System and method for predicting motor eccentricity level using topology data analysis

Abstract

A system and method for detecting motor eccentricity faults is disclosed. The method includes extracting fault-related features via topological data analysis (TDA) of motor current signals and applying these fault-related features to motor eccentricity fault detection. The method further includes obtaining topological features from time-domain data and representing these topological features in a persistence diagram and a vectorized Betch sequence. The method further includes extracting fault-related features from the topological features obtained from the data that can be clearly related to not only the type of fault but also the fault severity level. The method further includes extracting the fault-related features from the TDA using a machine learning model to predict the motor eccentricity fault level for new eccentricity level data not present in the training data.

Description

[Technical Field]

[0001] This disclosure relates in general to motors, and more specifically to systems and methods for detecting motor operational failures. [Background technology]

[0002] Electric motors are widely used in various aspects of modern society, including factories, home appliances, and electric vehicles. With increasing use, and especially with the growth of the Internet of Things (IoT), monitoring motor operating conditions and detecting motor failures is becoming increasingly important. Motors can experience various failures, one of the most common being eccentric failure, which occurs when the air gap between the stator bore and rotor is not uniform.

[0003] Eccentricity failures can be classified into three types: static eccentricity, dynamic eccentricity, and mixed eccentricity. Static eccentricity occurs when the center of rotation coincides with the center of the rotor, but the center of the rotor is offset from the central axis of the stator bore. Dynamic eccentricity occurs when the center of rotation coincides with the central axis of the stator bore, but the center of the rotor is offset. Mixed eccentricity is a combination of both static and dynamic eccentricity.

[0004] There are various causes of motor eccentricity. Air gap eccentricity can damage other motor components and, if not corrected in time, can lead to machine failure using the motor. It is impossible to manufacture a motor with zero air gap eccentricity during the manufacturing process. Static eccentricity can result from imperfect alignment between the stator core assembly and the center of rotation, or from the stator core's deviation from a perfect circle. Similarly, small dynamic eccentricity can result from imperfect alignment between the rotor center and the axis of rotation, or from imperfect rotor shape. Over the operating life of a motor, the level of eccentricity can increase due to, for example, bearing degradation or mechanical degradation of the mounts, which can cause physical displacement of the stator assembly. Air gap eccentricity induces an unbalanced magnetic attraction (UMP) that counteracts the rotor's rigidity, and as eccentricity increases, it can lead to stator winding failure and friction between the rotor and stator, ultimately resulting in machine failure. Therefore, it is important to inspect electric motors for eccentricity during the manufacturing process for quality control and for operational safety and asset protection.

[0005] Vibration analysis and motor current signature analysis (MCSA) are the most widely used methods for detecting eccentric faults. UMP caused by air gap eccentricity results in increased vibration. This increased vibration can be monitored using accelerometers installed in the motor casing. In recent years, machine learning and deep learning techniques have been applied to the detection and classification of electromechanical faults based on measured vibration signals. However, vibration signals can be affected by noise from other sources, such as mechanical imbalances in the motor or external excitation in complex factory environments. Furthermore, the sensitivity of vibration analysis can vary depending on the sensor location on the motor casing. Therefore, identifying eccentric faults based solely on vibration signals is difficult.

[0006] MCSA has been proposed to address these problems. MCSA has the advantage of being easy to implement and cost-effective because it does not require the addition of dedicated sensors. MCSA detects eccentricity using stator current harmonics. In effect, the non-uniform air gap due to eccentricity causes further harmonics in the air gap permeance function and air gap flux. Some of these harmonics are reflected in the induced voltage of the stator windings and ultimately in the stator current. One challenge in detecting eccentric faults using MCSA is that many spatial harmonics caused by eccentricity can be reflected in the vibration signal, but not in the time harmonics and therefore not in the stator current. Furthermore, a particular stator current fault signature may depend on specific motor design parameters and is not universal for all motors. For example, certain combinations of stator lot number and rotor bar number have proven to make it more difficult to detect some fault signatures caused by static eccentricity.

[0007] Another method for analyzing eccentric failures is to use either time-step finite element simulations or circuit models based on the modified winding function method (MWFM). The above methods are primarily used for physics-based modeling. Finite element simulations can identify the failure frequency and its corresponding amplitude with greater accuracy, but they are time-consuming and require detailed geometric parameters and material properties of the motor. MWFM-based circuit models are much faster, but because the modeling process is simplified, they are not as accurate in identifying the amplitude of the failure component and still require specific motor design information beyond the nameplate, such as the nominal air gap dimensions, number of slots, and number of rotor bars for induction or synchronous machines.

[0008] Furthermore, applying data-driven methods to MCSA-based motor fault detection using only stator current signals is difficult. Unlike vibration signals, current components resulting from eccentric faults are generally several orders of magnitude smaller than the dominant fundamental component at the supply frequency. Machine learning techniques commonly used for time-domain signals and effective for vibration signals cannot effectively distinguish between stator current signals of machines under normal and faulty conditions. Therefore, before applying the signal to a data-driven machine learning model, it is generally necessary to extract the frequency components resulting from the fault using a feature extraction process based on a physical model built on expert domain knowledge and detailed spectral analysis of the measured stator current signal. Moreover, relatively long time-domain signals, typically ranging from several seconds to tens of seconds, are required to extract highly sensitive fault components from conventional spectral analysis.

[0009] Therefore, to detect motor failures, an effective method is desired that does not use physical models and signal processing processes, but rather identifies and extracts failure-related features from, ideally, shorter signal segments. [Overview of the Initiative]

[0010] Some embodiments are based on the recognition that there is a need for an effective solution to detect motor eccentric failures that is computationally more efficient and accurate than the conventional solutions described above.

[0011] Accordingly, a method for detecting motor eccentric failures is disclosed. This method includes extracting failure-related features of a motor, such as an induction motor or a synchronous motor, by performing topological data analysis (TDA) on a motor current signal, and applying them to the detection of motor eccentric failures. TDA is a mathematical process for extracting shape information from a data space. By applying TDA to time-series data, image data, sensor data, etc., the essential geometric characteristics of an object can be extracted. The TDA-based method for detecting motor eccentric failures disclosed herein includes obtaining topological features from time-domain data and representing these topological features in a persistence diagram and a vectorized Betti sequence. This method further includes extracting failure-related features from the topological features of the obtained data that can be clearly associated not only with the type of failure but also with the severity level of the failure. Furthermore, this method includes a machine learning model that uses the failure-related features extracted from TDA to predict the motor eccentric failure level for new eccentricity level data that is not present in the training data.

[0012] Some embodiments are based on the recognition that the TDA method is less sensitive to metric selection compared to other geometric methods, lacks coordinates, and extracts only the essential geometric properties of the object, making it more robust to noise.

[0013] Therefore, some embodiments are based on the recognition that TDA, along with the application of the principle of persistent homology, provides a highly effective data analysis method for failure analysis problems in fields such as image analysis, time series data analysis, sensor networks, chemistry, and materials science.

[0014] Some conventional methods are based on TDA applications that utilize persistent homology methods to reveal major shapes in the data space, ignoring smaller features or treating them as noise. However, various embodiments disclosed herein remove the major shapes and focus on smaller features in the persistent homology data space, such as time-series stator current data.

[0015] Therefore, some embodiments are based on the recognition that the extracted topology features, as described above, contain fault signatures. These fault signatures are distinguishable between data from the same motor with different static eccentricity levels, making them suitable for developing data-driven machine learning models to predict eccentric failures in motors.

[0016] Various embodiments provide methods and systems for identifying and extracting fault-related features using only small segments of a measured signal, without using physical models or signal processing processes.

[0017] The methods and systems disclosed herein can be used in at least two application scenarios, namely during the manufacturing stage and during the operating period of a motor, to detect eccentric failures of the motor.

[0018] During the manufacturing phase, the purpose is to inspect the manufactured motors and identify their eccentricity levels for quality control. Since a large number of identical motors are produced, data including a wide range of eccentricity levels is collected using test motors, and a model is developed to predict new data measured in other motors of the same type based on the collected data.

