Cage type motor broken bar fault diagnosis method for complex scene

Abstract

The invention provides a complex scene-oriented cage type motor broken bar fault diagnosis method, which comprises the following steps of: calculating a fault characteristic frequency based on a given frequency and a rotating speed of a cage type asynchronous motor, and obtaining a signal to be analyzed and the frequency of a maximum harmonic component of a stator current signal based on the stator current signal; filtering the to-be-analyzed signal based on an NFLMS adaptive filter to obtain a filtered signal; fFT analysis is carried out on the filtered signal, an amplitude spectral density value of a fault characteristic component and an amplitude spectral density value of a fundamental wave residual volume are respectively obtained based on a fault characteristic frequency and a given frequency, and an amplitude spectral density value of a maximum harmonic component is taken as a reference to respectively calculate an amplitude spectral density ratio of the fault characteristic component and an amplitude spectral density ratio of the fundamental wave residual volume; and judging whether the motor has a broken bar fault or not based on the characteristic component amplitude spectral density ratio and the fundamental wave residual quantity amplitude spectral density ratio. The robustness of the algorithm to the initial weight is enhanced, and the effect of fault feature extraction and diagnosis is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of electromechanical equipment status monitoring and fault diagnosis technology, and in particular to a broken bar fault diagnosis method for a cage motor. Background Art

[0002] Broken rotor bar fault is one of the common faults of cage-type asynchronous motors. In some important occasions, it is very necessary to diagnose the broken rotor bar fault through real-time detection. Since the rotor of the cage-type asynchronous motor has no direct electrical components, it is necessary to analyze and process the motor operating parameters to achieve accurate diagnosis of the broken bar fault. From the perspective of detecting and analyzing signals, there are mainly signals such as stator current, power-off voltage, torque, vibration, temperature, etc. Among them, the broken rotor bar fault diagnosis method based on stator current analysis is the most common. The basic principle of this method is as follows: the motor is directly powered by an industrial frequency power supply. Under normal circumstances, the stator current of the motor only contains the power supply frequency f0=50Hz; when a broken rotor bar fault occurs, a fault characteristic component with a frequency of (1±2s)f0 will also appear in the stator current, where the slip rate s=(n0-n) / n0, n0 is the synchronous speed, and n is the motor speed. Under normal circumstances, the stator current is directly powered by ... appear in the stator current, where the slip rate s=(n0-n) / n0, n0 is the synchronous speed, and n is the motor speed. c =(1-2s)f0 frequency component is used as the broken bar fault characteristic to determine whether there is a broken rotor bar fault. However, when the motor is running at rated speed, the speed n is close to n0, and the slip rate s is very small, close to 0. c is very close to the fundamental wave f0, and f c The component is about 0.02 to 0.05 times the f0 component. Therefore, if the spectrum analysis is performed directly, f c The component will be overwhelmed by the f0 component and f cannot be obtained. c In the field of signal processing, adaptive filters are widely used because of their high efficiency and stable signal processing capabilities. In order to accurately extract the f of the stator current c The commonly used method is as follows: first use an adaptive filter to process the stator current to filter out the f0 component as much as possible, and then use spectrum analysis to determine whether there is f in the stator current. c Finally, perform broken bar fault diagnosis.

[0003] When a motor is powered directly by a commercial power supply, the stator current has a simple frequency component. Using an adaptive filter based on the least mean square (LMS) algorithm for rotor bar fault diagnosis can achieve excellent results, with high fault diagnosis accuracy. However, current motors generally use variable frequency speed regulation, where the motor is powered and controlled by a frequency converter. The harmonic components of the stator current are complex due to the frequency converter's influence. These components include not only the frequency converter output frequency and its integer harmonics, but also interharmonics and noise interference. If a rotor bar fault occurs, the fault signature components are easily obscured by these complex harmonic components, making fault signature extraction extremely difficult. Furthermore, the complex harmonic components of the stator current increase the error signal as the adaptive filter approaches stability, resulting in a larger notch bandwidth and thus affecting the filter's filtering effectiveness. Therefore, the complex harmonic components and noise in variable frequency speed regulation have a significant negative impact on rotor bar fault diagnosis methods based on adaptive filters.

[0004] To improve the filtering performance of the adaptive LMS filter algorithm, many researchers have explored various approaches, including the introduction of fractional-order calculus and the variable step size algorithm (VSSA), achieving some significant research results. Combining fractional-order calculus with the LMS adaptive algorithm, the FLMS (Fast Least Mean Square) adaptive filter algorithm was proposed. The characteristics of the FLMS and the effective adjustment range of the fractional order were studied. Based on the characteristics of the object being analyzed, several improvements to the FLMS adaptive filter were proposed. Adjusting the fractional order increases the algorithm's flexibility, adding degrees of freedom for practical applications. Compared to traditional adaptive filtering algorithms, the algorithm significantly improves filtering performance. However, current research on motor rotor bar broken fault diagnosis based on adaptive filters primarily uses the LMS algorithm, whose performance needs to be improved. The FLMS algorithm provides a new approach for rotor bar broken fault diagnosis, potentially further improving fault diagnosis accuracy.

