System and method for detecting faults in the operation of a synchronous motor - Patents.com

The system uses static magnetic field analysis to determine the mutual position of stator and rotor in synchronous motors, effectively detecting bearing and eccentricity faults, enhancing fault detection accuracy and reducing maintenance costs.

JP2025502555AActive Publication Date: 2025-01-24MITSUBISHI ELECTRIC CORP
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Patent Information

Application Number
JP2024562559
Authority / Receiving Office
JP · JP
Patent Type
Applications
Current Assignee / Owner
Priority Date
2022-02-16
Filing Date
2022-12-14
Publication Date
2025-01-24
Estimated Expiration
2042-12-14

AI Technical Summary

Technical Problem

Existing methods for detecting failures in synchronous motors, such as reluctance and permanent magnet motors, face challenges in accurately identifying bearing and eccentricity faults due to variations in stator current magnitude with load, speed, and power ratings, and are hindered by background noise and sensor installation issues.

Method used

A system and method utilizing static magnetic field principles to determine the mutual position of the stator and rotor through a weighted sum over actual space basis functions, enabling efficient and compact representation of magnetic fields for online failure detection.

Benefits of technology

Enables accurate and efficient detection of various types of faults in synchronous motors, including bearing and eccentricity failures, by analyzing the interaction between the stator and rotor using static magnetic fields, reducing downtime and maintenance costs.

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Abstract

The present disclosure provides a system and method for detecting faults in the operation of a synchronous motor. The method includes collecting an electrical input and a measurement associated with the operation of the synchronous motor caused by the electrical input. The method further includes determining a series of points defining a mutual position of a stator and a rotor of the synchronous motor that results in a static magnetic field determined as a weighted sum over a real space basis function, the real space basis function being parameterized with pairs of adjacent points in the determined series of points and weighted with a surface charge density between corresponding adjacent points, the static magnetic field describing the measurement of the operation of the synchronous motor taking into account the electrical input. Furthermore, the method includes determining a fault in the operation of the synchronous motor based on the mutual position of the stator and the rotor of the synchronous motor.
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Description

[Technical field]

[0001] FIELD OF THE DISCLOSURE This disclosure relates generally to synchronous motors, such as reluctance motors and permanent magnet motors, and more particularly to systems and methods for detecting faults in the operation of synchronous motors. [Background technology]

[0002] Synchronous motors are widely used in various industrial applications including pumps, chemical, petrochemical, electrified transportation systems, etc. In many applications, synchronous motors operate under several unfavorable conditions such as high ambient temperature, high humidity, and overloading, which may result in malfunctions that result in serious economic losses due to high maintenance costs and unexpected downtime.

[0003] The causes of synchronous motor malfunctions are generally various categories of failures including drive inverter failure, stator winding insulation breakdown, broken rotor bar failure, and other mechanical failures. Several surveys of synchronous machine failures conducted by the IEEE Industry Application Society (IEEE-IAS) and the Japan Electrical Manufacturers' Association (JEMA) reveal that mechanical failures are the most common type of failure. Examples of mechanical failures include bearing failures and / or eccentricity failures of synchronous motors. Summary of the Invention [Problem to be solved by the invention]

[0004] Bearing faults can be detected by vibration and acoustic analysis. However, the accuracy of bearing fault diagnosis based on vibration or acoustic signals can be affected by background noise due to external mechanical excitation movements, while its sensitivity also varies based on the installation location of the sensor. An alternative approach for bearing fault detection is realized by analyzing the stator current of a synchronous motor. However, the magnitude of the stator current at the bearing fault signature frequency can vary with different loads, different speeds, and different power ratings of the synchronous motor itself, thus creating a challenge to identify the threshold stator current value for triggering a fault alarm at any operating condition.

[0005] Similarly, eccentricity faults in synchronous motors have been thoroughly studied over the past decades. Eccentricity faults can exist in the form of both static and dynamic eccentricity, called static eccentricity, or dynamic eccentricity, or mixed eccentricity faults. Eccentricity faults cause bearing damage, excessive vibration and noise, unbalanced synchronous pull, and stator-rotor friction that can cause synchronous motor damage under extreme conditions. Eccentricity faults can cause bearing failure or be caused by bearing failure. Therefore, in theory, similar fault detection methods can be applied to detect eccentricity faults in synchronous motors. However, in practice, it is difficult to detect different types of faults in synchronous motors, so different techniques are tailored to detect different types of faults.

[0006] Therefore, there is a need to provide a method for detecting different types of faults in synchronous motors.

[0007] It is an object of some embodiments to provide a system and method for determining different types of faults in the operation of a synchronous motor. Examples of synchronous motors include reluctance motors and permanent magnet motors. Examples of faults include mechanical faults, including different types of bearing faults and different types of eccentricity faults. Additionally or alternatively, it is an object of some embodiments to provide a method that can determine different types of faults from the same input. Additionally or alternatively, it is an object of some embodiments to provide a method that can determine different types of eccentricity faults in a synchronous motor, such as static eccentricity, dynamic eccentricity, or both. [Means for solving the problem]

[0008] The synchronous motor includes a stator and a rotor separated by an air gap. Some embodiments are based on the recognition that the synchronous motor includes an interface between different materials of the synchronous motor. For example, the synchronous motor includes two interfaces. A first interface is between the stator of the synchronous motor and the air in the air gap, and a second interface is between the air in the air gap and the rotor of the synchronous motor. The first interface between the stator and the air in the air gap is a single series of points, e.g., z 0 ,z 1 ,z 2 ,z 3 ,……,z N and the second interface between the air in the air gap and the rotor is represented by another series of points, e.g., y 0 ,y 1 ,y 2 ,y 3 ,……,y N The series of points thus forms the interfaces between the different materials of the synchronous motor. Furthermore, the series of points defines the relative positions of the stator and rotor.

[0009] Some embodiments are based on the realization that defects in the structure of a synchronous motor that result in misalignment of the rotor position with the stator position cause faults. In other words, the defects result in a change in the relative position of the stator and the rotor. Different types of defects result in different relative positions of the stator and the rotor. Therefore, if the relative position of the stator and the rotor can be determined online from measurements of the operation of the synchronous motor, the relative position of the stator and the rotor can be used to detect different types of faults. However, determining the relative position of the stator and the rotor is memory and computationally expensive. Therefore, it is an object of some embodiments to provide a practical approach suitable for online estimation of the structure of a synchronous motor for determining the relative position of the stator and the rotor.

