System and method for motor eccentricity level prediction using topological data analysis

Abstract

A system and method for motor eccentricity fault detection are disclosed. The method includes extracting fault-related features through topological data analysis (TDA) of a motor current signal and applying the fault-related features to motor eccentricity fault detection. The method also includes a process of obtaining topological features from the time domain data and representing them in a persistence map and a vectorized Betti sequence. The method also includes extracting fault-related features from topological features of the obtained data, which may not only be differentially associated with fault types but also be differentially associated with fault severity levels. Further, the method includes using a machine learning model to extract fault-related features from the TDA for predicting motor eccentricity fault levels, even for data from new eccentricity levels not visible in the training data.

Description

Technical Field

[0001] The present disclosure relates generally to electric machines, and more particularly to systems and methods for detecting operating faults in electric machines. Background Art

[0002] Electric motors are widely used in many aspects of modern society, such as factories, home appliances, electric vehicles, etc. With the increase in usage, monitoring the operating conditions of electric motors and detecting faults in electric motors has become important, especially with the growth of the Internet of Things. Different faults can occur in electric motors, one of the most common faults is eccentricity fault, which occurs when the air gap between the stator inner bore and the rotor is uneven.

[0003] Eccentricity faults can be divided into three categories, namely, static eccentricity, dynamic eccentricity and mixed eccentricity. Static eccentricity occurs when the center of the rotor is displaced from the center axis of the stator inner bore, while the center of rotation is still aligned with the center of the rotor. Dynamic eccentricity occurs when the center of rotation and the center axis of the stator inner bore are still aligned but the center of the rotor is displaced. Mixed eccentricity is a combination of static eccentricity and dynamic eccentricity.

[0004] There are many reasons that may cause motor eccentricity. If not corrected in time, air gap eccentricity can damage other components of the motor and cause failure of the machine using the motor. During the manufacturing stage, it is not feasible to produce a motor with zero air gap eccentricity. Static eccentricity may exist due to imperfect alignment between the stator core assembly and the center of rotation or the deviation of the stator core from a perfect circle. Similarly, small dynamic eccentricities may also exist due to imperfect alignment between the center of the rotor and the axis of rotation or imperfect shape of the rotor. Throughout the operating life of the motor, the eccentricity level may increase, for example due to bearing degradation or mechanical degradation of the mountings, resulting in physical displacement of the stator assembly. Air gap eccentricity causes unbalanced magnetic pull (UMP), which resists the rotor stiffness and may cause stator winding failure and friction between the rotor and stator with increased eccentricity, ultimately leading to machine failure. Therefore, it is important to check the eccentricity of the motor in the production stage for quality control and throughout 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. The UMP caused by air gap eccentricity leads to increased vibration. The increased vibration can be monitored by accelerometers mounted on the motor housing. Recently, machine learning and deep learning techniques have been applied to fault detection and classification of electric machines based on the measured vibration signals. However, vibration signals are often affected by noise from other sources, such as mechanical imbalance of the motor, excitation from external sources in complex factory environments, etc. In addition, the sensitivity of vibration analysis also varies depending on the location of the sensor on the motor housing. Therefore, it is challenging to identify eccentricity faults based solely on vibration signals.

[0006] MCSA has been proposed to address these issues. MCSA does not require additional dedicated sensors and therefore has the additional advantage of being simple to implement, thereby saving cost. MCSA uses stator current harmonics to detect eccentricity. In fact, the uneven air gap caused by eccentricity causes additional harmonics in the air gap permeability function and the air gap flux. Some of these harmonics will be reflected in the induced voltage in the stator winding and ultimately in the stator current. One challenge of eccentricity fault detection using MCSA is that a large number of spatial harmonics caused by eccentricity can be reflected in the vibration signal, but do not appear in the time harmonics and are not present in the stator current. In addition, certain stator current fault characteristics may depend on specific motor design parameters and are not universal for all motors. For example, it has been shown that under certain combinations of stator slots and the number of rotor bars, some fault characteristics due to static eccentricity are more difficult to detect.

[0007] Another approach for analyzing eccentricity faults is by using circuit models based on time-stepped finite element simulation or modified winding function method (MWFM). The above methods are mainly used for physics-based modeling methods. Finite element simulation provides higher accuracy in identifying fault frequencies and their corresponding magnitudes, but is also more time-consuming and requires detailed geometric parameters and material properties of the motor. Circuit models based on MWFM are much faster, but are not as accurate in identifying fault component magnitudes due to simplifications in the modeling process, and still require certain motor design information beyond the nameplate, such as the nominal air gap size, number of slots, and number of rotor bars for induction or synchronous motors.

[0008] It is also challenging to apply data-driven approaches to MCSA-based motor fault detection using only the stator current signal. Unlike vibration signals, the current component due to eccentricity faults is typically several orders of magnitude smaller than the dominant fundamental component at the power frequency. Commonly used machine learning techniques for time-domain signals that work well for vibration signals cannot effectively distinguish the stator current signals of the machine in healthy and fault conditions. Therefore, before the signal can be applied to a machine learning model for a data-driven approach, a feature extraction process based on a physical model built from expert domain knowledge and detailed spectral analysis of the measured stator current signal is typically required to extract the frequency components due to the fault. In addition, relatively long time-domain signals (typically between a few seconds and tens of seconds) are required to extract the extremely sensitive fault components from conventional spectral analysis.

[0009] Therefore, it is desirable to have an effective method to identify and extract fault-related features for motor fault detection without involving physical models and signal processing procedures and ideally from shorter signal segments. Summary of the invention

[0010] Some embodiments are based on the recognition that there is a need for an effective solution for motor eccentricity fault detection that is computationally efficient and more accurate than previous solutions described above.

[0011] Therefore, a method for motor eccentricity fault detection is disclosed. The method includes extracting fault-related features of a motor (e.g., an induction motor or a synchronous motor) by topological data analysis (TDA) of a motor current signal, and applying the extracted fault-related features to motor eccentricity fault detection. 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 the inherent geometric properties of an object. The TDA-based method for motor eccentricity fault detection disclosed in the present invention includes obtaining topological features from time domain data, and representing the topological features in a persistence graph and a vectorized Betti sequence. The method also includes extracting fault-related features from the topological features of the obtained time domain data, and the fault-related features can be associated not only with the fault type but also with the fault severity level. In addition, the method includes a machine learning model that uses the fault-related features extracted from TDA to predict the motor eccentricity fault level, even for data from new eccentricity levels that are not seen in the training data.

[0012] Some embodiments are based on the recognition that the TDA method is less sensitive to the choice of metric than other geometric methods, is coordinate-free, and extracts only intrinsic geometric properties of the object, which makes it more robust to noise.

[0013] To this end, some embodiments are based on the recognition that TDA together with the application of the principles of persistent homology provides data analysis methods that are very effective in failure analysis problems in fields such as image analysis, time series data analysis, sensor networks, chemistry and materials science.

[0014] Some previous methods are based on the application of TDA, which uses persistent coherence methods to reveal the dominant shape in the data space and ignores smaller features or treats them as noise. However, various embodiments disclosed herein provide filtering out the main shapes and focusing on small features in the data space, such as time series stator current data in persistent coherence.

[0015] To this end, some embodiments are based on the recognition that the topological features extracted in the manner described above do contain fault signatures: the fault signatures are different between data from the same motor with different static eccentricity levels, making them suitable for developing a data-driven machine learning model for predicting eccentricity faults in motors.

[0016] Various embodiments provide methods and systems for identifying and extracting fault-related features without involving physical models and signal processing procedures, and are achieved using only a small portion of the measured signal.

[0017] The method and system disclosed in this article can be used in at least two application scenarios for motor eccentricity fault detection: one application scenario is during the manufacturing stage, and the other application scenario is through the operation of the motor.

