System and method for predicting motor eccentricity levels 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] FIELD OF THE DISCLOSURE The present disclosure relates generally to motors, and more particularly to systems and methods for detecting operational faults in motors. [Background technology]

[0002] Electric motors are widely used in various aspects of modern society, such as factories, home appliances, and electric vehicles. As their use increases, especially with the growth of IoT, monitoring the operating status of motors and detecting motor faults is becoming increasingly important. Motors can experience a variety of failures, and one of the most common is eccentricity failure, which occurs when the air gap between the stator bore and rotor is not uniform.

[0003] Eccentricity faults can be classified into three types: static eccentricity, dynamic eccentricity, and mixed eccentricity. Static eccentricity occurs when the center of rotation is aligned with the center of the rotor, but the rotor center is offset from the central axis of the stator bore. Dynamic eccentricity occurs when the center of rotation is aligned with the central axis of the stator bore, but the rotor center 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, cause machine failures. It is impossible to manufacture a motor with zero air-gap eccentricity during manufacturing. Static eccentricity can be caused by imperfect alignment between the stator core assembly and the center of rotation or by deviation of the stator core from its true roundness. Similarly, small dynamic eccentricity can be caused by imperfect alignment between the rotor center and the rotation axis or by imperfect rotor geometry. Over the motor's operational life, the eccentricity level can increase due to, for example, bearing deterioration or mechanical deterioration of the mounts, causing physical misalignment of the stator assembly. Air-gap eccentricity induces unbalanced magnetic attraction (UMP) that counteracts the rotor's stiffness. As eccentricity increases, it can cause 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 manufacturing for quality control and during operation for safety and asset protection.

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

[0006] To address these issues, MCSA has been proposed. Its advantages include ease of implementation and reduced costs due to the lack of additional dedicated sensors. MCSA detects eccentricity using stator current harmonics. The uneven air gap caused by eccentricity effectively induces additional 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 to detecting eccentricity faults using MCSA is that many spatial harmonics caused by eccentricity may be reflected in the vibration signal but not in the time harmonics, which are not present in the stator current. Furthermore, specific stator current fault signatures may depend on specific motor design parameters and are not universal for all motors. For example, certain combinations of stator slot and rotor bar counts have proven more difficult to detect some fault signatures due to static eccentricity.

[0007] Another method for analyzing eccentricity faults is to use either time-stepping finite element simulation or a circuit model based on the modified winding function method (MWFM). The above methods are primarily used for physics-based modeling. Finite element simulation can identify the fault frequency and its corresponding amplitude with greater accuracy, but it is time-consuming and requires detailed geometric parameters and material properties of the motor. MWFM-based circuit models are much faster, but due to the simplified modeling process, they are less accurate in identifying the amplitude of the fault component and still require more than nameplate specific motor design information, such as the nominal air gap dimensions, number of slots, and number of rotor bars for induction or synchronous machines.

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

[0009] Therefore, an effective method for identifying and extracting fault-related features, ideally from shorter signal segments, without using physical models and signal processing processes, is desirable for detecting motor faults. Summary of the Invention

[0010] Some embodiments are based on the recognition that there is a need for an effective solution for detecting eccentricity faults in motors that is more computationally efficient and accurate than the conventional solutions described above.

[0011] Thus, a method for detecting eccentricity faults in a motor is disclosed. The method includes extracting fault-related features of a motor, such as an induction motor or a synchronous motor, by performing topological data analysis (TDA) on motor current signals and applying them to detecting eccentricity faults in the motor. TDA is a mathematical process for extracting shape information from a data space. TDA can be applied to time-series data, image data, sensor data, etc. to extract essential geometric characteristics of an object. The TDA-based method for detecting eccentricity faults in a motor disclosed herein includes acquiring topological features from time-domain data and representing these topological features with a persistence diagram and a vectorized Betti sequence. The method further includes extracting fault-related features from the topological features of the acquired data that can be clearly associated not only with the type of fault but also with the severity level of the fault. Furthermore, the method includes a machine learning model that predicts the eccentricity fault level of a motor for new eccentricity level data not included in the training data using the fault-related features extracted from TDA.

[0012] Some embodiments are based on the recognition that TDA methods are less sensitive to the choice of metric compared to other geometric methods and are more robust to noise because they are coordinate-free and extract only essential geometric properties of the object.

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

[0014] Some conventional methods are based on the application of TDA, which utilizes persistent homology techniques to reveal dominant shapes in a data space and ignore smaller features or consider them noise. However, various embodiments disclosed herein remove dominant shapes and focus on smaller features in the persistent homology data space, such as time-series stator current data.

[0015] As such, some embodiments are based on the recognition that the topological features extracted as described above comprise fault signatures that distinguish between data from the same motor with different static eccentricity levels and are therefore suitable for developing data-driven machine learning models for predicting motor eccentricity failures.

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

[0017] The methods and systems disclosed herein can be used in at least two application scenarios to detect eccentricity faults in motors: during the manufacturing stage and during operation of the motor.

[0018] During the manufacturing stage, the purpose is to inspect manufactured motors and identify the eccentricity level for quality control. Since the same type of motor is mass-produced, test motors are used to collect data covering a wide range of eccentricity levels, and based on the collected data, a model is developed to predict new data measured on other motors of the same type.

