A Motor Fault Diagnosis Method Based on Frequency Map and EFA-BP Deep Learning

Abstract

The present invention discloses a motor fault diagnosis method based on frequency maps and EFA-BP deep learning, including: classifying four types of motor faults (bearing misalignment, stator coil inter-turn short circuit, rotor bar breakage, and outer bearing damage) by detecting the motor current signal; using frequency transformation to convert it from the time domain to the frequency domain and completing data preprocessing; converting the preprocessed signal from the frequency spectrum to a frequency map, thereby completing the extraction of the characteristics of the motor fault; proposing a hybrid model based on electromagnetics and the firefly algorithm to effectively solve complex problems such as motor fault processing and enhance the prediction ability of the artificial neural network for motor faults; constructing an EFA-BP classification algorithm to complete the classification of the conditions and fault types of healthy and faulty motors for testing. Based on the automatic memory of EFA and optimizing the parameters to the minimum prediction error, the classification model can significantly reduce the calculation time, improve the prediction accuracy, and perform well in motor fault diagnosis.

Description

Technical Field

[0001] The present invention relates to the technical field of motor fault diagnosis, and particularly relates to a motor fault diagnosis method based on a frequency diagram and EFA-BP deep learning. Background Technique

[0002] Motors in industrial production are very common devices. During the production process, once a motor fails, it will not only affect the motor itself, but also hinder the production and manufacturing process of products. Therefore, the fault prediction and health management of motors are of great significance to industrial development. Generally, motor fault diagnosis is divided into two stages. One is the analysis and feature extraction of fault signals, and the other is fault classification. Among them, in the stage of analysis and feature extraction of motor fault signals, traditional methods include feature extraction methods based on time-domain analysis and frequency-domain analysis. The method based on time-domain analysis is to extract time-domain parameters, and the motor is diagnosed for faults according to the sensitivity of the time-domain parameters to abnormal motor fault signals. Its feature performance is generally not very clear and the representativeness is insufficient. For a relatively complex system, the operation is cumbersome and not intuitive enough to see the relationship between the information contained and the faults. Compared with the time-domain analysis method, the method based on frequency-domain analysis can find the corresponding characteristic frequency components from the fault signals and analyze them, and can extract deeper fault characteristics. However, since the frequency spectra caused by motor faults are generally relatively complex, it is difficult to identify the types of specific motor faults from these frequency spectra.

[0003] In the fault classification stage, the goal is to classify data features according to different fault types, which is also the difficulty of fault diagnosis. At present, since machine learning algorithms have the ability to dig out hidden rules from data and can handle complex prediction or classification problems, they are often used as classification models for motor faults. Among them, the commonly used ones are: decision tree, support vector machine, neural network and other methods. Among these methods, the application scope of the decision tree is limited, and the determination of the occurrence probability of various solutions is sometimes subjective, which may lead to decision-making errors; the main disadvantage of the support vector machine is that it is relatively difficult to implement for large-scale training samples, and there are difficulties in solving multi-classification problems. Relatively speaking, the unique non-linear adaptive information processing ability of artificial neural networks can overcome the defects of traditional artificial intelligence methods in unstructured information processing. However, the main problem of neural networks is that when the data is insufficient, the neural networks cannot work, and its theory and learning algorithms need to be further improved and enhanced. If the artificial neural network can be combined with other traditional methods, it will help to promote the continuous development of artificial intelligence and fault processing technology. Summary of the Invention

[0004] Objective of the Invention: Aiming at the problems pointed out in the background technology, the present invention provides a motor fault diagnosis method based on frequency maps and EFA-BP deep learning. By using the method of frequency maps and EFA-BP deep learning, the diagnosis process of motor faults can be successfully completed only by using the stator current signal of the motor.

[0005] Technical Solution: The present invention discloses a motor fault diagnosis method based on frequency maps and EFA-BP deep learning, which includes the following steps:

[0006] Step (1): Under the stable no-load operation of the motor, simulate four motor faults, namely bearing misalignment, inter-turn short circuit of the stator winding, rotor bar breakage, and outer ring bearing damage, collect the stator current signal under the motor fault state, and obtain the time series data under five kinds of coupled load changes, that is, the time series motor fault state current signal;

[0007] Step (2): Use frequency transformation to convert the time series motor fault state current signal from the time domain to the frequency domain, and complete data preprocessing; convert the preprocessed signal from the frequency spectrum to a frequency map (PLT), and perform necessary normalization calculations, divide the data into test and training data, record and store the data, and establish a fault database, so as to complete the feature extraction of motor faults;

[0008] Step (3): Propose a hybrid model (EFA) based on the field approach (FA) and the firefly algorithm (EA). Assume that all fireflies are magnetized, and the charge of the firefly depends on its objective value. Moreover, all fireflies can participate in the search and processing, so as to ensure that in the exploration stage, the fireflies of EFA can quickly find the target area, and in the exploitation stage, the fireflies of EFA can perform effective local search in these areas and find the best solution;

[0009] Step (4): Construct an EFA-BP classification algorithm, and use EFA to train the weight and offset parameters of the BP neural network, so as to complete the classification of the conditions and fault types of healthy and faulty motors for testing.

[0010] Further, in the step (1), the five kinds of coupled load changes are 0, 25%, 50%, 75% and 100% respectively. Use a clamp-on current transformer to measure the stator current flowing through the motor, obtain the state data of four motor faults, namely bearing misalignment, inter-turn short circuit of the stator winding, rotor bar breakage, and outer ring bearing damage, that is, the time series motor fault state current signal, and store the fault state signal.