[0010] Some embodiments are based on the realization that the structure of a synchronous motor can be represented by the material distribution of its components during the operation of the synchronous motor. For example, the distribution of a magnetic field can be determined using magnetostatic principles, which can be used to explain the operation of a synchronous motor. As a result, magnetostatic principles can be linked to the structure of a synchronous motor to its operation and can therefore be used to analyze the structure of a synchronous motor during its operation.

[0011] Magnetostatics is the study of magnetic fields in systems in which the current is steady state (does not change with time). Magnetostatics is the magnetic equivalent of electrostatics in which the charge is stationary. However, in many cases the magnetization does not need to be static, and the equations of the static field can be used to predict fast synchronous switching events that occur on sub-nanosecond time scales. The static field is even a good approximation when the current is not static, as long as it does not alternate rapidly. Static fields are typically used in micromagnetics applications such as modeling magnetic storage devices, such as in computer memories, but static field focusing can be achieved by permanent magnets or by passing a current through a coil of wire whose axis is coincident with the beam axis. Hence, static fields can be used to analyze the construction of synchronous motors.

[0012] Some embodiments are based on the realization that the electrical output corresponding to an electrical input can be explained by learning the mutual position of the stator and rotor online based on the principle of static magnetic field. In particular, some embodiments are based on the realization that there is a relationship between the mutual position of the stator and rotor of a synchronous motor and the static magnetic field. In addition, some embodiments are based on the realization that there is a relationship between the electrical input, the static magnetic field that the synchronous motor generates in response to the electrical input, and the electrical output or measurement of the operation of the synchronous motor. Hence, different static magnetic fields are determined for different mutual positions of the stator and rotor. Furthermore, a static magnetic field is selected that explains the electrical output taking into account the electrical input. The mutual position corresponding to the selected static magnetic field is the current / actual mutual position.

[0013] In this manner, by evaluating different relative positions of the stator and rotor, the relative position of the stator and rotor that best matches the electrical output given the electrical input can be determined using the static magnetic field.Faults can then be determined based on the determined relative positions of the stator and rotor.However, to do so, an efficient and compact representation of the static magnetic field is required.

[0014] For example, the static magnetic field can be estimated using finite element analysis (FEA) and / or finite difference analysis, which can be considered a variant of FEA. However, FEA typically solves potentials that require boundary values ​​at locations larger than the region of interest. As a result, the static magnetic field determined using FEA is represented as a set of points in space surrounding and including the synchronous motor. Such a representation is inconvenient and memory consuming. For example, the FEA method requires at least 5000 points to represent a simple motor with a cylindrical shape.

[0015] Another approach to solving the static magnetic field is to use the eigenfunction expansion (EE) method. The EE method expresses the solution in terms of eigenfunctions and automatically satisfies the partial differential equations. However, the EE method only works for motors whose component geometry matches the polar coordinates. Therefore, to use the EE method, the geometry of any component of the motor must be approximated as a sector and / or a combination of sectors, which is not always practical.

[0016] Therefore, there is a need for an alternative 2-D magnetic field solver and an efficient and compact representation of the static magnetic field discovered using this solver that is suitable for online fault detection during operation of synchronous motors.

[0017] Some embodiments are based on the realization that the static magnetic field can be represented as a weighted sum over real-space basis functions. Each real-space basis function is analytical and parameterized by a series of points forming the interfaces of different materials inside the synchronous motor, and weighted by the surface charge density. In particular, a real-space basis function is a function that represents a pair of adjacent points, e.g., point z 1 and z 2 and the surface charge density between corresponding adjacent points, e.g., point z 1 and z 2 and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density between the motor and the surface charge density

[0018] Therefore, different static magnetic fields for different mutual positions at different times are found by calculating a weighted sum over real space basis functions, parameterized with a series of points representing interfaces between different materials and weighted by surface charge density, for each mutual position. Further, a static magnetic field is selected that describes the electrical output given the electrical input. Further, a series of points defining the mutual positions of the stator and rotor is determined from the selected static magnetic field. Additionally, a fault in the operation of the synchronous motor is determined based on the mutual positions of the stator and rotor.

[0019] In this way, some embodiments use a new representation of the static magnetic field of a synchronous motor as a weighted sum over real space basis functions. Moreover, such a representation of the static magnetic field is a compact and memory-efficient representation of the static magnetic field, which is suitable for online control or monitoring of the synchronous motor. With this improvement, some embodiments design a fault detector suitable for online estimation of different types of faults in the synchronous motor.

[0020] Accordingly, one embodiment discloses a fault detection apparatus for detecting faults in the operation of a synchronous motor including a stator and a rotor separated by an air gap. The fault detector comprises a processor and a memory having instructions stored thereon, which, when executed by the processor, causes the fault detector to collect, via a communication channel including one or a combination of a wired communication link and a wireless communication link, an electrical input for controlling operation of the synchronous motor and a measurement of the operation of the synchronous motor caused by the electrical input, and to determine a series of points defining a mutual position of a stator and a rotor of the synchronous motor and forming interfaces of different materials inside the synchronous motor that result in a static magnetic field determined as a weighted sum over real space basis functions, the real space basis functions being parameterized with pairs of adjacent points in the determined series of points and weighted with a surface charge density between corresponding adjacent points, the static magnetic field describing the measurement of the operation of the synchronous motor taking into account the electrical input, and further to determine a fault in the operation of the synchronous motor based on the mutual position of the stator and rotor of the synchronous motor, and to transmit, via the communication channel, one or a combination of an indication of the fault in the operation of the synchronous motor and a control command selected based on the fault.

[0021] Accordingly, another embodiment discloses a method for detecting a fault in operation of a synchronous motor including a stator and a rotor separated by an air gap, the method including: collecting, via a communication channel including one or a combination of a wired communication link and a wireless communication link, an electrical input for controlling the operation of the synchronous motor and a measurement of the operation of the synchronous motor caused by the electrical input; determining a series of points defining a mutual position of the stator and rotor of the synchronous motor and forming an interface of different materials inside the synchronous motor resulting in a static magnetic field determined as a weighted sum over a real space basis function, the real space basis function being parameterized with pairs of adjacent points of the determined series of points and weighted with a surface charge density between corresponding adjacent points, the static magnetic field describing the measurement of the operation of the synchronous motor taking into account the electrical input; and determining a fault in operation of the synchronous motor based on the mutual position of the stator and rotor of the synchronous motor; and transmitting, via the communication channel, one or a combination of an indication of the fault in operation of the synchronous motor and a control command selected based on the fault.