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

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

[0021] According to another embodiment, a method for detecting eccentricity faults in a motor including a stator and a rotor separated by an air gap is disclosed. The method includes collecting, via a communication channel including one or a combination of a wired communication link and a wireless communication link, a feedback electrical signal of the motor's operation, including time series data of three-phase currents measured during operation of the motor. The method further includes forming a three-phase point cloud by mapping data points of the time series data to a three-dimensional space of 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. The method further includes transmitting, via the communication channel, one or a combination of an indicator indicative of the classified eccentricity of the motor and a control command selected based on the classified eccentricity.

[0022] Embodiments of the present disclosure will now be further described with reference to the accompanying drawings, which are not necessarily to scale, emphasis instead being placed upon illustrating the principles of embodiments of the present disclosure. [Brief explanation of the drawings]

[0023] [Figure 1A] FIG. 1 is a schematic diagram illustrating a motor fault detection system according to some embodiments of the present disclosure. [Figure 1B] FIG. 1 is a schematic diagram illustrating a motor, according to some embodiments of the present disclosure. [Figure 2A] FIG. 1 is a schematic diagram illustrating a motor, according to some embodiments of the present disclosure. [Figure 2B] FIG. 10 is a schematic diagram illustrating static eccentricity faults, according to some embodiments of the present disclosure. [Figure 2C] FIG. 10 is a schematic diagram illustrating a dynamic eccentricity fault, according to some embodiments of the present disclosure. [Figure 2D] FIG. 10 is a schematic diagram illustrating a mixed eccentricity fault, in accordance with some embodiments of the present disclosure. [Figure 3]FIG. 1 is a schematic diagram illustrating an experimental setup of a motor, according to some embodiments of the present disclosure. [Figure 4] 10A-10C illustrate graphical representations of time domain current signals for different eccentricity levels of a motor, in accordance with some embodiments of the present disclosure. [Figure 4 Continued] 10A-10C are diagrams (continued) illustrating graphical representations of time domain current signals for different eccentricity levels of a motor, in accordance with some embodiments of the present disclosure. [Figure 5A] FIG. 1 illustrates an exemplary method for determining motor faults, according to some embodiments of the present disclosure. [Figure 5B] FIG. 1 illustrates an exemplary method for determining motor faults, according to some embodiments of the present disclosure. [Figure 6] FIG. 10 illustrates a graphical representation of three-phase point clouds for different eccentricity levels, in accordance with some embodiments of the present disclosure. [Figure 6 Continued] 10A-10C are diagrams (continued) illustrating graphical representations of three-phase point clouds for different eccentricity levels, according to some embodiments of the present disclosure. [Figure 7A] 1A and 1B illustrate exemplary representations of data points in a finite metric space, in accordance with some embodiments of the present disclosure. [Figure 7B] FIG. 1 illustrates an exemplary representation of a barcode in a finite metric space, in accordance with some embodiments of the present disclosure. [Figure 8] FIG. 1 illustrates an exemplary method for persistent homology computation of 3-phase point groups in finite metric spaces, in accordance with some embodiments of the present disclosure. [Figure 9] FIG. 2 illustrates a graphical representation of a persistence diagram in accordance with some embodiments of the present disclosure. [Figure 10] FIG. 10 illustrates persistence diagrams of three-phase currents for six different eccentricity levels, in accordance with some embodiments of the present disclosure. [Figure 10 Continued] 10A-10C are diagrams (continued) illustrating persistence diagrams of three-phase currents for six different eccentricity levels, in accordance with some embodiments of the present disclosure. [Figure 11]FIG. 2 illustrates a Betti sequence or Betti curve corresponding to a persistence diagram, according to some embodiments of the present disclosure. [Figure 12] FIG. 10 illustrates Betti sequences or curves associated with different three-phase currents, in accordance with some embodiments of the present disclosure. [Figure 12 Continued] 10A-10C are diagrams (continued) illustrating Betti sequences or curves associated with different three-phase currents, according to some embodiments of the present disclosure. [Figure 13] 10A-10C illustrate time domain plots of different eccentricity levels in accordance with some embodiments of the present disclosure. [Figure 14] FIG. 1 illustrates t-Distributed Stochastic Neighbor Embedding (t-SNE) plots for H0 and H1 Betti curves, in accordance with some embodiments of the present disclosure. [Figure 15] FIG. 10 illustrates prediction results in accordance with some embodiments of the present disclosure. [Figure 16] FIG. 10 illustrates prediction results in accordance with some embodiments of the present disclosure. [Figure 17A] FIG. 10 illustrates prediction results in accordance with some embodiments of the present disclosure. [Figure 17B] FIG. 10 illustrates prediction results in accordance with some embodiments of the present disclosure. [Figure 17C] FIG. 10 illustrates prediction results in accordance with some embodiments of the present disclosure. [Figure 17D] FIG. 10 illustrates prediction results in accordance with some embodiments of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0024] In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. It will be apparent to one skilled in the art that one or more embodiments may be practiced without these specific details. Additionally, devices and methods are shown as block diagrams in order to avoid obscuring the present disclosure.

[0025] As used in this specification and claims, the terms "for example," "for example," "such as," and "comprises," "has," "includes," and other verb forms thereof, when used in conjunction with a list of one or more components or other items, should be construed as open-ended, meaning not to exclude other additional components or items from this list. The term "based on" means based at least in part on. It should further be understood that the phraseology and terminology used herein are for descriptive purposes and should not be regarded as limiting. Any headings used herein are for convenience only and have no legal or limiting effect.

