A gearbox compound fault diagnosis method based on optimal legendre multiwavelet frequency band

Abstract

The application discloses a gearbox compound fault diagnosis method based on an optimal Legendre multi-wavelet frequency band, and relates to the technical field of rotating machinery fault diagnosis and artificial intelligence technology. The genetic algorithm is used to optimize the structural parameters of the proposed model, i.e., the number of Legendre multi-wavelets, the level of wavelet decomposition and the number of hidden layer neurons of a BP neural network classifier, and an improved self-adaptive threshold denoising algorithm based on the optimized frequency band of the Legendre multi-wavelet is proposed, so that the strong noise interference in a complex environment is effectively removed; and the standard deviation + kurtosis, entropy + skewness statistical features are extracted and input into the BP neural network, so that the high-precision diagnosis problem of the gearbox compound fault with label noise and a small sample is effectively solved, the problem that a deep neural network is difficult to design and train due to a complex structure is avoided, and the online fault diagnosis of the rotating machinery is more easily realized.

Description

Technical Field

[0001] This invention relates to the field of interdisciplinary technology of rotating machinery fault diagnosis and artificial intelligence, specifically a gearbox composite fault diagnosis method based on optimal Legendre multi-wavelet frequency bands. Background Technology

[0002] The health of the gearbox directly affects the normal operation of rotating machinery. Accurate identification and prediction of fault types can effectively prevent significant losses. However, different types of gearbox failures can easily couple together, and fault signals are susceptible to contamination by strong noise. Furthermore, in real-world environments, incorrect labeling is unavoidable due to operator error. Machinery is typically in normal operating condition, meaning only a limited number of fault samples can be collected. Therefore, the lack of typical fault samples—the small sample problem—remains a major challenge in diagnosing mechanical equipment faults.

[0003] There are generally three methods for diagnosing complex gearbox faults: model-based methods, knowledge-driven methods, and data-driven methods. Model-based methods primarily rely on mathematical models of the mechanical operation process. Therefore, they require a sufficient understanding of the mathematical models of the mechanical equipment system. However, developing effective mathematical models for mechanical fault diagnosis is often difficult. Knowledge-driven methods largely rely on domain knowledge. However, they require a deep understanding of the causal relationships between faults and symptoms in mechanical equipment, which can be quite challenging for many technicians, hindering their accurate identification of fault types. In contrast, the rapid development of artificial intelligence has enabled data-driven methods to offer more significant benefits for mechanical equipment fault diagnosis in practical applications. This approach does not require extensive mathematical models or domain knowledge and can find suitable classification schemes from raw data. Traditional machine learning-based fault diagnosis methods require complex manual selection of fault features, which is difficult to meet the needs of analyzing various fault data in engineering practice. Training a deep learning model in practical applications typically requires a large number of labeled samples. Generative adversarial networks, diffusion models, and transfer learning are used to augment existing fault sample datasets, but deep models are difficult to train.

[0004] Denoising algorithms based on wavelet transform are widely used in signal processing to improve the signal-to-noise ratio of fault detection and diagnosis by estimating thresholds. However, simple denoising algorithms often fail to adequately eliminate noise because its frequencies overlap with the fault characteristic signals.

[0005] Therefore, a new solution is needed to address the above problems. Summary of the Invention

[0006] The purpose of this invention is to provide a gearbox composite fault diagnosis method based on optimal Legendre multi-wavelet frequency bands. Addressing the problem of high-precision diagnosis of gearbox composite faults under conditions of strong noise interference, label noise, and limited fault samples, this invention constructs a Max min objective function and uses a genetic algorithm and gradient descent learning algorithm to learn the optimal value between high diagnostic accuracy and low signal energy loss, obtaining optimized network structure parameters (number of Legendre multi-wavelets, wavelet decomposition level, number of neurons in the hidden layer of the BP neural network). An improved adaptive denoising algorithm is proposed for each optimal Legendre wavelet frequency band to effectively remove strong noise interference. Based on the statistical feature combination of standard deviation + kurtosis and entropy + skewness, the features of gearbox composite faults are effectively extracted, avoiding the complex feature selection algorithms of traditional machine learning methods and the difficulties of deep networks in feature extraction and learning, thus effectively solving the problem of high-precision diagnosis of gearbox composite faults under small sample conditions.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a gearbox composite fault diagnosis method based on optimal Legendre multi-wavelet frequency bands, comprising at least the following steps:

[0008] Step 1: Data acquisition, using the PHM 2009 composite gearbox fault dataset;

[0009] Step 2: Initialize the algorithm;

[0010] Step 3: Sample processing, allocate 75% of the total samples for each gearbox failure category to the training samples and 25% to the test samples;

[0011] Step 4: Legendre multi-wavelet decomposition process, including initial values ​​of network parameters and implementation of Legendre multi-wavelet decomposition;

[0012] Step 5: Improved adaptive threshold denoising algorithm;

[0013] Step 6: Feature extraction. For each denoised optimal Legender multi-wavelet high-frequency band and the undenoised Legender multi-wavelet low-frequency band, calculate the statistical feature combination standard deviation + kurtosis and entropy + skewness as the feature input of the BP neural network.

[0014] Step 7: Train the BP neural network, normalize the obtained optimal features to between 0 and 1, and train the BP neural network through the gradient descent learning algorithm. Then, pass the normalized result of the optimal features obtained on the test sample to the BP neural network to calculate the test diagnosis accuracy, so as to complete the performance evaluation of the proposed method.

[0015] Step 8: Fusion of genetic algorithm and improved adaptive threshold denoising algorithm. If the accuracy of fault diagnosis does not reach the expected diagnostic accuracy, update the decomposition level of multiwavelet, the number of Legendre multiwavelets, and the number of neurons in the BP neural network through genetic algorithm, and repeat steps 4 to 7 to obtain higher fault diagnosis accuracy.

[0016] Step 9: Output the results. If the accuracy of the fault diagnosis reaches the expected accuracy, output the highest diagnostic accuracy and the corresponding multi-wavelet decomposition level, the number of Legendre multi-wavelets, and the number of neurons in the BP neural network.

[0017] Furthermore, the gearbox model in the PHM 2009 composite gearbox fault dataset is ER-10K;

[0018] The PHM 2009 composite gearbox fault dataset contains six different health conditions for gearbox fault signals. Each signal is collected under five conditions: low load and speeds of 30, 35, 40, 45, and 50 Hz. The sampling frequency for each signal is 66.7 kHz, and the sampling time is 8 seconds.

[0019] Furthermore, the initial algorithm includes at least the number of iteration steps for initializing the genetic algorithm, the number of iteration steps for the gradient descent algorithm, the decomposition level, the number of Legendre wavelets, the number of hidden layer neurons in the BP neural network, the number of chromosomes, the crossover probability, the mutation probability, the training samples and test samples, the training error of the BP neural network at the end of the iteration, and the expected fault diagnosis accuracy.

[0020] Furthermore, step 5 includes at least the following steps:

[0021] S1: Noise estimation in the optimal high-frequency band of Legendre multi-wavelet:

[0022] Let W = [w1, w2, ..., w N ] is a vector consisting of the squares of the Legendre multiwavelet coefficients for each optimal high-frequency band, arranged in ascending order;

[0023] First, let the minimum value r of the risk vector R obtained by calculating the vector W using formula (1) be obtained. b (b th r) is used as an unbiased risk estimate, as shown in equation (1):

[0024]

[0025] Then, using the index b corresponding to the risk value, the square w of the Legendre multiwavelet coefficient at the corresponding position in vector W is selected. bAs the minimum risk coefficient

[0026] Therefore, the improved threshold estimate is given by equation (2):

[0027]

[0028] S2: Experiment-based threshold parameter selection:

[0029] According to formula (2), the Legendre multi-wavelet coefficients of the optimal decomposition level are used to estimate the optimal threshold, where the parameter σ is the standard deviation of the optimal high-frequency band signal, and η is a parameter determined by numerical simulation experiments according to different application scenarios.