[0019] In the operating life of a motor, it may not always be possible to obtain data on all possible eccentricity levels. However, measurement data can be collected during inspection when the eccentricity level is still low. Therefore, some embodiments are based on the understanding that a model can be built on initial measurements and used to predict the eccentricity level according to subsequent measurements where failures are expected to become more severe over time.

[0020] Accordingly, several embodiments disclose fault detectors for detecting eccentricity of a motor including a stator and rotor separated by an air gap. The fault detector comprises a processor and a memory storing instructions that, when executed by the processor, cause the fault detector to collect feedback electrical signals of motor operation, including time-series data of three-phase currents measured during the motor's operating period, via a communication channel including one or a combination of a wired communication link and / or a wireless communication link. The processor is further configured to form a three-phase point cloud by mapping data points of the time-series data into a three-dimensional space of three-phase currents. The processor is further configured to extract a topological representation of the topological features of the three-phase point cloud using topology data analysis (TDA). The processor is further configured to classify the motor's eccentricity based on the extracted topological representation. Furthermore, the processor is configured to transmit, via the communication channel, one or a combination of an index indicating the classified eccentricity of the motor and / or a control command selected based on the classified eccentricity.

[0021] According to another embodiment, a method for detecting an eccentricity fault of a motor including a stator and a rotor separated by an air gap is disclosed. The method includes collecting a feedback electrical signal of the operation of the motor including time series data of three-phase currents measured during the operation of the motor via a communication channel including one or a combination of a wired communication link and a wireless communication link. The method further includes forming a three-phase point cloud by mapping data points of the time series data into a three-dimensional space of the three-phase currents. The method further includes extracting a topological representation of topological features of the three-phase point cloud using topological data analysis (TDA). The method further includes classifying the eccentricity of the motor based on the extracted topological representation. Further, the method includes transmitting via the communication channel one or a combination of an indicator indicating the classified eccentricity of the motor and a control command selected based on the classified eccentricity.

[0022] Hereinafter, embodiments of the present disclosure will be further described with reference to the accompanying drawings. The drawings are not necessarily drawn to scale. Instead, the drawings may be emphasized to illustrate the principles of the embodiments of the present disclosure.

Brief Description of the Drawings

[0023] [Figure 1A] According to some embodiments of the present disclosure, it is a schematic diagram showing a motor fault detection system. [Figure 1B] According to some embodiments of the present disclosure, it is a schematic diagram showing a motor. [Figure 2A] According to some embodiments of the present disclosure, it is a schematic diagram showing a motor. [Figure 2B] According to some embodiments of the present disclosure, it is a schematic diagram showing a static eccentricity fault. [Figure 2C] According to some embodiments of the present disclosure, it is a schematic diagram showing a dynamic eccentricity fault. [Figure 2D] According to some embodiments of the present disclosure, it is a schematic diagram showing a mixed eccentricity fault. [Figure 3]This is a schematic diagram showing an experimental setup for a motor according to some embodiments of the present disclosure. [Figure 4] This figure shows a graphical representation of a time-domain current signal at different eccentricity levels of a motor, according to some embodiments of the present disclosure. [Figure 4 Continued] The following is a (continued) figure showing a graphical representation of a time-domain current signal at different eccentricity levels of a motor, according to some embodiments of the present disclosure. [Figure 5A] This figure shows an exemplary method for determining motor failure according to some embodiments of the present disclosure. [Figure 5B] This figure shows an exemplary method for determining motor failure according to some embodiments of the present disclosure. [Figure 6] This figure shows a graphical representation of three phase point groups with different eccentricity levels, according to some embodiments of the present disclosure. [Figure 6 Continued] The following is a (continued) figure showing a graphical representation of three-phase point groups with different eccentricity levels, according to some embodiments of the present disclosure. [Figure 7A] This figure shows an exemplary representation of data points in a finite metric space according to some embodiments of the present disclosure. [Figure 7B] This figure shows an exemplary representation of a barcode in a finite metric space according to some embodiments of the present disclosure. [Figure 8] This figure shows an exemplary method for calculating the persistent homology of a three-phase point group in a finite-metric space, according to some embodiments of the present disclosure. [Figure 9] This figure shows a graphical representation of a persistence diagram according to some embodiments of the present disclosure. [Figure 10] This figure shows persistence diagrams of three-phase currents for six different eccentricity levels, according to some embodiments of the present disclosure. [Figure 10 Continued] The following is a diagram (continued) showing persistence diagrams of three-phase currents for six different eccentricity levels, according to some embodiments of the present disclosure. [Figure 11]This figure shows a Betti sequence or Betti curve corresponding to a persistence diagram, according to some embodiments of the present disclosure. [Figure 12] This figure shows a Betti sequence or Betti curve related to different three-phase currents according to some embodiments of the present disclosure. [Figure 12 Continued] The following is a diagram (continued) showing a Bettis sequence or Bettis curve related to different three-phase currents, according to some embodiments of the present disclosure. [Figure 13] This figure shows time-domain plots of different eccentricity levels according to some embodiments of the present disclosure. [Figure 14] This figure shows t-dispersive stochastic adjacency embedding (t-SNE) plots for the H0 Betti curve and the H1 Betti curve, according to some embodiments of the present disclosure. [Figure 15] This figure shows the prediction results according to some embodiments of the present disclosure. [Figure 16] This figure shows the prediction results according to some embodiments of the present disclosure. [Figure 17A] This figure shows the prediction results according to some embodiments of the present disclosure. [Figure 17B] This figure shows the prediction results according to some embodiments of the present disclosure. [Figure 17C] This figure shows the prediction results according to some embodiments of the present disclosure. [Figure 17D] This figure shows the prediction results according to some embodiments of the present disclosure. [Modes for carrying out the invention]

[0024] In the following description, many specific details are provided for illustrative purposes to provide a complete understanding of this disclosure. It will be obvious to those skilled in the art that one or more embodiments can be carried out without these specific details. Furthermore, the apparatus and methods are shown as block diagrams so as not to obscure this disclosure.

[0025] Where used herein and in the claims, the terms “for example,” “as an example,” and “like,” as well as the verbs “equip,” “have,” “include,” and their other verb forms, when used with a list of one or more components or other items, should be interpreted as open-ended, meaning that no other additional components or items are excluded from the list. The term “based on” means based on at least partially. Furthermore, it should be understood that the expressions and terms used herein are for illustrative purposes only and should not be considered restrictive. Any headings used herein are for convenience only and have no legal or restrictive effect.

[0026] Figure 1A is a schematic diagram showing a fault detection system for a motor, for example, motor 101, according to some embodiments of the present disclosure. In one example, the system for detecting operational faults may include motor 101, sensors 105A, 105B, and 105C, a fault detector 100A, and a communication channel 107. Motor 101 is an AC motor in which the rotation of the motor shaft is synchronized with the frequency of the supply current in a steady state. Examples of synchronous motors include reluctance motors and permanent magnet motors. Sensors 105A, 105B, and 105C are connected to motor 101. According to a particular embodiment, sensors 105A, 105B, and 105C may be current sensors and voltage sensors for obtaining the current and voltage of each winding of motor 101. Other sensors are also conceivable, including torque sensors, environmental (temperature, humidity, etc.) sensors, and other types of sensors used to assist in the operation, maintenance, or management of motor 101. In one example, sensors 105A, 105B, and 105C are connected to the motor 101 via wireless or wired connection and collect data from the motor 101.

[0027] The communication channel 107 may include a medium that can transmit data from the motor 101 to the fault detector 100A. Examples of the communication channel 107 may include, but are not limited to, a dedicated short-range communication (DSRC) network, a mobile ad-hoc network (MANET), an internet-based mobile ad-hoc network (IMANET), a wireless sensor network (WSN), a wireless mesh network (WMN), the internet, cellular networks such as Long-Term Evolution (LTE) networks, cloud networks, wireless fidelity (Wi-Fi) networks, and / or wireless local area networks (WLANs). Various devices within the system for detecting operational faults of the motor 101 can operate to connect to the communication channel 107 according to various wireless communication protocols. Examples of such wireless communication protocols may include, but are not limited to, IEEE 802.11, 802.11p, 802.15, 802.16, 1609, Wi-MAX (Worldwide Interoperability for Microwave Access), WAVE (Wireless Access in Vehicular Environments), cellular communication protocols, transmission control protocols and Internet protocols (TCP / IP), user datagram protocol (UDP), hypertext transfer protocol (HTTP), Long-Term Evolution (LTE), file transfer protocol (FTP), ZigBee®, EDGE, infrared (IR), and / or Bluetooth® communication protocols.

