System and method for fault detection based on robust damped signal demixing

Abstract

A system for detecting faults in a motor is provided. The system includes an interface; a memory for storing a computer-implemented program including a signal sampling program, a matrix formation program, an optimization formation program, a matrix bundle program, an optimization solver, and lookup data including predetermined system parameters related to the fault; and a processor. The processor, using the computer-implemented program, performs the following steps: generating a signal matrix based on an acquired signal for an input time domain; forming an optimization problem with a low-rank constraint using the optimization formation program; solving the optimization problem using one of the optimization solvers to demix the signal matrix into a low-rank matrix, a spike interference matrix, and a Gaussian noise matrix; extracting a damping index parameter from the low-rank matrix using the matrix bundle program; and determining a fault related to the induction motor by identifying each of the measured system parameters of the induction motor based on the lookup data.

Description

Technical Field

[0001] The present invention generally relates to systems and methods for monitoring electric machines, and more particularly, to systems and methods for fault detection of electric machines based on robust damping signal demixing. Background Art

[0002] Electric motors are widely used in a variety of applications, including power plants, manufacturing plants, home appliances, and electric vehicles. Electric motors can be subject to a variety of faults, such as bearing failures, broken rotor bars, and winding shorts. These faults can reduce the lifespan of the motor or even lead to sudden, catastrophic failure. For example, when the motor is running at high speed, bearing failures can cause excessive vibration and friction. Therefore, there is a need to detect faults in electric motors to mitigate the losses caused by such failures. Summary of the Invention

[0003] Different technologies currently used for fault detection include, but are not limited to, vibration and acoustic signal analysis, electromagnetic field monitoring, temperature measurement, infrared recognition, and stator current spectrum analysis.

[0004] To monitor motor operation online and detect faults immediately, it is necessary to analyze the rotating motor's timing signals (vibration or current signals) and extract characteristic fault signatures for further analysis. However, due to the noisy operating environment and the motor's varying load, the measured signals are often a mixture of normal operating signals, fault signals, spike interference, transient signals caused by sudden changes in load or supply voltage, and Gaussian white noise. For example, even if a fault signature in the stator current is minimal, its magnitude can vary with different loads. As a result, it can be difficult to distinguish the fault signature from normal operating signals and noise.

[0005] To decompose signals and detect fault signatures, classical methods such as Fourier transform and wavelet transform are suitable for static operation. However, for motors operating under transient conditions, these classical methods perform poorly in extracting fault signatures due to their varying magnitudes.

[0006] The Hilbert-Huang transform (HHT) is another method for decomposing signals and analyzing their components. HHT uses empirical mode decomposition (EMD) to decompose the signal into so-called intrinsic mode functions (IMFs) with trends, and applies the Hilbert spectrum analysis (HSA) method to the IMFs to obtain instantaneous frequency data. The HHT method is designed to work well for unstable and nonlinear data. However, it is more of an empirical method without theoretical guarantees.

[0007] Another technique for fault characterization detection is based on compressed sensing, which utilizes the super-resolution characteristics of compressed sensing technology to extract fault characterization in a very short time, so that it can be assumed that the motor is operating in a steady state for a short period of time.

[0008] According to an embodiment of the present invention, a method for detecting faults during operation of a motor is provided. The method measures a stator current signal supplying power to the motor in the time domain, wherein the measurement includes sampling the signal at a sampling rate of at least twice the fundamental frequency of the stator current for a certain period of time during operation of the induction motor. A processor demixes a set of damped signals having non-zero amplitude, spike interference, and noise in the time domain, such that the set of damped signals includes the fundamental frequency of the operating signal, one or more possible fault signals, and other harmonic damped signals, and determines a fault signal corresponding to a potential fault based on the signal frequency and magnitude. If the set of damped signals includes a fault characteristic frequency corresponding to the fault, the method detects a fault in the motor.

[0009] Some embodiments of the present invention may provide systems and methods suitable for performing motor fault detection based on analyzing the stator current supplied to the motor or the vibration signal of the motor during operation. In this way, fault detection can be performed continuously and simultaneously with the operation of the motor without having to restart the motor.