[0030] S3: Improved soft thresholding denoising algorithm:

[0031] Based on the threshold estimation in formula (2), the improved soft thresholding denoising algorithm is as follows:

[0032]

[0033] in, The adaptive weighting coefficient model is constructed. It is important to note that through this unbiased risk estimation, different thresholds λ can be obtained in different optimal Legendre multi-wavelet high-frequency bands, thus the improved algorithm is more helpful in removing complex noise interference.

[0034] S4: Evaluation of the improved denoising algorithm:

[0035] The performance of the improved adaptive threshold denoising algorithm is evaluated using the root mean square error (RMSE). The specific formula for calculating the performance of the improved adaptive threshold denoising algorithm using the RMSE is Equation (4):

[0036]

[0037] Where N0 is the number of sample points, x i It is the i-th element of the original signal, y i It is the i-th element of the denoised signal reconstructed using the inverse Legendre multiwavelet transform;

[0038] A lower RMSE value indicates that the denoising algorithm has better denoising performance.

[0039] Furthermore, the fusion of the genetic algorithm and the improved adaptive threshold denoising algorithm includes at least the following steps:

[0040] S1: The fitness function of the genetic algorithm adopts the expected accuracy of fault diagnosis, specifically as shown in equation (5):

[0041]

[0042] Where TP, TN, FP and FN represent true positives, true negatives, false positives and false negatives, respectively;

[0043] S2: The weight coefficients of the BP neural network are learned through the gradient descent algorithm. When the loss function reaches the predetermined lower limit or the number of iterations reaches the predetermined maximum value, the adjustment process of the network weight coefficients stops. At this time, if the fault diagnosis accuracy does not reach the target, a genetic algorithm is used to further select better values ​​of the network structure parameters.

[0044] S3: Let GA(·) represent the optimization process of the genetic algorithm for the network structure parameters, GD(·) represent the learning process of the weight coefficients of the BP neural network, and Fitness(·) represent the fitness function of the genetic algorithm. The designed Max min objective function is Equation (6):

[0045]

[0046] Where n, p, and ξ represent the decomposition level, the number of Legendre multi-wavelets, and the number of hidden layer neurons in the BP neural network, respectively, and λ represents the optimal unbiased risk estimation threshold in each optimal Legendre multi-wavelet high-frequency band.

[0047] Compared with the prior art, the beneficial effects of the present invention are:

[0048] 1. This invention improves the Rigrsure threshold selection method by establishing a soft threshold weight model and incorporating experimental parameters to enhance threshold estimation. It proposes an adaptive threshold denoising algorithm that improves upon each optimized Legendre multi-wavelet band. This improved adaptive threshold denoising algorithm for optimized bands can effectively eliminate strong noise, label noise, and interference from unknown environments under complex operating conditions, while preserving important fault characteristic components in each optimal band.

[0049] 2. In this invention, the Legendre multi-wavelet frequency band optimization is achieved by constructing a Max min objective function and using a genetic algorithm and gradient descent learning algorithm. This optimization avoids the need for traditional methods to obtain network structure parameters (number of Legendre wavelet bases, decomposition level, number of neurons in the hidden layer of the BP neural network) through a large number of experiments.

[0050] 3. This invention selects a traditional and effective combination of statistical features—standard deviation + kurtosis and entropy + skewness—to effectively extract features of gearbox composite faults. The fundamental reason for the effectiveness of this method lies in the fact that environmental noise interference is removed in the optimized Legendre multi-wavelet frequency band; the frequency domain of the optimized Legendre multi-wavelet decomposition layer can fully characterize the complex features of gearbox composite faults. That is, by using simple statistical features to enter a simple classifier, high-precision diagnosis of gearbox composite faults under complex conditions can be achieved. This invention avoids the complex feature selection of traditional machine learning methods and avoids the use of deep networks to extract features, thus effectively solving the problem of high-precision diagnosis of gearbox composite faults under small sample conditions.