[0018] During the manufacturing phase, the goal is to inspect the manufactured motors and identify the eccentricity level for quality control purposes. Since many motors of the same model will be mass-produced, data covering a wide range of eccentricity levels is collected using test motors, and based on this collected data, a model is developed to make predictions for new data measured on other motors of the same type.

[0019] It is not possible to have data for all possible eccentricity levels during the operational life of the motor. However, measurement data collected during inspections when the eccentricity level is still low are available. Therefore, some embodiments are based on the recognition that a model can be built based on these earlier measurements and used to predict the eccentricity level based on later measurements, where faults are expected to become more severe over time.

[0020] Therefore, some embodiments disclose a fault detector for detecting the eccentricity of a motor, the motor comprising a stator and a rotor separated by an air gap. The fault detector comprises a processor and a memory, the memory having instructions stored thereon, the instructions when executed by the processor causing the fault detector to collect an electrical feedback signal of the motor operation through a communication channel comprising one or a combination of a wired communication link and a wireless communication link, the electrical feedback signal comprising time series data of three-phase current measured during a time period of motor operation. The processor is also configured to map the data points of the time series data into a three-dimensional space of the three-phase current to form a three-phase point cloud. The processor is also configured to extract a topological representation of the topological features of the three-phase point cloud using topological data analysis (TDA). The processor is also configured to classify the eccentricity of the motor based on the extracted topological representation. In addition, the processor is configured to send an indication of the classified eccentricity of the motor and one or a combination of control commands selected based on the classified eccentricity through a communication channel.

[0021] According to another embodiment, a method for detecting an eccentricity fault in an electric motor is disclosed, the electric motor comprising a stator and a rotor separated by an air gap. The method comprises collecting an electrical feedback signal of the operation of the electric motor, the electrical feedback signal comprising time series data of three-phase current measured during a time period of the operation of the electric motor. The method further comprises mapping the data points of the time series data into a three-dimensional space of the three-phase current to form a three-phase point cloud. The method further comprises extracting a topological representation of topological features of the three-phase point cloud using topological data analysis (TDA). The method further comprises classifying the eccentricity of the electric motor based on the extracted topological representation. In addition, the method comprises sending one or a combination of an indication of the classified eccentricity of the electric motor and a control command selected based on the classified eccentricity via a communication channel.

[0022] The presently disclosed embodiments will be further explained with reference to the accompanying drawings. The drawings shown are not necessarily drawn to scale, with emphasis instead generally being placed upon illustrating the principles of the presently disclosed embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] [ Figure 1A ]

[0024] Figure 1A A schematic diagram illustrating a fault detector system for an electric machine according to some embodiments of the present disclosure is shown.

[0025] [ Figure 1B ]

[0026] Figure 1B A schematic diagram of an electric machine according to some embodiments of the present disclosure is shown.

[0027] [ Figure 2A ]

[0028] Figure 2A A schematic diagram illustrating an electric machine according to some embodiments of the present disclosure is shown.

[0029] [ Figure 2B ]

[0030] Figure 2B A schematic diagram illustrating a static eccentricity fault according to some embodiments of the present disclosure is shown.

[0031] [ Figure 2C ]

[0032] Figure 2C A schematic diagram illustrating a dynamic eccentricity fault according to some embodiments of the present disclosure is shown.

[0033] [ Figure 2D ]

[0034] Figure 2D A schematic diagram illustrating a hybrid eccentricity fault according to some embodiments of the present disclosure is shown.

[0035] [ Figure 3 ]

[0036] Figure 3 A schematic diagram illustrating an experimental setup for an electric machine according to some embodiments of the present disclosure is shown.

[0037] [ Figure 4 ]

[0038] Figure 4 A graphical representation of a time domain current signal illustrating different eccentricity levels in an electric machine according to some embodiments of the present disclosure is shown.

[0039] [ Figure 5A ]

[0040] Figure 5A An exemplary method for determining a fault in an electric machine according to some embodiments of the present disclosure is shown.

[0041] [ Figure 5B ]

[0042] Figure 5B An exemplary method for determining a fault in an electric machine according to some embodiments of the present disclosure is shown.

[0043] [ Figure 6 ]

[0044] Figure 6 A graphical representation of a three-phase point cloud for different eccentricity levels is shown according to some embodiments of the present disclosure.

[0045] [ Fig. 7A ]

[0046] Fig. 7A An exemplary representation of data points in a finite metric space according to some embodiments of the present disclosure is shown.

[0047] [ Figure 7B ]

[0048] Figure 7B An exemplary representation of a barcode of a finite metric space is shown according to some embodiments of the present disclosure.

[0049] [ Figure 8 ]

[0050] Figure 8 An exemplary method of persistent homology computation of a three-phase point cloud in a finite metric space according to some embodiments of the present disclosure is shown.

[0051] [ Fig. 9 ]

[0052] Fig. 9 A graphical representation of a persistence graph according to some embodiments of the present disclosure is shown.

[0053] [ Fig.10 ]

[0054] Fig.10 Persistence graphs of three-phase currents for six different eccentricity levels are shown according to some embodiments of the present disclosure.

[0055] [ Fig.11 ]

[0056] Fig.11 A Betti sequence or Betti curve corresponding to a persistence graph is shown according to some embodiments of the present disclosure.

[0057] [ Fig.12 ]

[0058] Fig.12 Betti sequences or Betti curves associated with different three-phase currents are shown according to some embodiments of the present disclosure.

[0059] [ Fig.13 ]

[0060] Fig.13 A time domain graph is shown for different eccentricity levels according to some embodiments of the present disclosure.

[0061] [ Fig.14 ]

[0062] Fig.14 t-Distributed Stochastic Neighbor Embedding (t-SNE) plots of H0 and H1 Betti curves are shown according to some embodiments of the present disclosure.

[0063] [ Fig.15 ]

[0064] Fig.15 Prediction results according to some embodiments of the present disclosure are shown.

[0065] [ Fig.16 ]

[0066] Fig.16 Prediction results according to some embodiments of the present disclosure are shown.

[0067] [ Fig.17A ]

[0068] Fig.17A Prediction results according to some embodiments of the present disclosure are shown.

[0069] [ Fig. 17B ]

[0070] Fig. 17B Prediction results according to some embodiments of the present disclosure are shown.

[0071] [ Fig. 17C ]

[0072] Fig. 17C Prediction results according to some embodiments of the present disclosure are shown.

[0073] [ Fig.17D ]

[0074] Fig.17D Prediction results according to some embodiments of the present disclosure are shown. DETAILED DESCRIPTION

[0075] In the following description, for the purpose of explanation, many specific details are set forth in order to provide a thorough understanding of the present disclosure. However, it is apparent to those skilled in the art that the present disclosure can be practiced without these specific details. In other cases, only in order to avoid obscuring the present disclosure, devices and methods are shown in block diagram form.

[0076] As used in this specification and claims, the terms "for example," "for example," and "such as," and the verbs "include," "have," "comprise," and other verb forms thereof, when used in conjunction with a list of one or more components or other items, are each interpreted as open-ended, meaning that the list is not to be viewed as excluding other additional components or items. The term "based on" means based, at least in part, on. In addition, it should be understood that the wording and terminology employed herein are for descriptive purposes and should not be considered limiting. Any headings used in this specification are for convenience only and have no legal or limiting effect.

[0077] Figure 1A A schematic diagram of a fault detector system for a motor (e.g., motor 101) according to some embodiments of the present disclosure is shown. In an example, a system for detecting an operating fault may include motor 101, sensors 105A, 105B, 105C, a fault detector 100A, and a communication channel 107. Motor 101 is an AC motor in which, in a steady state, the rotation of the motor shaft is synchronized with the frequency of the supply current. Examples of synchronous motors include reluctance motors and permanent magnet motors. Sensors 105A, 105B, 105C are connected to motor 101. According to certain embodiments, sensors 105A, 105B, 105C may be current sensors and voltage sensors for obtaining the current and voltage of each winding of motor 101. Other sensors may be envisioned, including torque sensors, environmental sensors (temperature, humidity, etc.), and other types of sensors for assisting the operation, maintenance, or management of motor 101. In an example, sensors 105A, 105B, 105C are connected to motor 101 via wireless or wired connections to collect data from motor 101.