[0022] Accordingly, another embodiment discloses a non-transitory computer-readable storage medium including a program executable by a processor to execute a method for detecting a fault in operation of a synchronous motor including a stator and a rotor separated by an air gap, the method including: collecting, via a communication channel including one or a combination of a wired communication link and a wireless communication link, an electrical input for controlling the operation of the synchronous motor and a measurement of the operation of the synchronous motor caused by the electrical input; determining a series of points, the series of points defining a mutual position of the stator and rotor of the synchronous motor and forming an interface of different materials inside the synchronous motor resulting in a static magnetic field determined as a weighted sum over a real space basis function, the real space basis function being parameterized with pairs of adjacent points of the determined series of points and weighted with a surface charge density between corresponding adjacent points, the static magnetic field describing the measurement of the operation of the synchronous motor taking into account the electrical input; and determining a fault in operation of the synchronous motor based on the mutual position of the stator and rotor of the synchronous motor; and transmitting, via the communication channel, one or a combination of an indication of the fault in operation of the synchronous motor and a control command selected based on the fault.

[0023] The presently disclosed embodiments will be further described with reference to the accompanying drawings, in which: The drawings are not necessarily to scale, and instead, emphasis is generally placed upon illustrating the principles of the presently disclosed embodiments. [Brief description of the drawings]

[0024] [Figure 1A] FIG. 1 illustrates a schematic diagram of a synchronous motor according to an embodiment of the present disclosure. [Figure 1B] FIG. 2 illustrates a detailed block diagram of a fault detector for detecting faults in the operation of a synchronous motor according to an embodiment of the present disclosure. [Figure 2A] FIG. 1 shows a schematic diagram illustrating a healthy synchronous motor, according to some embodiments of the present disclosure. [Figure 2B] FIG. 1 shows a schematic diagram illustrating a static eccentricity fault, according to some embodiments of the present disclosure. [Figure 2C] FIG. 1 shows a schematic diagram illustrating a dynamic eccentricity fault, according to some embodiments of the present disclosure. [Figure 2D] FIG. 1 shows a schematic diagram illustrating a mix of both static and dynamic eccentricity faults, according to some embodiments of the present disclosure. [Diagram 3] FIG. 2 shows a schematic diagram illustrating the interface of different materials within a synchronous motor according to some embodiments of the present disclosure. [Figure 4] FIG. 1 illustrates a schematic diagram of the use of a static magnetic field to analyze the structure of a synchronous motor, according to some embodiments of the present disclosure. [Diagram 5] 1 illustrates a block diagram of a method for determining a sequence of points defining the relative positions of a stator and a rotor of a synchronous motor according to an embodiment of the present disclosure. [Figure 6] 4 shows a block diagram of a method for determining a sequence of points defining the mutual position of a stator and a rotor of a synchronous motor according to another embodiment of the present disclosure; [Figure 7] FIG. 2 illustrates a table of columns of example data stored in a memory of a fault detector according to an embodiment of the present disclosure. [Figure 8] FIG. 2 illustrates a schematic diagram of a classifier for classifying fault type and severity according to an embodiment of the present disclosure. [Figure 9] FIG. 1 shows a block diagram illustrating an H-solver according to an embodiment of the present disclosure. [Figure 10] FIG. 2 shows a block diagram illustrating a B-solver according to an embodiment of the present disclosure. [Figure 11] FIG. 1 shows a block diagram illustrating a BH solver according to an embodiment of the present disclosure. [Figure 12A] FIG. 1 illustrates a diagram showing a cylinder geometry of finite thickness according to an embodiment of the present disclosure. [Figure 12B] FIG. 13 illustrates a table column showing a comparison of results from different solvers according to an embodiment of the present disclosure. [Figure 13A] FIG. 2 shows a schematic diagram illustrating rotor geometry according to an embodiment of the present disclosure. [Figure 13B]FIG. 1 illustrates a graph of torque as a function of electrical angle according to an embodiment of the present disclosure. [Figure 14] FIG. 2 illustrates a block diagram of a method for detecting faults in the operation of a synchronous motor according to an embodiment of the present disclosure. [Figure 15] FIG. 1 is a schematic diagram illustrating a computing device that can be used to implement the systems and methods of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0025] For purposes of explanation, numerous specific details are set forth in the following to provide a thorough understanding of the present disclosure. However, it will be apparent to those skilled in the art that the present disclosure may be practiced without these specific details. In other instances, the apparatus and methods are shown in block diagram form solely to avoid obscuring the present disclosure.

[0026] As used in the specification and claims, the terms "for example," "for instance," and "such as," as well as the verbs "comprising," "having," "including," and other forms of these verbs, when used in conjunction with a list of one or more components or other items, should each be construed as open-ended, meaning that the list should not be considered to exclude further components or items. The term "based on" means based at least in part on. Furthermore, it should be understood that the style and terminology used herein are for purposes of illustration and should not be considered limiting. Any headings used herein are for convenience only and should not be considered to have any legal or limiting effect.

[0027] FIG. 1A illustrates a schematic diagram of a synchronous motor 101 according to an embodiment of the present disclosure. The synchronous motor 101 is an AC motor whose shaft rotation is synchronous with the frequency of the supply current in a steady state. Examples of synchronous motors include reluctance motors and permanent magnet motors. The synchronous motor 101 includes a stator 103, a rotor 105, a main shaft 107, and two bearings 109A and 109B. Sensors 111A, 111B, and 111C are connected to the synchronous motor 101. According to a particular embodiment, the sensors 111A, 111B, and 111C may be current and voltage sensors for obtaining the current and voltage of each winding of the synchronous motor 101. Other sensors are contemplated, including torque sensors, environmental sensors (temperature, humidity, etc.), and other types of sensors used to assist in the operation, maintenance, or management of the synchronous motor 101.