[0026] 1A is a schematic diagram illustrating a fault detection system for a motor, e.g., motor 101, in accordance with some embodiments of the present disclosure. In one example, the system for detecting operational faults may include motor 101, sensors 105A, 105B, and 105C, fault detector 100A, and communication channel 107. Motor 101 is an AC motor in which the rotation of the motor shaft is synchronized to 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 certain embodiments, sensors 105A, 105B, and 105C may be current and voltage sensors for acquiring the current and voltage of each winding of motor 101. Other sensors are also contemplated, 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 motor 101 via wireless or wired connections to collect data from motor 101.

[0027] The communication channel 107 may include any medium over which data from the motor 101 can be communicated 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, a cellular network such as a long-term evolution (LTE) network, a cloud network, a wireless fidelity (Wi-Fi) network, and / or a wireless local area network (WLAN). Various devices in a system for detecting operating faults in the motor 101 are operable 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, Worldwide Interoperability for Microwave Access (Wi-MAX), Wireless Access in Vehicular Environments (WAVE), cellular communication protocols, Transmission Control Protocol and Internet Protocol (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 a fault during operation of the motor 101. 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 the sensors 105A, 105B, and 105C. The memory 140 stores the sensor data. In one example, the memory 140 can persistently store the sensor data. In another example, the memory 140 can temporarily store the sensor data for a predetermined period of time. This period may be determined based on user / operator 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 goals / interests. In one embodiment, the sensor data collected from the 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. The sensor data collected from the sensors 105A, 105B, and 105C may include a feedback electrical signal indicative of the operation of the motor 101. The feedback electrical signal may include time-series data of three-phase currents measured during the operation of the motor 101. The fault detector 100A may form a three-phase point cloud by mapping data points of the time-series data to a three-dimensional space of the three-phase currents. The fault detector 100A may extract a topological representation of topological features of the three-phase point cloud using TDA. The fault detector 100A may classify the eccentricity of the motor based on the extracted topological representation. In one example, the classified eccentricity includes a type of eccentricity and a severity level of the eccentricity. The fault detector 100A may transmit, via the communication channel 107, one or a combination of an indicator indicative of the classified eccentricity of the motor and a control command selected based on the classified eccentricity.In one embodiment, the processor 120 of the fault detector 100A can cause the output interface 150 to transmit, via the communication channel 107, one or a combination of an indication of the classified eccentricity of the motor and a control command selected based on the classified eccentricity. The fault detector 100A can select the control command based on the type of eccentricity and the severity level of the eccentricity. In one example, the output interface 150 can transmit, via the communication channel 107, the indication of the classified eccentricity and the control command to a user or system operating the motor 101. The indication of 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. Operations performed by the fault detector 100A to detect a fault during operation of the motor 101A are described below with reference to FIGS. 5A and 5B.

[0029] FIG. 1B illustrates 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 main shaft 106, and two bearings 108A and 108B. Eccentricity failures in the motor 101 typically result from manufacturing or operating errors that cause an uneven air gap between the stator 104 and the rotor 102. In one example, an eccentricity 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. Types of eccentricity are described in more detail with reference to FIGS. 2A, 2B, 2C, and 2D.

[0030] 2A, 2B, 2C, and 2D are schematic diagrams illustrating different types of eccentricity faults in accordance with 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. An eccentricity fault is a type of motor fault that results from the formation of an uneven air gap between stator 104 and rotor 102.

[0031] 2A is a schematic diagram illustrating a motor 101 according to some embodiments of the present disclosure. The motor 101 shown in FIG. 2A is an example of a normal motor without any eccentricity 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 and has no eccentricity faults, and the air gap 124(A) between the stator 104 and the rotor 102 is uniform at different locations.

[0032] 2B is a schematic diagram illustrating a static eccentricity fault, according to some embodiments of the present disclosure. Points O and O are coincident but offset from the center O of the stator bore. A static eccentricity fault exists because the rotor 102 always rotates around point O, and the air gap 124 (B) between the stator 104 and the rotor 102 is not uniform at different locations.

[0033] 2C is a schematic diagram illustrating a dynamic eccentricity fault, according to some embodiments of the present disclosure. The center of rotation Ow of the rotor 102 coincides with the stator center Os, while the rotor center Or orbits around the point Ow. Because the rotor does not rotate around its own center of mass, the air gap 124 (C) changes with the rotor's rotation angle and varies dynamically.

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

[0035] Static eccentricity of motors is usually generated during the manufacturing process. Static eccentricity faults can develop into mixed eccentricity during motor operation due to unbalanced magnetic attraction force, which can eventually cause machine failure, so early detection is important.

[0036] FIG. 3 is a schematic diagram illustrating an experimental setup for a motor 101 in accordance with some 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 a fault associated with the motor 101. The experimental setup shown in FIG. 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 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, two pairs of air gap sensors are used to measure the air gap 124. The first pair of air gap sensors may be located at a position indicated by (x1, y1). The second pair of air gap sensors may be located at a position indicated by (x2, y2). In one embodiment, the stator 104 of the motor 101 is mounted on a linear stage, which allows 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 air gap 124 on the load side, and the second pair of displacement sensors is installed on the opposite side to the side facing the air gap 124. The two pairs of displacement sensors 105C detect when the motor 101 moves at an angular velocity ω r The horizontal (x-axis) and vertical (y-axis) dimensions of the air gap 124 are measured while the motor 101 is operating at 100°C. A power brake is connected to the motor 101, which acts as the 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. Phase current sensors are used to measure the phase current signals 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 the 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 the 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 sensors and the air gap sensor 105C is recorded, for example, at a sampling frequency of 10 kHz and under no load. By way of example, but not limitation, the eccentricity levels may be set to 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively. These percentages are defined as the ratio of the maximum air gap deviation to the nominal air gap size. From the data from the air gap sensor 105C, the actual static eccentricity of the air gap 124 is remarkably close to the initial setting, within 3% in all cases. Furthermore, a small dynamic eccentricity level of approximately 6% exists in all cases, according to the air gap sensor readings. This mixed eccentricity effect generates a sideband signal of fc = fs ± fr, where fs is the supply frequency and fr is the rotational frequency.