[0011] Further, in the step (2), the specific process of using frequency transformation to convert the time series motor fault state current signal from the time domain to the frequency domain and complete data preprocessing is as follows:

[0012] Step (2)a: Use the discrete Fourier transform (DFT) to convert the previously generated time series motor current signal into a spectrum, which is specifically defined as follows:

[0013]

[0014] W N = e 2πi / N

[0015] where A(n) is the complex expression of the discrete Fourier transform; W N is the Nth root in the complex Fourier series; X(j) is the given sampling signal, j = 0, 1,..., N - 1, and N is the number of sampling points;

[0016] Step (2)b: Preprocessing, perform three data preprocessing schemes on the above spectrum data:

[0017] First, assume that all motor faults do not exceed 500Hz. Using the data clipping preprocessing technique, truncate the motor state data within the range of 0 - 500Hz;

[0018] Second, clip the data again and change the amplitude of the unimportant signal frequencies to zero to avoid noise;

[0019] Third, make the signal amplitudes of the working frequency and its sideband frequencies much larger than those of other modal frequencies.

[0020] Furthermore, in step (2), convert the preprocessed signal from the spectrum to a frequency map, specifically as follows:

[0021] Step (2)c: Define the metric space M and let B(j) ∈ M, that is, the point on the jth column of the previously defined spectrum B. Then the frequency map is defined as the difference between the signals on the jth column and the ith row, and then divided by the resolution. The definition formula is as follows:

[0022] PLT(j,i) = (B(j) - B(i) T ) / λ

[0023] where λ is the mapping resolution, used to measure the error between the signals B(j) and B(i) on the jth column and the ith row. Thus, the matrix PLT(j,i) is converted into a color map, and after normalizing its data, it is mapped to the RGB map.

[0024] Furthermore, in step (3), the hybrid model EFA based on electromagnetics and the firefly algorithm is as follows:

[0025] Step (3)a: Initialization

[0026] First, set the initial population of fireflies to be uniformly distributed within the upper and lower boundaries, which is specifically defined as follows:

[0027] x o =bl k +β(bu k -bl k )

[0028] Among them, k ,bl k are the upper and lower boundaries of the kth coordinate respectively; β is a random number in [0,1];

[0029] Step (3) b: Local search. The local search process is completed by the following formula:

[0030]

[0031] Among them, ε is a random number vector, α t is the trade-off coefficient of the tth iteration, L(s) is the distribution function;

[0032] Step (3)c: Firefly flight movement

[0033] First, EFA's Firefly Inspired Attraction F g and the repulsive force F r , the i-th firefly is only affected by the F from the next better and worse fireflies g and F r Then, all fireflies are ranked according to their objective function values; all fireflies in the population move based on the EA method. In this way, the interference from many fireflies can be alleviated and the optimal solution can be found quickly. The flight movement process of magnetic fireflies is as follows:

[0034]

[0035] Among them, F g and F r are attractive and repulsive forces, defined by:

[0036]

[0037]

[0038] q i is the charge at the ith point, which is defined as follows:

[0039]

[0040] f(x) is the objective function.

[0041] Furthermore, β in step (3)a is determined by Logistic mapping, and its mapping expression is as follows:

[0042] β n+1 = μ1β n (1 - β n ), β n ∈(0, 1)

[0043] In the formula, the control parameter μ1 ∈ (0, 4]. When 3.75 < μ1 ≤ 4, chaotic phenomenon occurs, and the generated solution β n+1 ∈(0, 1). The closer the control parameter μ1 is to 4, the closer the value range of the solution is to being evenly distributed throughout the [0, 1] region.

[0044] Furthermore, the ε parameter, α t and L(s) in step (3)b are determined as follows:

[0045] 1) The Tent mapping in the chaotic mapping equation is used to determine the ε parameter, and its mapping expression is as follows:

[0046]

[0047] In the formula, when the control parameter μ2 ∈ (0, 1), the solution x n+1 ∈(0, 1) will be generated. When μ2 = 0.5, a uniform distribution sequence will be generated, and the chaotic system will be in a short - period state at this time. When the initial value x = μ2, the system will become a periodic system;

[0048] 2) α t is the trade - off coefficient of the t - th iteration, and its calculation expression is as follows:

[0049] α t = α0γ t

[0050] where α0 is the initial trade - off coefficient; α t is the trade - off coefficient at the t - th iteration; γ is the adaptive parameter 0 < γ < 1;

[0051] 3) L(s) is a distribution function, and its definition is as follows:

[0052]

[0053] where s is the power - law distribution, τ is the exponent, and the calculations of u and v follow the normal distribution, specifically as follows:

[0054]

[0055]

[0056] σ v = 1

[0057]

[0058] Γ(z) is the gamma function, which is determined by the following formula:

[0059]

[0060] Furthermore, in step (4), an EFA-BP classification algorithm is constructed, and the weights and offset parameters of the BP neural network are trained using EFA. Specifically:

[0061] Step (4)a: Determine the basic structure of the BP neural network, build the structure of the neural network, and initialize its relevant parameters;

[0062] Step (4)b: Use the firefly initialization of the weights and offset parameters in the BP algorithm by the hybrid model EFA based on electromagnetism and firefly algorithm. For each specific firefly individual, set its fluorescence intensity and perception radius;

[0063] Step (4)c: Calculate the output values of the input layer nodes, hidden layer nodes, and output layer nodes of the BP network, calculate the fitness for each firefly individual, and effectively store the maximum value among them;

[0064] Step (4)d: Based on the fluorescence intensity, continuously update each firefly individual, search for unknown neighborhoods within the perception range of the individual, perform flight movement updates, and train its weights and offset parameters using EFA;

[0065] Step (4)e: After the position update, according to the fitness value calculated by the firefly individual, judge whether it reaches the termination condition of the training target. If it is satisfied, execute the next step; otherwise, return to the previous step;

[0066] The fitness value judgment error formula is as follows:

[0067]

[0068] where D j is the target output, and Y j is the actual output;

[0069] Step (4)f: Convert the received position information into the corresponding weights and thresholds of the neural network;

[0070] Step (4)g: Judge whether the termination condition is satisfied, that is, whether the set error target is reached. If it is reached, output the result and end the algorithm; otherwise, return to (d) and continue training until the termination condition is met.