[0028] A fault detector 113 is connected to the synchronous motor 101. The fault detector 113 is configured to detect faults in the operation of the synchronous motor 101. Sensor data collected from the sensors 111A, 111B, 111C are input to an input interface 115 of the fault detector 113. The sensor data may also be stored in a memory 117. The sensor data is then processed by a processor 119 and, depending on the purpose / interest of a user, may be output to an output interface 121 or stored in the memory 117 of the fault detector 113. Details of the fault detector 113 are described below with reference to FIG. 1B.

[0029] 1B illustrates a detailed block diagram of the fault detector 113 according to an embodiment of the present disclosure. The fault detector 113 includes a network interface controller (NIC) 123 adapted to connect the fault detector 113 to a network 127 (also referred to as a communication channel) via a bus 125. Through the network 127, wirelessly or through a wired link, the fault detector 113 collects electrical inputs 129 for controlling the operation of the synchronous motor 101 and measurements of the operation of the synchronous motor 101 caused by the electrical inputs. The electrical inputs include one or a combination of current or voltage of each winding, and the measurements include one or a combination of output torque and mutual inductance between different windings.

[0030] Further, in some implementations, a human machine interface (HMI) 131 in the fault detector 113 connects the fault detector 113 to a keyboard 133 and a pointing device 135. The pointing device 135 may include a mouse, a trackball, a touchpad, a joystick, a pointing stick, a stylus, or a touch screen, among others. Furthermore, the fault detector 113 includes an application interface 137 for connecting the fault detector 113 to an application device 139 for performing various operations. The fault detector 113 may also include a control interface 141 for connecting the fault detector 113 to the synchronous motor 101. For example, the fault detector 113 may control the synchronous motor 101 via the control interface 141. Additionally, the fault detector 113 may be connected via the bus 125 to a display interface 143 adapted to connect the fault detector 113 to a display device 145, such as a computer monitor, a television, a projector, or a mobile device, among others.

[0031] The fault detector 113 further includes a processor 119 and a memory 117 that stores instructions executable by the processor 119. The processor 119 may be a single-core processor, a multi-core processor, a computing cluster, or any number of other configurations. The memory 117 may include a random access memory (RAM), a read-only memory (ROM), a flash memory, or any other suitable memory system. The processor 119 is connected to one or more input and output devices via a bus 125. The stored instructions implement a method for detecting faults in the operation of the synchronous motor 101.

[0032] The processor 119 is configured to detect faults in the operation of the synchronous motor 101. The faults include mechanical faults, including, for example, different types of bearing faults and different types of eccentricity faults of the synchronous motor 101. The different types of bearing faults include cage defects, outer ring defects, inner ring defects, and ball defects. The different types of eccentricity faults include, for example, static eccentricity faults, dynamic eccentricity faults, or both.

[0033] 2A-2D are schematic diagrams illustrating different types of eccentricity faults according to some embodiments of the present disclosure. Any synchronous motor, such as the synchronous motor 101, includes a stator 103 and a rotor 105 separated by an air gap 201 therebetween. An eccentricity fault is a type of motor fault resulting from the formation of an uneven air gap between the stator 103 and the rotor 105. FIG. 2A shows a normal synchronous motor 101. Point Ow is the center of rotation, point Os is the center of the stator 103, and point Or is the center of the rotor 105. If the three points Ow, Os, and Or are coincident, the synchronous motor 101 is normal and there is no eccentricity fault.

[0034] 2B is a schematic diagram illustrating a static eccentricity fault according to some embodiments of the present disclosure. Points Or and Ow are coincident but offset from the center Os of the stator. Since the rotor 105 always rotates around the center point Ow, a static eccentricity fault exists, and the air gap 201 between the stator 103 and the rotor 105 is not uniform at different locations.

[0035] 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 105 is aligned with the stator center Os, but the rotor center Or orbits around the point Ow. Since the rotor 105 does not rotate around its own center of mass, the air gap length 201 varies and changes dynamically with the rotation angle of the rotor 105.

[0036] FIG. 2D is a schematic diagram illustrating a mixture of both static and dynamic eccentricity faults, called mixed eccentricity, according to some embodiments of the present disclosure. Points Or, Os, and Ow are not aligned with each other. In this case, both static and dynamic eccentricity faults are present. From the faults shown in FIGS. 2B-2D, it can be seen that the air gap 201 is not uniform, i.e., there is a bias in the air gap.

[0037] According to an embodiment, the synchronous motor 101 includes an interface between different materials of the synchronous motor 101. FIG. 3 shows a schematic diagram illustrating an interface between different materials inside the synchronous motor 101 according to some embodiments of the present disclosure. Here, there are two interfaces between different materials of the synchronous motor 101. A first interface 301 is between the stator 103 and the air in the air gap 201, and a second interface 303 is between the air in the air gap 201 and the rotor 105. The first interface 301 between the stator 103 and the air in the air gap 201 is a single series of points, e.g., z 0 ,z 1 ,z 2 ,z 3 ,……,z N and a second interface 303 between the air in the air gap 201 and the rotor 105 is represented by another series of points, e.g., y 0 ,y 1 ,y 2 ,y 3 ,……,y N The series of points thus forms the interfaces between the different materials of the synchronous motor 101. Furthermore, the series of points defines the mutual position of the stator 103 and the rotor 105.

[0038] Some embodiments are based on the realization that defects in the structure of the synchronous motor 101 that result in misalignment of the rotor position with the stator position cause the fault. In other words, the defects result in a change in the mutual position of the stator 103 and the rotor 105. Different types of defects result in different mutual positions of the stator 103 and the rotor 105. Therefore, if the mutual position of the stator 103 and the rotor 105 can be determined online from collected measurements, the mutual position of the stator 103 and the rotor 105 can be used to detect different types of faults. However, determining the mutual position of the stator 103 and the rotor 105 has a high memory and computational cost. Therefore, it is an objective of some embodiments to provide a practical approach suitable for online estimation of the structure of the synchronous motor 101 for determining the mutual position of the stator 103 and the rotor 105.

[0039] Some embodiments are based on the realization that the structure of the synchronous motor 101 can be represented by the material distribution of its components during the operation of the synchronous motor 101. For example, the distribution of the magnetic field can be defined using magnetostatic principles, which can be used to explain the operation of the synchronous motor 101. As a result, magnetostatic principles can link the structure of the synchronous motor 101 to its operation and can therefore be used to analyze the structure of the synchronous motor 101 during its operation.