[0039] 4 shows a block diagram 400 including a graphical representation of time-domain current signals at different eccentricity levels of motor 101, according to some embodiments of the present disclosure. Block diagram 400 includes results of measurements performed by sensors 105A, 105B, and 105C on motor 101 at different eccentricity levels. In one example, three-phase current signals associated with stator 104 are measured at eccentricity levels set at, 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 with the eccentricity level set at 1.5%. Graph 400B shows the results of measurements performed by sensors 105A, 105B, and 105C on motor 101 with the eccentricity level set at 17.2%. Graph 400C shows the results of measurements performed by sensors 105A, 105B, and 105C on motor 101 with the eccentricity level set at 24.1%. Graph 400D shows the results of measurements performed by sensors 105A, 105B, and 105C on motor 101 with the eccentricity level set at 40.3%. Graph 400E shows the results of measurements performed by sensors 105A, 105B, and 105C on motor 101 with the eccentricity level set at 47.1%. Graph 400F shows the results of measurements performed by sensors 105A, 105B and 105C on motor 101 with the eccentricity level set at 64.6%.

[0041] The time-domain current signal is sampled at a sampling frequency of, for example, 10 kHz. As a non-limiting example, the time-domain signal shown in the graphical representation of FIG. 4 is formed by plotting approximately 1,000 data samples of the time-domain current signal. Because the fundamental component is dominant, it is difficult to directly distinguish the eccentricity level from the time-domain current signal shown in FIG. 4. The TDA method and the process of applying the TDA method to extract eccentricity fault features and predict eccentricity levels are introduced.

[0042] FIG. 5A illustrates an exemplary method 500A for determining faults in a motor 101, according to some embodiments of the present disclosure. According to one embodiment of the present disclosure, the method 500A is used to train a machine learning model for determining faults in the motor 101 using a TDA process. The method 500A determines topological features that persist across different scales by applying the TDA process to time-domain current signals associated with the stator 104 of the motor 101. The topological features associated with point cloud representations of samples of the time-domain current signals for different eccentricity levels may be provided to the machine learning model as training data for identifying eccentricity faults and levels of eccentricity faults. The steps and their order illustrated in FIG. 5A are exemplary and may include various alternatives, equivalents, or derivations, without being limited to the order of execution. The steps of the method 500A of FIG. 5A and their various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., an optical disk, a memory card, or a hard drive) storing instructions executable by the processor 120.

[0043] At 502, the fault detector 100A can collect, via a communication channel 107, which can include one or a combination of a wired communication link and a wireless communication link, feedback electrical signals of the operation of the motor 101, including time series data of time-domain current signals measured during the operation of the motor 101. In one embodiment, the time series data of the time-domain current signals includes three-phase current signals associated with the stator 104, which are measured at eccentricity levels set, 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 FIGS. 3 and 4. The time-domain current signals are measured over a predetermined period of time depending on a sampling rate employed to divide the time-domain current signals. In one example, but not limited to, the time-domain current signals are measured over a period of 0.01 seconds at a sampling rate of 10 kHz.

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

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

[0046] At 508, the fault detector 100A can extract a topological representation of topological features of the three-phase point cloud by performing a persistent homology calculation 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 a persistent homology representation. The persistent homology representation can include one or a combination of a persistence barcode and a persistence diagram. The persistence barcode is described with reference to FIGS. 7A and 7B. The persistence diagram is described with reference to FIG. 9. In one example, the fault detector 100A can calculate persistent homologies of the three-phase point cloud corresponding to each eccentricity level for a zero-dimensional hole H0 and a one-dimensional hole H1. The zero-dimensional hole H0 may also be referred to as an H0 feature, which corresponds to multiple clusters formed by connected components in the three-phase point cloud. The one-dimensional hole H1 may also be referred to as an H1 feature, which corresponds to the hole formed by the space enclosed by the connected components around the 3-phase 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 investigating data structures such as 3-phase point clouds of time series data. Persistent homology is robust to perturbations in the time series data, is independent of dimensionality and coordinates, and provides a compact representation of qualitative features of the time series data.

[0047] A 3-phase point cloud is represented as a finite metric space. From a topological point of view, a finite metric space does not contain any interesting information. Therefore, it is necessary to compactify the point cloud at different resolution scales and analyze the evolution of the shape across different resolution scales. Qualitative features are given by topological invariants. The variation of the topological invariants across different resolution scales is represented in a compact way, summarizing the "shape" of the time series data.

[0048] A method for performing persistent homology calculations of 3-phase point groups in finite metric spaces will be described in detail with reference to FIG.