[0071] Furthermore, the specific process of step (4)c is as follows:

[0072] (1) Input the motor fault data into the BP neural network, and calculate the output Y of the i-th neuron in the input layer through forward calculation i It is:

[0073] Y i = f(x i )

[0074] where x i is the motor fault data;

[0075] (2) Calculate the output of the hidden layer:

[0076] The output of the h-th neuron is:

[0077]

[0078] Y h = f(I h )

[0079] where w hi , θ i are the weights and thresholds of the hidden layer neurons;

[0080] (3) Calculate the output values of all neurons in the output layer:

[0081] The output formula of the j-th output neuron is as follows:

[0082]

[0083] Y j = f(I j )

[0084] where w jh , θ j are the weights and thresholds of the output layer neurons.

[0085] Beneficial effects:

[0086] The present invention uses a frequency map and an EFA-BP deep learning method to successfully complete the process of motor fault diagnosis only using the motor stator current signal, and correctly predicts five motor states, including four fault types, bearing shaft deviation, stator coil inter-turn short circuit fault, rotor bar breakage, outer bearing ring damage, and a healthy motor. Among them, in the extraction of motor fault features, a frequency map-based extraction method is proposed: on the one hand, frequency transformation technology is used to convert the sampled current signal from the time domain to the frequency domain and complete data preprocessing; on the other hand, a frequency map (PLT) generation method is proposed to convert the preprocessed signal from the frequency spectrum to a frequency map (PLT), and necessary normalization calculations are performed. The data is divided into test and training data, the data is recorded and stored, and a fault database is established, thus completing the extraction of the features of the motor fault. In terms of the fault classification model, a deep learning model based on EFA-BP is proposed: on the one hand, a hybrid model (EFA) based on electromagnetics (FA) and the firefly algorithm (EA) is proposed. It is assumed that all fireflies are magnetized, and the charge of a firefly depends on its target value. Moreover, all fireflies can participate in the search and processing, so as to ensure that in the exploration stage, the fireflies of EFA can quickly find the target area, and in the development stage, the fireflies of EFA can perform effective local searches in these areas and find the best solution; on the other hand, an EFA-BP classification algorithm is constructed, and EFA is used to train the weight and offset parameters of the BP neural network, thus completing the classification of the conditions and fault types of the healthy and faulty motors for testing.

[0087] Experiments show that the method proposed by the present invention can still obtain satisfactory fault prediction results without using the motor load change as the input data label. The overall prediction accuracy is 90.82%, and the recall rate is 91.42%. Among them, based on the frequency map and EFA-BP, it is easy to predict the bearing shaft deviation fault and the healthy motor condition, and can also better predict the stator coil inter-turn short circuit fault, rotor bar breakage, and outer bearing ring damage fault. On the other hand, since only the motor stator current signal is used to complete the diagnosis of the motor fault, this method can reduce the hardware resources used, lower the sampling frequency and sample size, is suitable for the hardware implementation of embedded systems, and has better application prospects. Brief Description of the Drawings

[0088] Figure 1 It is a schematic diagram of the motor fault signal acquisition system;

[0089] Figure 2 It is the shape and size parameters of the motor;

[0090] Figure 3 It is the three-period time series sample of the stator current (five motor conditions, three loads of 0, 50%, and 100%);

[0091] Figure 4 is the frequency spectrum of a healthy motor;

[0092] Figure 5 is the frequency spectrum of a healthy motor after data processing;

[0093] Figure 6 are the spectrograms under five faulty motor states;

[0094] Figure 7 is the frequency graph PLT (operating frequency: 500 Hz);

[0095] Figure 8 is the EFA search process flow;

[0096] Figure 9 is the motor fault classification process based on the frequency graph;

[0097] Figure 10 is the weight and bias training process of the EFA-optimized BP neural network;

[0098] Figure 11 is the comparison of the effects between EFA-BP and the BP classifier;

[0099] Figure 12 is the comparison of the training error effects between EFA-BP and the BP classifier. Detailed implementation manner

[0100] To better explain the present invention for easy understanding, the technical solution of the present invention will be described in detail below. The following embodiments are explanations of the present invention, and the present invention is not limited to the following embodiments.

[0101] Aiming at the motor fault problem commonly existing in manufacturing production equipment, the present invention proposes a motor fault diagnosis method based on frequency graph and EFA-BP deep learning. First, the stator current signal under the motor fault state is collected to obtain the time series data from five load changes, completing the collection of the motor fault signal; then, the motor fault features are extracted by using the frequency graph-based method. The specific implementation steps are as follows: on the one hand, the frequency transformation is used to convert it from the time domain to the frequency domain and complete the data preprocessing; on the other hand, the frequency graph (PLT) generation method is used to convert the preprocessed signal from the frequency spectrum to the frequency graph (PLT), and the necessary normalization calculation is performed. The data is divided into test and training data, the data is recorded and stored, and a fault database is established, thus completing the extraction of the motor fault features;

[0102] The present invention also proposes a hybrid model (EFA) based on electromagnetics (FA) and the firefly algorithm (EA), and constructs an EFA-BP classification algorithm. The weights and offset parameters of the BP neural network are trained using EFA, so as to complete the classification of the conditions and fault types of healthy and faulty motors for testing, and finally establish a mapping relationship between features and motor faults. The present invention processes four fault states of the motor, namely bearing misalignment, inter-turn short circuit of the stator coil, rotor bar breakage, and outer bearing damage, and can realize autonomous fault diagnosis of the motor.