[0040] Magnetostatics is the study of magnetic fields in systems where the current is steady state (does not change with time). Magnetostatics is the magnetic equivalent of electrostatics where the charge is stationary. The magnetization does not have to be static, and the equations for the static field can be used to predict fast synchronous switching events that occur on sub-nanosecond time scales. The static field is even a good approximation when the current is not static, as long as it does not alternate rapidly. Static fields are typically used in micromagnetics applications such as modeling magnetic storage devices such as in computer memories, but static field focusing can be achieved by permanent magnets or by passing a current through a coil of wire whose axis coincides with the beam axis. Hence, static fields can be used to analyze the structure of the synchronous motor 101.

[0041] FIG. 4 illustrates a schematic diagram of the use of a static magnetic field to analyze the structure of a synchronous motor 101, according to some embodiments of the present disclosure. Some embodiments are based on the realization that, based on the principles of static magnetic fields, the mutual position of the stator 103 and the rotor 105 can be learned online to explain the electrical output corresponding to the electrical input. In particular, some embodiments are based on the realization that there is a relationship between the mutual position 407 of the stator 103 and the rotor 105 of the synchronous motor 101 and the static magnetic field 403. In addition, some embodiments are based on the realization that there is a relationship between the electrical input 401, the static magnetic field 403 generated by the synchronous motor 101 in response to the electrical input, and the electrical output or measurement 405 of the operation of the synchronous motor 101. Thus, different static magnetic fields are determined for different mutual positions of the stator 103 and the rotor 105. Furthermore, a static magnetic field is selected that explains the electrical output 405 taking into account the electrical input 401. The mutual position corresponding to the selected static magnetic field is the current / actual mutual position.

[0042] In this manner, by evaluating different mutual positions 407 of the Stator 103 and the Rotor 105, the mutual position of the Stator 103 and the Rotor 105 can be determined using the static magnetic field 403, which describes the electrical output 405 given the electrical input 401. Furthermore, faults can be determined based on the determined mutual positions of the Stator 103 and the Rotor 105. However, to do so an efficient and compact representation of the static magnetic field is required.

[0043]

number

[0044] Here, each real space basis function [B r (Z|{z i},{λ i})] is analytical and is a series of points [{z i Specifically, each real space basis function is parameterized by a pair of adjacent points, e.g., a point z 1 and z 2 and the surface charge density between corresponding adjacent points, e.g., point z 1 and z 2 The surface charge density is found by iteratively matching the boundary conditions on the interface imposed by Maxwell's equations. The determination of the surface charge density is illustrated in Figure 9. From (1) it can be seen that the magnetic field at any point on the two-dimensional plane can be found by a weighted sum over real-space basis functions using the succession of points and the corresponding surface charge density as input parameters for the real-space basis functions. The expression of the static magnetic field as a weighted sum over real-space basis functions provides a compact representation of the static magnetic field. In addition, such an expression is independent of the load on the motor.

[0045] Therefore, the processor 119 determines different static magnetic fields for different mutual positions at different times by calculating, for each mutual position, a weighted sum over real space basis functions parameterized with a series of points representing interfaces between different materials and weighted by surface charge densities corresponding to different pairs of adjacent points in the series of points. The processor 119 further selects a static magnetic field that describes the electric output 405 given the electric input 401. The processor 119 further determines, from the selected static magnetic field, a series of points that define the mutual positions of the stator 103 and the rotor 105. The processor 119 further determines a fault in the operation of the synchronous motor 101 based on the mutual positions of the stator 103 and the rotor 105.

[0046] The overall method for determining the succession of points defining the relative positions of the stator 103 and rotor 105 is described below with reference to FIG.

[0047] 5 illustrates a block diagram of a method 500 for determining a series of points defining the mutual positions of the stator 103 and rotor 105 of the synchronous motor 101, according to an embodiment of the present disclosure. In block 501, the method 500 includes determining different static magnetic fields based on different mutual positions of the stator 103 and rotor 105. According to an embodiment, the processor 119 calculates the different static magnetic fields by calculating a weighted sum over real space basis functions for each mutual position, the real space basis functions being parameterized with a series of points representing interfaces between different materials inside the synchronous motor 101 and weighted by surface charge densities corresponding to various pairs of adjacent points in the series of points.

[0048] At block 503, the method 500 includes the processor 119 calculating, for each of the different static magnetic fields, an electrical output of the synchronous motor operation given the electrical input.

[0049] At block 505, the method 500 includes the processor 119 selecting a static magnetic field that results in an electrical output of the synchronous motor 101 operation that is closest to the measured value of the synchronous motor 101 operation.

[0050] At block 507, the method 500 includes the processor 119 selecting a sequence of points that define the relative positions of the stator 103 and rotor 105 of the synchronous motor 101 based on the selected static magnetic field.

[0051] Additionally or alternatively, in some embodiments, different parameters of the real space basis functions, i.e., the succession of points and the corresponding surface charge densities, can be pre-determined offline and stored in memory 117. During online operation, processor 119 retrieves the different parameters of the real space basis functions from memory 117 and determines different static magnetic fields based on the retrieved parameters.

[0052] FIG. 6 illustrates a block diagram of a method 600 for determining a series of points, where different parameters of the real space basis functions are pre-determined offline, according to an embodiment of the present disclosure.

[0053] At block 601, the method 600 includes determining offline different parameters of the real space basis functions, i.e., the succession of points and the corresponding surface charge densities. At block 603, the method 600 includes storing the determined different parameters of the real space basis functions in memory 117.

[0054] At block 605, the method 600 includes the processor 119 retrieving, during online operation, different parameters of the real space basis functions from the memory 117. Further, at block 607, the method 600 includes the processor 119 determining different static magnetic fields based on the retrieved parameters.

[0055] At block 609, the method 600 includes the processor 119 calculating, for each of the different static magnetic fields, an electrical output of the operation of the synchronous motor 101 given the electrical input. At block 611, the method 600 includes the processor 119 selecting the static magnetic field that results in an electrical output of the operation of the synchronous motor 101 that is closest to the measured value of the operation of the synchronous motor 101. At block 613, the method 600 includes the processor 119 selecting a series of points from the selected static magnetic fields that define the mutual position of the stator 103 and the rotor 105.