[0028] The fault detector 100A can detect faults in the motor 101 during operation. The fault detector 100A may include an input interface 110, a memory 140, a processor 120, and an output interface 150. The input interface 110 of the fault detector 100A receives sensor data from sensors 105A, 105B, and 105C. The memory 140 stores the sensor data. In one example, the memory 140 can permanently store the sensor data. In another example, the memory 140 can temporarily store the sensor data for a predetermined period. This period may be determined based on the user / operator's goals / interests. The sensor data is then processed by the processor 120 and may be output to the output interface 150 or stored in the memory 140, depending on the user / operator's goals / interests. In one embodiment, the sensor data collected from sensors 105A, 105B, and 105C is provided to the fault detector 100A via a communication channel 107, which may include a wired or wireless communication link for communicating the sensor data. Sensor data collected from sensors 105A, 105B, and 105C may include a feedback electrical signal indicating the operation of motor 101. The feedback electrical signal includes time-series data of three-phase current measured during the operation of motor 101. The fault detector 100A can form a three-phase point cloud by mapping data points of the time-series data into a three-dimensional space of three-phase current. The fault detector 100A can extract a topological representation of the topological features of the three-phase point cloud using TDA. The fault detector 100A can classify the motor eccentricity based on the extracted topological representation. In one example, the classified eccentricity includes the type of eccentricity and the severity level of the eccentricity. The fault detector 100A can transmit, via communication channel 107, either an index indicating the classified eccentricity of the motor, or a control command selected based on the classified eccentricity, or a combination thereof.In one embodiment, the processor 120 of the fault detector 100A can cause the output interface 150 to transmit, via the communication channel 107, either an index indicating the classified eccentricity of the motor or a control command selected based on the classified eccentricity, or a combination thereof. The fault detector 100A can select a control command based on the type of eccentricity and the severity level of the eccentricity. In one example, the output interface 150 can transmit the index indicating the classified eccentricity and the control command via the communication channel 107 to the user or system operating the motor 101. The index indicating the classified eccentricity and the control command can cause the user or system to take corrective action to eliminate the eccentricity in the motor 101. The actions performed by the fault detector 100A to detect faults in operation of the motor 101A will be described later with reference to Figures 5A and 5B.

[0029] Figure 1B shows a schematic diagram 100B of a motor 101 according to one embodiment of the present disclosure. The motor 101 includes a rotor 102, a stator 104, a spindle 106, and two bearings 108A and 108B. Eccentric failure of the motor 101 is typically due to manufacturing or operating errors that cause an uneven air gap between the stator 104 and the rotor 102. In one example, eccentric failure occurs when the rotation axis 103 of the motor 101 does not coincide with the axis of symmetry. In one example, the eccentricity of the motor 101 may be static eccentricity, dynamic eccentricity, or mixed eccentricity. The types of eccentricity will be described in detail with reference to Figures 2A, 2B, 2C, and 2D.

[0030] Figures 2A, 2B, 2C, and 2D are schematic diagrams illustrating different types of eccentric failures according to some embodiments of the present disclosure. An AC electric motor, such as motor 101, includes a stator 104 and a rotor 102 separated by an air gap 124. Eccentric failure is one type of motor failure resulting from the formation of an uneven air gap between the stator 104 and the rotor 102.

[0031] Figure 2A is a schematic diagram showing a motor 101 according to some embodiments of the present disclosure. The motor 101 shown in Figure 2A is an example of a normal motor without any eccentric faults. Point Ow is the center of rotation, point Os is the center of the stator 104, and point Or is the center of the rotor 102. When the three points Ow, Os, and Or coincide, the motor 101 is normal, free from eccentric faults, and the air gap 124(A) between the stator 104 and the rotor 102 is uniform at different locations.

[0032] Figure 2B is a schematic diagram illustrating a static eccentric failure according to some embodiments of the present disclosure. Points Or and Ow coincide but are offset from the center Os of the stator bore. A static eccentric failure exists because the rotor 102 always rotates around point Ow, and the air gap 124(B) between the stator 104 and the rotor 102 is not uniform in different places.

[0033] Figure 2C is a schematic diagram illustrating a dynamic eccentric failure according to some embodiments of the present disclosure. The rotation center Ow of the rotor 102 coincides with the stator center Os, but the rotor center Or revolves around point Ow. Because the rotor does not rotate around its own center of mass, the air gap 124(C) changes dynamically as the rotor rotation angle changes.

[0034] Figure 2D is a schematic diagram illustrating a mixed eccentric fault according to some embodiments of the present disclosure. A mixture of both static and dynamic eccentricity is a mixed eccentric fault where points Or, Os, and Ow do not coincide with each other. In this case, both static and dynamic eccentric faults are present.

[0035] Typically, static eccentricity in motors is generated during the manufacturing process. Early detection is crucial because static eccentricity failures can develop into mixed eccentricity during motor operation due to unbalanced magnetic attraction, ultimately leading to machine failure.

[0036] Figure 3 is a schematic diagram showing an experimental setup for a motor 101 according to several embodiments of the present disclosure. In one embodiment, the experimental setup is used to generate data that can be collected, analyzed, and used to identify the type and severity of failures associated with the motor 101. The experimental setup shown in Figure 3 may include different components for connecting to the motor 101 via an interface. In one example, sensor 105A may refer to, but is not limited to, a speed sensor such as a tachometer for measuring the angular velocity or rotational speed ωr of the motor 101. In one example, sensor 105B may refer to, but is not limited to, an acceleration sensor. In one example, sensor 105C may refer to, but is not limited to, an air gap sensor. In one embodiment, the air gap 124 is measured using two pairs of air gap sensors. The first pair of air gap sensors may be installed at the position indicated by (x1, y1). The second pair of air gap sensors may be installed at the position indicated by (x2, y2). In one embodiment, the stator 104 of the motor 101 is mounted on a linear stage, thereby allowing the position of the stator 104 to be adjusted horizontally (x-axis) using a pair of micrometers. The stator 104 is provided with two pairs of air gap sensors 105C. The first pair of displacement sensors is installed on the side facing the load-side air gap 124, and the second pair of displacement sensors is installed on the opposite side from the side facing the air gap 124. The two pairs of displacement sensors 105C detect the angular velocity ω of the motor 101. r While operating, the horizontal (x-axis) and vertical (y-axis) dimensions of the air gap 124 are measured. A power brake is connected to the motor 101 and functions as a load 125.

[0037] In one example, various eccentricity levels are generated by adjusting the air gap 124 between the stator 104 and the rotor 102. A phase current sensor is used to measure the phase current signal corresponding to each eccentricity level. In one embodiment, a 0.75 kW three-phase two-pole pair squirrel-cage induction motor with a nominal air gap size of 0.28 mm is used as motor 101. In another embodiment, a 0.75 kW three-phase synchronous motor with a nominal air gap size of 0.28 mm is used as motor 101. The line voltage is 200 V and the frequency is 60 Hz.

[0038] In one embodiment, six eccentricity levels are generated when the motor 101 is stationary. For each eccentricity level, data from the phase current sensor and the air gap sensor 105C are recorded, for example, at a sampling frequency of 10 kHz and under no-load conditions. As an example, the eccentricity levels may be set to 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively, but are not limited to these. These percentages are defined as the ratio of the maximum air gap displacement to the nominal air gap size. From the data of the air gap sensor 105C, the actual static eccentricity of the air gap 124 is remarkably close to the initial setting, with a difference of less than 3% in all cases. Furthermore, according to the readings of the air gap sensor, there is a small dynamic eccentricity level of approximately 6% in all cases. This mixed eccentricity effect generates a sideband signal of fc = fs ± fr, where fs is the supply frequency and fr is the rotation frequency.