[0103] Figure 1 The motor fault signal acquisition system in the embodiment of the present invention is shown as follows:

[0104] The motor fault signal acquisition system consists of a motor, a clamp-on current transformer, an oscilloscope, a multi-channel data acquisition instrument, and a computer. The experiment is carried out under the stable no-load operation of the motor, mainly collecting the stator current signals of the motor in the normal state and the fault state. Finally, the collected signals are sent to the computer for fault diagnosis processing.

[0105] Combined with Figure 1 , a motor fault diagnosis method based on frequency diagram and EFA-BP deep learning includes the following steps:

[0106] Step 1: Under the stable no-load operation of the motor, collect the stator current signals of the motor in the normal state and the fault state;

[0107] (1) Test object

[0108] In the embodiment of the present invention, a DC motor with model 775 is used as the test motor. Under five coupling load change conditions (0, 25%, 50%, 75%, and 100%), the stator current flowing through the motor is measured with a clamp-on current transformer, and the range of the clamp-on current transformer is adjusted to 10A. The current signals of the healthy motor and the faulty motor are collected once every three seconds, and a total of 150 data are collected. Four kinds of motor faults are artificially simulated, namely bearing misalignment, inter-turn short circuit of the stator winding, rotor bar breakage, and outer ring bearing damage.

[0109] The external shape and dimension parameters of the motor are shown in Figure 2 , and the motor specifications and parameters are shown in Table 1.

[0110] Table 1 775 motor parameters

[0111]

[0112] (2) Motor fault conditions

[0113] In specific implementation, four aspects of faults of the test motor are respectively investigated, namely bearing misalignment, inter-turn short circuit fault, rotor bar breakage, and outer ring bearing fault.

[0114] 1) Bearing misalignment

[0115] When the motor is eccentrically coupled to its load, bearing misalignment faults will occur. Installation, replacement or damage of the motor base can all lead to bearing shaft misalignment faults.

[0116] 2) Stator inter-turn short circuit

[0117] Due to the long operation cycle of the motor, the insulation aging of the stator coil will cause the motor to overheat. In severe cases, it will lead to inter-turn short circuit. In implementation, first test two adjacent turns of the motor stator winding, artificially damage their insulation and make them contact, so as to simulate the stator inter-turn short circuit fault of the motor.

[0118] 3) Rotor bar breakage fault

[0119] Excessive current caused by long-term overload will lead to rotor breakage faults. In implementation, simulate the rotor bar breakage fault by directly drilling a hole on one side of the bar.

[0120] 4) Outer ring bearing fault

[0121] Outer ring damage is a common bearing fault, which will cause the bearing to vibrate when passing through the damaged area. In implementation, drill a hole in the outer ring of the test motor, apply conductive heat to the hole, and remove the drilling residue to ensure that there is no physical deformation, so as to simulate the outer ring bearing fault.

[0122] (3) Data acquisition

[0123] Conduct experimental simulations on the test motors, collect 150 three-second current signals of each motor, obtain time series data under five load changes, and plot three full-cycle current sampling signal waves.

[0124] Figure 3 Give the test data of the three-cycle time series samples of the stator current (five motor conditions, three loads of 0, 50% and 100%). It can be seen from this that among the five motor conditions under three different motor loads, since the healthy motor consumes less energy than the faulty motor, the motion upper limit of the healthy motor exceeds the current amplitude of all faulty motors.

[0125] Step 2: Propose a method for extracting motor fault characteristics based on frequency diagrams. First, use frequency transformation technology to convert it from the time domain to the frequency domain and complete data preprocessing. Next, convert the preprocessed signal from the spectrum to a frequency diagram (PLT), so as to complete the extraction of the characteristics of the motor fault. The main steps are as follows:

[0126] Step 2(a): Spectrum generation

[0127] Fourier analysis (DTFT) is a tool for converting a time series signal into a frequency spectrum, and the Discrete Fourier Transform (DFT) therein is used to analyze discrete time samples. Since the motor fault is a digital sampling signal, the Discrete Fourier Transform is used to convert the previously generated time series motor current signal into a frequency spectrum. The specific definition is as follows:

[0128] Given the sampling signal X(j), j = 0, 1, …, N - 1, where N is the number of sampling points, equation (1) gives the complex expression of the Discrete Fourier Transform, and equation (2) is the Nth root in the complex Fourier series.

[0129]

[0130] W N =e 2πi / N (2)

[0131] In implementation, the frequency spectrum of the healthy motor signal is obtained, as Figure 4 shown.

[0132] Step 2(b): Preprocessing

[0133] Three data preprocessing schemes are implemented on the above frequency spectrum data to avoid potential noise and simplify the learning process of the fault classification system.

[0134] First, based on the fact that increasing the frequency range will reduce the resolution of the frequency plot (PLT), thus leading to a decrease in the classification performance of the EFA-ANN neural network, it is assumed that all motor faults do not exceed 500 Hz. Using the data clipping preprocessing technique, the motor state data is truncated within the range of 0 - 500 Hz; second, the data is clipped again to change the signal frequency amplitudes of unimportant parts to zero to avoid noise; finally, the signal amplitudes of the operating frequency (65 Hz) and its sideband frequencies (about 62 - 68 Hz) are made much larger than those of other modal frequencies.

[0135] Figure 5 is the frequency spectrum of the healthy motor condition after preprocessing.

