) pertains to a computer-generated representation that accurately reproduces the attributes and operational capabilities of a tangible system, hence facilitating the emulation of its performance and state. The utilization of the word in question was initially documented in the scholarly publication by Hernández et al. in 1997 [30], marking its introduction into contemporary industrial discourse. The field of DT has witnessed significant advancements through several research articles, leading to notable improvements. The implementation of DT techniques varies depending on the specific research objectives pursued. The efficacy of utilizing DT in the context of predictive maintenance has been demonstrated to effectively identify defects inside induction motors, hence mitigating operational downtime and minimizing associated maintenance expenses. The method being presented utilizes the losses and efficiency of IMs (induction motors) as indicators to detect and diagnose faults. The development of the DT model is grounded in the utilization of the double cage electrical equivalent circuit model including an accurate stray load loss model selected in [31]. This model effectively encompasses the dynamic behavior of induction motors across many operational scenarios. The efficacy of the proposed methodology is assessed through the utilization of a dataset comprising five motors. This dataset encompasses one motor that is free from any faults and four motors that exhibit various defects. The purpose of this dataset is to validate the effectiveness of the provided method.

The primary contributions and novelty of this research study are outlined as follows:

• We introduce an innovative fault detection and diagnosis technique for IMs that utilizes the results of a previously established efficiency model-based digital shadow approach [32]. This approach provides real-time data on losses and efficiency.
• We find 33 exhaustive and uncorrelated sources that influence the motor parameters and losses and hence the efficiency of the motor. These common sources are also associated with the effects of various faults.
• We developed two new tables from these common sources to highlight the losses impacted by these sources.

  Table 1. Sources considering the losses expression.

  Sources\Losses	Stator Joule Loss	Core Loss	Rotor Joule Loss	Mechanical Loss	Stray Loss
  Air density				√
  Air resistance (windage)				√
  Applied magnetic field		√
  Bearing friction				√
  Belt and pulley friction				√
  Belt leakage flux					√
  Brush friction				√
  Core geometry and construction		√
  Fan				√
  Harmonics	√		√		√
  Harmonics in air gap MMF					√
  Incremental leakage flux					√
  Magnetic saturation in tooth tips					√
  Material properties/Core material conductivity		√
  Motor casing				√
  Operating frequency	√	√	√
  Operating temperature	√	√	√
  Overhang leakage flux					√
  Peripheral leakage flux					√
  Proximity effect	√		√
  Resistance of rotor winding for slip ring motor			√
  Resistance of stator winding	√
  Rotor bar design for squirrel cage motor			√
  Rotor leakage flux			√		√
  Rotor speed			√	√	√
  Rotor–stator interaction				√
  Seal friction				√
  Skin effect	√		√
  Sliding contacts				√
  Skew leakage flux					√
  Stator leakage flux	√				√
  Variation in slot permeance					√
  Zig-zag leakage flux					√

  lists the sources of losses, while

  Table 2. The common sources that are impacted when faults occur.

  Sources\Faults	Turn-to-Turn	Coil-to-Coil	Phase-to-Phase	Phase-to-Ground	Broken Rotor Bar	Broken End Ring	Phase Unbalance	Single Phasing	Outer Race	Inner Race	Rolling Element	Cage/Train	Unbalanced Rotor	Bowed Rotor	Misaligned Rotor
  Air density							√	√
  Air resistance (windage)													√
  Applied magnetic field								√
  Bearing friction									√	√	√
  Belt and pulley friction															√
  Brush friction												√
  Core geometry and construction														√
  Fan												√
  Harmonics			√	√
  Harmonics in air gap MMF	√
  Incremental leakage flux	√
  Magnetic saturation in tooth tips				√
  Material properties/Core material conductivity											√
  Motor casing									√
  Operating frequency														√
  Operating temperature							√	√
  Overhang leakage flux	√	√	√	√
  Peripheral leakage flux	√	√	√	√
  Proximity effect			√
  Resistance of rotor winding for slip ring motor							√
  Resistance of stator winding							√
  Rotor bar design for squirrel cage motor					√
  Rotor leakage flux					√
  Rotor speed						√
  Rotor–stator interaction													√
  Seal friction										√
  Skin effect	√	√
  Sliding contacts					√	√
  Skew leakage flux		√
  Stator leakage flux		√
  Variation in slot permeance				√
  Zig-zag leakage flux	√

  associates these sources as specific causes of motor failures.
• We propose a loss-based fault detection network that outlines an overview of the algorithm for fault detection that is outlined below. In this network, the relationship between losses and faults is made through the motor parameters and shared sources. This network is the primary innovation of this paper.