[0039] Figure 4 shows a block diagram 400 including a graphical representation of time-domain current signals of motor 101 at different eccentricity levels, according to some embodiments of the present disclosure. Block diagram 400 includes the results of measurements performed by sensors 105A, 105B, and 105C on motor 101 at different eccentricity levels. In one example, the three-phase current signals associated with stator 104 are measured at eccentricity levels set to, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively.

[0040] In one example, Graph 400A shows the results of measurements performed by sensors 105A, 105B, and 105C on motor 101 at an eccentricity level set to 1.5%. Graph 400B shows the results of measurements performed by sensors 105A, 105B, and 105C on motor 101 at an eccentricity level set to 17.2%. Graph 400C shows the results of measurements performed by sensors 105A, 105B, and 105C on motor 101 at an eccentricity level set to 24.1%. Graph 400D shows the results of measurements performed by sensors 105A, 105B, and 105C on motor 101 at an eccentricity level set to 40.3%. Graph 400E shows the results of measurements performed by sensors 105A, 105B, and 105C on motor 101 at an eccentricity level set to 47.1%. Graph 400F shows the results of measurements performed by sensors 105A, 105B, and 105C on motor 101 at an eccentricity level set to 64.6%.

[0041] The time-domain current signal is sampled, for example, at a sampling frequency of 10 kHz. As an example without limitation, the time-domain signal shown in the graph representation in Figure 4 is formed by plotting approximately 1000 data samples of the time-domain current signal. Because the fundamental wave component is dominant, it is difficult to directly distinguish the eccentricity level from the time-domain current signal shown in Figure 4. The TDA method and the process of applying the TDA method to extract eccentric fault features and predict the eccentricity level are introduced.

[0042] Figure 5A shows an exemplary method 500A for determining a motor 101 failure according to some embodiments of the present disclosure. According to one embodiment of the present disclosure, method 500A is used to train a machine learning model for determining a motor 101 failure using a TDA process. Method 500A determines topological features that persist across different scales by applying the TDA process to a time-domain current signal associated with the stator 104 of the motor 101. Topological features associated with a point cloud representation of a sample of the time-domain current signal for different eccentricity levels may be provided to the machine learning model as training data for identifying eccentric failures and levels of eccentric failure. The steps and their sequence shown in Figure 5A are exemplary and may include various alternatives, equivalents, or derivatives, not limited to their execution order. The steps of method 500A in Figure 5A and their various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., optical disk, memory card, or hard drive) that stores instructions executable by the processor 120.

[0043] In 502, the fault detector 100A can collect feedback electrical signals of motor 101 operation, including time-series data of time-domain current signals measured during the operation of motor 101, via a communication channel 107 which includes either or a combination of a wired communication link and / or a wireless communication link. In one embodiment, the time-series data of time-domain current signals includes three-phase current signals associated with stator 104, which are measured at eccentric levels set to, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively. The time-domain current signals are described in detail with reference to Figures 3 and 4. The time-domain current signals are measured over a predetermined period, depending on the sampling rate employed to divide the time-domain current signals. In one example, the time-domain current signals are measured over a period of 0.01 seconds at a sampling rate of 10 kHz, but are not limited to this.

[0044] In 504, the fault detector 100A can divide each time-domain current signal of the three-phase time-domain current signal into data points of length L. As shown in Figure 4, the length L of the data sample may be set to 1000, but is not limited to this. The length L defines the precision of the divided time-domain current signals.

[0045] In 506, the fault detector 100A can form a group of three phase points corresponding to each eccentricity level by mapping data points of time-series data into a three-dimensional space of the three-phase current signal. In one example, the eccentricity levels may be set to 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively, but are not limited to these. A set of data points having a defined distance is called a point group. The three phase point groups corresponding to each eccentricity level are described with reference to Figure 6.

[0046] In 508, the fault detector 100A can extract a topological representation of the topological features of the three-phase point cloud by performing persistent homology calculations on the three-phase point cloud using TDA. The persistent homology calculation examines the three-phase point cloud at different scales. The fault detector 100A can determine the topological representation as the persistent homology representation. The persistent homology representation may include one or a combination of a persistence barcode and / or a persistence diagram. The persistence barcode is described with reference to Figures 7A and 7B. The persistence diagram is described with reference to Figure 9. In one example, the fault detector 100A can calculate the persistent homology of the three-phase point cloud corresponding to each eccentricity level for a 0-dimensional hole H0 and a 1-dimensional hole H1. The 0-dimensional hole H0 may also be called an H0 feature corresponding to multiple clusters formed by connected components within the three-phase point cloud. A one-dimensional hole H1 may also be called an H1 feature, corresponding to a hole formed by the space enclosed by connected components around a triphase point cloud. In one example, the topological features tracked by persistent homology may include H0 features and H1 features. Persistent homology is a TDA tool for examining data structures such as triphase point clouds of time series data. Persistent homology is robust to perturbations in time series data, is dimensional and coordinate-independent, and provides a compact representation of the qualitative features of time series data.

[0047] A three-phase point cloud is represented as a finite-metric space. From a topological perspective, a finite-metric space contains no interesting information. Therefore, it is necessary to condense the point cloud at different resolution scales and analyze the evolution of its shape across these different resolution scales. Qualitative features are given by topological invariants. The variation of topological invariants across different resolution scales is represented in a compact way and summarizes the "shape" of the time-series data.

[0048] A method for performing persistent homology calculations of a three-phase point group in a finite-metric space is described in detail with reference to Figure 8.

[0049] In 510, the fault detector 100A can convert the H0 homology and H1 homology of the three-phase point group into Betti sequences with fixed lengths L1 and L2, respectively. The topological features extracted in 508 are used as input or training data for a regression model or machine learning model. However, it is more convenient to represent the topological features using vectors of the same length. For this purpose, the fault detector 100A derives a Betti sequence or Betti curve from the persistence diagram of time-series data of three-phase currents with different eccentricities. The Betti sequence is described in detail with reference to Figures 9 and 10.

[0050] In 512, the fault detector 100A can provide training data to a machine learning model. The machine learning model may include a regression model or a neural network. During the training phase of the machine learning model, the mean squared error of the eccentricity level predicted by the model is matched with the ground truth eccentricity level obtained from the eccentricity level data 514. In one example, the eccentricity level data 514 is the labels of the segmented time-domain current signal and the time-series data of the time-domain current signal. The eccentricity level data 514 may also indicate the conditions under which the time-domain current signal is collected.

[0051] A machine learning model may be trained to predict the eccentricity level of the motor 101. In one example, the machine learning model may be trained in a supervised manner to classify different topological representations labeled by eccentricity type, eccentricity severity level, or both. The predicted eccentricity includes the eccentricity type and eccentricity severity level. For example, the eccentricity type may include, but is not limited to, static eccentricity, dynamic eccentricity, or mixed eccentricity. The eccentricity level may indicate the degree of the air gap 124 between the stator 104 and rotor 102 of the motor 101. The training data provided to the machine learning model is labeled data containing one or a combination of the Betch sequence derived in 510, eccentricity level data 514, or data points corresponding to a three-phase time-domain current signal.

[0052] Figure 5B shows an exemplary method 500B for determining a motor 101 failure according to one embodiment of the present disclosure. Method 500B determines topological features that persist across different scales by applying TDA to a time-domain current signal associated with the stator 104 of the motor 101. Topological features associated with a point cloud representation of a sample of the time-domain current signal for different eccentricity levels may be provided to a trained machine learning model as training data for identifying eccentric failures and levels of eccentric failure. The steps and their sequence shown in Figure 5B are exemplary and may include various alternatives, equivalents, or derivatives, not limited to their execution order. The steps of the method in Figure 5B and their various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., optical disk, memory card, or hard drive) that stores instructions executable by the processor 120.