[0136] In the same way, the frequency spectra of five faulty motor states can be obtained, as Figure 6 shown. Among them, the signals with obvious frequency amplitudes are caused by motor faults, but due to the complexity of the frequency spectra, it is difficult to identify the types of specific motor faults from these frequency spectra.

[0137] Step 2(c): Generating the frequency plot (PLT)

[0138] A method for generating the frequency plot (PLT) is proposed, as follows:

[0139] Define the metric space M and let B(j) ∈ M, which is the point on the j-th column of the previously defined spectrum B. Then the frequency map (PLT) is defined as the difference between the signals on the j-th column and the i-th row, divided by the resolution, as shown in equation (3).

[0140] PLT(j,i) = (B(j) - B(i) T ) / λ (3)

[0141] where λ is the mapping resolution, which is used to measure the error between the signals B(j) and B(i) on the j-th column and the i-th row. Thus, the matrix PLT(j,i) is converted into a color map, and after normalizing its data, it is mapped to the RGB map. In implementation, its range is defined as: λ = 0.001 ± (0 - 0.0005). After a series of experimental comparisons and verifications based on the specific sampled motor state data, finally λ = 0.0012 is determined to generate the characteristic frequency map (PLT).

[0142] Figure 7 The frequency map (PLT) is generated from the motor state spectrum within the range of 500 Hz.

[0143] where the resolution of each map is 256 × 256. In the vertical and horizontal directions, the brightly colored lines represent the high-amplitude spectra. Therefore, the motor operating frequency of 65 Hz has the brightest color. Another bright line represents other frequencies with significant amplitudes, which are caused by different motor faults.

[0144] Step 3: Propose a hybrid model (EFA) based on the Firefly Algorithm (FA) and the Electromagnetism-Like Algorithm (EA).

[0145] In this patent, the Firefly Algorithm (FA) and the Electromagnetism-Like Algorithm (EA) are used to solve the problem of motor fault classification. Since using FA and EA alone both have the disadvantages of premature convergence and divergence, this patent proposes a new hybrid model (EFA) based on FA and EA. Experimental verification shows that the Firefly Algorithm based on Electromagnetism (EFA) is an effective optimization algorithm that can solve complex problems and can enhance the prediction ability of artificial neural networks for motor faults.

[0146] The Firefly Algorithm based on Electromagnetism (EFA) is a new hybrid algorithm that combines the Firefly Algorithm (FA) and the Electromagnetism-Like Algorithm (EA). In FA, the brightness of the firefly is determined by the objective function. Fireflies tend to move closer to brighter fireflies and are not affected by darker fireflies; on the other hand, EA is an exclusion mechanism that mimics attraction to solve the global optimization problem. In EA, each point converges and moves towards the highly attractive valleys and away from the steep hills, but EA is ineffective in local search.

[0147] In EFA, it is assumed that all fireflies are magnetized, the charge of the fireflies depends on their target value, and all fireflies can participate in the search and processing, so that the fireflies will be close to attractive fireflies. In each iteration, all fireflies are ranked, and fireflies only attract or repel adjacent fireflies. In this way, the fireflies in EFA will not be scattered like in EA. Therefore, in the exploration stage, the fireflies of EFA can quickly find the target area, and in the development stage, the fireflies of EFA can perform effective local searches in these areas and find the best solution. The specific process is as follows:

[0148] Step 3(a): Initialization

[0149] First, the initial population of fireflies is set to be evenly distributed within the upper and lower boundaries, as shown in formula (4):

[0150] x o =bl k +β(bu k -bl k ) (4)

[0151] Among them, k ,bl k are the upper and lower boundaries of the kth coordinate respectively; β is a random number in [0,1]; in the process of determining β, the chaotic mapping method is adopted to ensure that the β parameter has an irregular motion state that is non-repeatable and unpredictable.

[0152] In the field of optimization, chaotic mapping can be used to replace the random number generator in the algorithm to generate chaotic numbers between [0,1]. Using this chaotic number to initialize the population parameters will increase its ergodicity, thereby affecting the iterative process of the algorithm, thereby achieving better results than pseudo-random numbers. In this patent, Logistic mapping is used to determine the β parameter, and its mapping expression is as follows:

[0153] β n+1 =μ1β n (1-β n ),β n ∈(0,1) (5)

[0154] In formula (5), the control parameter μ1∈(0,4]. When 3.75<μ1≤4, chaos occurs and the solution β n+1 ∈(0,1), the closer the control parameter μ1 is to 4, the closer the solution value range is to being evenly distributed in the entire [0,1] region. In implementation, based on the specific experimental verification results, μ1=0.38 and the initial value β1=0.2 are taken.

[0155] Step 3(b): Local Search

[0156] The EFA inherits the development capabilities of FA and EA and can perform local searches near each coordinate. Each firefly determines its moving direction through coordinates. As a result, the probability of finding a better position gradually increases. The local search process of the EFA is completed through Equation (6):

[0157]

[0158] where ε is a random number vector, and here the chaotic mapping equation is adopted to increase the ergodicity of ε.

[0159] In implementation, the Tent mapping in the chaotic mapping equation is used to determine the ε parameter, and its mapping expression is as follows:[[]]

[0160]

[0161] In Equation (7), when the control parameter μ2 ∈ (0, 1), the solution x n+1 ∈ (0, 1) will be generated. When μ2 = 0.5, a uniformly distributed sequence will be generated, and the chaotic system is in a short-period state at this time. When the initial value x = μ2, the system will become a periodic system. According to the specific experimental verification results, the control parameter μ2 = 0.6 and the initial value ε1 = 0.2 are taken.