[0005] On the one hand, the FLMS algorithm is not limited to fixed-step-size algorithms. By combining it with a variable-step-size algorithm (VSSA), the algorithm's convergence speed can be further improved and steady-state error can be reduced. VSSA adjusts the step size based on the error signal; a larger error signal increases the step size, resulting in a variety of VSSA variants. However, few VSSAs consider the influence of signal harmonics, making them less adaptable to applications with large variations in harmonic content.

[0006] On the other hand, the simulation analysis of the relevant research results assumes that the initial phase φ0 of the input signal of the adaptive filter is 0° and the initial weight w0 is selected as a specific value. Figure 1The adaptive filter shown generally takes a phase shift φ p =90°. Initial weight w0, initial phase φ0, phase shift φ p The selection of is often not taken seriously, so the analysis results are based on ideal conditions. Although the filtering effect is good, the adaptability to the analysis object is poor, and the actual analysis results applied to engineering projects will have large deviations. In fact, the initial phase φ0=0° and the phase shift φ p =90° is not necessarily the optimal combination and requires further study based on actual conditions. In practical applications, the harmonic components and noise of the collected signal vary, and its initial phase is also uncertain. This can cause the FLMS adaptive filter to have a significant difference from the ideal filtering effect, sometimes not being good enough, and in some cases even failing to converge. Summary of the Invention

[0007] To address the technical problem that existing methods lack adaptability to the analysis object due to their failure to consider harmonic components, the initial phase of the input signal, the initial weights of the adaptive filter, and phase shift, this paper proposes a method for diagnosing broken-bar faults in squirrel-cage motors for complex scenarios. This fault diagnosis method utilizes a novel FLMS algorithm (NFLMS) and a novel variable-step-size algorithm (NVSSA), taking into account the influence of the adaptive filter's initial weights and harmonic components. Furthermore, by selecting the initial phase and phase shift of the input signal, the algorithm's robustness to the initial weights is enhanced, improving the effectiveness of fault feature extraction and diagnosis.

[0008] In order to achieve the above object, the technical solution of the present invention is achieved as follows:

[0009] A method for diagnosing broken bar faults in squirrel-cage motors for complex scenarios, including the following steps:

[0010] S1: Real-time acquisition of the given frequency f0 of the inverter, the speed of the cage asynchronous motor and the stator current signal;

[0011] S2: Calculate the fault characteristic frequency f based on the given frequency f0 and the speed of the cage asynchronous motor c , based on the stator current signal, obtain the frequency f of the maximum harmonic component of the signal to be analyzed and the stator current signal r ;

[0012] S3: Filter the signal to be analyzed based on the NFLMS adaptive filter to obtain a filtered signal;

[0013] S4: Perform FFT analysis on the filtered signal based on the fault characteristic frequency f c The amplitude spectrum density value of the fault characteristic component and the amplitude spectrum density value of the fundamental wave residual are obtained by taking the frequency f0 as the given frequency, and ther The amplitude spectrum density value of the maximum harmonic component is used as a reference to calculate the amplitude spectrum density ratio R of the fault characteristic component. c and the fundamental residual amplitude spectral density ratio R f ;

[0014] S5: Based on the characteristic component amplitude spectral density ratio R c and the fundamental residual amplitude spectral density ratio R f Determine whether the motor has a broken bar fault.

[0015] Furthermore, the frequency f of the maximum harmonic component of the signal to be analyzed and the stator current signal is obtained based on the stator current signal. r The method is:

[0016] S2.1: Determine the signal to be analyzed by performing peak value judgment on the stator current signal;

[0017] S2.2: Obtain the frequency f of the maximum harmonic component by performing FFT analysis on the signal to be analyzed r and its amplitude spectral density values.

[0018] Furthermore, the method for filtering the signal to be analyzed based on the NFLMS adaptive filter is:

[0019] S3.1: Randomly initialize weights; sample the signal to be analyzed and the reference signal respectively;

[0020] S3.2: Calculate the error ε(n) based on each sample value of the signal to be analyzed;

[0021] S3.3: Calculate the variable step size μ based on the improved variable step size algorithm NVSSA according to the error ε(n) THD (n);

[0022] S3.4: Combined with variable step size μ THD (n) Update weights using the weight update iterative formula of the NFLMS algorithm;

[0023] S3.5: Repeat steps S3.2 to S3.4 until the weights converge or all sampling points are processed to obtain the filtered signal.

[0024] Furthermore, the method for calculating the error ε(n) according to each sampling value of the signal to be analyzed is:

[0025] ε(n)=d(n)-y(n)=d(n)-w1(n)x1(n)-w2(n)x2(n)

[0026] Where d(n) is the sample value of the signal to be analyzed in the nth sampling period, y(n) is the output of the nth sampling period, w1(n) and w2(n) are the weights of the nth sampling period, and x1(n) and x2(n) are the sample values ​​of the reference signal in the nth sampling period.

[0027] Furthermore, the variable step size μ is calculated based on the improved variable step size algorithm NVSSA according to the error ε(n) THD (n) The method is:

[0028] S3.31: Perform Fourier transform on the signal to be analyzed x0(t) to obtain the frequency domain amplitude spectrum, extract the fundamental amplitude A1, and the amplitudes of each harmonic A2, A3, ..., A m , calculate the distortion rate:

[0029]

[0030] S3.32: Calculate variable step size μ based on distortion rate THD (n).