[0053] In 516, the fault detector 100A can collect feedback electrical signals of motor 101 operation, including time-series data of time-domain current signals measured during the same motor 101 operation period used in 502 during training of the machine learning model, via a communication channel 107 including either or a combination of a wired communication link and / or a wireless communication link. In another embodiment, the operation period may vary depending on the sampling rate of the data points. In one embodiment, the time-series data of time-domain current signals includes three-phase current signals associated with the stator 104, which are measured at eccentric levels set to, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively. The time-domain current signals are described in detail with reference to Figures 3 and 4.

[0054] In 518, the fault detector 100A can divide each time-domain current signal of the three-phase time-domain current signal into data points of length L. As shown in Figure 4, the length L of the data sample may be set to 1000, but is not limited to this. The length L defines the precision of the divided time-domain current signals.

[0055] In 520, the fault detector 100A can form a group of three phase points corresponding to each eccentricity level by mapping data points of time-series data into a three-dimensional space of the three-phase current signal. In one example, the eccentricity levels may be set to 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively, but are not limited to these. A set of data points having a defined distance is called a point group. For example, Figure 6 shows a graphical representation of three phase point groups of different eccentricity levels according to another embodiment of the present disclosure. Each three phase point group is formed for a three-phase current signal measured at a particular eccentricity level. The distance between data points may be, for example, a Euclidean distance or a Minkowski distance. Both Euclidean and Minkowski distances are defined by numerical data. However, this embodiment is not entirely limited to numerical data defining the distance between data points. In another example, distances can be defined even if the data is categorical data rather than numerical data.

[0056] In 522, the fault detector 100A can extract the topological representation of the topological features of the three-phase point cloud by performing persistent homology calculations on the three-phase point cloud using TDA. For example, the fault detector 100A can calculate the persistent homology of the three-phase point cloud corresponding to each eccentricity level for a 0-dimensional hole H0 and a 1-dimensional hole H1.

[0057] In 524, the fault detector 100A can convert the H0 homology and H1 homology of the three-phase point group into Betti sequences having fixed lengths L1 and L2, respectively. The fault detector 100A derives a Betti sequence or Betti curve from persistence diagrams of time-series data of three-phase currents at different eccentricity levels. The Betti sequence is described in detail with reference to Figures 9 and 10.

[0058] In 526, the fault detector 100A can provide a machine learning model trained in 512 with either or a combination of data points corresponding to the Betch sequence or time-domain current signal derived in 524. In one embodiment, the fault detector 100A can classify different topological representations, labeled by eccentricity type, eccentricity severity level, or both, by running a machine learning model trained in a supervised manner in 512. The trained machine learning model can classify the eccentricity of the motor 101 based on the extracted topological representations. In one embodiment, the trained machine learning model can classify the eccentricity of the motor 101 based on either or a combination of the Betch sequence or data points derived in 524. The eccentricity level prediction value 528 includes the eccentricity type and the eccentricity severity level. In one example, the machine learning model may be a regression model trained in 512 to extrapolate labeled levels of eccentricity severity used to train the regression model in 512.

[0059] Figure 6 shows a block diagram 600 including a graphical representation of three phase point groups with different eccentricity levels, according to one embodiment of the present disclosure. The block diagram 600 may include three phase point groups with different eccentricity levels set to, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively.

[0060] In one example, Graph 600A shows the three-phase point group of a three-phase current signal measured at an eccentricity level set to 1.5%. Graph 600B shows the three-phase point group of a three-phase current signal measured at an eccentricity level set to 17.2%. Graph 600C shows the three-phase point group of a three-phase current signal measured at an eccentricity level set to 24.1%. Graph 600D shows the three-phase point group of a three-phase current signal measured at an eccentricity level set to 40.3%. Graph 600E shows the three-phase point group of a three-phase current signal measured at an eccentricity level set to 47.1%. Graph 600F shows the three-phase point group of a three-phase current signal measured at an eccentricity level set to 64.6%.

[0061] Each three-phase point group is formed for a three-phase current signal measured at a specific eccentricity level. The distance between data points within a particular point group may be, for example, a Euclidean distance or a Minkowski distance. Both Euclidean and Minkowski distances are defined by numerical data. However, this embodiment is not entirely limited to numerical data defining the distance between data points. In another example, the distance can be defined even if the data is categorical rather than numerical.

[0062] Since the dominant component of a three-phase current signal is a periodic wave with a fundamental frequency, the most important shape is a large circle in 3D space. The most important shape is the dominant shape of the three-phase point cloud. In the case of an ideal sinusoidal signal, the shape of the three-phase point cloud is a perfect circle. However, if components other than the fundamental frequency are present, the points on the three-dimensional point cloud will deviate from a perfect circle. Components other than the fundamental frequency are caused by faults such as eccentric faults and are called fault components. Because the amplitude of fault components is very small, it is difficult to distinguish different levels of eccentricity based solely on the shape of the three-phase point cloud. Components other than the fundamental frequency can result in topological features other than the dominant shape of the three-phase point cloud. Therefore, if any eccentric fault occurs in the operation of the motor 101, the topological features of the three-phase point cloud of the three-phase current may include at least one dominant shape and at least one shape other than the dominant shape.

[0063] After the TDA process, topology features can be extracted from the three-phase point cloud, and these extracted topology features can be provided to a machine learning model to train a machine learning model for predicting the eccentricity level of the motor 101.

[0064] Figure 7A shows an exemplary representation 700A of a data point in a finite metric space according to one embodiment of the present disclosure. The data point is located in region R 2 It is represented as follows. The distance between two data points is called the filtration radius r. For different r values, the space S is composed of vertices, edges, triangles, or higher-dimensional polyhedra. rHowever, it is constructed according to specific rules. In one example, an edge between two points i and j is included, and all edges are S, only if the Euclidean distance between points i and j is less than or equal to the filtration radius r. r Triangles are included only if they are in S r A tetrahedron is included only if it is located in space S. Using homology, r Several features of space S can be measured. r The features or topological features may include components, holes, and / or voids.

[0065] 700A-1 shows an exemplary point cloud when the filtration radius r is close to zero (r=0). When r=0, no topological features, such as edges or vertices, are formed, and all data points in the point cloud are represented as distinct data points with no connection features between them. As the filtration radius r increases, topological features begin to appear in the point cloud. 700A-2 shows an exemplary point cloud when the filtration radius r is set to 0.6. 700A-3 is an example of a point cloud where holes appear when the filtration radius r is set to 1.1. In one example, holes begin to appear when the filtration radius r=1.1. 700A-4 shows an exemplary point cloud when the filtration radius r is set to 1.6. In one example, when the filtration radius r=1.6, holes that appeared when the radius value was small are still present in the point cloud, but the radius of the holes is reduced compared to the holes shown in 700A-3. 700A-5 shows an exemplary point cloud when the filtration radius r is set to 2.1. In one example, when the filtration radius r = 2.1, the holes in the point cloud disappear.

[0066] The duration of features such as holes can be represented using a finite set of intervals known as persistence barcodes. The left endpoint of an interval represents the generation of a feature, and the right endpoint of an interval represents the disappearance of that feature. For example, Figure 7B shows an exemplary representation of a barcode in a finite metric space according to one embodiment of the present disclosure. As the filtration radius increases, a topological feature, such as a hole, appears at a first value of the filtration radius r, r1 (e.g., r=1.1). As the filtration radius r further increases, the size of the hole begins to decrease, and the hole gradually disappears at a second value of the filtration radius r, r2 (e.g., r=2.1). The first value of the filtration radius r, r1, represents the generation of a hole, and the second value of the filtration radius r, r2, represents the disappearance of a hole. The persistence of a hole can be represented as a pair (r1, r2). The persistence may be visualized as an interval or bar known as a persistence bar from r1 to r2. The persistence bar is a visual representation of the persistence of a hole. The set of persistence bars for each topology feature in a three-phase point cloud is called a persistence barcode.

[0067] Figure 8 shows an exemplary method 800 for calculating the persistent homology of a three-phase point group in a finite-metric space, according to some embodiments of the present disclosure. The steps and their order shown in Method 800 of Figure 8 are exemplary and may include various alternatives, equivalents, or derivatives, not limited to their execution order. The steps and their various alternatives in Method 800 of Figure 8 may be embodied in hardware or software, including a computer-readable storage medium (e.g., an optical disk, memory card, or hard drive) that stores instructions executable by the processor 120.