[0056] Further, in some embodiments, the processor 119 determines the fault based on the sequence of the selected points. Specifically, the processor 119 determines the type and severity of the fault based on the parameters of the selected static magnetic field real space basis function. For example, different types and severity of the fault associated with different parameters of the real space basis function are stored in the memory 117. In addition, in some embodiments, the memory 117 stores control commands corresponding to each type and severity of the fault.

[0057] FIG. 7 illustrates a tabular column 700 of example data stored in memory 117 according to an embodiment of the present disclosure. Different parameters 701, such as parameter 1 through parameter N, and corresponding fault types 703, fault severity 705, and control commands 707 are stored in memory 117. If the parameter of the selected static magnetic field real space basis function corresponds to parameter 1 709, the processor 119 selects bearing fault 711 as the fault type and high fault severity 713 from memory 117. Further, the processor 119 selects a "Stop" 715 control command. The processor executes the "Stop" 715 control command to stop the synchronous motor 101 to protect the synchronous motor 101 from a fault. In another example, if the parameter of the selected static magnetic field real basis function corresponds to parameter 2 717, the processor 119 selects static eccentric fault 719 as the fault type and medium fault severity 721 from memory 117. Further, the processor 119 selects the control command, decelerate 723 the synchronous motor 101. The processor executes the control command, decelerate 723 the synchronous motor 101 to decelerate the synchronous motor 101. Further, in some implementations, the control command also includes a change in the load and / or input power of the synchronous motor 101.

[0058] In some embodiments, the fault type and severity may also be referred to as a fault indication. The processor 119 transmits one or a combination of the fault indication and the selected control command. Additionally or alternatively, in some embodiments, a classifier may be used to classify the fault type and severity based on the relative positions of the stator 103 and the rotor 105.

[0059] 8 illustrates a schematic diagram of a classifier 801 for classifying fault types and severity, according to an embodiment of the present disclosure. In an embodiment, the classifier 801 may be a neural network-based classifier. For example, the classifier 801 corresponds to an artificial neural network, such as a convolutional neural network, a recurrent neural network, a forward propagation neural network, etc., trained to classify fault types and severity based on the relative positions of the stator 103 and the rotor 105. The classifier 801 is used by the processor 119 to classify fault types and severity based on the relative positions of the stator 103 and the rotor 105.

[0060] Some embodiments are based on the realization that the surface charge density λ is required to solve the static magnetic field. According to an embodiment, the H-solver can be formulated to solve the static magnetic field for the surface charge density λ. The H-solver formulation is mathematically described below.

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[0065] The H-solver is introduced based on the relationship between the surface charge density λ(s) and H given by (6).

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[0070] A B solver is introduced based on the relationship between the surface current density K(s) and B given by (9).

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[0082] 13A shows a schematic diagram illustrating the geometry of a rotor according to an embodiment of the present disclosure. rotor =0.6cm outer circle 1301 and major axis 0.7r rotor and minor axis 0.3r rotor and the inner ellipse 1303 of θ = 0. These values ​​are chosen randomly. The dashed circle 1305 is the surface for torque calculations using equation (16).

[0083] FIG. 13B illustrates a control circuit for controlling the electrical angle θ according to an embodiment of the present disclosure. ele 13 shows a graph 1307 of torque as a function of . The results using the direct Lorentz force law (Eq. (14)) and the stress tensor (Eq. (16)) are in good agreement. Eq. (16) requires the B field at the dashed circle 1305 to be substantially equal to the B field resulting from the surface current density and the surface charge density.

[0084] 14 illustrates a block diagram of a method 1400 for detecting a fault in the operation of a synchronous motor according to an embodiment of the present disclosure. At block 1401, the method 1400 includes collecting an electrical input for controlling the operation of the synchronous motor and a measurement of the operation of the synchronous motor caused by the electrical input.

[0085] In block 1403, the method 1400 includes determining a series of points defining the relative positions of the stator and rotor of the synchronous motor that results in a static magnetic field determined as a weighted sum over real space basis functions, the real space basis functions being parameterized by pairs of adjacent points in the determined series of points and weighted by the surface charge density between corresponding adjacent points, the generated static magnetic field describing a measurement of the operation of the synchronous motor given the electrical input.

[0086] At block 1405, the method 1400 includes determining a fault in operation of the synchronous motor based on a relative position of a stator and a rotor of the synchronous motor. Further, at block 1407, the method 1400 includes transmitting an indication of the fault in operation of the synchronous motor.

[0087] 15 is a schematic diagram illustrating a computing device 1500 for implementing the method and system of the present disclosure. The computing device 1500 includes a power supply 1501, a processor 1503, a memory 1505, and a storage device 1507, all of which are connected to a bus 1509. Furthermore, a high-speed interface 1511, a low-speed interface 1513, a high-speed expansion port 1515, and a low-speed expansion port 1517 can be connected to the bus 1509. In addition, a low-speed connection port 1519 is connected to the bus 1509. Furthermore, an input interface 1521 can be connected to an external receiver 1523 and an output interface 1525 via the bus 1509. The receiver 1527 can be connected to an external transmitter 1529 and a transmitter 1531 via the bus 1509. Also, an external memory 1533, an external sensor 1535, a machine 1537, and an environment 1539 can be connected to the bus 1509. Additionally, one or more external input / output devices 1541 can be connected to the bus 1509. A network interface controller (NIC) 1543 can be adapted to connect to a network 1545 through the bus 1509 to, among other things, render data or other data on a third party display device, a third party imaging device, and / or a third party printing device external to the computing device 1500.

[0088] The memory 1505 can store instructions executable by the computer device 1500, as well as any data that can be utilized by the methods and systems of the present disclosure. The memory 1505 can include random access memory (RAM), read only memory (ROM), flash memory, or any other suitable memory system. The memory 1505 can be one or more volatile memory units and / or one or more non-volatile memory units. The memory 1505 can also be another form of computer-readable medium, such as a magnetic disk or an optical disk.