[0078] The communication channel 107 may include a medium through which data from the motor 101 may be transmitted 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 the system for detecting an operational fault in the motor 101 may be operatively connected 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 (BT) communication protocols.

[0079] The fault detector 100A can detect a fault in the 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 sensors 105A, 105B, 105C. The memory 140 stores the sensor data. In an example, the memory 140 can store the sensor data permanently. In another example, the memory 140 can temporarily store the sensor data within a predefined time period. The time period can be determined based on user / operator goals / interests. The sensor data is then processed by the processor 120 and output to the output interface 150, or can be stored in the memory 140, depending on the user / operator goals / interests. In an embodiment, the sensor data collected from the sensors 105A, 105B, 105C is provided to the fault detector 100A via a communication channel 107, which may include a wired communication link or a wireless communication link for transmitting sensor data. The sensor data collected from the sensors 105A, 105B, 105C may include an electrical feedback signal of the operation of the motor 101. The electrical feedback signal includes time series data of three-phase current measured during the operation time period of the motor 101. The fault detector 100A may map the data points of the time series data into the three-dimensional space of the three-phase current to form a three-phase point cloud. The fault detector 100A may use TDA to extract a topological representation of the topological features of the three-phase point cloud. The fault detector 100A may classify the eccentricity of the motor based on the extracted topological representation. In an example, the classified eccentricity includes an eccentricity type and an eccentricity severity level. The fault detector 100A may send one or a combination of an indication of the classified eccentricity of the motor and a control command selected based on the classified eccentricity through the communication channel 107. In an embodiment, the processor 120 of the fault detector 100A may cause the output interface 150 to send one or a combination of an indication of the classified eccentricity of the motor and a control command selected based on the classified eccentricity through the communication channel 107. The fault detector 100A may select a control command based on the type of eccentricity and the severity level of the eccentricity. In an example, the output interface 150 may send an indication of the classified eccentricity and a control command to a user or system operating the motor 101 via the communication channel 107. The indication of the classified eccentricity and the control command may enable the user or system to take corrective action to remove the eccentricity in the motor 101. Figure 5A and Figure 5B The operation performed by the fault detector 100A for detecting a fault in operation of the motor 101A is explained in detail.

[0080] Figure 1BA schematic diagram 100B of a motor 101 according to an embodiment of the present disclosure is shown. The motor 101 includes a rotor 102, a stator 104, a main shaft 106, and two bearings 108A and 108B. The eccentricity failure of the motor 101 is usually caused by manufacturing errors or operating errors, which makes the air gap between the stator 104 and the rotor 102 uneven. In an example, when the rotation axis 103 of the motor 101 does not coincide with the symmetry axis. In an example, the eccentricity in the motor 101 can be one of static eccentricity, dynamic eccentricity, or mixed eccentricity. Reference Figure 2A , Figure 2B , Figure 2C and Figure 2D Explain the description of the eccentricity type in detail.

[0081] Figure 2A , Figure 2B , Figure 2C and Figure 2D is a schematic diagram illustrating different types of eccentricity faults according to some embodiments of the present disclosure. Any AC electric motor, such as motor 101, includes a stator 104 and a rotor 102 separated by an air gap 124 therebetween. An eccentricity fault is a type of motor fault caused by the formation of unequal air gaps between the stator 104 and the rotor 102.

[0082] Figure 2A A schematic diagram illustrating an electric machine 101 according to some embodiments of the present disclosure is shown. Figure 2A The motor 101 shown in FIG. 1 is an example of a healthy motor without any type of eccentricity fault. 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 healthy, meaning there is no eccentricity fault, and the air gap 124 (A) between the stator 104 and the rotor 102 is uniform at different positions.

[0083] Figure 2B A schematic diagram illustrating a static eccentricity fault according to some embodiments of the present disclosure is shown. Points Or and Ow coincide, but are offset from the center Os of the stator inner hole. Since the rotor 102 always rotates around the center point Ow, a static eccentricity fault exists, and the air gap 124 (B) between the stator 104 and the rotor 102 is not uniform at different locations.

[0084] Figure 2C A schematic diagram illustrating a dynamic eccentricity fault according to some embodiments of the present disclosure is shown. The rotation center Ow of the rotor 102 is aligned with the stator center Os, but the rotor center Or is orbiting around the point Ow. Since the rotor does not orbit around its own center of mass, the air gap 124 (C) will vary and change dynamically depending on the rotation angle of the rotor.

[0085] Figure 2D A schematic diagram illustrating a hybrid eccentricity fault according to some embodiments of the present disclosure is shown. A mixture of static eccentricity and dynamic eccentricity is a hybrid eccentricity, where points Or, Os and Ow are not aligned with each other. In this case, both static eccentricity fault and dynamic eccentricity fault exist.

[0086] Typically, static eccentricity of a motor is created during the manufacturing process. It is important to detect static eccentricity faults at an early stage because it can evolve into a compound eccentricity on motor operation due to unbalanced magnetic pull and eventually lead to failure of the machine.

[0087] Figure 3 A schematic diagram illustrating an experimental setup for an electric machine 101 according to some embodiments of the present disclosure is shown. In an embodiment, the experimental setup is used to generate data that can be collected, analyzed, and used to identify the type and severity of faults associated with the electric machine 101. Figure 3 The experimental setup shown may include different components to interface with the motor 101. In the example, the sensor 105A may refer to, but is not limited to, a speed sensor (such as a tachometer) to measure the angular velocity or rotational speed ω of the motor 101. r . In an example, sensor 105B may refer to but is not limited to an acceleration sensor. In an example, sensor 105C may refer to but is not limited to an air gap sensor. In an embodiment, two pairs of air gap sensors are used to measure the air gap 124. The first pair of air gap sensors may be mounted at a position represented by (x1, y1). The second pair of air gap sensors may be mounted at a position represented by (x2, y2). In one embodiment, the stator 104 of the motor 101 is mounted on a linear stage so that the position of the stator 104 can be adjusted in the horizontal direction (x-axis) by a pair of micrometers. Two pairs of air gap sensors 105C are mounted on the stator 104. The first pair of displacement sensors are mounted on the side of the load side facing the air gap 124, and the second pair of displacement sensors are mounted on the side opposite to the side facing the air gap 124. When the motor 101 is at an angular velocity ω r In operation, the two pairs of displacement sensors 105C measure the size of the air gap 124 in the horizontal direction (x-axis) and the vertical direction (y-axis). A dynamic brake is connected to the motor 101 and acts as a load 125 .

[0088] In the example, the air gap 124 between the stator 104 and the rotor 102 is adjusted to produce various eccentricity levels. Phase current sensors are used to measure phase current signals corresponding to each eccentricity level. In an embodiment, a 0.75kW three-phase 2-pole pair squirrel cage induction motor with a nominal air gap size of 0.28mm is used as the motor 101. In another embodiment, a 0.75kW three-phase synchronous motor with a nominal air gap size of 0.28mm is used as the motor 101. The line voltage and frequency are 200V and 60Hz, respectively.

[0089] In one embodiment, six eccentricity levels are generated when the motor 101 is stationary. Data from the phase current sensors and the air gap sensor 105C are recorded for each eccentricity level at a sampling frequency of, for example, 10 kHz under no-load conditions. In the example, but not limited to this, the eccentricity level can be set to 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively, where the percentage is defined as the ratio of the maximum air gap deviation to the nominal air gap size. According to the data of the air gap sensor 105C, the actual static eccentricity of the air gap 124 is significantly close to the initial setting, with the difference within 3% in all cases. In addition, according to the air gap sensor readings, there is a small dynamic eccentricity level of about 6% for all cases. This mixed eccentricity effect produces a sideband signal at fc=fs±fr, where fs is the power frequency and fr is the rotation frequency.