[0068] First, the time-series data, represented by a three-phase point cloud formed by data points sampled from the time-series data, is provided to the processor 120 for persistent homology calculation 508.

[0069] In 508-1, a simplicial complex of the three-phase point cloud is identified for each eccentricity level. In one embodiment, a topological representation of the topological features of the three-phase point cloud is extracted using TDA. A simplicial complex is a set of basic topological features or simplices, such as points, edges, or triangles. However, the features or simplices are not limited to points, edges, or triangles. Tetrahedra or other higher-dimensional polyhedra may be used as topological features or simplices. In one embodiment, a Rips complex is used as an algorithm to extract a topological representation of the topological features of the three-phase point cloud. However, other algorithms may be used to construct simplicial complexes. A simplicial complex is defined by a threshold r called the filtration radius, and includes only complexes where the Euclidean distance between each pair of points is less than or equal to the filtration radius r.

[0070] In section 508-2, the homology is determined from the constructed simplicial complex using linear algebra. For example, H0 homology counts the number of connected components, and H1 homology counts the number of holes.

[0071] In 508-3, persistent homology is obtained throughout the filtration process by calculating homology at different filtration radii r and tracking the generation and disappearance of topological features at values ​​corresponding to the filtration radius r. The generation and disappearance of topological features define the lifetime of the topological features for different filtration radii r.

[0072] There are various ways to represent persistent homology, and persistence diagrams are one of the most common options. A persistence diagram shows (b,d)=b,d∈R 2and a set of points satisfying d > b, where each point corresponds to the generation and disappearance of topological features within the corresponding simplicial complex group. Specifically, each point (b, d) indicates a topological feature "generated" at radius b and "disappeared" at radius d. There are various algorithms for performing the filtration of the Rips complex and the calculation of the persistence diagram, which can be implemented by several software packages. Referring to FIG. 9, the persistence diagram is described. Referring to FIG. 10, the H0 and H1 persistence diagrams of three-phase current data at six different eccentricity levels are described.

[0073]

Number

[0074] Then, the points on the Betti sequence are obtained from the sum.

Number

[0075] Topological features in persistent homology are a function of the filtration radius r. The representation of persistent homology is obtained through filtration by calculating persistent homology using different filtration radii r as thresholds and tracking the lifetimes of different topological features at the corresponding thresholds. By limiting the maximum filtration range, "large" features in the data can be excluded, leaving only the "small" features in the data. In one example, TDA can remove "large" features or dominant shapes from topological features. In the case of motor fault detection, the fault-related features have much smaller amplitudes compared to the dominant fundamental signal corresponding to the power frequency. Small filtration radius r maxBy selecting this option, the dominant fundamental signal can be excluded, and fault-related features obtained from topology calculations for persistent homology represented by persistence diagrams and / or Betch sequences can be shown. Furthermore, excluding fundamental signals using TDA is not very complex and does not require knowing the exact power supply frequency. In contrast, conventional signal processing methods require knowing the exact frequency of the fundamental signal in order to remove it. In contrast to conventional model-based MCSA methods, the exact frequency components associated with eccentric faults do not need to be explicitly identified by the physical model.

[0076] Figure 9 shows a graphical representation 900 of a persistence diagram according to some embodiments of the present disclosure. The graphical representation 900 includes persistence diagram 900A and persistence diagram 900B. The persistence diagram is R 2 A finite number of points within and the diagonal Δ={(x,y)∈R} 2This is a multi-set that is the sum of multiple sets of points on |x=y}, and each point on the diagonal has infinite multiplicity. Persistence diagram 900A is an H1 persistence diagram when the eccentricity level is set to 1.5%. The horizontal axis of persistence diagram 900A represents the generation of a topological feature, such as a hole. The vertical axis of persistence diagram 900A represents the disappearance of that topological feature. Persistence diagram 900A is a set of persistence barcodes for all H1 features in the three-phase point cloud when the eccentricity level is set to 1.5%. Each persistence barcode in persistence diagram 900A represents the generation and disappearance of the corresponding H1 feature. A persistence barcode begins with the generation of the corresponding H1 feature and ends with the disappearance of the corresponding H1 feature. The generation of an H1 feature indicates the filtration radius r at which the H1 feature begins to appear. The disappearance of an H1 feature indicates the filtration radius r at which the H1 feature begins to disappear. Therefore, persistence diagram 900A shows the lifespan of each H1 feature in the three-phase point cloud when the eccentricity level is set to 1.5%. As shown in persistence diagram 900A, fewer or only one feature is generated and disappears with a large filtration radius. As an example, a feature is called a major feature if it has a large filtration radius of disappearance and generation compared to other topological features in the three-phase point cloud. As shown in persistence diagram 900A, the persistence barcode for a major feature is represented by the barcode in the upper left of persistence diagram 900A. A minor feature is a topological feature that has a small filtration radius of disappearance and generation compared to a major feature in the three-phase point cloud. As shown in persistence diagram 900A, the persistence barcode for a minor feature is represented by the barcode in the lower left of persistence diagram 900A. As shown in persistence figure 900A, most small features have smaller generation and disappearance filtration radii. Persistence figure 900B visualizes the small features shown in persistence figure 900A more clearly. In persistence figure 900B, the ranges on the horizontal and vertical axes are reduced, for example, to r=0.06 for generation and r=0.065 for disappearance.

[0077] Figure 10 shows a graphical representation 1000 of the persistence diagram of three-phase current for six different eccentricity levels according to some embodiments of the present disclosure. The graphical representation 1000 includes, but is not limited to, H0 and H1 persistence diagrams for different eccentricity levels set to 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively. In one embodiment, the H0 and H1 persistence diagrams of three-phase current data for six different eccentricity levels may be calculated using a three-phase point cloud for the six different eccentricity levels. The most notable difference between these diagrams is the H1 feature corresponding to the small holes formed by adjacent points. For an ideal sine wave, the point cloud can form only one large hole. For small eccentricity levels, the deviation from the ideal circle is small, and only small features are formed in the H1 diagram. As the eccentricity level increases, the deviation of the points from the ideal circle increases, and these points are more likely to form small circles during the filtering process 508-2 to obtain the persistence diagram. Therefore, as the level of eccentricity increases, more features appear in the H1 persistence diagram.

[0078] In one example, 1000A shows the H0 and H1 persistence diagrams of three-phase current data for an eccentricity level set to 1.5%. 1000B shows the H0 and H1 persistence diagrams of three-phase current data for an eccentricity level set to 17.2%. 1000C shows the H0 and H1 persistence diagrams of three-phase current data for an eccentricity level set to 24.1%. 1000D shows the H0 and H1 persistence diagrams of three-phase current data for an eccentricity level set to 40.3%. 1000E shows the H0 and H1 persistence diagrams of three-phase current data for an eccentricity level set to 47.1%. 1000F shows the H0 and H1 persistence diagrams of three-phase current data for an eccentricity level set to 64.6%.

[0079] Figure 11 shows a Betch sequence or Betch curve corresponding to a persistence diagram according to some embodiments of the present disclosure. Block diagram 1100 includes a Betch curve 1100A corresponding to an H0 persistence diagram and a Betch curve 1100B corresponding to an H1 persistence diagram. The H0 persistence diagram and the H1 persistence diagram are distinct from each other. The number of points in the H0 persistence diagram and the H1 persistence diagram is not fixed for different input data corresponding to three-phase currents. To provide these topological features to a machine learning model, the H0 homology and H1 homology are converted to an H0 Betch sequence and an H1 Betch sequence having lengths L1 and L2, respectively. In one example, for both the H0 homology and the H1 homology, lengths L1 and L2 are fixed at 1024, but the filtering ranges are [0,0.07] and [0,0.14], respectively.