[0089] The storage device 1507 may be adapted to store supplemental data and / or software modules used by the computer device 1500. The storage device 1507 may include a hard drive, an optical drive, a thumb drive, an array of drives, or any combination thereof. Additionally, the storage device 1507 may include computer readable media such as a floppy disk device, a hard disk device, an optical disk device, or an array of devices including a tape device, a flash memory or other similar solid state memory device, or a storage area network or other configuration of devices. The instructions may be stored on an information carrier. The instructions, when executed by one or more processing devices (e.g., the processor 1503), perform one or more methods as described above.

[0090] The computing device 1500 can optionally be linked through a bus 1509 to a display or user interface (HMI) 1547 adapted to connect the computing device 1500 to a display device 1549 and a keyboard 1551, which may include, among others, a computer monitor, a camera, a television, a projector, or a mobile device. In some implementations, the computing device 1500 may include a printer interface for connecting to a printing device, which may include, among others, a liquid inkjet printer, a solid ink printer, a large scale commercial printer, a thermal printer, a UV printer, or a dye-sublimation printer.

[0091] The high-speed interface 1511 manages bandwidth-intensive operations of the computing device 1500, and the low-speed interface 1513 manages low-bandwidth-intensive operations. Such an allocation of functions is merely an example. In some implementations, the high-speed interface 1511 can be coupled to the memory 1505, the user interface (HMI) 1547, the keyboard 1551, and the display 1549 (e.g., through a graphics processor or accelerator), and can be coupled to a high-speed expansion port 1515 that can accept various expansion cards via a bus 1509. In some implementations, the low-speed interface 1513 is coupled to a storage device 1507 and a low-speed expansion port 1517 via a bus 1509. The low-speed expansion port 1517, which can include various communication ports (e.g., USB, Bluetooth, Ethernet, wireless Ethernet), can be coupled to one or more input / output devices 1541. The computing device 1500 can be connected to a server 1553 and a rack server 1555. The computing device 1500 may be implemented in a number of different forms. For example, the computing device 1500 may be implemented as part of a rack server 1555.

[0092] The following description provides exemplary embodiments only and is not intended to limit the scope, applicability, 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. It is contemplated that various changes may be made to the function and arrangement of elements without departing from the spirit and scope of the disclosed subject matter as set forth in the appended claims.

[0093] Specific details are given in the above description to provide a thorough understanding of the embodiments. However, those skilled in the art will appreciate 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 diagram form in order to avoid obscuring the embodiments in unnecessary detail. In other instances, well-known processes, structures, and techniques may be shown without unnecessary detail in order to avoid obscuring the embodiments. Additionally, like reference numbers and names in the various drawings refer to like elements.

[0094] Also, the individual embodiments may be described as a process that is depicted as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a block diagram. Although a flowchart may describe operations as a sequential process, many of the operations may be performed in parallel or simultaneously. In addition, the order of operations may be rearranged. A process may be terminated when its operations are completed, but may have additional steps not discussed or included in the diagram. Moreover, not all operations in any process specifically described may occur in all embodiments. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, or the like. When a process corresponds to a function, the end of the function may correspond to a return of the function to the calling function or to the main function.

[0095] Additionally, embodiments of the disclosed subject matter may be implemented, at least in part, either manually or automatically. The manual or automated implementation may be performed or at least assisted through machine, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware, or microcode, the program code or code segments to perform the necessary tasks may be stored on a machine-readable medium. A processor(s) may perform the necessary tasks.

[0096] The various methods or processes outlined herein may be coded as software executable on one or more processors employing any one of a variety of operating systems or platforms. In addition, 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 as desired in various embodiments.

[0097] The embodiments of the present disclosure may be implemented as a method, an example of which is provided. The order of operations performed as part of the method may be determined in any suitable manner. Thus, the embodiments may be configured to perform operations in an order different from that illustrated, which may include performing some operations simultaneously, although in the illustrated embodiment they are shown as a sequence of operations.

[0098] Although the present disclosure has been described with reference to certain preferred embodiments, it should be understood that various other variations and modifications are possible within the spirit and scope of the disclosure. It is therefore the aspect of the appended claims to cover all such variations and modifications that come within the true spirit and scope of the disclosure.

Claims

1. 1. A fault detector for detecting faults in the operation of a synchronous motor including a stator and a rotor separated by an air gap, the fault detector comprising a processor and a memory having instructions stored thereon that, when executed by the processor, cause the fault detector to: collecting, via a communication channel including one or a combination of a wired communication link and a wireless communication link, electrical inputs for controlling operation of the synchronous motor and measurements associated with operation of the synchronous motor caused by the electrical inputs; determining a series of points defining the mutual positions of the stator and the rotor of the synchronous motor and forming interfaces of different materials inside the synchronous motor resulting in a static magnetic field determined as a weighted sum over real space basis functions, the real space basis functions being parameterized by pairs of adjacent points in the determined series of points and weighted by surface charge densities between corresponding adjacent points, the static magnetic field describing the measurement of the operation of the synchronous motor taking into account the electrical input; and determining a fault in operation of the synchronous motor based on a relative position of the stator and the rotor of the synchronous motor; A fault detector for transmitting, via the communication channel, one or a combination of an indication of a fault in operation of the synchronous motor and a selected control command based on the fault.

2. To determine the succession of points defining the relative positions of the stator and the rotor, the processor further comprises: and determining different static magnetic fields based on different mutual positions of the stator and the rotor by calculating a weighted sum over the real space basis functions for each mutual position, the real space basis functions being parameterized with a series of points representing interfaces between different materials inside the synchronous motor and weighted by a surface charge density determined by iteratively matching boundary conditions for the interfaces imposed by Maxwell's equations, the processor further comprising: calculating, for each of the different static magnetic fields, an electrical output of the operation of the synchronous motor taking into account the electrical input; selecting a static magnetic field that produces the electrical output of the synchronous motor that is closest to the measured value of the operation of the synchronous motor; selecting a series of points from the selected static magnetic field that define the relative positions of the stator and the rotor of the synchronous motor; The fault detector of claim 1 , configured as follows:

3. To determine the succession of points defining the mutual positions of the stator and the rotor of the synchronous motor, the processor further comprises: and configured to retrieve different parameters of the real space basis functions stored in the memory, the different parameters including different successions of points and corresponding surface charge densities determined for different mutual positions of the stator and the rotor of the synchronous motor, the processor further comprising: determining different static magnetic fields based on the extracted parameters; calculating, for each of the different static magnetic fields, an electrical output of the operation of the synchronous motor taking into account the electrical input; selecting a static magnetic field that produces the electrical output of the synchronous motor operation that is closest to the measured value of the synchronous motor operation; From the selected static magnetic field, a series of points are selected that define the mutual positions of the stator and the rotor of the synchronous motor. The fault detector of claim 1 , configured as follows:

4. The fault detector of claim 3 , wherein the electrical output of operation of the synchronous motor comprises a torque, and the processor is further configured to calculate the torque based on the Lorentz force law and an external magnetic field.