[0051] 4. This invention verifies the effectiveness and robustness of its proposed method through extensive comparative experiments on the PHM 2009 gearbox fault dataset (Prognostics and Health Management, from the IEEE International Conference on Prediction and Health Management 2009). The proposed method demonstrates 100% diagnostic accuracy on this gearbox dataset without noise interference. Under three conditions—6dB noise, a label-to-noise ratio of 0.05, and a limited number of fault samples (10)—the proposed method achieves diagnostic accuracies of 99.83%, 95.33%, and 90.80%, respectively, outperforming methods based on Daubechies wavelets. Attached Figure Description

[0052] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This is a schematic diagram of the overall process of the present invention. Detailed Implementation

[0054] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0055] Please see Figure 1 A method for diagnosing complex faults in gearboxes based on optimal Legendre multi-wavelet frequency bands includes at least the following steps:

[0056] Step 1: Data acquisition, using the PHM 2009 composite gearbox fault dataset;

[0057] Step 2: Initialize the algorithm;

[0058] Step 3: Sample processing. Allocate 75% of the total samples for each gearbox failure category to the training samples and 25% to the test samples. To avoid specificity and randomness, the training and test samples are randomly selected, and this random experiment is repeated 10 times.

[0059] Step 4: The Legendre multi-wavelet decomposition process includes initializing the network parameters and implementing the Legendre multi-wavelet decomposition. Specifically, it uses three Legendre multi-wavelets, and the level of the Legendre multi-wavelet decomposition is 2.

[0060] Step 5: Improved adaptive threshold denoising algorithm;

[0061] Step 6: Feature extraction. For each denoised optimal Legender multi-wavelet high-frequency band and the undenoised Legender multi-wavelet low-frequency band, calculate the statistical feature combination standard deviation + kurtosis and entropy + skewness as the feature input of the BP neural network.

[0062] Step 7: Train the BP neural network, normalize the obtained optimal features to between 0 and 1, and train the BP neural network through the gradient descent learning algorithm. Then, pass the normalized result of the optimal features obtained on the test sample to the BP neural network to calculate the test diagnosis accuracy, so as to complete the performance evaluation of the proposed method.

[0063] Step 8: Fusion of genetic algorithm and improved adaptive threshold denoising algorithm. If the accuracy of fault diagnosis does not reach the expected diagnostic accuracy, update the decomposition level of multiwavelet, the number of Legendre multiwavelets, and the number of neurons in the BP neural network through genetic algorithm, and repeat steps 4 to 7 to obtain higher fault diagnosis accuracy.

[0064] Step 9: Output the results. If the accuracy of the fault diagnosis reaches the expected accuracy, output the highest diagnostic accuracy and the corresponding multi-wavelet decomposition level, the number of Legendre multi-wavelets, and the number of neurons in the BP neural network.

[0065] The gearbox model used in the PHM 2009 composite gearbox fault dataset is ER-10K;

[0066] The PHM 2009 composite gearbox fault dataset contains six different gearbox fault signals, each collected under five conditions: low load and speeds of 30, 35, 40, 45, and 50 Hz. The sampling frequency for each signal is 66.7 kHz, and the sampling time is 8 seconds. This results in 533,312 sampling points for each operating condition and speed, and a total of 2,666,560 sample points across the five speed conditions. For each composite fault signal, 4,096 data points are used as one sample, for a total of 600 samples. To best meet practical diagnostic needs, 450 samples are randomly selected for each health condition as training samples, and the remaining 150 samples are used to test the diagnostic accuracy of the proposed method. Furthermore, to match the composite fault patterns in composite fault diagnosis, the fault labels are set to a multi-label format, allowing a single composite fault label to represent fault information from multiple locations.

[0067] The specific descriptions of the six composite fault types of the gearbox and their corresponding tag arrays are shown in Table 1.