[0080] From the H1 Betti sequence, it has been observed that the number of features as a function of filtration distance changes with the eccentricity level. While differences in H0 features cannot be inferred from the persistence diagram, the trend of the H0 Betti sequence is observable. When the filtration radius r is 0, all 1024 data points are unconnected. Therefore, all Betti sequences start from 1024. As the filtration radius r increases, more neighboring points are connected. Consequently, the number of features (i.e., the number of disconnected clusters) begins to decrease. Eventually, all points are connected, leaving only one feature. The higher the eccentricity level, the larger the amplitude of the fault component, and the data points move away from each other as they deviate from a larger circle. Therefore, points are connected in later stages, these H0 features persist longer, and the area under the H0 Betti curve increases monotonically with the eccentricity level. The changes in the Betti curve are due to eccentricity.

[0081] Figure 12 shows a graphical representation 1200 of a Betti sequence or Betti curve associated with different three-phase currents, according to some embodiments of the present disclosure. The graphical representation 1200 includes a Betti curve 1200A corresponding to an H0 persistence diagram obtained from five different data segments with the same eccentricity level set to 17.2%, a Betti curve 1200B corresponding to an H1 persistence diagram obtained from five different data segments with the same eccentricity level set to 17.2%, a Betti curve 1200C corresponding to an H0 persistence diagram obtained from five different data segments with the same eccentricity level set to 64.6%, and a Betti curve 1200D corresponding to an H1 persistence diagram obtained from five different data segments with the same eccentricity level set to 64.6%. A key feature of persistent homology is its robustness. In other words, the robustness of persistent homology suggests that similar data structures yield similar persistent homology. The Betti curves exhibit good consistency. The similarity of the Betti curves shown in Figure 12 suggests that the TDA process can be used to remove time variations between different samples of time-series data, and that fault signatures can be extracted using relatively short data segments.

[0082] From the above analysis, the proposed TDA process is effective in revealing small fault signatures embedded in large background signals and in isolating signals from different fault levels.

[0083] The calculated Betti curves are used in data-driven methods for eccentric fault detection, quantification, and prediction.

[0084] Figure 13 shows time-domain plots 1300 of different eccentricity levels according to several embodiments of the present disclosure. In one embodiment, eccentricity level data of motor 101 are measured and divided into a total of 1170 samples, each sample having a length of 1024 data points. As an example, eccentricity level data are measured for six different eccentricity levels, set to, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively. As described with reference to Figures 5A and 5B, a Betti curve is calculated for the measured eccentricity level data. In one embodiment, a t-distributed stochastic neighborhood embedding (t-SNE) plot is used to visualize the distinction between signals of different eccentricity levels. The t-SNE plot is a commonly used tool to represent the similarity of high-dimensional data, both time-series data of three-phase current and the calculated Betti curve, in a lower dimension.

[0085] Figure 14 shows t-SNE plots 1400 for the H0 Betch curve and the H1 Betch curve according to one embodiment of the present disclosure. The t-SNE plot 1400 includes t-SNE plot 1400A for the H0 Betch curve and t-SNE plot 1400B for the H1 Betch curve. As shown in Figure 14, data from all eccentricity levels are mixed with time-series data of the three-phase current. The data segments shown in Figure 14 are similar, for example, because they are dominated by a dominant 60 Hz signal. However, the data samples from both the H0 Betch sequence and the H1 Betch sequence are clustered according to their respective eccentricity levels, thus showing similarity between data samples obtained from the same eccentricity level.

[0086] The dominant 60Hz signal, as shown in Figure 6, has a large hole in the point cloud and therefore corresponds only to feature values ​​in the large filtering radius of the H1 Betch sequence, having little effect on the Betch curve profile. In this sense, the Betch curve with a threshold applied acts as a "nudge filter" that effectively removes the dominant time-domain signal, thus amplifying the behavior of small signals where fault signatures exist. This threshold can be applied without knowing the exact frequency of the dominant signal.

[0087] Figure 15 shows a prediction result 1500 according to several embodiments of the present disclosure. In one embodiment, the prediction result 1500 includes a root mean square evaluation of the time-domain representation of the phase current data. In one embodiment, motor eccentric fault detection can be applied to two application scenarios, namely the manufacturing stage and the operating period of a motor such as motor 101.

[0088] During the manufacturing phase, the goal is to inspect the manufactured motors and identify the eccentricity level for quality control. Since many identical motors are produced, a test motor is used to collect data containing a wide range of eccentricity levels. Based on this collected data, a model is developed to predict new data measured on other identical motors. To replicate this scenario, all eccentricity level data is shuffled and split into a training dataset and a test dataset with a 0.8 / 0.2 split ratio. The machine learning model is trained on the training dataset and then applied to the test dataset. While many different models can be developed, the capabilities of TDA can be demonstrated using results from a simple k-nearest neighbor (k-NN) regression model. For given new data, the k-NN regression model searches for nearest neighbors from the training dataset and predicts the eccentricity level as the average level of these neighbors. As is evident from the results shown in Figure 15, for time-domain phase current data, the k-NN regression model performs poorly on new data, with a mean squared error (RMSE) of approximately 10% and a mean absolute error (MAE) of approximately 9.4%.

[0089] Figure 16 shows a prediction result 1600 according to several embodiments of the present disclosure. In one embodiment, the prediction result 1600 may include a root mean square evaluation using a Betch sequence. As an example, an H0 Betch sequence may be given as a training dataset for a k-NN regression model. For a given new data converted to an H0 Betch sequence, the k-NN regression model searches for nearest neighbors from the training dataset and predicts the mean level of these neighbors as the eccentricity level. As is evident from the results shown in Figure 16, the RMSE is reduced to 1.6% and the MAE is reduced to 0.7% with the H0 Betch sequence. This result demonstrates the effectiveness of using a Betch sequence for time-domain topology current data for interpolation purposes.

[0090] During the motor's operating life, data for all possible eccentricity levels may not be available. Measurement data can be collected during inspections when the eccentricity level is still low. A model can be built based on these initial measurements, and this model can be used to predict eccentricity levels according to later measurements where failures are expected to become more severe over time. Therefore, experimental data obtained from four small eccentricity levels can be designated as the training set, and the last two levels as the test dataset, to check the predictive ability of the trained model.

[0091] Figure 17A shows a prediction result 1700A according to some embodiments of the present disclosure. In one embodiment, the prediction result 1700A is based on a quadratic regression model trained on time-series data of three-phase current. As an example, the time-series data of three-phase current may be given as a training dataset for a quadratic regression model and then used to make predictions for new data. For a given new data of three-phase current in the time domain, the quadratic regression model searches for nearest neighbors from the training dataset and predicts the mean level of these neighbors as the eccentricity level. Figure 17A shows the best prediction result obtained using a quadratic regression model trained on time-series data of three-phase current.

[0092] Figure 17B shows a prediction result 1700B according to one embodiment of the present disclosure. In one embodiment, the prediction result 1700B is based on a regression model trained on an H0 Betch sequence. For example, an H0 Betch sequence of time-series data of three-phase current may be given as the training dataset for a quadratic regression model. For a given new data of the H0 Betch sequence, the quadratic regression model searches for nearest neighbors from the training dataset and predicts the average level of these neighbors as the eccentricity level. Figure 17B shows the best prediction result obtained using a quadratic regression model trained on an H0 Betch sequence.

[0093] Figure 17C shows prediction results 1700C according to some embodiments of the present disclosure. In one embodiment, the prediction results are based on a regression model trained on an H1 Betch sequence. As an example, an H1 Betch sequence of time-series data of three-phase current may be given as the training dataset for a quadratic regression model. For a given new data of the H1 Betch sequence, the quadratic regression model searches for nearest neighbors from the training dataset and predicts the average level of these neighbors as the eccentricity level. Figure 17C shows the best prediction result obtained using a quadratic regression model trained on an H1 Betch sequence.

[0094] Figure 17D shows prediction results according to several embodiments of the present disclosure. In one embodiment, the prediction results are based on a regression model trained on H0 and H1 Betch sequences. As an example, both H0 and H1 Betch sequences of time-series data of three-phase current may be given as the training dataset for a quadratic regression model. For a given new data set of H0 and H1 Betch sequences, the quadratic regression model searches for nearest neighbors from the training dataset and predicts the mean level of these neighbors as the eccentricity level. Figure 17D shows the best prediction result obtained using a quadratic regression model trained on H0 and H1 Betch sequences.