[0090] Figure 4 A block diagram 400 including a graphical representation of time domain current signals for different eccentricity levels in an electric machine 101 according to some embodiments of the present disclosure is shown. The block diagram 400 includes measurements performed by sensors 105A, 105B, 105C on the electric machine 101 for different eccentricity levels. In an example, three-phase current signals associated with the stator 104 are measured for eccentricity levels that are respectively set to, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%.

[0091] In the example, graph 400A shows the measurement results performed by sensors 105A, 105B, 105C on motor 101 for an eccentricity level set to 1.5%. Graph 400B shows the measurement results performed by sensors 105A, 105B, 105C on motor 101 for an eccentricity level set to 17.2%. Graph 400C shows the measurement results performed by sensors 105A, 105B, 105C on motor 101 for an eccentricity level set to 24.1%. Graph 400D shows the measurement results performed by sensors 105A, 105B, 105C on motor 101 for an eccentricity level set to 40.3%. Graph 400E shows the measurement results performed by sensors 105A, 105B, 105C on motor 101 for an eccentricity level set to 47.1%. Graph 400F shows measurements performed by sensors 105A, 105B, 105C on motor 101 for an eccentricity level set to 64.6%.

[0092] The time domain current signal is sampled at a sampling frequency of, for example, 10 kHz. As an example, but not limited to, approximately 1000 data samples of the time domain current signal are plotted to represent Figure 4 The time domain signal in the graphical representation of . Figure 4 The time domain current signal shown, it is difficult to directly distinguish the eccentricity level because the fundamental component is dominant. The TDA method and the process of applying TDA to eccentricity fault feature extraction and eccentricity level prediction are introduced.

[0093] Figure 5A An exemplary method 500A for determining faults in an electric machine 101 according to some embodiments of the present disclosure is shown. According to an embodiment of the present disclosure, the method 500A is used to train a machine learning model for determining faults in the electric machine 101 using a TDA process. The method 500A applies a TDA process to a time-domain current signal associated with a stator 104 of the electric machine 101 to determine topological features that persist across different scales. The topological features associated with the point cloud representation of samples of the time-domain current signal at different eccentricity levels can be fed to the machine learning model as training data for identifying eccentricity faults and eccentricity fault levels. Figure 5A The steps identified in the description and their order are exemplary and may include various alternatives, equivalents or derivatives thereof, including but not limited to the order of execution thereof. Figure 5A The steps of method 500A and its various alternatives may be embodied in hardware or software including a computer-readable storage medium (eg, a CD, a memory card, or a hard drive) that includes instructions executable by processor 120.

[0094] At 502, the fault detector 100A may collect an electrical feedback signal of the operation of the motor 101 through a communication channel 107 including one or a combination of a wired communication link and a wireless communication link, the electrical feedback signal including time series data of a time domain current signal measured during a time period of the operation of the motor 101. In an embodiment, the time series data of the time domain current signal includes a three-phase current signal associated with the stator 104, such that the three-phase current signal is measured for eccentricity levels respectively set to, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%. Reference Figure 3 and Figure 4 The description of the time domain current signal is explained in detail. The time domain current signal is measured during a predefined time period according to the sampling rate used to segment the time domain current signal. In an example, for a sampling rate of 10 kHz, the time domain current signal is measured during a time period of, but not limited to, 0.01 seconds.

[0095] At 504, the fault detector 100A may split each of the time-domain current signals of the three phases into data points of length L. Figure 4 As shown, the length L of the data sample can be set to, but not limited to, 1000. The length L defines the accuracy of the segmented time-domain current signal.

[0096] At 506, the fault detector 100A may map the data points of the time series data into the three-dimensional space of the three-phase current signal to form a three-phase point cloud corresponding to each eccentricity level. In the example, the eccentricity level may be set to, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively. A collection of data points with a distance definition is referred to as a point cloud. Reference Figure 6 Explain the description of the three-phase point cloud corresponding to each eccentricity level.

[0097] At 508, the fault detector 100A may perform a persistent coherence calculation on the three-phase point cloud to extract a topological representation of the topological features of the three-phase point cloud using TDA. The persistent coherence calculation examines the three-phase point cloud at different scales. The fault detector 100A may determine the topological representation as a persistent coherent representation. The persistent coherent representation may include one or a combination of a persistent barcode and a persistent map. Fig. 7A and Figure 7B Explains the description of the persistent barcode. Fig. 9 Explanation of the description of the persistence diagram. In an example, the fault detector 100A can calculate the persistence homology of the three-phase point cloud corresponding to each eccentricity level for the 0-dimensional hole H0 and the 1-dimensional hole H1. 0 Also known as H 0Features, which correspond to multiple clusters formed by connected components in the three-phase point cloud. The 1-dimensional hole H1 can also be called H 1 Features, which correspond to holes formed by the space surrounded by connected components in the three-phase point cloud. In an example, the topological features tracked by persistent homology may include H 0 Features and H 1 Features. Persistent homology is a tool in TDA for investigating the structure of data (e.g., a three-phase point cloud of time series data). Persistent homology is robust to perturbations of time series data, independent of dimension and coordinates, and provides a compact representation of qualitative features of time series data.

[0098] The three-phase point cloud is represented as a finite metric space. From a topological point of view, a finite metric space does not contain any information of interest. Therefore, a thickening of the point cloud at different resolution scales is required, followed by an analysis of the evolution of the resulting shape across different resolution scales. Qualitative features are given by topological invariants. The variation of such topological invariants across different resolution scales is represented in a compact way to summarize the "shape" of the time series data.

[0099] refer to Figure 8 The description of the method for the persistent homology computation of three-phase point clouds in a finite metric space is explained in detail.

[0100] At 510, the fault detector 100A can convert the H0 coherence and H1 coherence of the three-phase point cloud into Betti sequences of fixed lengths L1 and L2, respectively. The topological features extracted at 508 are used as input or training data for a regression model or a machine learning model. However, it is more convenient to represent the topological features with vectors of the same length. To this end, the fault detector 100A derives a Betti sequence or a Betti curve from a persistence diagram of the time series data of the three-phase currents at different eccentricity levels. Reference Fig. 9 and Fig.10 Explain the description of the Betty sequence in detail.

[0101] At 512, the fault detector 100A can feed the training data to the machine learning model. The machine learning model can include a regression model or a neural network. During the training phase of the machine learning model, the mean square 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 the example, the eccentricity level data 514 is a label of the segmented time domain current signal and 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 was collected.

[0102] The machine learning model can be trained to predict the eccentricity level of the motor 101. In an example, the machine learning model can be trained in a supervised manner to classify different topological representations labeled with eccentricity type, eccentricity severity level, or both. The prediction of eccentricity includes the eccentricity type and the eccentricity severity level. As an example, but not limited to this, the eccentricity type may include static eccentricity, dynamic eccentricity, or mixed eccentricity. The eccentricity level can indicate the degree of the air gap 124 between the stator 104 and the rotor 102 of the motor 101. The training data fed to the machine learning model is labeled data, which includes one or a combination of the Betty sequence derived at 510, the eccentricity level data 514, or data points corresponding to the time domain current signals of the three phases.

[0103] Figure 5B An exemplary method 500B for determining faults in an electric machine 101 according to an embodiment of the present disclosure is shown. The method 500B applies TDA to a time-domain current signal associated with a stator 104 of the electric machine 101 to determine topological features that persist across different scales. The topological features associated with a point cloud representation of samples of the time-domain current signal at different eccentricity levels can be fed to a trained machine learning model for predicting and identifying eccentricity faults and levels of eccentricity faults. Figure 5B The steps identified in the description and their order are exemplary and may include various alternatives, equivalents or derivatives thereof, including but not limited to the order of execution thereof. Figure 5B The steps of the process and its various alternatives may be embodied in hardware or software including a computer-readable storage medium (eg, a CD, a memory card, or a hard drive) that includes instructions executable by the processor 120.