[0031] Furthermore, the variable step size μ is calculated based on the distortion rate. THD The method of (n) is: calculate the harmonic complexity adjustment parameter α(THD) according to the distortion rate:

[0032]

[0033] The variable step size μ is calculated based on the harmonic complexity adjustment parameter α(THD) and the error ε(n) using the variable step size calculation formula THD (n):

[0034]

[0035] Among them, β0 and m0 are both positive numbers to be determined.

[0036] Furthermore, the weight update iteration formula of the NFLMS algorithm is:

[0037]

[0038] Among them, i (n) = d(n) - w i (n)x i (n)-w j (n-1)x j (n), w j (n), w i (n) is the weight of the nth sampling period, x j (n), x i(n) is the sampling value of the reference signal in the nth sampling period, d(n) is the sampling value of the signal to be analyzed in the nth sampling period, when i = 1, j = 2; when i = 2, j = 1; α is the order of the fractional order; Γ(·) represents the Gamma function.

[0039] Furthermore, the calculated characteristic component amplitude spectral density ratio R c and the fundamental residual amplitude spectral density ratio R f The method is:

[0040] Calculate the amplitude spectral density ratio of the fault characteristic component:

[0041] Among them, V r is the amplitude spectrum density of the maximum harmonic component, V c is the amplitude spectrum density of the fault characteristic component;

[0042] Calculate the fundamental residual amplitude spectral density ratio:

[0043] Among them, V f is the amplitude spectral density of the fundamental wave residual.

[0044] Furthermore, when sampling the reference signal described in step S3.1, the phase shift φ p The value range is 60°~80°.

[0045] Furthermore, the method for determining the signal to be analyzed in step S2.1 is: taking the maximum value point of the first fundamental wave period as the starting point of the signal to be analyzed, and taking data with a length of N0 as the signal to be analyzed.

[0046] Beneficial effects of the present invention:

[0047] The broken bar fault feature extraction and diagnosis method based on the NFLMS adaptive filter proposed in the present invention can solve the problems of the influence of initial weight, initial phase, phase shift and harmonic components, has strong adaptability to harmonics and noise, ensures the convergence of the adaptive filter, and can also guarantee a stable and effective filtering effect in complex and changeable scenarios, thereby greatly improving the effect of fault feature extraction and diagnosis after adaptive filtering. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0049] Figure 1 Flow chart of the method of the present invention.

[0050] Figure 2 This is the principle diagram of the FLMS adaptive filter.

[0051] Figure 3 FIG. 4 is a schematic diagram of the NFLMS adaptive filter principle of the present invention.

[0052] Figure 4 is the current signal amplitude spectrum with a given frequency of 40 Hz.

[0053] Figure 5 This is the result diagram of the influence of initial value on broken bar fault feature extraction under FLMS algorithm + VSSA variable step size algorithm.

[0054] Figure 6 This is a diagram showing the effect of the initial phase on the NFLMS adaptive filter of the present invention.

[0055] Figure 7 This is a diagram showing the effect of the phase shift on the NFLMS adaptive filter according to the present invention.

[0056] Figure 8 The initial weight of the present invention affects the NFLMS adaptive filter, where (a) is the phase shift φ p =60°, (b) is the phase shift φ p =70°, (c) is the phase shift φ p =80°.

[0057] Figure 9 This is the FFT analysis result of the signal after filtering by the overall method of the present invention after improving the initial phase, phase shift, initial weight and adding the distortion rate. DETAILED DESCRIPTION

[0058] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0059] A broken bar fault diagnosis method for squirrel cage motors in complex scenarios, such as Figure 1 As shown, the steps are:

[0060] S1: Get the given frequency f0 of the inverter, the speed n of the cage asynchronous motor and the stator current signal in real time.

[0061] S2: Calculate the fault characteristic frequency f based on the given frequency f0 and the speed of the cage asynchronous motorc , based on the stator current signal, obtain the frequency f of the maximum harmonic component of the signal to be analyzed and the stator current signal r .

[0062] Calculate the broken bar fault characteristic frequency f c The method is as follows: Step 1, calculate the slip rate s = (n0-n) / n0, n0 is the synchronous speed, in this example n0 = 30f0; Step 2, calculate f c =(1-2s)f0. In the subsequent analysis, the purpose is to eliminate the influence of the fundamental component and effectively extract the frequency f c Components, and according to f c The component size and other related indicators can be used to determine whether there is a broken bar fault.

[0063] Because the stator current signal is affected by harmonics and noise, it is still approximately a periodic signal. According to the reference signal requirement of the adaptive filter, the signal to be analyzed here is a cosine signal with an initial phase of 0. Therefore, the starting point of the signal to be analyzed is the maximum point.

[0064] The method of obtaining the signal to be analyzed and the maximum harmonic component f of the stator current signal based on the stator current signal is as follows: r The method is:

[0065] S2.1: Determine the signal to be analyzed by performing peak value judgment on the stator current signal. That is, the maximum value point of the first fundamental wave cycle is used as the starting point of the signal to be analyzed, and data with a length of N0 is taken as the signal to be analyzed.

[0066] S2.2: Obtain the frequency f of the maximum harmonic component by performing FFT analysis on the signal to be analyzed r and its amplitude spectral density values.

[0067] S3: Filter the signal to be analyzed based on the NFLMS adaptive filter to obtain a filtered signal.