[0068] Table 1. Six types of combined faults in gearboxes

[0069]

[0070]

[0071] The position of the fault type in Table 1 represents the position of the fault in the multi-label array.

[0072] The initial algorithm should include at least the number of iterations for the initial genetic algorithm, the number of iterations for the gradient descent algorithm, the decomposition level, the number of Legendre wavelets, the number of hidden layer neurons in the BP neural network, the number of chromosomes, the crossover probability, the mutation probability, the training samples and test samples, the training error at the end of the BP neural network iteration, and the expected fault diagnosis accuracy.

[0073] In real-world engineering environments, acquired gearbox vibration signals often encounter significant noise interference, employee mislabeling, and a limited number of fault samples, posing a substantial challenge to high-precision fault diagnosis. To reduce the impact of noise on fault diagnosis, this invention designs an improved adaptive threshold denoising algorithm on the optimized Legendre multi-wavelet high-frequency band, as follows:

[0074] S1: Noise estimation in the optimal high-frequency band of Legendre multi-wavelet:

[0075] Let W = [w1, w2, ..., w N ] is a vector consisting of the squares of the Legendre multiwavelet coefficients for each optimal high-frequency band, arranged in ascending order;

[0076] First, let the minimum value r of the risk vector R obtained by calculating the vector W using formula (1) be obtained. b (b th r) is used as an unbiased risk estimate, as shown in equation (1):

[0077]

[0078] Then, using the index b corresponding to the risk value, the square w of the Legendre multiwavelet coefficient at the corresponding position in vector W is selected. b As the minimum risk coefficient

[0079] Therefore, the improved threshold estimate is given by equation (2):

[0080]

[0081] S2: Experiment-based threshold parameter selection:

[0082] According to formula (2), the Legendre multi-wavelet coefficients of the optimal decomposition level are used to estimate the optimal threshold, where the parameter σ is the standard deviation of the optimal high-frequency band signal, and η is a parameter determined by numerical simulation experiments according to different application scenarios.

[0083] S3: Improved soft thresholding denoising algorithm:

[0084] Based on the threshold estimation in formula (2), the improved soft thresholding denoising algorithm is as follows:

[0085]

[0086] in, The adaptive weighting coefficient model is constructed. It is important to note that through this unbiased risk estimation, different thresholds λ can be obtained in different optimal Legendre multi-wavelet high-frequency bands, thus the improved algorithm is more helpful in removing complex noise interference.

[0087] S4: Evaluation of the improved denoising algorithm:

[0088] The performance of the improved adaptive threshold denoising algorithm is evaluated using the root mean square error (RMSE). The specific formula for calculating the root mean square error is Equation (4):

[0089]

[0090] Where N0 is the number of sample points, x i It is the i-th element of the original signal, y iIt is the i-th element of the denoised signal reconstructed using the inverse Legendre multiwavelet transform;

[0091] A lower RMSE value indicates that the denoising algorithm has better denoising performance.

[0092] The fusion of genetic algorithms and improved adaptive thresholding denoising algorithms includes at least the following steps:

[0093] The method proposed in this invention combines a genetic algorithm with an improved adaptive threshold denoising algorithm. Specifically, the genetic algorithm is used to optimize three network structure parameters: the number of Legendre multi-wavelets, the decomposition level, and the number of hidden layer neurons in the BP neural network, thereby obtaining the optimal Legendre multi-wavelet high-frequency band information under complex conditions. Then, the improved adaptive threshold denoising algorithm is applied to each optimal Legendre multi-wavelet high-frequency band to effectively remove complex noise interference.

[0094] S1: The fitness function of the genetic algorithm adopts the expected accuracy of fault diagnosis, specifically as shown in equation (5):

[0095]

[0096] Where TP, TN, FP and FN represent true positives, true negatives, false positives and false negatives, respectively;

[0097] S2: The weight coefficients of the BP neural network are learned through the gradient descent algorithm. When the loss function reaches the predetermined lower limit or the number of iterations reaches the predetermined maximum value, the adjustment process of the network weight coefficients stops. At this time, if the fault diagnosis accuracy does not reach the target, a genetic algorithm is used to further select better values ​​of the network structure parameters.