[0049] In 510, the fault detector 100A can convert the H0 and H1 homologies of the three-phase point clouds 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. To this end, the fault detector 100A derives Betti sequences or Betti curves from persistence diagrams of time series data of three-phase currents with different eccentricities. Betti sequences are described in detail with reference to Figures 9 and 10.

[0050] At 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 from 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 a segmented time-domain current signal and a label of the time series data of the time-domain current signal. The eccentricity level data 514 can also indicate the conditions under which the time-domain current signal is collected.

[0051] The 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 value includes the eccentricity type and the eccentricity severity level. By way of 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 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 including one or a combination of data points corresponding to the Betch sequence derived in 510, the eccentricity level data 514, or three-phase time-domain current signals.

[0052] FIG. 5B illustrates an exemplary method 500B for determining faults in the motor 101 according to one embodiment of the present disclosure. The method 500B determines topological features that persist across different scales by applying TDA to time-domain current signals associated with the stator 104 of the motor 101. The topological features associated with point cloud representations of samples of the time-domain current signals for different eccentricity levels may be provided to a trained machine learning model as training data for identifying eccentricity faults and levels of eccentricity faults. The steps and their order illustrated in FIG. 5B are exemplary and may include various alternatives, equivalents, or derivations, without being limited to the order of execution. The steps of the method of FIG. 5B and their various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., an optical disk, a memory card, or a hard drive) storing instructions executable by the processor 120.

[0053] At 516, the fault detector 100A can collect, via a communication channel 107, including one or a combination of a wired communication link and a wireless communication link, feedback electrical signals of the operation of the motor 101, including time series data of time-domain current signals measured during the same operation period of the motor 101 used at 502 during training of the machine learning model. 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 the time-domain current signals includes three-phase current signals associated with the stator 104, measured at eccentricity levels set, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively. Time-domain current signals are described in detail with reference to FIGS. 3 and 4.

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

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

[0056] At 522, 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. In one example, the fault detector 100A can calculate persistent homology of the three-phase point cloud corresponding to each eccentricity level for the zero-dimensional hole H0 and the one-dimensional hole H1.

[0057] At 524, the fault detector 100A can convert the H0 and H1 homologies of the three-phase point clouds into Betti sequences with fixed lengths L1 and L2, respectively. The fault detector 100A derives Betti sequences or Betti curves from persistence diagrams of time series data of three-phase currents at different eccentricity levels. Betti sequences are described in detail with reference to FIGS. 9 and 10.

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

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

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

[0061] Each three-phase point cloud is formed for three-phase current signals measured at a particular eccentricity level. The distance between data points in a particular point cloud may be, for example, Euclidean distance or Minkowski distance. Both Euclidean distance and Minkowski distance are defined using numerical data. However, this embodiment is not limited to using numerical data to define the distance between data points. In another example, distances can also be defined when the data is categorical rather than numerical.

[0062] Because the dominant components of the three-phase current signal are periodic waves with a fundamental frequency, the most significant shape is a large circle in 3D space. The most significant shape is the dominant shape of the three-phase point cloud. For 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 deviate from a perfect circle. Components other than the fundamental frequency are caused by faults such as eccentricity faults and are called fault components. Because the fault components have very small amplitudes, it is difficult to distinguish different eccentricity levels from the shape of the three-phase point cloud alone. Components other than the fundamental frequency may result in topological features other than the dominant shape of the three-phase point cloud. Therefore, if an eccentricity fault occurs during 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, topological features can be extracted from the three-phase point cloud, and the extracted topological features can be provided to a machine learning model to train the machine learning model for predicting the eccentricity level of the motor 101.

[0064] 7A shows an example representation 700A of data points in a finite metric space according to one embodiment of the present disclosure. The data points are located in a region R 2 The distance between two data points is called the filtering radius r. For different values ​​of r, the space S consisting of vertices, edges, triangles, or higher-dimensional polyhedra ris constructed based on a specific rule. In one example, an edge between two points i and j is included if and only if the Euclidean distance between points i and j is less than or equal to the filtering radius r, and all edges are included in S r The triangle is included if and only if all face triangles are in S r Using homology, the space S r It is possible to measure several features of the space S r The features or topological features may include moieties, holes, and / or voids.

[0065] 700A-1 shows an example point cloud when the filtering radius r is close to zero (r=0). When r=0, topological features, such as edges or vertices, are not formed, and all data points in the point cloud are represented as separate data points with no connecting features between them. As the filtering radius r increases, topological features begin to appear in the point cloud. 700A-2 shows an example point cloud when the filtering radius r is set to 0.6. 700A-3 shows an example point cloud in which holes appear when the filtering radius r is set to 1.1. In one example, holes begin to appear when the filtering radius r=1.1. 700A-4 shows an example point cloud when the filtering radius r is set to 1.6. In one example, when the filtering radius r=1.6, the holes that appeared at smaller radius values ​​are still present in the point cloud, but the hole radii are reduced compared to the holes shown in 700A-3. 700A-5 shows an example point cloud when the filtering radius r is set to 2.1. In one example, when the filtering radius r=2.1, holes in the point cloud disappear.

[0066] The lifetime of a feature, such as a hole, can be represented using a finite interval set known as a persistence barcode. The left endpoint of the interval represents the creation of the feature, and the right endpoint of the interval represents the disappearance of the feature. For example, FIG. 7B shows an example representation 700B of a barcode in a finite metric space according to one embodiment of the present disclosure. As the filtration radius increases, a topological feature, e.g., a hole, appears at a first value r1 of the filtration radius r (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 r2 of the filtration radius r (e.g., r=2.1). The first value r1 of the filtration radius r indicates the creation of the hole, and the second value r2 of the filtration radius r indicates the disappearance of the hole. The persistence of the hole can be represented as the 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 hole's persistence. The collection of persistence bars for each topological feature in the 3-phase point cloud is referred to as a persistence barcode.