[0068] The working principle of FLMS adaptive filter is as follows Figure 2 As shown in the figure, d(t) is the input original current signal (that is, the signal to be analyzed), x(t) is the reference signal, where x(t) = C·cos(2πf0t), where C is the amplitude and f0 is the frequency of the component to be filtered out. d(n), x1(n), and x2(n) are the sampled values ​​of d(t), x1(t), and x2(t) in the nth sampling period, respectively. w1(n) and w2(n) are weights, and the error is ε(n) = d(n)-y(n), where y(n) is the filter output. Usually, the phase shift is φ p =90°.

[0069] In order to balance the convergence speed and filtering effect of the adaptive filter, the adaptive filter usually uses a variable step size μ(n) instead of a fixed step size μ. When using a variable step size, the weight correction process is:

[0070] w k (n+1)=w k (n)+2μ(n)ε(n)x k (n) (1)

[0071] Where k = 1, 2.

[0072] The minimum mean square error function of the traditional LMS adaptive filter is:

[0073] J(n)=E[|ε(n)| 2 ] (2)

[0074] Among them, E represents expectation.

[0075] The cost function equation in formula (2) can be transformed into:

[0076]

[0077] Where L = 2, w k (n) is the weight, x k (n) is the sample value of the reference signal x(t).

[0078] The nth iteration of the adaptive filter with the first-order derivative term is:

[0079]

[0080] The FLMS algorithm is an LMS adaptive filtering algorithm based on the fractional gradient descent method. The following describes the principle of the FLMS adaptive filtering algorithm.

[0081] Based on the principle of LMS algorithm, the FLMS algorithm can be obtained, and its nth iteration is:

[0082]

[0083] Where α is the order of the fractional order, which is generally a real number between 0 and 1.

[0084] Thus, the fractional-order cost function equation is:

[0085]

[0086] After simplification, we get:

[0087]

[0088] In the formula, the symbol Γ represents the Gamma function, Dα w k (n) indicates the value of w k (n) Find the fractional order of α.

[0089] Substituting formula (7) into formula (5), we can get:

[0090]

[0091] Formula (8) is the final iterative process of the FLMS algorithm.

[0092] NFLMS adaptive filter: The present invention combines Figure 2 The FLMS adaptive filter shown in FIG, proposes an NFLMS adaptive filter, such as Figure 3 As shown, the weight update method of the FLMS adaptive filter is mainly improved.

[0093] For the function λ(t)=(tc) ν , the corresponding fractional derivative can be expressed as:

[0094]

[0095] Wherein, 0≤n-1≤α<n,ν>n-1, α represents the order of the fractional order, n represents the sampling number, ν is the power exponent, Γ represents the Gamma function, c is a constant, and t is the function independent variable.

[0096] Next, for the quadratic function f(t)=(at+b) 2 ,a≠0, introduce the initial value τ0 through transformation, and discuss the influence of the initial value τ0 of t:

[0097]

[0098] According to formula (9), the α-order gradient of the quadratic function f(t) can be derived as:

[0099]

[0100] The constant term has no effect on the extreme points of a given quadratic function, that is, the extreme points of f(t) and f(t)+constant are the same. Therefore, Equation (11) can be modified as follows:

[0101]

[0102] Thus, according to formula (9), we can obtain:

[0103]

[0104] Transform the cost function J(n) and change the weight w j (n) split into w j(n-1)+[w j (n)-w j (n-1)], construct a form similar to formula (10):

[0105]

[0106] Where, i (n) = d(n) - w i (n)x i (n)-w j (n-1)x j (n), the algorithm takes into account the weight w of the previous iteration j (n-1) The impact on the current state: when i=1, j=2; when i=2, j=1.

[0107] correspond Thus, according to formula (12) and formula (13), the fractional derivative of the cost function J(n) can be obtained:

[0108]

[0109] Therefore, the weight update iteration formula of the NFLMS algorithm is expressed as:

[0110]

[0111] NVSSA principle: Adaptive filters using variable step sizes generally achieve better filtering results than fixed step sizes. This aspect has been extensively studied in the literature and will not be further explored here. This paper selects the VSSA variable step size algorithm, as shown in Equation (17), and analyzes and improves upon it.

[0112]

[0113] Here, α0, β0, and m0 are all undetermined positive numbers. To distinguish the e exponent, ε(n) is used to represent the error signal at time n. When the motor is powered by a commercial power supply, the power supply harmonics are very low, and ideal conditions are achieved. In this case, setting α0 = 1.5, β = 0.6, and m0 = 1 achieves good results.

[0114] When the motor is controlled by a frequency converter, the harmonics of the stator current signal are very complex, which leads to a prolonged transition process of the adaptive filter. After the filter stabilizes, the error signal is still large, which results in a large step size obtained according to formula (17), which is not conducive to extracting the broken bar fault characteristics. For this reason, it is necessary to improve the variable step size algorithm VSSA according to the harmonic characteristics of the frequency converter. The complexity of the stator current signal harmonics is the main reason for the increase of |ε(n)|, and the parameter α needs to be adjusted according to the complexity of the harmonics. Since the harmonic distortion rate is an important indicator reflecting the degree of signal harmonics, a VSSA variable step size algorithm based on the harmonic distortion rate is proposed on the basis of the VSSA variable step size algorithm shown in formula (17). The present invention is called the improved variable step size algorithm NVSSA (novel VSSA, NVSSA). The details are as follows:

[0115]

[0116] Among them, THD is the distortion rate.