[0010] Furthermore, some embodiments of the present invention provide systems and methods that can perform fault detection by measuring a noise signal of a motor that may be disturbed by spike interference and has varying load conditions.

[0011] Some embodiments of the present invention are based on the recognition that, under fault conditions, the resulting stator current supplying an induction motor is a mixture of a damped exponential signal, Gaussian white noise, and spike interference. This is because the stator current includes harmonics of the fundamental frequency of the power supply generating the stator current, as well as fault frequency components caused by the fault. The spike interference is caused by changing load or operating conditions or some other disturbance.

[0012] Some embodiments of the present invention are based on the recognition that parameter estimation of the damping exponent has been extensively studied in a noise-free setting. Well-established methods for solving this problem include the Prony method, which involves polynomial root-finding operations, and the matrix pencil method, which forms a matrix pencil based on the input signal and solves a generalized eigenvalue problem. However, both methods are very sensitive to noise.

[0013] Some embodiments of the present invention are based on the recognition that data preprocessing methods based on the singular value decomposition (SVD) of Hankel matrices have been proposed for matrix bundle methods and have been found to be more optimal for denoising if the noise is random Gaussian noise.

[0014] Some embodiments of the present invention are based on the recognition that the Hankel matrix formed by the sum of damping exponents is low rank.

[0015] Some embodiments of the present invention are based on the recognition that robust principal component analysis (RPCA) has been shown to be very effective in extracting low-rank matrices from observations contaminated by spike noise.

[0016] These insights lead to the realization that a combination of demixing damped signals using matrix bundling, RPCA, spike noise, and Gaussian noise enables the reconstruction of real signals using sparse driving techniques to denoise low-rank Hankel matrices for the matrix bundling method.

[0017] Therefore, one embodiment of the present invention discloses a method for detecting a fault during operation of a motor. The method includes the following steps: measuring a signal of a current supplied to the motor in the time domain; demixing a set of damped signals having non-zero amplitude, spike interference, and noise so that the set of damped signals includes the fundamental frequency of the operating signal, one or more possible fault signals, and other harmonic damped signals; and determining a fault signal corresponding to a potential fault based on the signal frequency and magnitude.

[0018] The demixing includes forming a Hankel matrix of the time domain measurement, denoising the Hankel matrix using a convex robust parameter estimation (CRPE) or non-convex robust parameter estimation (NRPE) method, and analyzing the denoised Hankel matrix using a matrix bundle method to obtain parameters of the damping signal. The steps of the method are performed by a processor.

[0019] Another embodiment discloses a system for operating an electric motor, the system comprising: a power supply for supplying power to the electric motor with a stator current having a fundamental frequency; a sensor for measuring a signal of the stator current supplying power to the electric motor in a time domain, wherein the measurement comprises sampling the signal at a sampling rate of at least twice the fundamental frequency of the stator current for a certain period of time during operation of the induction motor; a processor demixing a set of damped signals having non-zero amplitude, spike interference, and noise in the time domain so that the set of damped signals comprises the fundamental frequency of the operating signal, one or more possible fault signals, and other harmonic damped signals, and determining a fault signal corresponding to a potential fault based on the signal frequency and magnitude.

[0020] The presently disclosed embodiments will be further explained with reference to the accompanying drawings, which are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the presently disclosed embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1A is a block diagram of a system for detecting a fault in a motor during operation according to an embodiment of the present invention;

[0022] Figure 1B is a diagram illustrating a system for detecting a fault in a motor during operation according to an embodiment of the present invention;

[0023] Figure 2 is a block diagram of a method for detecting a fault of a motor according to one embodiment of the present invention;

[0024] Figure 3 is a block diagram of a method for denoising a Hankel matrix of a measurement result according to another embodiment of the present invention; and

[0025] Figure 4 is an exemplary plot of a signal of a stator current supplying power to a motor and a demixed damped signal including a fundamental operating frequency component, a fault-characterizing damped signal, Gaussian noise, and spike interference.