[0162] In addition, α t is the trade-off coefficient of the t-th iteration, and its calculation expression is as follows:[[]]

[0163] α t = α0γ t (8)

[0164] where α0 is the initial trade-off coefficient; α t is the trade-off coefficient at the t-th iteration; γ is the adaptive parameter 0 < γ < 1.

[0165] Finally, L(s) is the distribution function, and its definition is as follows:[[]]

[0166]

[0167] where s is the power-law distribution, τ is the exponent, and the calculations of u and v follow the normal distribution, specifically as follows:[[]]

[0168]

[0169]

[0170] where: σ v = 1 (12)

[0171]

[0172] Γ(z) is the gamma function, which is determined by the following formula:

[0173]

[0174] Step 3(c): The flight motion of fireflies

[0175] First, the fireflies in EFA generate attraction and repulsion forces. The i-th firefly is only affected by the attraction force (F g ) and the repulsion force (F r ) from the next better and worse fireflies, and then all fireflies are ranked according to their objective function values. All fireflies in the population move based on the EA method. In this way, the interference from many fireflies can be alleviated, and the best solution can be found quickly. The magnetic firefly flight motion process is as shown in Equation (15):

[0176]

[0177] where F g and F r are the attraction and repulsion forces, which are defined by Equation (16) and Equation (17).

[0178]

[0179]

[0180] where q i is the charge at the i-th point, which is defined as follows:

[0181]

[0182] where f(x) is the objective function. It can be seen that fireflies with better objective values have higher charges.

[0183] During the optimization process, EFA uses weights (1 - α) and α to control the influence of the attraction force F g and the repulsion force F r . In the early stage of optimization, α decreases from 1 to 0, and the fireflies are mainly affected by the repulsion force F r to explore the target area. In the later stage of optimization, the attraction force F g increases, and the repulsion force F r decreases to help the fireflies explore the optimal solution in the most effective area, which helps EFA find a better classifier solution.

[0184] In each iteration, the EFA selects the best firefly according to the objective function value. The best firefly conducts local search by flying around its position, while other fireflies search within their respective areas. At the end of each iteration, the best firefly is selected, and the process continues until the termination criterion is met.

[0185] The flowchart of the EFA search process is shown in Figure 8 .

[0186] Step 4: Build a motor fault classification model of an artificial neural network (EFA - BP) based on the Electromagnetic Field - assisted Firefly Algorithm (EFA). Use the EFA to train the weight and offset parameters of the BP neural network, thereby completing the classification of the conditions and fault types of healthy and faulty motors for testing.

[0187] In implementation, the generated frequency map (PLT) feature data is divided into training and test data sets. Using the selected EFA - BP model parameters, the model training of the PLT features is carried out through the learning mode, and its training performance is evaluated. Then, using another set of test PLT data, the trained classification model is tested, and its test performance is evaluated. Finally, the training and test performances are compared.

[0188] The motor fault classification process based on the frequency map is as shown in Figure 9 follows:

[0189] The weight and bias update process of the BP neural network optimized by the EFA is as shown in Figure 10 follows.

[0190] First, the historical data is divided into learning and test data. Then, the learning data is divided into training and validation data with ratios of 80% and 20% respectively. The model is trained using the EFA algorithm and the training data, and then the trained neural network is verified using the validation data. When the optimal neural network model is found, the test data is used to evaluate the model performance. Specifically, it mainly includes the following steps:

[0191] Step (4)a: Determine the basic structure of the BP neural network, build the structure of the neural network, and initialize its related parameters, such as the target error, maximum number of training times parameters, etc.

[0192] Step (4)b: Use the fireflies of the EFA to initialize the weight and offset parameters in the BP algorithm. For each specific firefly individual, set its fluorescence and perception radius.

[0193] Step (4)c: Calculate the output values of the input layer, hidden layer, and output layer nodes of the BP network, and calculate the fitness for each firefly individual, and effectively store the maximum value among them. The specific process is as follows;

[0194] (1) Input the motor fault data into the BP neural network and calculate the output Y of the i-th neuron in the input layer through forward calculation i :

[0195] Y i = f(x i ) (19)

[0196] where x i is the motor fault data

[0197] (2) Calculate the output of the hidden layer

[0198] The output of the h-th neuron is:

[0199]

[0200] where w hi , θ i are the weights and thresholds of the hidden layer neurons

[0201] (3) Calculate the output values of all neurons in the output layer

[0202] The output formula of the j-th output neuron is as follows:

[0203]

[0204] where w jh , θ j are the weights and thresholds of the output layer neurons

[0205] Step (4)d: Based on the fluorescence intensity, continuously update each firefly individual, search for unknown neighborhoods within the perception range of the individual, perform flight movement updates, and use EFA to train its weight and offset parameters

[0206] Step (4)e: After the position update, according to the fitness value calculated by the firefly individual, determine whether it reaches the termination condition of the training goal. If it is satisfied, execute the next step; otherwise, return to the previous step

[0207] The fitness value judgment error formula is as follows:

[0208]

[0209] where D j is the target output, and Y j is the actual output

[0210] Step (4)f: Convert the received position information into the corresponding weights and thresholds of the neural network

[0211] Step (4)g: Determine whether the termination condition is met, that is, the set error target is reached. If so, output the result and end the algorithm; otherwise, return to (d) and continue training until the termination condition is met.

[0212] Step 5: Based on the above technology, build an experimental platform to complete the specific implementation of motor fault classification. The following test experiments are mainly completed:

[0213] (1) Motor fault diagnosis experiment

[0214] First, establish five EFA-BP models. Collect 150 data for each motor, extract the fault features of the corresponding frequency diagram, and send them into the corresponding classifier model to complete the classification of the health status and fault types of the healthy and faulty motors for testing. Focus on four aspects of faults, namely bearing misalignment, inter-turn short circuit fault, rotor bar breakage, and outer ring bearing fault. The fault diagnosis classification effect is shown in Table 2.