[0117] The specific method of filtering the signal to be analyzed based on the NFLMS adaptive filter is:

[0118] S3.1: Randomly initialize the weights to values ​​in the range of [-1; -1] to [1; 1]; sample the signal to be analyzed and the reference signal separately.

[0119] The signal to be analyzed is d0(t), the reference signal is x0(t), and the reference signal x0(t) is subjected to φ p =60°~80° phase shift, in this embodiment, φ p =70° as an example, synchronous sampling is performed on the signal to be analyzed d0(t), the reference signal x0(t), and the phase-shifted signal of the reference signal x0(t) to obtain the sampling value d(n) of the signal to be analyzed, the sampling value x1(n) of the reference signal, and the sampling value x2(n) after phase shift.

[0120] S3.2: Calculate the error ε(n) based on each sample value of the signal to be analyzed.

[0121] ε(n)=d(n)-y(n)=d(n)-w1(n)x1(n)-w2(n)x2(n)

[0122] Among them, w1(n) and w2(n) are the weights of the nth sampling period, and x1(n) and x2(n) are the sampling values ​​of the nth sampling period.

[0123] S3.3: Calculate the variable step size μ based on the improved variable step size algorithm NVSSA according to the error ε(n) THD (n).

[0124] S3.31: Calculate the distortion rate THD: Perform Fourier transform on the signal to be analyzed x0(t) to obtain the frequency domain amplitude spectrum, extract the fundamental amplitude A1, and the amplitudes of each harmonic A2, A3, ..., A m Calculate the distortion rate THD:

[0125]

[0126] S3.32: Calculate the harmonic complexity adjustment parameter α(THD) based on the distortion rate, and calculate the variable step size μ based on the harmonic complexity adjustment parameter α(THD) and the error ε(n) using the variable step size calculation formula THD (n).

[0127] S3.4: Combined with NVSSA algorithm, the step size is changed to μ THD (n), and update the weight using the NFLMS algorithm’s weight update iteration formula:

[0128]

[0129] Among them, i (n) = d(n) - w i (n)x i (n)-w j (n-1)x j (n), w j (n), w i (n) is the weight of the nth sampling period, x j (n), x i (n) is the sampling value of the reference signal in the nth sampling period, when i=1, j=2; when i=2, j=1; α is the order of the fractional order; Γ(·) represents the Gamma function.

[0130] S3.4: Repeat steps S3.2 to S3.4 until the weights converge or all sampling points are processed.

[0131] S4: Perform FFT analysis on the filtered signal to obtain the fault characteristic component (whose frequency is f c ) and the amplitude spectrum density value of the fundamental wave residual (whose frequency is the fundamental wave frequency f0), and the amplitude spectrum density value of the maximum harmonic component (whose frequency is f r ) is used as a reference to calculate the characteristic component amplitude spectrum density ratio R c and the fundamental residual amplitude spectral density ratio R f The details are as follows:

[0132] Fault characteristic component amplitude spectral density ratio:

[0133] Among them, V ris the amplitude spectrum density of the maximum harmonic component, V c is the amplitude spectral density of the fault characteristic component.

[0134] Fundamental wave residual amplitude spectral density ratio:

[0135] Among them, V f is the amplitude spectral density of the fundamental wave residual.

[0136] S5: Based on the characteristic component amplitude spectral density ratio R c and the fundamental residual amplitude spectral density ratio R f Determine whether the motor has a broken bar fault.

[0137] If R c ≥0.3 and R c ≥R f , then there is a broken bar fault in the motor, otherwise the motor is normal.

[0138] Experimental process analysis:

[0139] Broken bar fault feature extraction and diagnosis based on FLMS adaptive filter: Broken bar fault diagnosis method based on stator current analysis is the most common method. The basic principle of this method is as follows: the motor is directly powered by industrial frequency power supply. When the motor is normal, its stator current only contains f0 = 50Hz frequency component; when the motor has a broken bar fault, the stator current also contains a fault characteristic component with a frequency of (1±2s)f0, where the slip rate s = (n0-n) / n0, n0 is the synchronous speed, and n is the motor speed. Under normal circumstances, the f in the stator current is used as the reference frequency. c =(1-2s)f0 frequency component is used as the broken bar fault feature to determine whether there is a broken bar fault.

[0140] However, when the motor is running at rated speed, the speed n is close to n0 and the slip rate s is very small. At this time, the fault characteristic frequency f c It is very close to the fundamental frequency f0, and the fault characteristic frequency component (frequency f c ) is about 0.02 to 0.05 times the fundamental frequency component (frequency f0). Therefore, although the stator current frequency component is simple, if the spectrum analysis is performed directly, the fault characteristic frequency component (frequency f c) will be overwhelmed by the fundamental frequency component (frequency f0), making it impossible to obtain the fault characteristic frequency component. Currently, variable frequency speed regulation of electric motors is becoming increasingly popular. In this case, the motor is powered and controlled by a frequency converter. Affected by the frequency converter, the harmonic components of the motor stator current are complex, including not only the frequency converter output frequency and its integer harmonics, but also interharmonics and noise interference. If a broken bar fault occurs, the fault characteristic component is easily obliterated by the complex harmonic components, making fault feature extraction very difficult. This places higher demands on the fault feature extraction method. In order to accurately extract the fault characteristic frequency component of the stator current, the FLMS adaptive filter is first used to process the stator current, filtering out the fundamental frequency component as much as possible. Spectral analysis is then used to determine whether the stator current contains the fault characteristic frequency component, and finally, the broken bar fault diagnosis is performed.