[0026] Although the above drawings illustrate the presently disclosed embodiments, other embodiments are also contemplated, as mentioned in the discussion. This disclosure presents exemplary embodiments by way of representation and not limitation. Those skilled in the art can devise numerous other modifications and embodiments that fall within the scope and spirit of the principles of the presently disclosed embodiments. DETAILED DESCRIPTION

[0027] 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 exemplary embodiments will provide those skilled in the art with an enabling description for implementing one or more exemplary embodiments. Various changes to the function and arrangement of elements are contemplated without departing from the spirit and scope of the disclosed subject matter as set forth in the appended claims.

[0028] In the following description, specific details are given to provide a thorough understanding of the embodiments. However, it will be understood by those skilled in the art that these embodiments can be put into practice without these specific details. For example, the systems, processes and other elements in the disclosed subject matter can be shown as components in block diagram form to avoid obscuring these embodiments with unnecessary details. In other cases, well-known processes, structures and technologies can be shown without unnecessary details to avoid obscuring these embodiments. In addition, the same reference numerals and marks in the various drawings represent the same elements.

[0029] In addition, various embodiments may be described as processes, which may be depicted as flowcharts, flow diagrams, data flow diagrams, structure diagrams, or block diagrams. Although a flowchart may describe operations as sequential processes, many operations may be performed in parallel or simultaneously. In addition, the order of the operations may be rearranged. A process may terminate when its operations are completed, but may have additional steps not discussed or included in the figure. Furthermore, not all operations in any particularly described process may occur in all embodiments. A process may correspond to a method, function, procedure, subroutine, subprogram, etc. When a process corresponds to a function, the termination of the function may correspond to the function returning to the calling function or main function.

[0030] Furthermore, 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, the 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.

[0031] Figure 1A is a schematic diagram of a system 100 for monitoring an exemplary electric machine according to one embodiment of the present invention. In this example, electric machine 10 , operated by a power supply and controller 11 , is a synchronous or asynchronous electric machine having a rotating rotor and a stationary stator.

[0032] The system 100 includes a sensor (electrical signal sensor) 120 for measuring a signal of the stator current that supplies power to the motor (or induction motor) 10 in the time domain. The measurement includes sampling the signal for a certain period of time at a sampling rate of at least twice the fundamental frequency of the stator current during steady-state operation of the induction motor. According to certain embodiments, the electrical signal sensor 120 may be a current or vibration sensor for acquiring current and vibration data about the motor 10. For example, the sensor 120 may be configured to sense current data from one or more of the multiple phases of the motor 10. More specifically, in the case where the motor is a three-phase motor, the current and voltage sensors sense current and voltage data from the three phases of the three-phase motor. Although certain embodiments of the present invention will be described with reference to a multi-phase motor, other embodiments of the present invention may be applied to other multi-phase motors.

[0033] The processor 130 is configured to determine a set of frequencies having non-zero amplitudes in the frequency domain such that a reconstructed signal formed by the frequencies having non-zero amplitudes approximates a signal measured in the time domain. The determination includes searching within a subband including a fundamental frequency that is subject to a sparsity condition of the signal in the frequency domain.

[0034] The system 100 also includes a memory device 140 for storing signal measurements and various parameters and coefficients used to perform signal analysis.

[0035] Figure 1Bis a diagram illustrating a system 100 for detecting a fault in a motor during operation according to an embodiment of the present invention. The system 100 may further include an input / output interface 150 configured to acquire a signal from the sensor 120 and, if the set of frequencies having non-zero amplitudes includes a frequency different from the main frequency, the input / output interface transmits a signal (output data) for the fault to the motor control system 110 via the network 50. In addition, the memory device 140 includes a computer executable program for detecting a fault in the motor. The computer executable program includes a signal sampling program 141, a matrix forming program 142, a matrix bundle program 143, and an optimization solver 220 configured to execute a non-convex robust parameter estimation (NRPE) method and a convex robust parameter estimation (CRPE) method using the processor 130. Therefore, the processor 130 is configured to execute, in response to a signal from the sensor 120 via the I / O interface 150, the following steps: acquiring a signal regarding the motor for an input time domain via the sensor; generating a signal matrix based on the acquired signal for the input time domain; forming an optimization problem with a low-rank constraint using an optimization formulation procedure; demixing the signal matrix into a low-rank matrix, a spike interference matrix, and a Gaussian noise matrix by solving the optimization problem using one of the optimization solvers; extracting a damping index parameter from the low-rank matrix using a matrix bundle procedure; and determining a fault regarding the induction motor by identifying each parameter in the measured system parameters of the induction motor based on the lookup data. The process of the steps is described below.