[0215] The number of iterations and the population number in the algorithm are 500 and 300 respectively. The EFA-BP step size is 0.08. The threshold and weight values are between [-1, 1], and the learning rate is 0.2.

[0216] Table 2 Fault diagnosis classification effect

[0217]

[0218] In Table 2, the first model classifies bearing misalignment (fault 1), and its recall rate is 96.2% and the precision is 95.8%. The second and third models correspond to stator inter-turn fault (fault 2) and rotor bar breakage (fault 3) respectively, and their performances are average, with precisions of 87.6% and 90.8% respectively. The fourth model corresponds to outer ring bearing damage (fault 4), and its performance is the worst. In the experiment, when predicting fault 4, it is easy to predict it as fault 2, resulting in relatively serious confusion.

[0219] (2) Comparison of different classifier models

[0220] During the implementation, the proposed EFA-BP algorithm is experimentally verified and compared with the BP neural network. The parameter values of the two algorithms are the same (as described above). Build EFA-BP and BP classifier models respectively. After training the models, compare the network error values of the trained networks. The classification effect is as Figure 11 .

[0221] Finally, randomly select 15 groups of samples, send the fault samples into the trained model for testing, and finally obtain the diagnostic effect as shown in Table 3.

[0222] Table 3 Comparison of experimental results (error)

[0223]

[0224] As can be seen from the above charts, the prediction result of EFA - BP is the best, and the absolute value of its prediction error is significantly smaller than that of BP. Since the training samples contain motor fault information, compared with the traditional BP neural network, EFA - BP shows obvious advantages in motor fault diagnosis, has a high diagnosis accuracy rate, and can obtain a diagnosis effect far higher than that of the BP neural network.

[0225] Finally, the training times and training error curves of the two algorithms in the convergent situation are obtained, as shown in Table 4 and Figure 12 .

[0226] Table 4 Execution training times of the two algorithms

[0227]

[0228] As can be seen from the above charts, in terms of overall performance, the average training times of the BP algorithm are larger, while those of the EFA - BP algorithm are smaller. Thus, it can be seen that optimizing the BP neural network structure with the electromagnetic - based firefly algorithm (EFA) has achieved a relatively significant improvement in its performance, has a relatively fast convergence speed, and has obvious advantages in motor fault diagnosis.

Claims

1. A motor fault diagnosis method based on a frequency diagram and EFA-BP deep learning, characterized in that It includes the following steps: Step (1): Under the condition of stable no-load operation of the motor, simulate four kinds of motor faults, namely bearing misalignment, inter-turn short circuit of stator winding, rotor bar breakage and outer ring bearing damage, collect the stator current signal under the motor fault state, and obtain the time series data under five kinds of coupled load changes, namely the current signal of the motor fault state in the time series; Step (2): Use frequency transformation to convert the current signal of the motor fault state in the time series from the time domain to the frequency domain, and complete data preprocessing; convert the preprocessed signal from the spectrum to a frequency map (PLT), and perform necessary normalization calculations, divide the data into test and training data, record and store the data, and establish a fault database, so as to complete the feature extraction of the motor fault; Step (3): Propose a hybrid model (EFA) based on the field algorithm (FA) and the firefly algorithm (EA). Assume that all fireflies are magnetized, the charge of the firefly depends on its target value, and all fireflies can participate in the search and processing, so as to ensure that in the exploration stage, the fireflies of EFA can quickly find the target area, and in the development stage, the fireflies of EFA can perform effective local search in these areas and find the best solution; Step (4): Construct an EFA-BP classification algorithm, and use EFA to train the weight and offset parameters of the BP neural network, so as to complete the classification of the conditions and fault types of healthy and faulty motors for testing.

2. The motor fault diagnosis method based on frequency map and EFA-BP deep learning according to claim 1, characterized in that, In the step (1), the five kinds of coupled load change situations are 0, 25%, 50%, 75% and 100% respectively. Use a clamp-on current transformer to measure the stator current flowing through the motor, obtain the state data of four kinds of motor faults, namely bearing misalignment, inter-turn short circuit of stator winding, rotor bar breakage and outer ring bearing damage, that is, the current signal of the motor fault state in the time series, and store the fault state signal.

3. The motor fault diagnosis method based on the frequency diagram and EFA-BP deep learning according to claim 1, characterized in that, In the step (2), the specific process of using frequency transformation to convert the current signal of the motor fault state in the time series from the time domain to the frequency domain and completing data preprocessing is as follows: Step (2)a: Use the discrete Fourier transform (DFT) to convert the previously generated time series motor current signal into a spectrum, and the specific definition is as follows: W N = e 2πi / N where A(n) is the complex expression of the discrete Fourier transform; W N is the Nth root in the complex Fourier series; X(j) is the given sampling signal, j = 0, 1, …, N−1, and N is the number of sampling points; Step (2)b: Preprocessing, implement three data preprocessing schemes for the above spectrum data: First, assume that all motor faults do not exceed 500Hz, and use the data clipping preprocessing technology to truncate the motor state data within the range of 0 - 500Hz; Second, clip the data again, change the signal frequency amplitude of unimportant signals to zero to avoid noise; Third, make the signal amplitudes of the working frequency and its sideband frequencies much larger than other modal frequencies.