[0141] Evaluation criteria: Since the frequency of the broken bar fault characteristic component is f c =(1-2s)f0. In the case of variable frequency speed regulation, the fundamental frequency f0 is no longer the power frequency, but the given frequency of the inverter. Therefore, the frequency f of the fault characteristic component is c In the experimental system of the present invention, the number of pole pairs of the cage asynchronous motor is p=2, and the rated speed is n1=1430r·min. -1 , the power frequency is 50Hz, the motor is controlled by a frequency converter, and a typical working state is selected for testing. The sampling frequency of the stator current signal is f s =1000Hz, and the number of sampling points is N = 4096. To facilitate comparative analysis, the stator current signal is normalized. Below, we take the stator current signal with a given frequency of 40Hz as an example, assuming that i0 and i1 represent the original current signal and the signal after adaptive filtering, respectively. The analysis results of i0 are shown in Table 1, where n is the motor speed, V r The maximum harmonic component (frequency is f) after fast Fourier transform of the original current signal i0 r )’s amplitude spectral density value.

[0142] Table 1 Fault characteristic frequency and frequency of maximum harmonic component at given frequency 40 Hz

[0143]

[0144] Since adaptive filtering aims to remove the fundamental component from the signal and further reveal the characteristic component of a broken bar fault, while other frequency components are largely unaffected by filtering, the fault characteristic component and the residual fundamental component are crucial for fault diagnosis. To quantitatively compare the effectiveness of adaptive filtering, the largest harmonic component in the original current signal i0, excluding the fundamental, is used as the reference component for analysis.

[0145] The evaluation criteria include the characteristic component amplitude spectral density ratio R c , fundamental wave residual amplitude spectrum density ratio R f and the total error E of adaptive filtering s , where R c Indicates the component f after FFT of signal i1 c With the reference component f r The ratio of the amplitude spectral density values ​​of f Indicates the fundamental wave residual after FFT of signal i1 and the reference component f r The ratio of the amplitude spectral density values ​​of s Represents the total error of adaptive filtering ∑|ε(n)|. R c It can be shown that the characteristic component f c The extraction effect directly affects the judgment of broken bar fault; R f It can reflect the effect of filtering out the fundamental wave; E s It can reflect the transition process and final error of the adaptive filter.

[0146] Harmonic distribution and mathematical description of stator current signal: FFT analysis is performed on the actual stator current signal with a given frequency of 40Hz, and the amplitude spectrum is obtained as follows: Figure 4 As shown in the figure, the amplitude spectrum is normalized based on the fundamental wave. In order to clearly observe the harmonic situation, the maximum value in the figure is 0.2. The actual stator current signal selected here was collected when a broken stator fault occurred. It can be seen that the signal contains relatively complex harmonic components. The broken stator fault characteristic component is submerged by the fundamental wave leakage. The reference component frequency f r is 60Hz.

[0147] The stator current signal can be described as:

[0148]

[0149] Where f0, A0, φ0 are the frequency, amplitude and initial phase of the fundamental component respectively; f i 、A i 、φ i are the frequency, amplitude and initial phase of the harmonic components (i=1~m, m is a positive integer); η(k) is the noise.

[0150] Since the characteristic component of the broken bar fault is close to the fundamental component, the harmonics with smaller amplitudes can be ignored in the simulation analysis. Without considering the initial phase influence of the harmonic components, according to the main harmonic distribution of the actual measured signal, the four harmonic components with larger amplitudes are selected to construct the signal as follows:

[0151] d(k)=0.03cos(2πkf c )+A0·cos(2πkf0+φ0)

[0152]

[0153] Where, the amplitude of each harmonic at a given frequency of 40 Hz is shown in Table 2.

[0154] Table 2 Main frequency components when the given frequency is 40Hz

[0155]

[0156] The influence of initial value on the broken bar fault feature extraction based on FLMS adaptive filter: The influence of initial weight w0 and initial phase φ0 on FLMS adaptive filter is discussed below. The initial weight w0 ranges from [-1; -1] to [1; 1] with an interval of 0.1; the initial phase φ0 ranges from -180° to 180° with an interval of 1°. p = 90°, the initial weight w0 ranges from [-1; -1] to [1; 1], with an interval of 0.1, for a total of 400 points; the initial phase φ0 ranges from -180° to 180°, with an interval of 1°, for a total of 360 points. The number of points here is the total number of points in the traversal analysis, 400*360=144000. The characteristic component amplitude spectral density ratio R is obtained c , fundamental wave residual amplitude spectrum density ratio R f and the total error E of adaptive filtering s The changes in Figure 5 As shown. In the Matlab simulation program, a for loop is used, the outer loop is the initial phase φ0, and the inner loop is the initial weight w0. Therefore, it can be seen from the figure that the fundamental wave residual amplitude spectrum density is greater than R f and the total error E of adaptive filtering s The value has a more obvious trend of changing with the initial phase. The initial weight w0 and initial phase φ0 have a great influence on the filtering result of the FLMS adaptive filter. Under some values ​​of the initial weight w0 and initial phase φ0, the fundamental wave residual amplitude spectral density ratio R f and the total error E of adaptive filtering s Both change with the initial weight and phase, but the fundamental residual amplitude spectral density is greater than R f Greater than 0.5 and the total error E of adaptive filtering s A value greater than 400 is obviously abnormal. f and the total error E of adaptive filtering s The value is far beyond the normal value. At this time, the FLMS adaptive filter is not converged, which shows that the FLMS adaptive filter is less robust to the initial weight w0 and initial phase φ0.

