The methodology of this study can be described under three main sections: creating the digital model, constructing the predictive maintenance workflow, and testing the predictive maintenance algorithm. In this section, the methodology of the study is explained.
2.1. Creating the Digital Twin Model
The first step in the methodology is creating the digital twin model for use throughout the study. In this step, the aim was to build a high-fidelity physical model of the real-life physical object or system under focus. The three main parts of this step are modeling the behavior of the individual components, modeling the behavior of the overall system (collection of components), and finally, modeling the sensors and fine-tuning the parameters [5
], as shown in Figure 1
The system modeled consists of a motor and gearbox. The circuit includes components from electrical, thermal, rotational motion, and translational motion domains. The system represents the motor circuit of the main driver of a metal sheet roller machine. Two main base components of the model are the universal (electrical and mechanical components) motor, driven by a DC voltage source, and the gearbox, which reduces the rotation of the motor. The DC-driven universal motor of the circuit is designed based on electrical (Kirchhoff’s voltage law) and mechanical (Newton’s second law of motion) equations. The two governing equations of the motor are
(Kirchhoff’s voltage law), where
is the input voltage,
is the motor resistance,
is the motor current,
is the motor inductance, and
is the back electromotive force, and
(Newton’s law), where
is the electromotive torque,
is the load torque,
is the total inertia,
is the angular velocity, and
is the angular friction. The two equations are connected by the relationship between electromotive force and angular velocity (
is the back electromotive force constant), as well the relationship between the torque and current (
is the torque constant). Figure 2
below shows a simple physics-based schematic of a DC-driven universal motor [16
However, as stated, this study was focused on investigating the vibration signals. Thus, one of the key parts of the model is the vibration signal created by the subsystem that transforms the total rotational displacement at the output of the motor and gearbox to translational motion via masses and springs. The vibration signal is measured from the spring-damper chain found in this subsystem. The thermal domain components are temperature sensors, which can monitor the heat exchange between the motor and the environment. All measurements are gathered by respective sensors placed in the model (electrical sensors, thermal sensors, translational motion sensors, and rotational motion sensors). The main technical challenge in the model creation step was obtaining a reliable and accurate vibration output signal compatible with the digital twin model. With the initial version of the twin model, adding a subsystem that directly generates a vibration signal failed to yield desired results due to the operation mechanisms of the existing fault models. To ensure a satisfactory vibration output, the digital model was renovated, and several obsolete fault models and sensors were removed and replaced by new fault subsystems, as well as a subsystem to generate a vibration signal, creating more accurate vibrations from the digital twin. Another challenge was to find a suitable consistency tolerance for the solver configuration of the model. The default value for the consistency tolerance (
) provided by Simulink caused some simulations to raise error flags, and the interruption of the whole simulation process, due to calculational insensitivities of the motor current signals. This consistency tolerance was alleviated to
to eliminate false error flags and obtain a smoother simulation process. The digital twin model was constructed in MATLAB Simulink, and all simulations/data generation and gathering related to the twin model were carried out in MATLAB. Figure 3
below shows the digital twin model created in MATLAB Simulink.
Fault modeling is a key part of a digital twin model used in predictive maintenance [17
]. In this study, the main emphasis of the model was also the fault modeling. Two fault types were investigated and modeled in this study: gearbox tooth faults and vibration sensor errors. The tooth fault was modeled by inserting an undesired faulty torque at a fixed position (an error in a fixed tooth) in the turn of the gearbox shaft. A value of this disturbance torque of 0I indicates no error in the model. A visualization for gearbox tooth faults is shown in Figure 4
. The second type of error source is in vibration sensors. In order to represent both the measurement errors and the intrinsic mechanical errors of these sensors, a simple offset was inflicted in the measurement of the vibration sensors; a value of 0 in this offset indicates no error in the measurement of vibration signals.
Both errors (gearbox tooth fault and vibration sensor drift) described in the previous paragraph are modeled as subsystems in the diagram shown in Figure 3
above. Another subsystem shown in the diagram functions as a tachometer, in case it was needed. Although this subsystem was not used in this study, it is potentially valuable in further work. The tachometer’s output (output of the subsystem) contains pulses that correspond to the rotations of the motor and the gearbox.