[0098] S3: Let GA(·) represent the optimization process of the genetic algorithm for the network structure parameters, GD(·) represent the learning process of the weight coefficients of the BP neural network, and Fitness(·) represent the fitness function of the genetic algorithm. The designed Max min objective function is Equation (6):

[0099]

[0100] Where n, p, and ξ represent the decomposition level, the number of Legendre multi-wavelets, and the number of hidden layer neurons in the BP neural network, respectively, and λ represents the optimal unbiased risk estimation threshold in each optimal Legendre multi-wavelet high-frequency band.

[0101] On the PHM 2009 dataset, the optimal network structure parameters obtained by the method proposed in this invention are shown in Table 2:

[0102] Table 2. Optimal network structure parameters obtained by the method proposed in this invention

[0103]

[0104] As shown in Table 2, the optimal structure of the BP neural network consists of one input layer with 12 input neurons, three hidden layers with 12, 56, and 26 neurons each, and one output layer with 12 neurons. The threshold denoising method proposed in this invention has an optimal multi-wavelet decomposition level of 1, a multi-wavelet number of 3, and an experimental parameter η of 1.2.

[0105] This embodiment utilizes a genetic algorithm to optimize the proposed model's structural parameters: the number of Legendre multi-wavelets, the level of wavelet decomposition, and the number of hidden layer neurons in the classifier's BP neural network. It also proposes an adaptive threshold denoising algorithm based on improved frequency band optimization using Legendre multi-wavelets, effectively removing strong noise interference from complex environments. Furthermore, by extracting fault statistical features and combining standard deviation + kurtosis and entropy + skewness as inputs to the BP neural network, it effectively solves the problem of high-precision diagnosis of complex gearbox faults with label noise and small sample sizes. This avoids the design and training difficulties associated with deep neural networks due to their complex structure, making online fault diagnosis of rotating machinery easier to achieve.

[0106] A method for verifying the method of the present invention under complex conditions is proposed for the above embodiments;

[0107] To verify the effectiveness of the fault diagnosis method proposed in this invention, it was tested under conditions of strong noise interference, tag noise, and limited fault samples. Table 3 details the genetic algorithm configuration parameters involved in the experiments under three different conditions.

[0108] Table 3. Configuration parameters of genetic algorithm

[0109]

[0110] The fault diagnosis method proposed in this invention is compared with the Daubechies wavelet transform-based method to demonstrate that the proposed method has higher fault diagnosis accuracy than the traditional wavelet transform method. For clarity, the fault diagnosis methods involved in the experiment are abbreviated as follows:

[0111] Method 1: The method proposed in this invention, statistical characteristics (standard deviation + kurtosis);

[0112] Method 2: The method proposed in this invention, statistical characteristics (entropy + skewness);

[0113] Method 3: Based on the Daubechies wavelet transform method, statistical features (standard deviation + kurtosis);

[0114] Method 4: Based on the Daubechies wavelet transform method, statistical features (entropy + skewness).

[0115] Experimental results under different strong noise interference

[0116] Signal-to-noise ratios of -2, 0, 2, 4, and 6 dB were added to various fault signals in the gearbox to verify the noise immunity of the fault diagnosis method proposed in this invention. The accuracy of the four fault diagnosis methods under each signal-to-noise ratio condition is shown in Table 4.