[0104] At 516, the fault detector 100A may collect an electrical feedback signal of the operation of the motor 101 via a communication channel 107 including one or a combination of a wired communication link and a wireless communication link, the electrical feedback signal including time series data of a time-domain current signal measured during an operation time period of the motor 101, the time series data being the same as the time series data used at 502 during the training of the machine learning model. In another embodiment, the cycle of operation may vary according to the sampling rate of the data points. In an embodiment, the time series data of the time-domain current signal includes a three-phase current signal associated with the stator 104, such that the three-phase current signal is measured for eccentricity levels set to, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively. Reference Figure 3 and Figure 4 Explain the description of the time domain current signal in detail.

[0105] At 518, the fault detector 100A may split each of the time-domain current signals of the three phases into data points of length L. Figure 4 As shown, the length L of the data sample can be set to, but not limited to, 1000. The length L defines the accuracy of the segmented time-domain current signal.

[0106] At 520, the fault detector 100A may map the data points of the time series data into the three-dimensional space of the three-phase current signal to form a three-phase point cloud corresponding to each eccentricity level. In the example, the eccentricity level may be set to, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively. A collection of data points with distance definitions is referred to as a point cloud. For example, Figure 6 A graphical representation of a three-phase point cloud for different eccentricity levels according to another embodiment of the present disclosure is shown. Each three-phase point cloud is formed for a three-phase current signal measured for a specific eccentricity level. The distance between data points can be, for example, Euclidean distance or Minkowski distance. Both Euclidean distance and Minkowski distance are defined on digital data. However, the present embodiment is not limited to completely digital data to define the distance between data points. In another example, the distance can also be defined when the data is categorical rather than digital.

[0107] At 522, the fault detector 100A may perform persistent coherence calculation on the three-phase point cloud to extract a topological representation of topological features of the three-phase point cloud using TDA. In an example, the fault detector 100A may calculate persistent coherence of the three-phase point cloud corresponding to each eccentricity level for the 0-dimensional hole H0 and the 1-dimensional hole H1.

[0108] At 524, the fault detector 100A may convert the H0 coherence and H1 coherence of the three-phase point cloud into Betti sequences of fixed lengths L1 and L2, respectively. The fault detector 100A derives the Betti sequence or Betti curve from the persistence diagram of the time series data of the three-phase current for different eccentricity levels. Fig. 9 and Fig.10 Explain the description of the Betty sequence in detail.

[0109] At 526, the fault detector 100A may feed one or a combination of the Betty sequence or data points corresponding to the time-domain current signal derived at 524 to the machine learning model trained at 512. In an embodiment, the fault detector 100A may execute the machine learning model trained at 512 in a supervised manner to classify different topological representations labeled with eccentricity types, eccentricity severity levels, or both. The trained machine learning model may classify the eccentricity of the motor 101 based on the extracted topological representation. In an embodiment, the trained machine learning model may classify the eccentricity of the motor 101 based on one or a combination of the Betty sequence or data points derived at 524. The eccentricity level prediction 528 includes the eccentricity type and the eccentricity severity level. In an example, the machine learning model may be a regression model that is trained at 512 to infer the labeled eccentricity severity level used to train the regression model at 512.

[0110] Figure 6 A block diagram 600 including a graphical representation of a three-phase point cloud for different eccentricity levels according to an embodiment of the present disclosure is shown. The block diagram 600 may include three-phase point clouds at different eccentricity levels set to, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively.

[0111] In the example, the graph 600A shows a three-phase point cloud of a three-phase current signal measured for an eccentricity level set to 1.5%. The graph 600B shows a three-phase point cloud of a three-phase current signal measured for an eccentricity level set to 17.2%. The graph 600C shows a three-phase point cloud of a three-phase current signal measured for an eccentricity level set to 24.1%. The graph 600D shows a three-phase point cloud of a three-phase current signal measured for an eccentricity level set to 40.3%. The graph 600E shows a three-phase point cloud of a three-phase current signal measured for an eccentricity level set to 47.1%. The graph 600F shows a three-phase point cloud of a three-phase current signal measured for an eccentricity level set to 64.6%.

[0112] Each three-phase point cloud is formed for the three-phase current signal measured for a specific eccentricity level. The distance between the data points in a specific point cloud can be, for example, the Euclidean distance or the Minkowski distance. Both the Euclidean distance and the Minkowski distance are defined on digital data. However, the present embodiment is not limited to completely digital data to define the distance between data points. In another example, when the data is categorical rather than digital, the distance can also be defined.

[0113] Since the dominant component of the three-phase current signal is a periodic wave of the fundamental frequency, the most important shape is a large circle in 3D space. The most important shape is the dominant shape in the three-phase point cloud. For an ideal sinusoidal signal, the shape of the three-phase point cloud will be a perfect circle. However, when there are components other than the fundamental frequency, the points on the three-dimensional point cloud will deviate from the perfect circle. Components other than the fundamental frequency are generated by faults (such as eccentricity faults) and are called fault components. Since the amplitude of the fault component is much smaller, it is difficult to distinguish different eccentricity levels from the shape of the three-phase point cloud alone. Components other than the fundamental frequency can cause topological features other than the dominant shape in the three-phase point cloud. Therefore, when the operation of the motor 101 suffers from any eccentricity fault, the topological features in 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.

[0114] After the TDA process, topological features can be extracted from the three-phase point cloud, and the extracted topological features can be fed into a machine learning model for training and eccentricity level prediction of the motor 101.

[0115] Fig. 7A FIG. 7 shows an exemplary representation 700A of data points in a finite metric space according to an embodiment of the present disclosure. The data points are represented in region R 2 The distance between two data points is called the filter radius r. For different values ​​of r, a space S consisting of vertices, edges, triangles, or higher-dimensional polyhedra is constructed based on certain rules. r In the example, an edge between two points i and j is included if and only if the Euclidean distance between them is no greater than the filter radius r, and an edge between two points i and j is included if and only if all its edges are in S r In the case of S, a triangle is included if and only if all its face triangles are in S r By using homology, the space S can be measured r Some characteristics of space S r Features or topological features may include components, holes and / or voids.

[0116] 700A-1 shows an exemplary point cloud when the filter radius r approaches zero (r=0). In the case of r=0, no topological features, for example, edges or vertices can be formed, and all data points in the point cloud can be represented as individual data points with no connecting features between them. As the filter radius r increases, topological features begin to appear in the point cloud. 700A-2 shows an exemplary point cloud when the filter radius r is set to 0.6. 700A-3 shows an exemplary point cloud in which holes appear when the filter radius r is set to 1.1. In one example, at the filter radius r=1.1, holes begin to appear. 700A-4 shows an exemplary point cloud when the filter radius r is set to 1.6. In one example, at the filter radius r=1.6, there are still holes in the point cloud that appear for smaller values ​​of the filter radius, but the radius of the holes is reduced compared to the holes at 700A-3. 700A-5 shows an exemplary point cloud when the filter radius r is set to 2.1. In one example, at a filter radius r = 2.1, the holes disappear in the point cloud.

[0117] The lifetime of a feature such as a hole can be represented using a finite set of intervals called persistence barcodes. The left endpoint of an interval represents the birth of a feature, while the right endpoint of the interval represents the death of the same feature. For example, Figure 7B An exemplary representation 700B of a barcode of a finite metric space according to an embodiment of the present invention is shown. As the filter radius increases, at a first value r of the filter radius r 1 As the filter radius r increases further, the size of the pores appears to decrease, and at a second value of the filter radius r r 2 (For example, r = 2.1) gradually disappears. The first value r of the filtering radius r 1 Mark the birth of the hole, filter the second value of radius r 2 Mark the extinction of a hole. The persistence of a hole can be represented as a pair (r1,r2). Persistence can be visualized as the transition from r 1 to r 2 The intervals or bars are called persistence bars. The persistence bars are a visual representation of the persistence of the holes. The set of persistence bars for each topological feature in the three-phase point cloud is called the persistence barcode.