[0067] 8 illustrates an exemplary method 800 for persistent homology computation of 3-phase point groups in finite metric spaces in accordance with some embodiments of the present disclosure. The steps illustrated in method 800 of FIG. 8 and their order are exemplary and may include various alternatives, equivalents, or derivations that are not limited to the order of execution. The steps of method 800 of FIG. 8 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 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 performing persistent homology calculation 508 .

[0069] In 508-1, a simplicial complex of the 3-phase point cloud is identified for each eccentricity level. In one embodiment, TDA is used to extract a topological representation of the topological features of the 3-phase point cloud. A simplicial complex is a collection of basic topological features or simplices, such as points, edges, or triangles. However, features or simplices are not limited to points, edges, or triangles. Tetrahedra or other higher-dimensional polyhedra may also be used as topological features or simplices. In one embodiment, the Rips complex is used as an algorithm to extract a topological representation of the topological features of the 3-phase point cloud. However, other algorithms may be used to construct the simplicial complex. A simplicial complex is defined by a threshold value r, referred to as 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 508-2, linear algebra is used to determine homology from the constructed simplicial complex. 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 birth and death of topological features at values ​​corresponding to the filtration radius r. The birth and death of topological features defines the lifetime of the topological features for different filtration radii r.

[0072] There are various ways to represent persistent homology, with persistence diagrams being one of the most common choices. A persistence diagram is a representation of a set of functions (b,d) = b,d∈R. 2and d>b, where each point corresponds to the creation and destruction of a topological feature in the corresponding simplicial complex. Specifically, each point (b, d) indicates a topological feature "created" at radius b and "destroyed" at radius d. There are various algorithms for filtering Rips complexes and computing persistence diagrams, which can be implemented by several software packages. The persistence diagram is described with reference to Figure 9. The H0 and H1 persistence diagrams of three-phase current data at six different eccentricity levels are described with reference to Figure 10.

[0073]

number

[0074] A point on the Betti sequence is then obtained from the sum.

number

[0075] The topological features in the persistent homology are a function of the filtering radius r. The representation of the persistent homology is obtained through filtering by calculating the persistent homology using different filtering radii r as thresholds and tracking the duration of different topological features at the corresponding thresholds. By limiting the maximum filtering range, it is possible to filter out "large" features in the data and leave only "small" features in the data. In one example, TDA can remove "large" features or dominant shapes from the topological features. In the case of motor fault detection, fault-related features have much smaller amplitudes compared to the dominant fundamental signal corresponding to the power supply frequency. For a small filtering radius r, maxBy selecting the dominant fundamental signal, we can filter out the fault-related features obtained from topology calculations on the persistence diagram and / or persistent homology expressed as a Betti sequence. Furthermore, filtering out the fundamental signal using TDA is less complex and does not require knowing the exact power supply frequency. In contrast to traditional signal processing methods, the exact frequency of the fundamental signal must be known to filter it out. In contrast to traditional model-based MCSA methods, the exact frequency components associated with the eccentricity fault also do not need to be explicitly identified by a physical model.

[0076] 9 illustrates a graphical representation 900 of a persistence diagram in accordance with some embodiments of the present disclosure. The graphical representation 900 includes a persistence diagram 900A and a persistence diagram 900B. The persistence diagram is a graph of R 2 A finite multiset of points in and the diagonal Δ={(x,y)∈R 2The H1 persistence diagram 900A is a multiset that is the union of a multiset 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 indicates the creation of a topological feature, e.g., a hole. The vertical axis of persistence diagram 900A indicates the disappearance of the topological feature. Persistence diagram 900A is a collection of persistence barcodes of 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 indicates the creation and disappearance of the corresponding H1 feature. A persistence barcode begins with the creation of the corresponding H1 feature and ends with the disappearance of the corresponding H1 feature. The creation of the H1 feature indicates the filtration radius r at which the H1 feature begins to appear. The disappearance of the H1 feature indicates the filtration radius r at which the H1 feature begins to disappear. Thus, persistence diagram 900A illustrates the lifetime of each H1 feature in a 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 destroyed with a larger filtration radius. As an example, a feature is referred to as a primary feature if it has a larger filtration radius for destruction and generation compared to other topological features in the three-phase point cloud. As shown in persistence diagram 900A, the persistence barcode of the primary feature is represented by the barcode in the upper left of persistence diagram 900A. A minor feature is a topological feature that has a smaller filtration radius for destruction and generation compared to the primary feature in the three-phase point cloud. As shown in persistence diagram 900A, the persistence barcode of the minor feature is represented by the barcode in the lower left of persistence diagram 900A. As shown in persistence diagram 900A, most of the small features have smaller birth and death filtering radii. Persistence diagram 900B more clearly visualizes the small features shown in persistence diagram 900A. In persistence diagram 900B, the ranges of the horizontal and vertical axes are reduced, e.g., r=0.06 for birth and r=0.065 for death.