5. 4. The fault detector of claim 3, wherein different types and severities of faults associated with the different parameters of the real space basis functions are stored in the memory, and the processor is further configured to select a fault type and severity, a control command, or both, from the memory based on the parameters of the selected real space basis function of the static magnetic field.

6. The fault detector of claim 5 , wherein the processor is further configured to control the synchronous motor based on the control command.

7. 2. The fault detector of claim 1, wherein the indication of the fault includes a type and severity of the fault, and the processor is further configured to execute a classifier trained to classify the type and severity of the fault based on a mutual position of the stator and the rotor.

8. 2. The fault detector of claim 1, wherein to solve for the static magnetic field, the processor is further configured to calculate a magnetic field strength based on an initial value of the surface charge density, and iteratively update the surface charge density based on a relationship between the surface charge density and the magnetic field strength until a termination condition is met.

9. 2. The fault detector of claim 1, wherein to solve for the static magnetic field, the processor is further configured to calculate a magnetic flux density based on an initial value of a surface current density, and iteratively update the surface current density based on a relationship between the surface current density and the magnetic flux density until a termination condition is met.

10. The processor further comprises: assigning initial values ​​to the surface charge density and surface current density; calculating a magnetic field strength based on the initial value of the surface charge density; updating the surface current density based on the magnetic field strength; Calculating a magnetic flux density based on the updated surface current density; Update the surface charge density based on the magnetic flux density The fault detector of claim 1 , configured as follows:

11. 2. The fault detector of claim 1, wherein the electrical inputs include one or a combination of current and voltage in each winding of the synchronous motor, and the measurements include one or a combination of output torque and mutual inductance between different windings.

12. The fault detector of claim 1 , wherein the determined fault in operation of the synchronous motor includes one or a combination of a bearing fault and an eccentricity fault.

13. 1. A method for detecting faults in the operation of a synchronous 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, electrical inputs for controlling operation of the synchronous motor and measurements of the operation of the synchronous motor caused by the electrical inputs; determining a series of points defining the mutual positions of the stator and the rotor of the synchronous motor and forming interfaces of different materials inside the synchronous motor resulting in a static magnetic field determined as a weighted sum over real space basis functions, the real space basis functions being parameterized by pairs of adjacent points in the determined series of points and weighted by surface charge densities between corresponding adjacent points, the static magnetic field describing the measurement of the operation of the synchronous motor taking into account the electrical input; and determining a fault in operation of the synchronous motor based on a relative position of the stator and the rotor of the synchronous motor; and transmitting, via the communication channel, one or a combination of an indication of a fault in operation of the synchronous motor and a selected control command based on the fault.

14. To determine the succession of points defining the relative positions of the stator and the rotor, the method further comprises: determining different static magnetic fields based on different mutual positions of the stator and the rotor by calculating a weighted sum over the real space basis functions for each mutual position, the real space basis functions being parameterized with a series of points representing interfaces between different materials inside the synchronous motor and weighted by a surface charge density determined by iteratively matching boundary conditions for the interfaces imposed by Maxwell's equations, the method further comprising: calculating, for each of the different static magnetic fields, an electrical output of the operation of the synchronous motor taking into account the electrical input; selecting a static magnetic field that produces the electrical output of the synchronous motor that is closest to the measured value of the operation of the synchronous motor; and selecting from the selected static magnetic field a succession of points that define the mutual positions of the stator and the rotor of the synchronous motor.

15. To determine the succession of points defining the mutual positions of the stator and the rotor of the synchronous motor, the method further comprises: retrieving different parameters of the real space basis functions stored in a memory, the different parameters including different successions of points and corresponding surface charge densities determined for different mutual positions of the stator and the rotor of the synchronous motor, the method further comprising: determining different static magnetic fields based on the derived parameters; calculating, for each of the different static magnetic fields, an electrical output of the operation of the synchronous motor taking into account the electrical input; selecting a static magnetic field that produces the electrical output of the synchronous motor operation that is closest to the measured value of the synchronous motor operation; and selecting from the selected static magnetic field the succession of points that define the mutual positions of the stator and rotor of the synchronous motor.

16. 16. The method of claim 15, wherein different types and severities of faults associated with the different parameters of the real space basis functions are stored in the memory, and the method further comprises selecting a type and severity of fault, a control command, or both, from the memory based on the parameters of the selected real space basis functions of the static magnetic field.

17. The method of claim 16 , further comprising controlling the synchronous motor based on the control command.

18. 14. The method of claim 13, wherein the indication of the fault includes a type and severity of the fault, the method further comprising executing a classifier trained to classify the type and severity of the fault based on a mutual position of the stator and the rotor.

19. 14. The method of claim 13, wherein the electrical input comprises one or a combination of current and voltage in each winding of the synchronous motor, and the measurements comprise one or a combination of output torque and mutual inductance between different windings.

20. 1. A non-transitory computer readable storage medium comprising a program executable by a processor to perform a method for detecting faults in the operation of a synchronous 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, electrical inputs for controlling operation of the synchronous motor and measurements of the operation of the synchronous motor caused by the electrical inputs; determining a series of points defining the mutual positions of the stator and the rotor of the synchronous motor and forming interfaces of different materials within the synchronous motor resulting in a static magnetic field determined as a weighted sum over real space basis functions, the real space basis functions being parameterized by pairs of adjacent points in the determined series of points and weighted by surface charge densities between corresponding adjacent points, the static magnetic field describing the measurement of the operation of the synchronous motor taking into account the electrical input, the method further comprising: determining a fault in operation of the synchronous motor based on a relative position of the stator and the rotor of the synchronous motor; and transmitting, via the communication channel, one or a combination of an indication of a fault in operation of the synchronous motor and a selected control command based on the fault.

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