[0036] Figure 2 A block diagram of a method for detecting faults during operation of an electric motor according to one embodiment of the present invention is shown. System 100 detects noisy measurements 121 of a signal of a stator current supplying an induction motor, measured by sensor 120, in the time domain to form a noisy Hankel matrix 210. A processor 130 of system 100 is configured to denoise the noisy Hankel matrix using a CRPE method or a non-convex robust parameter estimation (NRPE) method to generate a low-rank Hankel matrix corresponding to a setting of a damping signal 220. A matrix bundle method 143 is then applied to the denoised Hankel matrix to determine a damping signal parameter 230. The damping signal parameter is used to compare with a fault characteristic frequency 240. If the fault frequency is present and its magnitude is greater than a threshold 250, a corresponding fault is detected 260, otherwise the motor operates under normal conditions 270.

[0037] For example, threshold 250 can be determined as follows. When there is a fault frequency component with a magnitude greater than a certain value (e.g., -30 dB of the fundamental frequency component) and the fault frequency is close to a characteristic fault frequency (e.g., within 5% of the characteristic fault frequency), system 100 detects a fault in step 260. In this case, the characteristic fault frequency can be determined by the mechanical structure of the motor (e.g., bearing size and number of balls) and rotor speed. The greater the magnitude of the fault frequency, the more likely a fault is present, such as a bearing inner race fault.

[0038] Mathematically, the system observes the time domain signal

[0039]

[0040] Here, y(t) is a noisy observation consisting of multiple damping exponentials, and their amplitude A j >0, damping coefficient α j ≤0, frequency f j >0, and the phase θ j ∈R, and their total number M is an unknown parameter. The noise η(t) can be modeled as a mixture of Gaussian noise g(t) and sparse spike interference s(t), that is, η(t) = g(t) + s(t). In particular, s(t) can be an unwanted interference or a series of system responses with a response time short compared to the sampling time, containing valuable information about the operating conditions of the circuit or motor.

[0041] The sampled signal x∈C N The Hankel matrix H p (x)∈C (N-p)×(p+1) Defined as:

[0042]

[0043] If the sampled signal x∈C N is the sum of M damping exponents, then by choosing p∈[M, NM], the Hankel matrix usually becomes a matrix of rank M≤p (i.e., low rank). In the absence of noise, the matrix bundle algorithm uses this low rank Hankel matrix to accurately estimate the exponential parameters. Therefore, in this work, our goal is to use the observation Hankel matrix Y=H p (y)∈C (N-p)×(p+1) To extract such a low-rank Hankel matrix H p (x) (where x is the sum of the estimated damping exponents), where y∈C Nare the sampled noisy observations. Additionally, if there are spikes, we should be able to extract a further sparse matrix. We rely on the assumption that M is small relative to N. Since p is fixed during the optimization process, we simplify the notation by using H(x) and drop the subscript p. Inspired by robust principal component analysis and the success of work in the compressive sensing community, we apply the nuclear norm to constrain the rank of H(x) and use the L1 norm to extract the sparse matrix S caused by the spikes. We assume that the residuals represent Gaussian noise. Combining these models leads to the convex robust parameter estimation (CRPE) problem

[0044]

[0045] Alternatively, non-convex robust parameter estimation (NRPE) utilizes rank constraints instead of nuclear norm regularization:

[0046]

[0047] Subject to the constraint that Rank(H(x))≤r(3)

[0048] where r represents the maximum number of damping exponents we wish to recover. If we have a priori estimate or knowledge of the number of damping exponents, then r can be set to be greater than or equal to that estimate, depending on the nature of the application. Thus, some embodiments of the present invention are based on the recognition that the NRPE optimization problem is less sensitive to hyperparameters than the CRPE optimization problem. However, since (3) is non-convex, the optimization algorithm may get stuck in a local minimum.