Our methodology is validated using experimental data of broken rotor bars and compared with recent state-of-the-art methods that employ vibration signals for FDD [33]. This comparative analysis reveals that our proposed methodology offers superior performance and reduced computational costs.

3. Proposed Methodology: Efficiency-Based Fault Detection

The proposed methodology utilizes the concept of a Digital Twin in the context of Industry 4.0 to establish an efficiency-based fault detection and diagnosis for IMs by monitoring, in real-time, the losses and efficiency of an induction motor through an efficiency model-based digital shadow first developed in [29] and improved in [32]. The primary objective of this approach is to detect failure and diagnose the type of failure.

The using digital shadow is established following Figure 2 as follows:

• The induction motor double cage model with iron resistance is used to model the motor in terms of efficiency
• The motor efficiency model is established by considering non-intrusive losses models such as stator joule, core, rotor, mechanical, and stray using the double cage circuit.
• The motor parameters are identified using 60 nameplate data of different SCIMs for the first method and using operational data of a SCIM for the improved method. These data are used as a dataset to train the proposed ANFIS models.
• As the parameter will be estimated in real-time to calculate losses and efficiency, the routine Newton–Raphson algorithm is used, which is computationally expensive, Hence, the Adaptive Neuro-Fuzzy Inference System algorithm is used.
• The ANFIS algorithm is trained and tested to learn the behavior of the double cage model and estimated motor parameters in real-time application.

The above steps summarized the process used by our proposed digital shadow to calculate in real-time the motor parameters. This system is one-way data visualization, which is the second step in the Digital Twin implementation according to the reference architecture model 4.0, which shows the synoptic of the proposed digital shadow. Figure 2 illustrates the data acquisition process.

3.1. Losses and Faults in Induction Motors: Theoretical Background

The initial performance of a newly developed machine is characterized by its ability to operate at rated conditions while consuming a minimal amount of energy at its rated power. Nevertheless, the performance of the system may decrease with time as a result of several circumstances, including the process of aging, thermal cycle, environmental impact, etc. To ensure the machine operates at its highest level of efficiency, the implementation of maintenance practices is crucial as it directly contributes to the reduction in energy consumption. Despite the significant correlation between maintenance and energy efficiency, both domains are frequently investigated in separate ways from each other. In a study conducted by [2], the significance of maintenance and frequently employed energy efficiency strategies is examined. The study makes it clear that maintenance is a fundamental practice of energy saving. In another study, the authors conducted a comprehensive literature review to examine the relationship between maintenance practices and energy conservation in commercial refrigeration environments [34]. The researchers found that the implementation of good maintenance practices plays a substantial role in enhancing the operational efficiency of refrigeration equipment. Lewis et al. conducted a study in which they analyzed three case studies within North American enterprises. Their findings indicated a significant correlation between energy management and maintenance management, suggesting that these two aspects are interdependent [3]. In [35], the author employed the same dataset used in the present study to introduce a fault detection method for induction motors. However, challenges such as computational costs and low detection precision pose obstacles to the accuracy and real-world implementation of the method. In a separate investigation, a model with a quantitative approach was established to make a connection between energy consumption, maintenance failure rates, and production within the context of energy-intensive manufacturing [36]. The objective of the suggested methodology is to establish a correlation between the power losses of a machine and its defects through motors’ dynamic parameters and fault sources by identifying the optimal combination of losses that enables the detection of machine faults. An examination is carried out on the origins of power losses in induction motors (IMs) within their operational environment and their influence on the estimated energy efficiency. Simultaneously, an investigation is conducted into the factors that affect IMs and lead to defects. This enables the identification of the distinct impact of each fault on motor parameters, and consequently, its losses. This is accomplished by implementing an induction motor loss-based fault detection network. Then, a case study on broken rotor bar fault is considered to validate the method. The condition monitoring of broken rotor bars can be achieved through digital shadow in two ways: with motor nameplate data when data are not available enough [29], or with historical data when operational data are available [32]. This methodology entails the continuous monitoring of data and the establishment of a pre-determined threshold. This threshold serves as a reference point, beyond which the identification of broken rotor bar faults becomes possible. To the best of our knowledge, there hasn’t been any research that has employed losses as a technique for identifying faults in induction motors by taking into account the motors’ dynamic parameters and the common sources between these parameters and the faults. The fault detection technique shown in Figure 3, while Figure 9 summarized the main steps of the proposed method.