[0118] Figure 8 An exemplary method 800 for persistent homology computation of a three-phase point cloud in a finite metric space is shown according to some embodiments of the present disclosure. Figure 8 The steps identified in method 800 and their order are exemplary and may include various alternatives, equivalents, or derivations thereof, including but not limited to the order of execution thereof. Figure 8The steps of method 800 and its various alternatives may be embodied in hardware or software including a computer-readable storage medium (eg, a CD, a memory card, or a hard drive) that includes instructions executable by processor 120.

[0119] First, time series data represented by a three-phase point cloud formed by data points sampled from the time series data is fed to the processor 120 for persistent coherence calculation 508 .

[0120] At 508-1, a simplex complex of the three-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 three-phase point cloud. The simplex 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. Tetrahedrons or other higher-dimensional polyhedrons 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 three-phase point cloud. However, other algorithms may also be used to construct the simplex complex. It is defined using a threshold r (called a filter radius) and includes pairwise Euclidean distances between points that only meet no greater than the filter radius r.

[0121] At 508-2, 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.

[0122] At 508-3, through the filtering process, by calculating the coherence using different filter radii r, tracking the birth and death of the topological feature at the corresponding value of the filter radius r, a persistent coherence is obtained. The birth and death of the topological feature defines the life of the topological feature for different filter radii r.

[0123] There are different ways to represent persistent homology, and persistence graphs are one of the most popular choices. A persistence graph is a set of points (b,d)|b,d∈R2 with d>b, where each point corresponds to the birth and death of a topological feature in the corresponding family of simplicial complexes. In particular, each point (b,d) represents a topological feature that is "born" at radius b and "dies" at radius d. There are different algorithms for filtering Lipps complexes and for computing persistence graphs, implementations of which are available in several software packages. Reference Fig. 9 Explains the description of the persistence graph. Fig.10 Description of the H0 persistence diagram and H1 persistence diagram explaining the three-phase current data for six different eccentricity levels.

[0124] Assume that D is a persistence graph with a finite number of off-diagonal points, where a = (b α ,dα ), and the maximum filter radius r max >0, set is [0,r max ], the Betti sequence of D is defined as is a vector of length M, the term β i The filter radius r around the point cloud in the data space in the persistence graph i The function is defined as:

[0125]

[0126] Then, the points on the Betti sequence are obtained from the following summation:

[0127] β i =∑ α∈D f α (r i ) (2)

[0128] The topological features in the persistent coherence are a function of the filter radius r. By computing the persistent coherence with different filter radii r as thresholds and tracking the lifetime of different topological features at the corresponding thresholds, a representation of the persistent coherence is obtained by filtering. By limiting the maximum filtering range, the "larger" features of the data can be excluded and only the "smaller" features of the data can be retained. In an example, TDA can filter out the "larger" features or dominant shapes from the topological features. In the case of motor fault detection, the amplitude of the fault-related features is much smaller compared to the dominant fundamental signal corresponding to the power supply frequency. By choosing the filter radius r max For smaller values ​​of , the dominant fundamental signal can be excluded and the fault-related features can be revealed from topological calculations in the persistence coherence represented as persistence diagrams and / or Betti sequences. Furthermore, excluding the fundamental signal using TDA is less complex and does not require knowing the exact power frequency. On the other hand, in conventional signal processing methods, the exact fundamental frequency needs to be known in order to filter it out. In contrast to conventional model-based MCSA methods, the exact frequency components associated with the eccentricity fault also do not need to be explicitly identified by the physical model.

[0129] Fig. 9 A graphical representation 900 of a persistence graph according to some embodiments of the present disclosure is shown. The graphical representation 900 includes a persistence graph 900A and a persistence graph 900B. A persistence graph is a multiset of R 2 The union of the finite point multiset in and the point multiset on the diagonal Δ={(x,y)∈R 2|x=y}, where each point on the diagonal has infinite multiplicity. Persistence graph 900A is an H1 persistence graph for an eccentricity level set to 1.5%. The horizontal axis of persistence graph 900A represents the birth of a topological feature (e.g., a hole). The vertical axis of persistence graph 900A represents the extinction of the same topological feature. Persistence graph 900A is a collection of persistence barcodes for all H1 features in a three-phase point cloud for an eccentricity level set to 1.5%. Each persistence barcode in persistence graph 900A indicates the birth and extinction of the corresponding H1 feature. The persistence barcode starts at the birth of the corresponding H1 feature and ends at the extinction of the corresponding H1 feature. The birth of an H1 feature indicates the filter radius r at which the H1 feature begins to appear. The extinction of an H1 feature indicates the filter radius r at which the H1 feature begins to disappear. In one manner, persistence graph 900A indicates the lifetime of each H1 feature in a three-phase point cloud for an eccentricity level set to 1.5%. As shown in persistence graph 900A, there are fewer features or only one feature that are born and die at large values ​​of the filter radius. As an example, when a feature has a larger filter radius value for extinction and birth compared to other topological features in the three-phase point cloud, the feature is called a primary feature. As shown in persistence graph 900A, the persistence barcode of the primary feature is represented by the barcode on the upper left side of persistence graph 900A. In addition, smaller features are those topological features that have smaller extinction and birth filter radius values ​​compared to the primary feature in the three-phase point cloud. As shown in persistence graph 900A, the persistence barcode of the smaller feature is represented by the barcode on the lower left side of persistence graph 900A. As shown in persistence graph 900A, most of the smaller features have a smaller range of filter radius for birth and extinction. Persistence graph 900B shows a clearer visualization of the smaller features shown in persistence graph 900A. In persistence graph 900B, the range of the horizontal and vertical axes is reduced, for example, r = 0.06 for birth and r = 0.065 for death.

[0130] Fig.10A graphical representation 1000 of a persistence diagram of a three-phase current at six different eccentricity levels according to some embodiments of the present disclosure is shown. The graphical representation 1000 includes H0 persistence diagrams and H1 persistence diagrams at different eccentricity levels set to, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%, respectively. In an embodiment, H0 persistence diagrams and H1 persistence diagrams of three-phase current data at six different eccentricity levels can be calculated using three-phase point clouds at six different eccentricity levels. The most obvious difference between these diagrams is the H1 feature, which corresponds to a small hole formed by adjacent points. For an ideal sine wave, its point cloud can only form a large hole. When the eccentricity level is small, the deviation from the ideal circle is small, and only a small number of small features are formed in the H1 diagram. When the eccentricity level increases, the deviation of the points from the ideal circle is larger, and these points are more likely to form small circles during the filtering process 508-2 of obtaining the persistence diagram. Therefore, as the eccentricity level increases, more features are displayed in the H1 persistence diagram.

[0131] In the example, 1000A shows the H0 persistence diagram and the H1 persistence diagram for the three-phase current data set to an eccentricity level of 1.5%. 1000B shows the H0 persistence diagram and the H1 persistence diagram for the three-phase current data set to an eccentricity level of 17.2%. 1000C shows the H0 persistence diagram and the H1 persistence diagram for the three-phase current data set to an eccentricity level of 24.1%. 1000D shows the H0 persistence diagram and the H1 persistence diagram for the three-phase current data set to an eccentricity level of 40.3%. 1000E shows the H0 persistence diagram and the H1 persistence diagram for the three-phase current data set to an eccentricity level of 47.1%. 1000F shows the H0 persistence diagram and the H1 persistence diagram for the three-phase current data set to an eccentricity level of 64.6%.