[0095] High RMSE and MAE (both close to 30%) indicate ineffective prediction. For Betch sequences, the inventors significantly improved prediction accuracy by extracting the mean values ​​of both H0 and H1 sequences and providing them to a quadratic regression model, reducing RMSE and MAE to 8.6% and 7.1%, respectively, when using both H0 and H1 Betch sequences.

[0096] Instead of quadratic regression models, other machine learning models such as support vector regression (SVR), Gaussian process regression (GPR), artificial neural networks (ANNs), and convolutional neural networks (CNNs) can also be used. However, these models tend to overfit to the training dataset and perform poorly on new data.

[0097] Compared to MCSA, which requires relevant domain knowledge and physical models to identify fault signatures, the TDA process, or the process described with reference to Figures 5A and 5B, for example, does not require a physical model to detect faults. By processing the input with TDA, the data is appropriately classified according to the fault level. This suggests the possibility of unsupervised learning for fault classification. Furthermore, prediction results can be improved by using only short time-domain data segments. In all tests, the length of the time-series data is 1024 points, or approximately 0.1 seconds. In contrast, conventional spectral analysis methods using MCSA often require several seconds or more of data to reliably identify fault components, in addition to the domain knowledge necessary to identify fault signatures. Due to these advantages, the proposed TDA method is promising for application to a wide range of fault detection.

[0098] The following description provides only exemplary embodiments and is not intended to limit the scope, application, or configuration of the Disclosure. Rather, the following description of exemplary embodiments will give a person skilled in the art an explanation that will enable the implementation of one or more exemplary embodiments. Various modifications to the function and arrangement of the elements are possible without departing from the spirit and scope of the subject matter set forth in the appended claims.

[0099] In the following description, specific details are given to provide a complete understanding of the embodiments. However, those skilled in the art will understand that the embodiments can be carried out even without these specific details. For example, systems, processes, and other elements in the disclosed subject matter may be shown as components in block diagrams so as not to obscure the embodiments with unnecessary details. Also, well-known processes, structures, and techniques may be shown without unnecessary details so as not to obscure the embodiments. Furthermore, similar reference numerals and names in different drawings refer to similar elements.

[0100] Furthermore, each embodiment may be described as a process shown as a flowchart, flow diagram, data flow diagram, structure diagram, or block diagram. Even if a flowchart describes the operation as a sequential process, many operations may be performed in parallel or simultaneously. Also, the order of operations may be changed. A process may be terminated when its operations are complete, but this process may include additional steps that are not discussed or illustrated. Furthermore, not all operations within a specifically described process are required to be included in all embodiments. A process may be a method, function, procedure, subroutine, subprogram, etc. If a process is a function, the termination of the function corresponds to returning the function to the calling function or the main function.

[0101] Furthermore, embodiments of the disclosed subject matter may be implemented manually or automatically, or at least partially. Manual or automatic implementations may be implemented, or at least assisted by, a machine, hardware, software, firmware, middleware, microcode, a hardware description language, or any combination thereof. If implemented in software, firmware, middleware, or microcode, the program code or code segments for performing the required tasks may be stored in a machine-readable medium. A processor can then perform the required tasks.

[0102] The various methods or processes outlined herein may be coded as software executable on one or more processors employing any one of various operating systems or platforms. Furthermore, such software may be written using any of several suitable programming languages ​​and / or programming tools or scripting tools, and may be compiled as executable machine language code or intermediate code that runs on a framework or virtual machine. Typically, the functions of program modules may be combined into various embodiments as desired, or distributed.

[0103] Embodiments of this disclosure may be embodied as methods provided as examples. The operations performed as part of this method may be ordered in any suitable manner. Thus, embodiments can be constructed that may include performing operations in a different order than those performed sequentially in exemplary embodiments, or performing several operations simultaneously.

[0104] While this disclosure has been described with reference to several preferred embodiments, it should be understood that various other modifications and alterations are possible within the spirit and scope of this disclosure. Accordingly, the appended claims cover all variations and alterations that fall within the true spirit and scope of this disclosure.

Claims

1. A fault detector for detecting eccentricity of a motor including a stator and rotor separated by an air gap, wherein the fault detector comprises a processor and a memory that stores instructions, when executed by the processor, to cause the fault detector to perform the following operations, the operations being: Collecting feedback electrical signals of the motor's operation, including time-series data of three-phase current measured during the motor's operation, via a communication channel including either or a combination of a wired communication link and a wireless communication link; By mapping the data points of the aforementioned time-series data onto the three-dimensional space of the three-phase current, a three-phase point group is formed. To extract the topological representation of the topological features of the three-phase point cloud using Topological Data Analysis (TDA), The eccentricity of the motor is classified based on the extracted topology representation, A fault detector comprising transmitting, via the communication channel, one or a combination of an index indicating the classified eccentricity of the motor and a control command selected based on the classified eccentricity.

2. The fault detector according to claim 1, wherein the classified eccentricity includes the type of eccentricity and the severity level of the eccentricity.

3. The fault detector according to claim 1, wherein the processor classifies the eccentricity by running a pre-supervised model to classify different topological representations indicated by the type of eccentricity, the severity level of the eccentricity, or both.

4. The fault detector according to claim 3, wherein the model is a regression model.

5. The fault detector according to claim 4, wherein the regression model includes extrapolation of the marked severity levels of the eccentric used for training.

6. The fault detector according to claim 3, wherein the model is a neural network.

7. The fault detector according to claim 1, wherein, in order to extract the topology features using the TDA, the processor is configured to perform persistent homology by examining the three-phase point cloud at different scales and to determine the topology representation as the representation of the persistent homology.

8. The fault detector according to claim 7, wherein the representation of the persistent homology includes one or a combination of a persistence barcode and a persistence diagram.

9. The fault detector according to claim 7, wherein the representation of the persistent homology is obtained by filtration, which involves calculating the persistent homology using different thresholds and tracking the duration of different topological features at the corresponding thresholds.

10. The topological features tracked by the persistent homology correspond to multiple clusters formed by the connected components in the three-phase point group. ０ Features and H corresponding to the hole formed by the space surrounded by the connecting component around the three-phase point group １ A fault detector according to claim 9, comprising the features.

11. The fault detector according to claim 1, wherein the processor is further configured to cause the fault detector to perform the conversion of the topological representation of the topological features into a Betti sequence or a Betti curve by executing the instructions.

12. The fault detector according to claim 11, wherein the processor is further configured to cause the fault detector to classify the eccentricity of the motor based on the Betch sequence or the Betch curve by executing the instructions.

13. The fault detector according to claim 1, wherein the TDA removes the dominant shape of the three-phase point group.

14. A method for detecting an eccentric failure in a motor including a stator and rotor separated by an air gap, wherein the method is: Collecting feedback electrical signals of the motor's operation, including time-series data of three-phase current measured during the motor's operation, via a communication channel including either or a combination of a wired communication link and a wireless communication link; By mapping the data points of the aforementioned time-series data onto the three-dimensional space of the three-phase current, a three-phase point group is formed. To extract the topological representation of the topological features of the three-phase point cloud using Topological Data Analysis (TDA), The eccentricity of the motor is classified based on the extracted topology representation, A method comprising transmitting, via the communication channel, one or a combination of an index indicating the classified eccentricity of the motor and a control command selected based on the classified eccentricity.

15. The method according to claim 14, wherein the classified eccentricity includes the type of eccentricity and the severity level of the eccentricity.

16. The method according to claim 14, further comprising running a pre-supervised model to classify different topological representations indicated by the type of eccentricity, the severity level of the eccentricity, or both.

17. The method according to claim 16, wherein the model is a regression model.

18. The method according to claim 17, wherein the regression model includes extrapolation of the marked severity levels of the eccentric used for training.

19. The method according to claim 16, wherein the model is a neural network.

20. Extracting the topological features using the TDA is Performing persistent homology, which includes examining the three-phase point group at different scales, The method according to claim 14, further comprising determining the topological representation as the representation of the persistent homology.

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