3.2. Interdependency of IM Losses and Faults: Feature Extraction

In this section, we will give the result of a survey of inefficiency sources, which means the internal and external sources that contribute to motor efficiency decrease. As shown in Figure 4, we account for a minimum of 33 sources of inefficiency in induction motors that we call common sources, which establish an interdependency between losses and faults through motor parameters. Even if one of these sources occurs, this can conduct in motor efficiency decrease. These sources impacted the motor power losses, and when a fault occurs in IMs, it causes some of these sources. Table 1 enumerates the sources of losses, while Table 2 correlates these sources with specific motor failures.

The occurrence of any failure in induction motors results in an elevation of motor losses, hence causing a subsequent decline in motor efficiency. If incipient defects are not identified and resolved promptly, they will lead to motor failure in the future. A decrease in efficiency at a specific threshold might serve as an indicator and contribute to the prevention of fault propagation and the subsequent reduction in associated losses. Hence, with regular monitoring of the operational efficiency of induction motors, it becomes feasible to identify potential defects and strategize maintenance actions accordingly. This approach can result in the implementation of cost-effective maintenance practices for induction motors. In the case of a singular BRB defect, there is a decrease in efficiency (Δη) of 2%. However, as the fault’s severity intensifies, this loss can escalate to 3% or 4%. In the event of a malfunction in the cooling system, there is a potential for heightened thermal strain on the insulation and windings, resulting in a steady state decline in Δη to 8% [4]. The observed correlation between fault occurrences and efficiency levels suggests a mutual reliance between losses and faults, hence establishing losses as potential markers for detecting faults. To offer fault detection approaches based on loss analysis, this study focuses on extracting loss characteristics from in-service IMs in both healthy and faulty conditions. The objective is to assess the impact of losses on each BRBF (basis function) and determine their contribution to fault identification.

Table 3. Efficiency loss under various fault conditions.

Fault	η1 (%)	η2 (%)	Δη (%)
Bearing damage	84	80	4
Failure of cooling system	81	73	8
One broken rotor bar (BRB)	75	73	2
Two broken rotor bar (BRB)	75	72	3
Three broken rotor bar (BRB)	75	71	4

summarizes the efficiency of motor depending on BRBF severity. Additionally, Figure 5 provides a summary of the proposed method’s flowchart.

3.3. Correlation-Based Feature Selection

The preceding analysis demonstrates a correlation between the occurrence of defects and losses in induction motors. The objective of this section is to determine the individual impact of each loss on the reduction in efficiency associated with a particular defect. Next, we will establish one, two, or three sets of losses that enable the distinct identification of a certain defect. These losses, whether employed individually or in combination, will serve as condition indicators. This study involves the graphical representation of losses and efficiency for both healthy and defective motors, with the aim of observing the effects of faults on machine losses and efficiency. As shown in Figure 6, from the common sources, we develop a fault diagnosis network.

One of the difficulties encountered in the practical application of this approach is the inability to directly measure losses in real-time on the physical machine.

Table 4. Comparison RMSE for efficiency and each loss: healthy data vs. 1, 2, 3, and 4 BRBF.

	Pjs	Pc	Pjr	Pm	Pstray	EE
1BRBF	17.667	0.0601	7.6877	2.322	0.0885	2.0005
2BRBF	27.5864	0.0485	25.5091	2.492	0.227	3.0009
3BRBF	37.576	0.0589	35.3361	2.662	0.0739	4.0002
4BRBF	46.4119	0.0488	44.5691	2.8279	0.0522	5.0005

shows the RMSE for efficiency and losses at rated condition in function of BRBF severity.

Consequently, we will rely on the digital representation of the machine, known as the machine digital shadow, to monitor losses for both broken and healthy machines, as depicted in Figure 7.