[0132] Fig.11 Betti sequences or Betti curves corresponding to persistence graphs according to some embodiments of the present disclosure are shown. Block diagram 1100 includes a Betti curve 1100A corresponding to an H0 persistence graph and a Betti curve 1100B corresponding to an H1 persistence graph. The H0 persistence graph and the H1 persistence graph are different from each other. The number of points in the H0 persistence graph and the H1 persistence graph is not fixed for different input data corresponding to three-phase currents. In order to feed these topological features to the machine learning model, the H0 coherence and the H1 coherence are converted into H0 Betti sequences and H1 Betti sequences of lengths L1 and L2, respectively. In the example, for both H0 coherence and H1 coherence, the lengths L1 and L2 are fixed at 1024, and the filtering ranges are [0, 0.07] and [0, 0.14], respectively.

[0133] From the H1 Betti sequence, it is observed that the number of features as a function of filter distance varies with the eccentricity level. In addition, although the difference in H0 features cannot be inferred from the persistence plot, the trend in the H0 Betti sequence is observable. When the filter radius r is 0, all 1024 data points are not connected. Therefore, all Betti sequences start at 1024. When increasing the filter radius r, more adjacent points are 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. With higher eccentricity levels, the amplitude of the fault component increases, and the data points are further separated from each other due to their deviation from the great circle. Therefore, the points are connected in subsequent stages, and these H0 features survive longer, and the area under the H0 Betti curve increases monotonically with the eccentricity level. The change in the Betti curve is due to eccentricity.

[0134] Fig.12 A graphical representation 1200 of Betti sequences or Betti curves associated with different three-phase currents according to some embodiments of the present disclosure is shown. The graphical representation 1200 includes a Betti curve 1200A corresponding to a H0 persistence graph from five different data segments set to the same eccentricity level of 17.2%, a Betti curve 1200B corresponding to a H1 persistence graph from five different data segments set to the same eccentricity level of 17.2%, a Betti curve 1200C corresponding to a H0 persistence graph from five different data segments set to the same eccentricity level of 64.6%, and a Betti curve 1200D corresponding to a H1 persistence graph from five different data segments set to the same eccentricity level of 64.6%. An important feature of persistent coherence is its robustness. Alternatively, the robustness of persistent coherence means that similar data structures produce similar persistent coherence. The Betti curves show good consistency. Fig.12 The similarity of the shown Betti curves means that the time fluctuations between different samples of the time series data can be filtered out by the TDA process, and the fault features can be extracted with relatively short data segments.

[0135] According to the above analysis, the proposed TDA process is effective in revealing small fault features embedded in large background signals and separating signals from different fault levels.

[0136] The calculated Betti curves are used in a data-driven approach for eccentricity fault detection, quantification, and prediction.

[0137] Fig.13A time domain graph 1300 of different eccentricity levels according to some embodiments of the present disclosure is shown. In one embodiment, eccentricity level data is measured for the motor 101 and is segmented into a total of 1170 samples, each sample being 1024 data points long. As an example, eccentricity level data is measured for six different eccentricity levels, which are respectively set to, but not limited to, 1.5%, 17.2%, 24.1%, 40.5%, 47.1%, or 64.6%. As shown in reference Figure 5A and Figure 5B As explained, the Betti curves are calculated for the measured eccentricity level data. In an embodiment, a t-distributed random neighbor embedding (t-SNE) plot is used to visualize the differences in signals of different eccentricity levels. The t-SNE plot is a commonly used tool to represent the similarity in low dimensions of high-dimensional data for both the time series data of the three-phase current and the calculated Betti curves.

[0138] Fig.14 1400 of the H0 Betti curve and the H1 Betti curve according to an embodiment of the present disclosure is shown. The t-SNE graph 1400 includes a t-SNE graph 1400A of the H0 Betti curve and a t-SNE graph 1400B of the H1 Betti curve. Fig.14 As shown, data from all eccentricity levels are mixed with the time series data of the three-phase currents. Fig.14 The data segments shown are similar in that they are dominated by, for example, a dominant 60 Hz signal. However, for both the H0 and H1 Betty sequences, the data samples do cluster according to their respective eccentricity levels, indicating similarities between data samples obtained from the same eccentricity levels.

[0139] Because Figure 6 The large hole in the point cloud shown, the dominant 60Hz signal corresponds only to the eigenvalues ​​at the large filter radius in the H1 Betti sequence, and has little effect on the profile of the Betti curve. In this sense, the Betti curve with the threshold applied acts as a "fine-tuning filter" that effectively removes the dominant time domain signal, and by doing so, it amplifies the behavior of the small signal where the fault signature resides. The threshold can be applied without knowing the exact frequency of the dominant signal.

[0140] Fig.15 The prediction result 1500 according to some embodiments of the present disclosure is shown. In an embodiment, the prediction result 1500 includes a root mean square evaluation in a time domain representation of the phase current data. In an embodiment, there may be two application scenarios for motor eccentricity fault detection: one scenario is at the manufacturing stage, and the other scenario is through the operation of the motor (such as motor 101).

[0141] During the manufacturing phase, the goal is to inspect the manufactured motors and identify the eccentricity level for quality control purposes. Since many motors of the same model will be produced in large quantities, it makes sense to collect data covering a wide range of eccentricity levels with test motors and develop models to make predictions on new data measured on other motors of the same type. To simulate this scenario, the data for all eccentricity levels were mixed and divided into training and test sets with a split ratio of 0.8 / 0.2. The machine learning model was trained on the training dataset and then applied to the test dataset. 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. For given new data, the k-NN regression model searches for the nearest neighbors from the training dataset and predicts the eccentricity level as the average level of these neighbors. From Fig.15 It is evident from the results shown that, using the 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%.

[0142] Fig.16 The prediction results 1600 according to some embodiments of the present disclosure are shown. In an embodiment, the prediction results 1600 may include a root mean square evaluation using a Betty sequence. As an example, an H0 Betty sequence may be given as a training data set for a k-NN regression model. For a given new data converted to an H0 Betty sequence, the k-NN regression model searches for the nearest neighbors from the training data set and predicts the eccentricity level as the average level of these neighbors. Fig.16 The results shown clearly show that, using the H0 Betti sequence, the RMSE is reduced to 1.6% and the MAE is reduced to 0.7%. This result shows the effectiveness of using the Betti sequence on the time domain phase current data for interpolation purposes.

[0143] During the working life of the motor, 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 earlier measurements and used to predict the eccentricity level from subsequent measurements, where faults are expected to become more severe over time. For this task, experimental data from four smaller eccentricity levels can be assigned as a training set, and the last two levels as a test data set to check the predictive ability of the trained model.

[0144] Fig.17APrediction results 1700A according to some embodiments of the present disclosure are shown. In an embodiment, the prediction results 1700A are based on a quadratic regression model trained on time series data of three-phase current. As an example, the time series data of the three-phase current can be given as a training data set for the quadratic regression model, which is then used for prediction of new data. For given new data of the three-phase current in the time domain, the quadratic regression model searches for the nearest neighbors from the training data set and predicts the eccentricity level as the average level of these neighbors. Fig.17A The best prediction results using a quadratic regression model trained on the time series data of three-phase current are shown.

[0145] Fig. 17B The prediction result 1700B according to an embodiment of the present disclosure is shown. In an embodiment, the prediction result 1700B is based on a regression model trained on the H0 Betti sequence. As an example, the H0 Betti sequence of the time series data of the three-phase current can be given as a training data set for the quadratic regression model. For a given new data of the H0 Betti sequence, the quadratic regression model searches for the nearest neighbors from the training data set and predicts the eccentricity level as the average level of these neighbors. Fig. 17B The best prediction results using a quadratic regression model trained on the H0 Betty sequence are shown.