[0117] Table 4. Average test accuracy of different methods under different signal-to-noise ratio conditions

[0118]

[0119] As can be seen from the experimental results in Table 4, Method 2 proposed in this invention achieves the highest diagnostic accuracy when the white noise applied to the vibration signal ranges from -2dB to 6dB. Specifically, the diagnostic accuracy of methods 3 and 4 based on traditional wavelet methods decreases significantly when the signal-to-noise ratio (SNR) decreases. When the SNR is 0dB, both methods 3 and 4 have an average test accuracy of less than 60%. In contrast, the proposed Method 1 has an average test accuracy of 95.17% and a minimum standard deviation of 2.63. Furthermore, Method 2, using the optimal feature combination entropy + skewness, has a higher average test accuracy than Method 1, which uses the optimal feature combination standard deviation + kurtosis.

[0120] Experimental results under different label noise

[0121] In real-world mechanical fault diagnosis scenarios, a small number of tags exhibit noise. To evaluate the performance of the proposed method under such tag noise conditions, datasets with tag noise ratios of 0%, 2%, 5%, and 10% were created. Ten validation experiments were conducted under each tag noise ratio condition. The average test accuracy of the experiments was then used as an evaluation metric for the performance of different fault diagnosis methods. The experimental results are described in detail in Table 5.

[0122] Table 5. Average test accuracy of the proposed method under different tag noise ratios.

[0123]

[0124] As shown in Table 5, when the tag-to-noise ratio changes from zero to 0.1, proposed methods 2 and 1 exhibit higher average test accuracy than methods 4 and 3. When the tag-to-noise ratio is 0.1, the average test accuracy of method 2 is above 91%. In contrast, the average diagnostic accuracy of methods 4 and 3 is only around 90%. This demonstrates that the proposed methods possess excellent fault identification and feature extraction capabilities in environments with noisy tags.

[0125] Experimental results under finite failure sample conditions

[0126] To evaluate the performance of the proposed method under limited fault sample conditions, a small sample dataset with a sample size ranging from 10 to 100 was set up, and the evaluation results are shown in Table 6.

[0127] Table 6. Average test accuracy of different methods under different limited fault sample conditions

[0128]

[0129]

[0130] As shown in Table 6, the average test accuracy of methods 1 and 2 proposed in this invention is higher than that of methods 3 and 4 when the number of fault samples is limited from 10 to 70. In particular, when the number of fault samples is 10, the average diagnostic accuracy of the proposed methods is as high as 90% or more. This indicates that the proposed methods successfully overcome the difficulty of deep learning models relying heavily on sufficient labeled training samples and exhibit good robustness under limited fault sample conditions.