The content of the digital physics-based model is as explained above. The last part of the modeling step is setting the parameters of the components of the twin, as shown in Figure 1
above. For this part, the parameters of the components were carefully tuned and set, after consulting the owner of the SPW machinery, the firm NOKSEL. To create conditions that were as close to reality as possible, all the parameters were set to the values provided by the owning firm, and if the exact value of a parameter could not be obtained, an approximation was made that was known to be correct to the nearest order of magnitude. As can be seen from Figure 3
above, the digital twin model contains 87 components, and in consequence, many parameters. These parameters include the electrical power, inertia and rated speed of the universal DC motor, voltage of the DC supply that drives the motor, follower-to-base teeth ratio of the gearbox, resulting losses of the system due to friction, and values of masses and inertias in the damping components. As can be understood from this variety of components, for the purpose of the digital twin, it is crucial to be as close to the real values of parameters as possible. If the parameters of components are unrealistic, the behavior and the output signals of the digital twin would not reflect the actual behavior of the SPW machinery. Thus, a precise co-operation was conducted with NOKSEL to fine-tune the component parameters. After the parameter calibration step, the modeling was completed. The main benefit of a physics-based digital twin model is the ability to generate synthetic data. In this study, the described digital twin model was constantly used to generate both healthy and faulty synthetic data, for use in the later stages, during the predictive maintenance algorithms development.
2.2. Predictive Maintenance Workflow
In general, a basic predictive maintenance workflow has four main steps [19
]: data acquisition, preprocessing, identifying condition indicators, and training. An image depicting these four steps can be seen in Figure 5
As shown in Figure 5
, the first step of the algorithm is acquiring the data to be worked on. Each predictive maintenance workflow begins with data, either synthetic or real-life data [12
]. In this study, synthetic data were generated via the digital twin model described in the previous subsection. The digital twin model is configured with error variables that describe the level of two error sources, namely gearbox tooth fault and sensor errors, as explained above. Changes in the values of these error variables in different simulation runs generate different vibration data. In order to ensure generalizability of the results, the values of error variables were assigned randomly in different simulations from a certain boundary of values. The synthetic data generation algorithm is briefly described in Algorithm 1 below. As well as the synthetic data, real life data were also used to test the created predictive maintenance algorithm (the testing process is explained in detail in the following section). Real life vibration data were acquired with a sampling period of 10 ms and the data included 411,863 datapoints. Furthermore, a frequency domain analysis was carried out to confirm the resemblance between the generated synthetic data and measured real-life data. Both real-life and synthetic data were transformed via the Fourier transform, and frequency contents were compared via power spectra and peak frequency analysis. The resulting graph of the power spectra analysis, shown in Figure 6
below reveals that the bandwidth of the synthetic data (spectrum shown in the bottom graph in Figure 6
) and the bandwidth of the real-life vibration data (spectrum shown in the top graph in Figure 6
) were both between approximately 30 and 45 Hz, and the peak frequencies were at approximately 39 Hz in both data. The boundary of power values for each data was also very close, indicated by the y
-axis of both graphs in Figure 6
|Algorithm 1 Synthetic Data Generation Algorithm|
|Input: Description of the List of Failures|
|(1) Develop Detailed Physics-Based Model of the Process|
|(2) Develop and Implement Modelling Strategies of the Failures|
|(3) Input Realistic Range of Variables Responsible of the Failures|
|Randomly vary the Variables Responsible of the Failures|
|Run Until Enough Data|
|Output: Supervised Dataset for Predictive Maintenance|
The next step of the predictive maintenance workflow is preprocessing. Preprocessing is essential for all applications of machine learning model development processes in the following step, extracting condition indicators [20
]. In this step, the raw data are manipulated and transformed into a form that facilitates the extraction of features and indicators. In this study, the preprocessing step consisted of three sub-steps. First, the first section of simulation outputs, called the transient response of the simulation, was removed to obtain the actual frequency contents of the signal. Then, the signals were filtered to reduce the noise. Lastly, in this step, each simulation was classified based on the type of error. There are two different error variables, and either of these may or may not induce an error based on its value; thus, four different classes emerge. If both error variables are in the boundary, such that they induce no error, the simulation is said to be in the healthy condition (Class 0), and if both error variables are in the error interval, the simulation is said to be in Class 3 (both variables induce error). In Class 1, there is only a gearbox tooth fault present in the simulation, and in Class 2, only vibration sensor drift error. Another challenge in the synthetic data generation process was determining the threshold levels for the error source variables, which indicates whether a simulation condition is healthy or faulty. As the values for the error variables were randomly given from a specified interval, choosing very small healthy condition boundaries resulted in domination of the sampling of faulty conditions, lowering the accuracy of identification of the healthy conditions in the classifier model training step, because the healthy condition class was under-sampled. Such a sampling inequality was overcome by broadening the threshold values specifying the healthy conditions, leading to a greater overall accuracy of the classifier. Figure 7
below shows an example simulation output before the preprocessing step (Figure 7
a) and after (Figure 7
b). Note that the first 5 s of the signal (the initial transient response) in Figure 7
a was removed, as well as the noise.