[0077] FIG. 10 illustrates a graphical representation 1000 of persistence diagrams of three-phase currents 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 at 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 three-phase point clouds for the six different eccentricity levels. The most noticeable difference between these diagrams is the H1 feature, which corresponds to a small hole formed by adjacent points. For an ideal sine wave, the point cloud can only form one large hole. At 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, with increasing eccentricity level, more features appear in the H1 persistence map.

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

[0079] FIG. 11 illustrates Betti sequences or curves corresponding to persistence diagrams according to some embodiments of the present disclosure. Block diagram 1100 includes Betti curve 1100A corresponding to the H0 persistence diagram and Betti curve 1100B corresponding to the H1 persistence diagram. The H0 and H1 persistence diagrams are different from each other. The number of points in the H0 and H1 persistence diagrams is not fixed for different input data corresponding to three-phase currents. To provide these topological features to the machine learning model, the H0 and H1 homologies are converted into H0 and H1 Betti sequences with lengths L1 and L2, respectively. In one example, for both the H0 and H1 homologies, the lengths L1 and L2 are fixed at 1024, while the filtering ranges are [0, 0.07] and [0, 0.14], respectively.

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

[0081] FIG. 12 illustrates a graphical representation 1200 of Betti sequences or curves 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 H persistence map obtained from five different data segments with the same eccentricity level set at 17.2%, a Betti curve 1200B corresponding to an H persistence map obtained from five different data segments with the same eccentricity level set at 17.2%, a Betti curve 1200C corresponding to an H persistence map obtained from five different data segments with the same eccentricity level set at 64.6%, and a Betti curve 1200D corresponding to an H persistence map obtained from five different data segments with the same eccentricity level set at 64.6%. An important feature of persistent homology is robustness. In other words, the robustness of persistent homology suggests that similar data structures yield similar persistent homologies. The Betti curves exhibit good consistency. The similarity of the Betch curves shown in Figure 12 suggests that the TDA process can be used to remove time variations between different samples of time series data, allowing fault signatures to 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 separating signals from different fault levels.

[0083] The calculated Betti curves are used in a data-driven approach to eccentricity fault detection, quantification and prediction.

[0084] FIG. 13 illustrates a time-domain plot 1300 of different eccentricity levels in accordance with some embodiments of the present disclosure. In one embodiment, eccentricity level data for the motor 101 is measured and divided into a total of 1,170 samples, each 1,024 data points long. As an example, the eccentricity level data is measured for six different eccentricity levels, including, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, and 64.6%, respectively. As described with reference to FIGS. 5A and 5B , a Betti curve is calculated for the measured eccentricity level data. In one embodiment, a t-distribution stochastic neighbor 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 provide a low-dimensional representation of the similarity of high-dimensional data, both the three-phase current time series data and the calculated Betti curve.

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

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

[0087] 15 illustrates a prediction result 1500 according to some embodiments of the present disclosure. In one embodiment, the prediction result 1500 includes a root-mean-square estimate of a time-domain representation of the phase current data. In one embodiment, motor eccentricity fault detection can be applied to two application scenarios: during the manufacturing stage and during operation of a motor, such as motor 101.

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

[0089] FIG. 16 illustrates prediction results 1600 according to some embodiments of the present disclosure. In one embodiment, the prediction results 1600 may include root-mean-square evaluation values ​​using Betti sequences. As an example, the H0 Betti sequences may be provided as a training data set for a k-NN regression model. Given new data converted to H0 Betti sequences, the k-NN regression model searches for nearest neighbors from the training data set and predicts the average level of these nearest neighbors as the eccentricity level. As can be seen from the results shown in FIG. 16, with the H0 Betti sequences, the RMSE is reduced to 1.6% and the MAE is reduced to 0.7%. This result demonstrates the effectiveness of using Betti sequences on time-domain topology current data for interpolation purposes.

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

[0091] FIG. 17A illustrates 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 currents. As an example, the time series data of three-phase currents may be provided as a training data set for the quadratic regression model and then used to predict new data. For given new data of time-domain three-phase currents, the quadratic regression model searches for nearest neighbor values ​​from the training data set and predicts the average level of these nearest neighbor values ​​as the eccentricity level. FIG. 17A illustrates the best prediction result obtained using the quadratic regression model trained on time series data of three-phase currents.

[0092] FIG. 17B illustrates 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 with an H0 Betch sequence. As an example, an H0 Betch sequence of three-phase current time series data may be provided as a training data set for a quadratic regression model. For a given new data of the H0 Betch sequence, the quadratic regression model searches for nearest neighbor values ​​from the training data set and predicts the average level of these nearest neighbor values ​​as the eccentricity level. FIG. 17B illustrates the best prediction result obtained using the quadratic regression model trained with the H0 Betch sequence.

[0093] FIG. 17C illustrates 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 three-phase current time series data may be provided as a training data set for a quadratic regression model. For a given new data set of the H1 Betch sequence, the quadratic regression model searches for nearest neighbor values ​​from the training data set and predicts the average level of these nearest neighbor values ​​as the eccentricity level. FIG. 17C illustrates the best prediction results obtained using a quadratic regression model trained on an H1 Betch sequence.

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

[0095] The high RMSE and MAE (both close to 30%) indicate ineffective prediction. For the vetch sequence, we significantly improved the prediction accuracy by extracting the mean values ​​of both the H0 and H1 sequences and feeding them into a quadratic regression model, reducing the RMSE and MAE to 8.6% and 7.1%, respectively, when using both the H0 and H1 vetch sequences.