[0146] Fig. 17C Prediction results 1700C according to some embodiments of the present disclosure are shown. In one embodiment, the prediction results are based on a regression model trained on an H1 Betty sequence. As an example, an H1 Betty sequence of time series data of three-phase current can be given as a training data set for a quadratic regression model. For a given new data of the H1 Betty sequence, the quadratic regression model searches for the nearest neighbors from the training data set and predicts the eccentricity level as the average level of these neighbors. Fig. 17C The best prediction results using a quadratic regression model trained on the H1 Betty sequence are shown.

[0147] Fig.17D The prediction results according to some embodiments of the present disclosure are shown. In an embodiment, the prediction results are based on a regression model trained on the H0 Betty sequence and the H1 Betty sequence. As an example, both the H0 Betty sequence and the H1 Betty sequence of the time series data of the three-phase current can be given as training data sets for the quadratic regression model. For given new data of the H0 Betty sequence and the H1 Betty sequence, the quadratic regression model searches for the nearest neighbors from the training data set and predicts the eccentricity level as the average level of these neighbors. Fig.17D The best prediction results using a quadratic regression model trained on the H0 Betty sequence and the H1 sequence are shown.

[0148] High RMSE and MAE (both close to 30%) indicate effective prediction failure. For the Betty sequence, we extract the average of both the H0 sequence and the H1 sequence and use them to fit a quadratic regression model that shows greatly improved prediction accuracy, where the RMSE and MAE are reduced to 8.6% and 7.1% respectively when both the H0 and H1 Betty sequences are used.

[0149] 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 instead of quadratic regression models. However, these models tend to overfit the training data set and perform worse extrapolation on new data.

[0150] Compared to MCSA, which requires domain knowledge and physical models to identify fault signatures, in TDA processes or for example, reference Figure 5A and Figure 5B The described process does not require a physical model for the fault. With the input processed by TDA, data clustering is appropriately performed according to the fault level. Therefore, the possibility of unsupervised learning for fault classification is suggested. Moreover, improved prediction results can be achieved by utilizing only short time domain data segments. In all tests, the length of the time series data is 1024 points or about 0.1 seconds. In contrast, traditional spectrum analysis methods with MCSA usually require several seconds or more of data in order to stably identify the fault component in addition to the domain knowledge required to identify the fault characteristics. These advantages make the proposed TDA method promising for application in a wide range of fault detection tasks.

[0151] The following description provides only exemplary embodiments and is not intended to limit the scope, applicability or configuration of the present disclosure. Instead, the following description of the exemplary embodiments will provide a description of implementations for implementing one or more exemplary embodiments to those skilled in the art. Various changes may be made to the functions and arrangements of the elements without departing from the spirit and scope of the disclosed subject matter set forth in the appended claims.

[0152] Specific details are given in the following description to provide a thorough understanding of the embodiments. However, it will be appreciated by those skilled in the art that the embodiments may be practiced without these specific details. For example, the systems, processes, and other elements in the disclosed subject matter may be shown as components in block diagram form so as not to obscure the embodiments with unnecessary details. In other cases, well-known processes, structures, and techniques may be shown without unnecessary details to avoid obscuring the embodiments. In addition, the same reference numerals and names in the various drawings indicate the same elements.

[0153] In addition, each embodiment can be described as a process depicted as a flow chart, a flow diagram, a data flow diagram, a structure diagram or a block diagram. Although a flow chart can describe an operation as a sequential process, many operations can be performed in parallel or concurrently. In addition, the order of the operations can be rearranged. The process can terminate when its operation is completed, but can have additional steps not discussed or included in the figure. In addition, not all operations in any particularly described process can occur in all embodiments. A process can correspond to a method, a function, a process, a subroutine, a subprogram, etc. When a process corresponds to a function, the termination of the function can correspond to the return of the function to the calling function or the main function.

[0154] In addition, embodiments of the disclosed subject matter may be implemented at least in part manually or automatically. Manual or automatic implementation may be performed or at least assisted by the use of a machine, hardware, software, firmware, middleware, microcode, hardware description language, or any combination thereof. When implemented in software, firmware, middleware, or microcode, program code or code segments that perform the necessary tasks may be stored in a machine-readable medium. A processor may perform the necessary tasks.

[0155] The various methods or processes outlined herein may be encoded as software that can be executed on one or more processors using any of a variety of operating systems or platforms. In addition, such software may be written using any of a variety of suitable programming languages ​​and / or programming or scripting tools, and may also be compiled into executable machine language code or intermediate code that is executed on a framework or virtual machine. Typically, the functions of program modules may be combined or distributed in various implementations as desired.

[0156] Embodiments of the present disclosure may be embodied as methods for which examples have been provided. The actions performed as part of the method may be ordered in any suitable manner. Thus, embodiments may be constructed in which the actions are performed in a different order than shown, which may include performing some actions simultaneously, even though shown as sequential actions in illustrative embodiments.

[0157] Although the present disclosure has been described with reference to certain preferred embodiments, it should be understood that various other adaptations and modifications may be made within the spirit and scope of the present disclosure. Therefore, the aspects of the appended claims cover all such changes and modifications that fall within the true spirit and scope of the present disclosure.

Claims

1. A fault detector for detecting eccentricity of an electric motor, the electric motor including a stator and a rotor separated by an air gap, the fault detector comprising: a processor; and a memory storing instructions which, when executed by the processor, cause the fault detector to: collect an electrical feedback signal of the operation of the electric motor through a communication channel including one or a combination of a wired communication link and a wireless communication link, the electrical feedback signal including time series data of three-phase currents measured during a period of operation of the electric motor; map data points of the time series data into a three-dimensional space of the three-phase currents to form a three-phase point cloud; use topological data analysis (TDA) to extract a topological representation of topological features of the three-phase point cloud; classify the eccentricity of the electric motor based on the extracted topological representation; and send, through the communication channel, one or a combination of an indication of the classified eccentricity of the electric motor and a control command selected based on the classified eccentricity.

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

3. The fault detector according to claim 1, wherein in order to classify the eccentricity, the processor executes a model previously trained in a supervised manner to classify different topological representations labeled with an eccentricity type, an eccentricity severity level, 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 an extrapolation of the labeled eccentricity severity level for the 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 topological features using the TDA, the processor is configured to: perform persistent homology, which 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 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 filtering by calculating the persistent homology using different thresholds and tracking the lifetimes of different topological features at the corresponding thresholds.

10. The fault detector according to claim 9, wherein The topological features tracked by the persistent coherence include H corresponding to the number of clusters formed by connected components in the three-phase point cloud. 0 The features and H corresponding to the holes formed by the space surrounded by the connected components in the three-phase point cloud 1 feature.

11. The fault detector according to 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 features into a Betti sequence or a Betti curve.

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

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

14. A method for detecting an eccentricity fault in an electric machine, the electric machine including a stator and a rotor separated by an air gap, the method comprises: collecting an electrical feedback signal of the operation of the electric machine through a communication channel including one or a combination of a wired communication link and a wireless communication link, the electrical feedback signal including time series data of three-phase currents measured during a time period of the operation of the electric machine; mapping data points of the time series data into a three-dimensional space of the three-phase currents to form a three-phase point cloud; using topological data analysis (TDA) to extract a topological representation of topological features of the three-phase point cloud; classifying the eccentricity of the electric machine based on the extracted topological representation; and sending, through the communication channel, one or a combination of an indication of the classified eccentricity of the electric machine and a control command selected based on the classified eccentricity.

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

16. The method according to claim 14, the method further comprises: executing a model previously trained in a supervised manner to classify different topological representations labeled with an eccentricity type, an eccentricity severity level, 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 an extrapolation of the labeled eccentricity severity level for the training.

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

20. The method according to claim 14, wherein using the TDA to extract the topological features further includes: performing persistent homology, the persistent homology including examining the three-phase point cloud at different scales; and determining the topological representation as a representation of the persistent homology.

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