[0131] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A method for diagnosing composite faults in gearboxes based on optimal Legendre multi-wavelet frequency bands, characterized in that: At least the following steps are included: Step 1: Data acquisition, using the PHM2009 composite gearbox fault dataset; Step 2: Initialize the algorithm; Step 3: Sample processing, allocate 75% of the total samples for each gearbox failure category to the training samples and 25% to the test samples; Step 4: Legendre multiwavelet decomposition; Step 5: Execute the improved adaptive thresholding denoising algorithm, including: Noise estimation in the optimal high-frequency band of the Legendre multiwavelet: Let W = [w1, w2, ..., w N ] is a vector composed of the squares of the Legendre multiwavelet coefficients of each optimal high-frequency band arranged in ascending order; The minimum value of the risk vector R calculated by formula (1) is taken as the unbiased risk estimate: ； The minimum value of the risk vector R is expressed as: Using the index b corresponding to the risk value, select the square w of the Legendre multiwavelet coefficient at the corresponding position in vector W. b As the minimum risk coefficient, the threshold is estimated by formula (2): Where σ is the standard deviation of the optimal high-frequency band signal, and η is a parameter determined by numerical simulation experiments according to different application scenarios; Based on the threshold estimation in formula (2), the improved adaptive threshold denoising algorithm is obtained as follows: ； in, The adaptive weighting coefficient model is constructed; the optimal unbiased risk estimation threshold λ on different optimal Legendre multi-wavelet high-frequency bands is obtained through unbiased risk estimation. Step 6: Feature extraction. For each denoised optimal Legender multi-wavelet high-frequency band and the undenoised Legender multi-wavelet low-frequency band, calculate the statistical feature combination standard deviation + kurtosis and entropy + skewness as the feature input of the BP neural network. Step 7: Train the BP neural network, normalize the obtained optimal features to between 0 and 1, and train the BP neural network through the gradient descent learning algorithm. Then, pass the normalized result of the optimal features obtained on the test sample to the BP neural network to calculate the test diagnosis accuracy, so as to complete the performance evaluation of the proposed method. Step 8: Fusion of the genetic algorithm and the improved adaptive threshold denoising algorithm. If the accuracy of fault diagnosis does not reach the expected accuracy, the decomposition level of the multi-wavelet, the number of Legendre multi-wavelets, and the number of neurons in the BP neural network are updated through the genetic algorithm, and steps 4 to 7 are repeated to obtain higher fault diagnosis accuracy. The fusion of the genetic algorithm and the improved adaptive threshold denoising algorithm includes the following steps: Step 8.1: The fitness function of the genetic algorithm adopts the expected accuracy of fault diagnosis, and the calculation formula is Equation (5): ； Wherein, TP, TN, FP and FN represent true positives, true negatives, false positives and false negatives, respectively; Step 8.2: The weight coefficients of the BP neural network are learned through the gradient descent algorithm. When the loss function reaches the predetermined lower limit or the number of iterations reaches the predetermined maximum value, the adjustment process of the network weight coefficients stops. At this time, if the fault diagnosis accuracy does not reach the target, a genetic algorithm is used to further select better values ​​of the network structure parameters. Step 8.3: Let GA(·) represent the optimization process of the genetic algorithm for the network structure parameters, GD(·) represent the learning process of the weight coefficients of the BP neural network, and Fitness(·) represent the fitness function of the genetic algorithm. The designed Max min objective function is Equation (6): Where n, p, and ξ represent the decomposition level, the number of Legendre multi-wavelets, and the number of hidden layer neurons in the BP neural network, respectively, and λ represents the optimal unbiased risk estimation threshold in each optimal Legendre multi-wavelet high-frequency band. Step 9: Output the results. If the accuracy of the fault diagnosis reaches the expected accuracy, output the highest diagnostic accuracy and the corresponding multi-wavelet decomposition level, the number of Legendre multi-wavelets, and the number of neurons in the BP neural network.

2. The gearbox composite fault diagnosis method based on optimal Legendre multi-wavelet frequency bands according to claim 1, characterized in that: The gearbox model in the PHM2009 composite gearbox fault dataset is ER-10K. The PHM2009 composite gearbox fault dataset contains six different health conditions for gearbox fault signals. Each signal is collected under five different conditions: speeds of 30, 35, 40, 45, and 50 Hz. The sampling frequency for each signal is 66.7 kHz, and the sampling time is 8 seconds.

3. The gearbox composite fault diagnosis method based on optimal Legendre multi-wavelet frequency bands according to claim 1, characterized in that: The initialization algorithm includes initializing the number of iteration steps of the genetic algorithm, the number of iteration steps of the gradient descent algorithm, the decomposition level, the number of Legendre wavelets, the number of hidden layer neurons of the BP neural network, the number of chromosomes, the crossover probability, the mutation probability, the training samples and test samples, the training error of the BP neural network at the end of iteration, and the expected fault diagnosis accuracy.

4. The gearbox composite fault diagnosis method based on optimal Legendre multi-wavelet frequency bands according to claim 1, characterized in that: The improved adaptive threshold denoising algorithm further includes: Experiment-based threshold parameter selection: According to formula (2), the Legendre multi-wavelet coefficients of the optimal decomposition level are used to estimate the optimal threshold. The performance of the improved adaptive threshold denoising algorithm is evaluated using the root mean square error, and the calculation formula is Equation (4): Where N0 is the number of sample points, x i It is the i-th element of the original signal, y i It is the i-th element of the denoised signal reconstructed using the inverse Legendre multiwavelet transform; A lower RMSE value indicates that the denoising algorithm has better denoising performance.

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