[0096] Instead of quadratic regression models, other machine learning models such as support vector regression (SVR) models, Gaussian process regression (GPR) models, 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 extrapolating to 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 physical models to detect faults. By processing the inputs with TDA, the data is appropriately classified according to the fault level. This suggests the possibility of unsupervised learning for fault classification. Furthermore, improved prediction results can be achieved 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 stably identify fault components, in addition to the domain knowledge required to identify fault signatures. These advantages make the proposed TDA method promising for widespread fault detection.

[0098] The following description provides exemplary embodiments only and is not intended to limit the scope, application, or configuration of the present disclosure. Rather, the following description of exemplary embodiments will provide those skilled in the art with an enabling description for implementing one or more exemplary embodiments. Various changes may be made in the function and arrangement of elements without departing from the spirit and scope of the subject matter as set forth in the appended claims.

[0099] In the following description, specific details are given to provide a thorough understanding of the embodiments. However, those skilled in the art will understand that the embodiments can be practiced 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 in unnecessary detail. Also, well-known processes, structures, and techniques may be shown without unnecessary detail so as not to obscure the embodiments. Furthermore, like reference numbers and names in the various drawings refer to like elements.

[0100] Each embodiment may also be described as a process, which is depicted as a flowchart, flow diagram, data flow diagram, structure diagram, or block diagram. Although a flowchart may describe operations as a sequential process, many operations may be performed in parallel or simultaneously. The order of operations may also be changed. A process may be terminated when its operations are completed, but the process may include additional steps not discussed or shown. Furthermore, not all operations within a specifically described process need be included in all embodiments. A process may be a method, a function, a procedure, a subroutine, a subprogram, etc. When a process is a function, the termination of the function corresponds to the function returning to the calling function or the main function.

[0101] Furthermore, embodiments of the disclosed subject matter may be implemented, at least in part, manually or automatically. The manual or automatic implementation may be implemented, or at least assisted, by machine, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented by software, firmware, middleware, or microcode, program code or code segments to perform the necessary tasks may be stored on a machine-readable medium. A processor may perform the necessary tasks.

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

[0103] The embodiments of the present disclosure may be embodied as methods, which are provided by way of example. The operations performed as part of the method may be ordered in any suitable manner. Thus, embodiments may be constructed that perform operations in an order different from the operations performed sequentially in the exemplary embodiments, and that may include performing some operations simultaneously.

[0104] Although the present disclosure has been described with reference to certain preferred embodiments, it should be understood that various other modifications and variations can be made within the spirit and scope of the present disclosure. It is therefore intended in the appended claims to cover all such variations and modifications as fall within the true spirit and scope of the present disclosure.

Claims

1. 1. A fault detector for detecting eccentricity in a motor including a stator and a rotor separated by an air gap, the fault detector comprising: a processor; and a memory storing instructions that, when executed by the processor, cause the fault detector to perform the following operations: collecting, via a communication channel including one or a combination of a wired communication link and a wireless communication link, a feedback electrical signal of the operation of the motor, the feedback signal including time series data of three-phase currents measured during operation of the motor; 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; extracting a topological representation of topological features of the three-phase point cloud using topological data analysis (TDA); and classifying the eccentricity of the motor based on the extracted topological representation; and transmitting, via the communication channel, one or a combination of an indicator indicative of the classified eccentricity of the motor and a control command selected based on the classified eccentricity.

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

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

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

5. The fault detector of claim 4 , wherein the regression model includes an extrapolation of the labeled severity levels of the eccentricity used for training.

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

7. 2. The fault detector of claim 1, wherein to extract the topological features using the TDA, the processor is configured to perform persistent homology that examines the three-phase point cloud at different scales and determine the topological representation as a representation of the persistent homology.

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

9. 8. The fault detector of claim 7, wherein the representation of the persistent homology is obtained through filtering by calculating the persistent homology using different thresholds and tracking the duration of different topological features at corresponding thresholds.

10. The topological features tracked by the persistent homology are represented as H ０ features and H corresponding to the holes formed by the spaces enclosed by the connected components around the three-phase point cloud. １ 10. The fault detector of claim 9, comprising:

11. 2. The fault detector of claim 1, wherein the processor is further configured to execute the instructions to cause the fault detector to convert the topological representation of the topological feature into a Betti sequence or a Betti curve.

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

13. The fault detector of claim 1 , wherein the TDA removes a dominant shape of the three-phase point cloud.

14. 1. A method for detecting eccentricity faults in a motor including a stator and a rotor separated by an air gap, the method comprising: collecting, via a communication channel including one or a combination of a wired communication link and a wireless communication link, a feedback electrical signal of the operation of the motor, the feedback signal including time series data of three-phase currents measured during operation of the motor; 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; extracting a topological representation of topological features of the three-phase point cloud using topological data analysis (TDA); and classifying the eccentricity of the motor based on the extracted topological representation; transmitting, via the communication channel, one or a combination of an indicator indicative of the classified eccentricity of the motor and a control command selected based on the classified eccentricity.

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

16. 15. The method of claim 14, further comprising: running a pre-trained model in a supervised manner to classify different topological representations labeled by the type of eccentricity, the severity level of the eccentricity, or both.

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

18. The method of claim 17 , wherein the regression model includes an extrapolation of the labeled severity levels of the eccentricity used for training.

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

20. Extracting the topological features using the TDA includes: performing persistent homology, which includes examining the three-phase point groups at different scales; and determining the topological representation as a representation of the persistent homology.

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