[0049] To solve the CRPE optimization problem, we introduce an auxiliary variable Z and add the constraint H(x)=Z to (2). Then, the augmented Lagrangian function of (2) becomes

[0050]

[0051] Where V∈C (N-p)×(p+1) is the Lagrange multiplier matrix, μ is the penalty parameter associated with the augmentation term, and<A,B> R =Re(Tr(B H A)). Application of ADMM results in Figure 3 The updating steps summarized in Algorithm 1 are shown in (a).

[0052] Reverse diagonal average operator is defined as

[0053]

[0054] where A∈C (N-p)×(p+1), and A(i;j) is the entry in A in the i-th row and j-th column. S τ (A) = sign(A) max{|A| - τ, 0} is a complex element-wise soft thresholding operator with threshold τ, where sign(A) = A / |A| for non-zero entries and 0 otherwise. max{·,·} is an element-wise maximum operator. Moreover, is a singular value soft thresholding operator with a threshold τ, where A = U diag(σ)W H The singular value decomposition f CRPE is the objective function of the CRPE optimization problem defined in (2).

[0055] The solver for the NRPE optimization problem outlined in Algorithm 2 is based on coordinate descent with projection. Tr(A) is the singular value truncation operator that implements the singular value decomposition on the input matrix A and returns a matrix constructed using the r largest singular values ​​of A. NRPE is the objective function of the NRPE optimization problem in (3). In the first experiment, we consider bearing fault detection of an induction motor, where the motor current consists of a 60 Hz operating signal and a 90 Hz sideband wave related to its rotational frequency component in the presence of Gaussian noise and spike interference. When a bearing fault or defect occurs, a damped frequency component in the current will be generated that depends on the fault location and bearing size. For example, a 73 Hz frequency component is caused by a cage defect in the outer ring. The magnitude of this defect frequency component is usually very small compared to the operating current signal, making bearing fault detection a very challenging problem. Nevertheless, its parameters (and sometimes the spike interference) are useful for evaluating the fault severity and operating conditions of the motor.

[0056] The noisy fault observation is formulated as follows:

[0057] y(t)=e 0t 1.0cos(2π60t+1.3)+e -4.2t 0.1cos(2π73t++0.2)+e -1.3t 0.3cos(3π90t+1.7)+g(t)+s(t).

[0058] We observe y for 1 second with 1000 samples. The signal-to-Gaussian noise ratio is 25 dB, and the spike interference has a cardinality of 1%, with the non-zero entries of the cardinality randomly selected with a magnitude uniformly sampled in [0, 5]. We Figure 4An example signal of the stator current 410 supplying power to the motor and the demixed damping signal are plotted in FIG. Using a matrix bundle method on the de-noised Hankel matrix, the noisy measurement result is demixed into the fundamental operating frequency component 420, the fault-characterizing damping signal 430, the Gaussian noise 440, and the spike interference 450.

[0059] The above-described embodiments of the present disclosure can be implemented in any of a number of ways. For example, these embodiments can be implemented using hardware, software, or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether located in a single computer or distributed across multiple computers. Such a processor can be implemented as an integrated circuit, with one or more processors included in the integrated circuit assembly. However, the processor can be implemented using circuits in any suitable format.

[0060] In addition, the various methods or processes outlined herein can be encoded as software, and the software can be performed on any one or more processors employing multiple operating systems or platforms. In addition, this software can be written using any one of multiple suitable programming languages ​​and / or programming or scripting tools, and can also be compiled into executable machine language code or intermediate code executed on framework or virtual machine. In various embodiments, the function of combination or distribution program can usually be used as needed. In some cases, the computer-implemented program used in embodiments of the present invention can be referred to as one or more program modules.