[0157] The previous section shows that the FLMS adaptive filter is less robust to initial phase φ0 and initial weight w0. The following discusses the impact of initial phase φ0 and initial weight w0 on the NFLMS adaptive filter.

[0158] Effect of initial phase on NFLMS adaptive filter: In the following analysis, the initial weight is w0 = [-0.9; -0.3], and the phase shift adopts the traditional value φ p =90°. Observe the effect of the initial phase φ0 on the NFLMS adaptive filter. The initial phase φ0 ranges from -180° to 180° with an interval of 1°, and we get R c 、R f and E s Changes such as Figure 6 As shown. It can be seen that R c 、R f and E s The change with the initial phase φ0 is very significant. This indicates that the NFLMS adaptive filter is not robust to the initial phase. Good initial phase values ​​are in the range of φ0 = -150° to -140°, -50° to -10°, and 140° to 150°. These values ​​are difficult to measure in the presence of harmonics and noise.

[0159] During actual signal acquisition, the initial phase φ0 of the acquired signal may be random. This patent analyzes the fundamental component, which has a large amplitude and whose phase essentially determines the initial phase of the acquired signal. While it is difficult to accurately determine the initial phase of the acquired signal due to the effects of harmonic components and noise, it is possible to approximate the specific points where φ0 = -180°, -90°, 0°, 90°, and 180°. However, the analysis results of the NFLMS adaptive filter corresponding to these specific points are unsatisfactory.

[0160] The initial phase φ0 = 0 corresponds to the peak value of the signal d(n), which is relatively easy to obtain. The following study is whether it is possible to adjust the phase shift φ when the initial phase φ0 = 0. p Get satisfactory results.

[0161] Phase shift φ p Impact on NFLMS adaptive filter: In the following analysis, the initial weight is w0 = [-0.9; -0.3], the initial phase is φ0 = 0°, and the phase shift φ is studied. p Impact on NFLMS adaptive filter. Phase shift φ p From -180° to 180°, the interval is 1°. Get R c 、R f and E s Changes such as Figure 7 As shown. It can be seen that R c、R f and E s With phase shift φ p The change is very obvious. s The pulse point indicates that the filter effect is not good and may not converge.

[0162] Common research is mostly based on the initial phase φ0=0° and the phase shift φ p =90°, the filtering effect is acceptable. c Yamato R f While small, φ p =-120°~-100°, 60°~80°, R c The value is larger. It is also more conducive to the extraction of fault features, and the NFLMS adaptive filter has a better filtering effect. Therefore, the traditional value φ can be p =90° is modified to 60°~80°. In this embodiment, the traditional value φ p =90° is changed to φ p =60° Figure 8 (a),φ p =70° Figure 8 (b), φ p =80° Figure 8 (c) Three cases Then select the signal starting from φ0=0° for analysis, and you can get satisfactory results.

[0163] The robustness of NFLMS adaptive filter to initial weights: In the following analysis, φ0 = 0°, φ p =60°, 70°, 80°, observe the effect of the initial weight w0 on the FLMS adaptive filter. w0 ranges from [-1; -1] to [1; 1] with an interval of 0.1, and obtains R c 、R f and E s Changes such as Figure 8 As shown. It can be seen that in the three cases, E s Basically does not change with w0, R c and R f The change with w0 is not obvious, and does not affect the broken bar fault feature extraction and diagnosis. This shows that the adaptive filter based on the NFLMS algorithm has good robustness to the initial weight w0.

[0164] The present invention has been introduced in the previous simulation experiment. Now we will conduct an actual measurement analysis of a motor with a broken stator fault. The given frequency is still 40Hz. To facilitate the comparison and analysis, the actual collected stator current signal and FFT analysis results are normalized. Take w0 = [-0.9; -0.3], φ p=70°, the FFT analysis results of the signal after NFLMS adaptive filter filtering are as follows Figure 9 As shown, at this time, the frequency of the reference component is 60Hz and its amplitude is 0.851. Based on this, we get R c =1.175, R f =0.482. The fault characteristics are obvious. According to the fault diagnosis method, it can be known that there is a broken bar fault. In addition, E s =245.152, which is close to the simulation experiment results.