Figure 8 presents the Root Mean Square Error (RMSE) values, which measure the discrepancy between a motor in a healthy state and one affected by a broken rotor bar fault. Additionally, it shows the impact of losses on the efficiency reduction caused by the BRBF. This is achieved by displaying the correlation coefficient between healthy and faulty data, simplifying the identification of loss combinations for BRBF detection and diagnosis. The findings indicate a significant correlation between the BRB fault and the stator, rotor, and mechanical losses, suggesting these losses are reliable indicators of the motor’s condition.

• Stator joule losses can be attributed to the presence of stator current. This is particularly evident when a broken rotor bar (BRB) defect occurs, as it introduces more components into the stator current. These additional components exhibit frequencies that are directly linked to the power frequency, slip, and the number of broken bars. The identification and utilization of fault signatures can be achieved by incorporating the stator current into the fault statement.
• Rotor loss deals with the dissipation of energy resulting from the phenomenon of Joule heating occurring within the rotor bars and end rings. The result is dependent on the precise slip value and the existing current in the rotor circuit. The occurrence of a BRB fault leads to an elevation in slip and an uneven distribution of current within the rotor. As a result, this phenomenon results in an elevation of rotor loss.
• Mechanical loss pertains to the dissipation of energy caused by the occurrence of friction within the bearings and the windage effects that arise in the air gap. The operational efficiency of the motor is dependent on variables such as its rotational velocity and the magnitude of the applied mechanical resistance. The presence of a BRB leads to a decrease in motor speed and an increase in load, which therefore causes a corresponding elevation in mechanical loss.

Table 5. Rated values of losses contribution for broken rotor bar fault of 1hp 3~SCIM, with 34 bar 220/380 V 3.02/1.75 A.

Fault	Psj(W)	Pc(W)	Prj(W)	Pmec(W)	PStray(W)	η1 (%)	η2 (%)	Δη (%)
Healthy Motor	127.444	9.7665	51.243	9.7885	9.7685	75	75	0
One Broken rotor bar	144.912	9.761	58.93	12.1105	9.7281	75	73	2
Two Broken rotor bar	154.901	9.7605	76.752	12.2805	9.82285	75	72	3
Three Broken rotor bar	164.929	9.7675	86.579	12.4505	9.78015	75	71	4
Four Broken rotor bar	173.7755	9.771	95.812	12.615	9.7485	75	70	5

summarized the BRBF values provided through the proposed method for 1hp 3~SCIM based on experimental data. Figure 9 summarized the main steps of the proposed method.

4. Results and Discussion

The technique under consideration is implemented utilizing the operational data of a three-phase squirrel cage induction motor with a power rating of 1 horsepower. The motor is equipped with a total of 34 rotor bars and functions at two distinct voltage levels, namely 220 V and 380 V. These voltage levels correspond to respective currents of 3.02 A and 1.75 A. The device exhibits a four-pole arrangement and functions at a frequency of 60 Hz. The motor exhibits a nominal torque of 4.1 Newton meters (Nm) and operates at a rated speed of 1715 revolutions per minute (rpm). The dataset utilized for the suggested methodology is comprehensively elucidated in the provided reference [33].

4.1. Validation of Efficiency-Based Broken Rotor Bar Fault Detection and Diagnosis for IMs

The dataset has been structured in a manner that facilitates the introduction of a BRB fault during regular operation. This fault is thereafter simulated for 55 s. The motor demonstrates typical operation during the initial 15 s interval, followed by the introduction of a solitary occurrence of BRB fault data over the final 10 s. This pattern is iterated, wherein two occurrences of BRB fault data are introduced for each subsequent 10 s interval, until the last 10 s interval where four instances of BRB fault data are injected. The algorithm is as follows Algorithm 1:

Algorithm 1 Condition-based algorithm for BRB fault detection and classification
Input: measured losses ${\mathit{P}}_{\mathit{j}\mathit{S}}$, ${\mathit{P}}_{\mathit{r}}$, ${\mathit{P}}_{\mathit{m}}$, $\mathit{\eta }$
Output: 1, 2, 3, & 4 BRB fault detection
1:	If $\eta$ > 75%  do
2:	Display: “The motor operates on healthy condition”
3:	Else
4:	Display: “Broken rotor bar is detected”
5:	$\mathbf{If} 75\% > \eta$ > 73%, & 145$\mathrm{W} > P_{jS}$ > 128 W, & 59$\mathrm{W} > P_r$ > 51 W, & 12$\mathrm{W} > P_m$ > 9 W, do
6:	Display: “1 BRB fault is detected”
7:	$\mathbf{Else} \mathbf{If} 73\% > \eta$ > 72%, & 155$\mathrm{W} > P_{jS}$ > 144 W, & 77$\mathrm{W} > P_r$ > 59 W, & 12$.3 \mathrm{W} > P_m$ > 12 W, do
8:	Display: “2 BRB fault is detected”
9:	Else If$72\% > \eta$ > 71%, & 164$\mathrm{W} > P_{jS}$ > 155 W, & 86$\mathrm{W} > P_r$ > 77 W, & 12$.5 \mathrm{W} > P_m$ > 12.3 W, do
10:	Display: “3 BRB fault is detected”
11:	Else If$71\% > \eta$ > 70%, & 174$\mathrm{W} > P_{jS}$ > 165 W, & 96$\mathrm{W} > P_r$ > 87 W, & 12$.7 \mathrm{W} > P_m$> 12.5 W, do
12:	Display: “4 BRB fault is detected”
13:	Else, do
14:	Display: “Fault condition is unknown”
15:	End if
16:	End if

As shown in Figure 10, the simulation illustrates that the presence of a broken rotor bar (BRB) in induction motors results in an elevation of stator joule loss, mechanical loss, and rotor loss. As a result, a decline in efficiency and performance is evident. The proposed approach is substantiated by the application of a simple condition-based algorithm, which proficiently detects and classifies BRB faults by taking into account efficiency and loss thresholds.

The presence of BRB fault in induction motors has been recognized as a substantial element leading to a considerable reduction in their overall efficiency. The aforementioned reduction can have a substantial impact on the electricity consumption of businesses that utilize these devices. To provide an example, the existence of a solitary BRBF possesses the capability to induce a decrease in motor effectiveness of approximately 2%. The power loss for a motor with a power rating of 1 horsepower is measured to be 28 watts, leading to an annual energy usage of 102.2 kilowatt-hours. The present computation is predicated on the assumption that the motor functions for 10 h on a daily basis.

4.2. Comparison of the Proposed Method to the State-of-the-Art

To evaluate the efficacy of the suggested methodology, a comparative analysis is performed with the current state-of-the-art approach. This evaluation is based on a set of predetermined metrics:

• Diagnostic Accuracy: This is the proportion of true results (both true positives and true negatives) in the population. It is a measure of the correctness of a diagnostic test [37]. The higher the diagnostic accuracy, the more reliable the diagnosis method is.

$$\mathrm{A}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{y}={\displaystyle \frac{True Positive+True Negative}{Total number of sample}}$$

(1)

• Recall: Also known as sensitivity, it measures the proportion of actual positives that are correctly identified [38]. In the context of induction motor diagnosis, it would refer to the ability of the diagnosis method to correctly identify faulty conditions.

$$\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}={\displaystyle \frac{True Positives }{True Positives+False Negatives}}$$

(2)

• F1-Score: The F1-score is the harmonic mean of precision and recall. It tries to find the balance between precision and recall [39]. A high F1 score means that you have low false positives and low false negatives, so you are correctly identifying real threats and you are not disturbed by false alarms.

$$\mathrm{F}1\text{-}\mathrm{s}\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}={\displaystyle \frac{2\times Precision\times Recall }{Precision+Recall}}$$

(3)

• Computational Efficiency: This refers to the computational resources used by the diagnosis method, such as time and memory. A method with high computational efficiency will be able to perform the diagnosis quickly and using less computational resources, which is particularly important in real-time monitoring systems [40].
• Early Fault Detection: This refers to the ability of the diagnosis method to detect faults at an early stage, before they develop into serious problems. Early fault detection allows for timely maintenance and can prevent costly downtime [41].
• Predictive Capability: This refers to the ability of the diagnosis method to predict future faults based on current and historical data [35]. A method with strong predictive capabilities can help plan maintenance activities and prevent unexpected failures.

Each of these metrics provides a different perspective on the performance of the diagnosis method, and they are all important for a comprehensive evaluation. A good diagnosis method should score high on all these metrics. However, there might be trade-offs between these metrics depending on the specific requirements of the application. For example, in some applications, early fault detection might be more important than computational efficiency, while in others, the opposite might be true.