4. The motor fault diagnosis method based on the frequency diagram and EFA-BP deep learning according to claim 3, wherein In the step (2), converting the preprocessed signal from the spectrum to a frequency map is specifically: Step (2)c: Define the metric space M, and let B(j) ∈ M, that is, the point on the j-th column of the previously defined spectrum B, then the frequency map is defined as the difference between the signals on the j-th column and the i-th row, and then divided by the resolution, and the definition formula is as follows: PLT(j,i) = (B(j) - B(i) T ) / λ Among them, λ is the mapping resolution, which is used to measure the error between the signals B(j) and B(i) on the j-th column and the i-th row. Thus, the matrix PLT(j, i) is converted into a color map. After normalizing its data, it is mapped to the RGB map.

5. The motor fault diagnosis method based on a frequency diagram and EFA-BP deep learning according to claim 1, wherein In step (3), the hybrid model EFA based on electromagnetism and the firefly algorithm is as follows: Step (3)a: Initialization First, the initial population of fireflies is set to be uniformly distributed within the upper and lower boundaries, and the specific definition is as follows: x o = bl k + β(bu k - bl k ) wherein, bu k , bl k are respectively the upper and lower boundaries of the k-th coordinate; β is a random number within [0, 1]; Step (3)b: Local search. The local search process is completed by the following formula: where ε is a random number vector, and α t is the trade-off coefficient at the t-th iteration, and L(s) is a distribution function; Step (3)c: The flight movement of fireflies First, the firefly excitation attraction F of the EFA g and the repulsive force F r , the i-th firefly is only affected by F from the next better and worse fireflies g and F r . Then, all fireflies are ranked according to their objective function values; all fireflies in the population move based on the EA method. In this way, the interference from many fireflies can be alleviated and the best solution can be found quickly. The magnetic firefly flight movement process is as follows: where F g and F r are the attractive and repulsive forces, defined by the following equation: q i is the charge at the i-th point and is defined as follows: f(x) is the objective function.

6. The motor fault diagnosis method based on the frequency diagram and EFA-BP deep learning according to claim 5, characterized in that In step (3)a, β is determined by using the Logistic map, and its mapping expression is as follows: β n+1 = μ1β n (1 - β n ), β n ∈(0, 1) In the formula, the control parameter μ1 ∈ (0, 4]. When 3.75 < μ1 ≤ 4, chaotic phenomena occur, and the generated solution β n+1 ∈ (0, 1). The closer the control parameter μ1 is to 4, the closer the value range of the solution is to being evenly distributed over the entire [0, 1] region.

7. The motor fault diagnosis method based on the frequency diagram and EFA - BP deep learning according to claim 5, wherein, In step (3)b, the ε parameter, α t and L(s) are determined as follows: 1) The Tent map in the chaotic map equation is used to determine the ε parameter, and its mapping expression is as follows: In the formula, when the control parameter μ2 ∈ (0, 1), the solution x will be generated. n+1 ∈ (0, 1). When μ2 = 0.5, a uniformly distributed sequence will be generated, and the chaotic system is in a short-period state at this time. When the initial value x = μ2, the system will become a periodic system. 2) α t is the trade-off coefficient of the t-th iteration, and its calculation expression is as follows: α t = α0γ t Among them, α0 is the initial trade-off coefficient; α t is the trade-off coefficient at the t-th iteration; γ is the adaptive parameter, where 0 < γ < 1; 3) L(s) is the distribution function, and its definition is as follows: Among them, s is the power-law distribution, τ is the exponent, and the calculations of u and v follow the normal distribution, specifically as follows: σ v = 1 Γ(z) is the gamma function, which is determined by the following formula:

8. The motor fault diagnosis method based on the frequency diagram and EFA - BP deep learning according to claim 1, characterized in that, In step (4), an EFA-BP classification algorithm is constructed, and the EFA is used to train the weight and offset parameters of the BP neural network. Specifically: Step (4)a: Determine the basic structure of the BP neural network, build the structure of the neural network, and initialize its relevant parameters; Step (4)b: Use the firefly initialization BP algorithm of the hybrid model EFA based on electromagnetism and the firefly algorithm to initialize the weight and offset parameters. For each specific firefly individual, set it as the fluorescence intensity and perception radius; Step (4)c: Calculate the output values of the input layer nodes, hidden layer nodes, and output layer nodes of the BP network, and calculate the fitness for each firefly individual, and effectively store the maximum value among them; Step (4)d: Based on the fluorescence intensity, continuously update each firefly individual, search for unknown neighborhoods within the perception range of the individual, perform flight movement updates, and use the EFA to train its weight and offset parameters; Step (4)e: After the position update, according to the fitness value calculated by the firefly individual, judge whether it reaches the termination condition of the training target. If it is satisfied, execute the next step; otherwise, return to the previous step; The fitness value judgment error formula is as follows: Among them, D j is the target output, and Y j is the actual output; Step (4)f: Convert the received position information into the corresponding weights and thresholds of the neural network; Step (4)g: Judge whether the termination condition is satisfied, that is, whether the set error target is reached. If it is reached, output the result and end the algorithm; otherwise, return to (d) and continue training until the termination condition is achieved.

9. The motor fault diagnosis method based on the frequency map and EFA-BP deep learning according to claim 8, wherein The specific process of step (4)c is as follows: (1) Input the motor fault data into the BP neural network and calculate the output Y of the i-th neuron in the input layer through forward calculation i as follows: Y i = f(x i ) where x i motor fault data; (2) Calculate the hidden layer output: The output of the h-th neuron is: Y h = f(I h ) where w hi and θ i are the weights and thresholds of the hidden layer neurons; (3) Calculate the output values of all neurons in the output layer: The output formula of the j-th output neuron is as follows: Y j = f(I j ) Among them, w jh , θ j are the weights and thresholds of the output layer neurons.

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