The following step was the identification of the condition indicators, also called features. Features are properties belonging to a particular dataset that change in an anticipated manner as the system itself changes or deteriorates [21
]. Condition indicators are features involved in many different areas of signal analysis, including time domain features (e.g., mean and standard deviation), frequency domain features (e.g., power bandwidth and peak frequency), and time–frequency domain features (e.g., special entropy and special kurtosis). In this study, the following 18 different features from time and frequency domains were extracted from the preprocessed data: signal mean, median, RMS value, variance, peak value, peak-to-peak value, skewness, kurtosis, crest factor, median absolute deviation (MAD), range of cumulative sum, correlation dimension, approximate entropy, Lyapunov exponent, peak frequency, high-frequency power, envelope power, and spectral kurtosis. As seen, the features used belong to the time domain, frequency domain, and time–frequency domain. These features were chosen as being well-established types of evaluating signal data, in particular, signals that have distinct frequency content, as in the case of vibration signals [22
]. After all 18 features were extracted from the data, neighborhood component analysis (NCA) was applied to the features for the two error sources in the model. NCA ensures that only relevant features (relevant condition indicators) are retained and that the others (those not useful in diversifying different error classes) are disregarded. This accelerates the final step of the predictive maintenance workflow, model training.
Model training is the final step of the predictive maintenance workflow of this study, as mentioned above. A trained model lies at the heart of the predictive maintenance algorithm. This model examines extracted condition indicators (or features), either to assess the system’s present state (fault detection and diagnosis) or to forecast its future state (remaining useful life prediction). After the features are extracted from the preprocessed data, and NCA is used to disregard undecisive features, and the remaining features are used to train a machine-learning model to determine the current error condition of the physics-based model. In both synthetic data and public dataset cases, the remaining features were the same, and for both cases, NCA decreased the number of features from 18 to 11: mean, median, peak, kurtosis, crest factor, MAD, range of cumulative sum, correlation dimension, approximate entropy, Lyapunov exponent, and envelope power. Determining the current condition of the digital twin model means assigning a class of error conditions to the current state of the model (according to current value of error variables) among the four error condition classes described earlier. Details of the model training are explained in the following subsection.
2.3. Testing the Predictive Maintenance Algorithm
The proposed predictive maintenance workflow described in the previous subsection was tested by two methods. The first test used bearing data provided by the public dataset of Case Western Reserve University (CWRU) [23
]. This dataset provides bearing test data for normal and faulty bearings, which resembles the results aimed at by generating synthetic data (healthy and faulty conditions). As with the synthetic data, the CWRU data also included four classes, one healthy and three faulty. Data in the public dataset were collected at 12,000 samples per second. These collections were continuous measurements, and in different time intervals, different fault conditions were exposed. However, in order to create enough different data elements, the continuous measurements were segmented by 1001 data points (in order to accord with the synthetic data, which consisted of 1001 data points for different simulations, as explained subsequently). In order to test the proposed predictive maintenance algorithm, the dataset was first preprocessed as explained in the previous subsection. Then, the features listed in Section 2.2
were extracted from the preprocessed data, and NCA was applied to eliminate unhelpful features. The process concluded with the training of the diagnosis model (the model that estimates the current state of the digital twin). This training involved the feature table composed of all 11 relevant features remaining after NCA, as listed in the previous section, for all data elements. Then, this feature table was used for training with many different state-of-art machine learning algorithms, such as SVM, ensemble trees, naïve Bayesian, KNN, and discriminant methods. The accuracy of these predictions was examined with different algorithms to assess the success of the proposed predictive maintenance algorithm. Of the many classification algorithms that were used to train the model, the 5 above-listed algorithms yielded the most accurate results for both the synthetic data and the public CWRU dataset during classification. Thus, the classification accuracy for these 5 algorithms is presented in the graphs and discussed in the next section, Results and Discussion.
The second test of the algorithm was conducted on the generated synthetic data. This test resembles the test with the public CWRU dataset but using the synthetic data from the digital twin model instead of the bearing data from the public dataset. These synthetic data were also a continuous measurement for each simulation. Each simulation was run with different error variable values and lasted 15 s. In the preprocessing, the first 5 s was removed as the transient response, leaving 1001 measurements (1001 data points) in each simulation. For each error variable, 50 random variables were used; thus, in total,
simulations were obtained, which means 2500 different elements were classified in the training model. The number of random variables (50) was deliberately chosen for computational efficiency, a priority in this study. In addition, 2500 simulations yielded a large enough dataset to run classification models, without producing very complex and time-consuming results. If computational efficiency had not been a concern, the number of different error variables could be increased, as discussed in the future work section. Once again, the features listed in Section 2.2
. were extracted from the data, and NCA was applied to eliminate unhelpful features. The resulting feature table (with the remaining 11 features listed above in Section 2.2
, as with the CWRU dataset case) was used in training with the same algorithms as listed in the previous paragraph, and once again, the accuracies of these predictions were examined to deduce the accuracy of the proposed algorithm. The overall, complete flowchart of the proposed workflow, including the synthetic data generation step, is shown in Figure 8
below. The classification accuracy results for the CWRU dataset and synthetic data are presented and discussed in the following section.