4.3. Discussion

Table 6. Comparative analysis of the proposed method and three contemporary techniques.

Metrics\References	The Proposed Method	[27]	[28]	[42]	[43]	[44]
Diagnosis Method	Efficiency-based Digital Twin	Ramanujan Digital Twin	Improved sparrow search algorithm, optimized random forest and Digital Twin-based	Novel sparse de-noising auto-encoder	Deep generative models	Digital Twin-enhanced semi supervised framework
Diagnostic Accuracy	99.99%	99.58	98.2%	93.20%	93.08	76%
Recall	0.98	0.96	0.97	NC	NC	NC
F1-score	0.99	0.98	0.98	0.93	NC	NC
Computational Efficiency	17.05 ms	322.56 ms	NC	238 ms	NC	NC
Early Fault Detection	YES	YES	YES	NO	YES	YES
Predictive Capability	YES	YES	NO	YES	YES	YES

presents an elaborate quantitative analysis, which compares the innovative methodology developed in this research with other recently documented methodologies for the identification and categorization of BRB in induction motors (IM). Upon conducting a comprehensive analysis of this comparison, it becomes evident that our proposed methodology has a high level of precision in detecting and categorizing damaged rotor bars. Significantly, a considerable body of empirical evidence indicates that the identification of BRB is enhanced by increased fault severity and mechanical loads. Furthermore, it is important to visually represent the temporal progression of fault frequency to authenticate the assessment of the operational condition of the induction motor. In this context, our proposed methodology effectively detecting the defective state, even during the initial transient phase, when subjected to only 25% of its specified mechanical force. This provides a visual representation of the changes in fault frequency over time, enhancing the diagnostic process by offering a valuable perspective. Finally, approach attains a 99.99% accuracy rate in the classification of all cases that were evaluated. The aforementioned accomplishment underscores the dependability, effectiveness, and applicability of our suggested methodology for identifying and categorizing faulty rotor bars. The work presented herein highlights the resilience of this technology, hence reaffirming its significance as a crucial tool in the field of induction motor diagnostics.

5. Conclusions and Future Works

This work presents a novel approach for detecting and diagnosing faults in induction motors (IMs) by utilizing losses and efficiency as condition indicators, leveraging the capabilities of Digital Twin (DT) technology. We develop a novel fault diagnosis network based on loss sources that use the correlation between fault and losses to facilitate the diagnosis. The approach we employed in our study involved utilizing an efficiency model-based digital shadow of induction motors (IMs) that was based on the double cage electrical equivalent circuit model. This model was chosen due to its ability to effectively represent the dynamic behavior of IMs across various operating situations. The methodology employed in our study involved the utilization of ANFIS-based techniques, as previously published in reference [32]. This approach was employed to extract and choose features as it can represent faulty and healthy motors to detect and diagnose BRB faults, leveraging data on efficiency and losses.

The validity of the method was established through the utilization of experimental data, followed by a comparative analysis with existing techniques that utilize vibration signals for fault detection and diagnosis. The results of our study indicate that the methodology we proposed achieved a good level of diagnosis accuracy, recall, F1-score, computational efficiency, ability to detect faults at an early stage, and predictive capability in identifying and categorizing faults in IMs.

The proposed study has several implications for both the theoretical and practical aspects of fault detection and diagnostics in the context of induction motors. The findings of the study indicate that losses and efficiency are more sensitive and reliable indicators for detecting and diagnosing faults in BRBs compared to vibration or current indications. Furthermore, the study demonstrated that the utilization of DT technology proved to be an effective methodology for simulating and forecasting the performance and state of intelligent machines across various scenarios.

The method we proposed also had certain conditions. To assure the validity and reliability of the DT model, it was necessary to have a significant degree of data quality, precision, and availability from the sensors and other data sources. The creation and updating of the DT model, particularly for large-scale or dynamic systems, necessitated a significant level of complexity and computational expenditure. The success of DT technology was contingent upon the accessibility and harmonization of software and hardware platforms that facilitated its implementation.

The method we have proposed also provides potential avenues for further investigation. The potential exists to broaden the scope of our methodology to encompass additional categories of faults or motors, including stator winding problems, bearing failures, and synchronous motors, among others. Additionally, it would be beneficial to evaluate the efficacy of our approach throughout various operating situations and loads, including factors such as fluctuating speed, varying torque, and diverse frequencies.