[0165] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for diagnosing broken bar faults in squirrel-cage motors for complex scenarios, characterized by: The steps are: S1: Real-time acquisition of the given frequency f0 of the inverter, the speed of the cage asynchronous motor and the stator current signal; S2: Calculate the fault characteristic frequency f based on the given frequency f0 and the speed of the cage asynchronous motor c , based on the stator current signal, obtain the frequency f of the maximum harmonic component of the signal to be analyzed and the stator current signal r ; S3: Filter the signal to be analyzed based on the NFLMS adaptive filter to obtain a filtered signal; S4: Perform FFT analysis on the filtered signal based on the fault characteristic frequency f c The amplitude spectrum density value of the fault characteristic component and the amplitude spectrum density value of the fundamental wave residual are obtained by taking the frequency f0 as the given frequency, and the r The amplitude spectrum density value of the maximum harmonic component is used as a reference to calculate the amplitude spectrum density ratio R of the fault characteristic component. c and the fundamental residual amplitude spectral density ratio R f ; S5: Based on the characteristic component amplitude spectral density ratio R c and the fundamental residual amplitude spectral density ratio R f Determine whether the motor has a broken bar fault.

2. The method for diagnosing broken bar faults of squirrel-cage motors for complex scenarios according to claim 1, characterized in that: The method of obtaining the signal to be analyzed and the frequency f of the maximum harmonic component of the stator current signal based on the stator current signal is as follows: r The method is: S2.1: Determine the signal to be analyzed by performing peak value judgment on the stator current signal; S2.2: Obtain the frequency f of the maximum harmonic component by performing FFT analysis on the signal to be analyzed r and its amplitude spectral density values.

3. The method for diagnosing broken bar faults of squirrel-cage motors for complex scenarios according to claim 2, characterized in that: The method for filtering the signal to be analyzed based on the NFLMS adaptive filter is: S3.1: Randomly initialize weights; The signal to be analyzed and the reference signal are sampled separately; S3.2: Calculate the error ε(n) based on each sample value of the signal to be analyzed; S3.3: Calculate the variable step size μ based on the improved variable step size algorithm NVSSA according to the error ε(n) THD (n); S3.4: Combined with variable step size μ THD (n) Update weights using the weight update iterative formula of the NFLMS algorithm; S3.5: Repeat steps S3.2 to S3.4 until the weights converge or all sampling points are processed to obtain the filtered signal.

4. The method for diagnosing broken bar faults of squirrel-cage motors for complex scenarios according to claim 3 is characterized in that: The method for calculating the error ε(n) according to each sample value of the signal to be analyzed is: ε(n)=d(n)-y(n)=d(n)-w1(n)x1(n)-w2(n)x2(n) Where d(n) is the sample value of the signal to be analyzed in the nth sampling period, y(n) is the output of the nth sampling period, w1(n) and w2(n) are the weights of the nth sampling period, and x1(n) and x2(n) are the sample values ​​of the reference signal in the nth sampling period.

5. The method for diagnosing broken bar faults of squirrel-cage motors for complex scenarios according to claim 4, characterized in that: The variable step size μ is calculated based on the improved variable step size algorithm NVSSA according to the error ε(n) THD (n) The method is: S3.31: Perform Fourier transform on the signal to be analyzed x0(t) to obtain the frequency domain amplitude spectrum, extract the fundamental amplitude A1, and the amplitudes of each harmonic A2, A3, ..., A m , calculate the distortion rate: S3.32: Calculate variable step size μ based on distortion rate THD (n).

6. The method for diagnosing broken bar faults of squirrel-cage motors for complex scenarios according to claim 5, characterized in that: The variable step size μ is calculated based on the distortion rate THD The method of (n) is: calculate the harmonic complexity adjustment parameter α(THD) according to the distortion rate: The variable step size μ is calculated based on the harmonic complexity adjustment parameter α(THD) and the error ε(n) using the variable step size calculation formula THD (n): Among them, β0 and m0 are both positive numbers to be determined.

7. The method for diagnosing broken bar faults of a squirrel-cage motor for complex scenarios according to any one of claims 3 to 6, characterized in that: The weight update iteration formula of the NFLMS algorithm is: Among them, i (n) = d(n) - w i (n)x i (n)-w j (n-1)x j (n), w j (n), w i (n) is the weight of the nth sampling period, x j (n), x i (n) is the sampling value of the reference signal in the nth sampling period, d(n) is the sampling value of the signal to be analyzed in the nth sampling period, when i = 1, j = 2; when i = 2, j = 1; α is the order of the fractional order; Γ(·) represents the Gamma function.

8. The method for diagnosing broken bar faults of a squirrel-cage motor for complex scenarios according to any one of claims 1 to 3, characterized in that: The calculated characteristic component amplitude spectral density ratio R c and the fundamental residual amplitude spectral density ratio R f The method is: Calculate the amplitude spectral density ratio of the fault characteristic component: Among them, V r is the amplitude spectrum density of the maximum harmonic component, V c is the amplitude spectrum density of the fault characteristic component; Calculate the fundamental residual amplitude spectral density ratio: Among them, V f is the amplitude spectral density of the fundamental wave residual.

9. The method for diagnosing broken bar faults of a squirrel-cage motor for complex scenarios according to any one of claims 3 to 5, characterized in that: When sampling the reference signal described in step S3.1, the phase shift φ p The value range is 60°~80°.

10. The method for diagnosing broken bar faults of squirrel-cage motors for complex scenarios according to claim 2 or 3, characterized in that: The method for determining the signal to be analyzed in step S2.1 is: taking the maximum value point of the first fundamental wave cycle as the starting point of the signal to be analyzed, and taking data with a length of N0 as the signal to be analyzed.

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