[0061] In addition, the embodiment of the present disclosure can be embodied as method, and the example of this method has been provided.The action performed as a part of this method can be sorted in any suitable manner.Therefore, even if it is shown as sequential action in the illustrative embodiment, it is also possible to construct an embodiment in which the action is performed in an order different from that illustrated, which may include performing some actions simultaneously. Moreover, the use of common terms such as "first", "second" to modify the claim element in the claims does not imply any priority, precedence or order of a claim element relative to another element, or the time sequence of the action of the method of execution, but is merely used as a mark for distinguishing a claim element with a specific name from another element with the same name (except using ordinal numbers), to distinguish these claim elements.

[0062] Although the present disclosure has been described with reference to certain preferred embodiments, it will be understood that various other changes and modifications may be made within the spirit and scope of the present disclosure. Therefore, it is intended that the appended claims cover all such changes and modifications as fall within the true spirit and scope of the present disclosure.

Claims

1. A system for detecting a fault in a motor, the system comprising: an interface configured to acquire a signal related to the motor for an input time domain via a sensor; a memory for storing a computer-implemented program comprising a signal sampling program, a matrix formation program, an optimization formation program, a matrix bundle program, an optimization solver, and lookup data comprising predetermined system parameters associated with the fault; as well as a processor, the processor being configured, when executing the computer-implemented program in conjunction with the interface and the memory, to perform: generating a signal matrix based on the acquired signal for the input time domain; formulating an optimization problem with a low-rank constraint using the optimization formulation procedure; Demixing the signal matrix into a low-rank matrix, a spike interference matrix, and a Gaussian noise matrix by solving the optimization problem using one of the optimization solvers; extracting damping exponential parameters from the low-rank matrix using the matrix bundle procedure; as well as determining a fault with the motor by identifying each of the measured system parameters of the motor based on the lookup data, The optimization procedure generates a convex robust parameter estimation CRPE optimization problem or a non-convex robust parameter estimation NRPE optimization problem, The low-rank matrix is ​​a Hankel matrix.

2. The system according to claim 1, wherein: The optimization solver is based on the convex robust parameter estimation CRPE method and the non-convex robust parameter estimation NRPE method.

3. The system according to claim 1, wherein: The input time domain represents a sampling period and a sampling frequency.

4. The system according to claim 1, wherein: The matrix bundle procedure is configured to obtain eigenvalues ​​and to calculate damping factors and frequencies using the eigenvalues.

5. The system according to claim 1, wherein The acquired signal is a current signal or a vibration signal based on the operation of the motor.

6. The system according to claim 1, wherein: The electric machine is an electric circuit, an electric motor or a generator.

7. A method for detecting a fault in a motor, the method comprising the following steps: acquiring a signal related to the motor in an input time domain via a sensor; generating a signal matrix based on the acquired signal for the input time domain; Use an optimization formulation procedure to formulate an optimization problem with low-rank constraints; Demixing the signal matrix into a low-rank matrix, a spike interference matrix, and a Gaussian noise matrix by solving the optimization problem using one of a plurality of optimization solvers; extracting damping exponential parameters from the low-rank matrix using a matrix bundle procedure; as well as determining a fault with the motor by identifying each of the measured system parameters of the motor based on lookup data, The optimization procedure generates a convex robust parameter estimation CRPE optimization problem or a non-convex robust parameter estimation NRPE optimization problem, The low-rank matrix is ​​a Hankel matrix.

8. The method according to claim 7, wherein: The optimization solver is based on the convex robust parameter estimation CRPE method and the non-convex robust parameter estimation NRPE method.

9. The method according to claim 7, wherein: The input time domain represents a sampling period and a sampling frequency.

10. The method according to claim 7, wherein: The matrix bundle procedure is configured to obtain eigenvalues ​​and to calculate damping factors and frequencies using the eigenvalues.

11. The method according to claim 7, wherein: The acquired signal is a current signal or a vibration signal based on the operation of the motor.

12. The method according to claim 7, wherein: The electric machine is an electric circuit, an electric motor or a generator.

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