A Transmission Fault Diagnosis Method Based on Wavelet Packet and Deep Autoencoder

Abstract

The present invention provides a gearbox fault diagnosis method based on wavelet packet and deep autoencoder, including: determining a wavelet basis function and a decomposition level, performing wavelet packet decomposition on an initial signal to obtain target decomposition coefficients, reconstructing the target decomposition coefficients according to a determined threshold to obtain a reconstructed signal; extracting the energies contained in different frequency bands of the reconstructed signal to form a feature vector, inputting the feature vector into an SDAE network for learning to extract deep features; performing forward unsupervised pre-training on the SDAE network and fine-tuning the trained SDAE network; selecting the structural parameters of the SDAE network based on a genetic algorithm; training and optimizing the weights of the SDAE network based on a genetic algorithm and a BP algorithm; and performing fault diagnosis on the deep features by using the optimized SDAE network. The present invention improves the denoising effect of the signal and the retention effect of effective components, and can accurately diagnose the gear faults of the gearbox.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent fault diagnosis, and particularly to a gearbox fault diagnosis method based on wavelet packet and deep autoencoder. Background Art

[0002] The application of using relevant theories of signal processing to detect faults in gearboxes is extensive. However, under actual working conditions of the gearbox, its vibration signal contains various noise interference signals and internal vibration coupling signals. When denoising the data, some frequency-domain information is easily lost, resulting in the loss of singular points that are sensitive to fault detection in non-stationary signals. Through the detection method of single signal processing, there are many disadvantages in some cases, and it is difficult to accurately abstract the fault feature expression. Therefore, it highly depends on the practical experience of engineering personnel. In addition, when using shallow models such as SVM (Support Vector Machine) and ELM (Extreme Learning Machine) for mechanical fault diagnosis, the self-learning ability of the model is limited, and it is difficult to well represent the complex mapping relationship between data and different fault states.

[0003] Therefore, there is an urgent need for a fault diagnosis method that can improve the signal-to-noise ratio of vibration signals and the model feature abstraction ability, and avoid local optimality in weight training. Summary of the Invention

[0004] Based on this, it is necessary to provide a gearbox fault diagnosis method based on wavelet packet and deep autoencoder for the above technical problems.

[0005] A gearbox fault diagnosis method based on wavelet packet and deep autoencoder includes the following steps: determining a wavelet basis function and the decomposition level, performing wavelet packet decomposition on the initial signal to obtain target decomposition coefficients, determining a corresponding threshold based on a threshold function, and reconstructing the target decomposition coefficients according to the threshold to obtain a reconstructed signal, where the threshold function is:

[0006]

[0007]

[0008] Among them, η(x, th, m) is a threshold function, x is the input signal, m is the adjustment coefficient, and th is the threshold; extract the energy contained in different frequency bands of the reconstructed signal to form a feature vector, and input the feature vector into the SDAE network for learning to extract deep features; perform forward unsupervised pre-training on the SDAE network, and fine-tune the trained SDAE network; select the structural parameters of the SDAE network based on the genetic algorithm; train and optimize the weights of the SDAE network based on the genetic algorithm and the BP algorithm; use the optimized SDAE network to perform fault diagnosis on the deep features.

[0009] In one embodiment, the extracting the energy contained in different frequency bands of the reconstructed signal to form a feature vector and inputting the feature vector into the SDAE network for learning to extract deep features specifically includes: performing wavelet packet decomposition on the initial signal, selecting the wavelet basis function of db8, with the decomposition level being 3 layers and a total of 8 frequency bands; obtaining the energy corresponding to each self-frequency band, and the formula is:

[0010]

[0011] Form a vector T from the energies of each sub-frequency band:

[0012]

[0013] Perform normalization processing on the vector T to obtain the feature vector:

[0014]

[0015] Input the feature vector into the SDAE network for learning to extract deep features.

[0016] In one embodiment, the performing forward unsupervised pre-training on the SDAE network specifically includes: using the gradient descent method to obtain the minimum value of the loss function, and the formula is:

[0017]

[0018] In the formula, is the gradient of the loss function, and the parameter η represents the learning rate; train the DAE model based on the minimum value of the loss function and stack it to form the trained SDAE model.

[0019] In one embodiment, the fine-tuning the trained SDAE network specifically includes: assuming that i is a neuron in the corresponding output layer l ni The corresponding residual is:

[0020]

[0021] The expression of the hidden layer residual is:

[0022]

[0023]

[0024] Among them, the parameter i refers to the i-th neuron in the l-th hidden layer, and the parameter j refers to the j-th neuron in the (l + 1)-th hidden layer, and ρ j represents the average activation value; the partial derivatives of the input and the mean square error function of the input with respect to the weight matrix W and the hidden layer threshold b are obtained respectively:

[0025]

[0026]

[0027] Update the weight parameters:

[0028]

[0029]

[0030] Among them, η represents the learning rate, that is, the rate of weight matrix and threshold update.

[0031] In one embodiment, the selection of the structural parameters of the SDAE network based on the genetic algorithm specifically includes: determining the number of nodes and the interval of the sparse parameter in each layer of the hidden layer of the SDAE network, encoding the number of nodes and the sparse parameter in the interval by binary coding, and decoding to obtain the network structure; obtaining the initial value, training the network structure according to the initial value; comparing the actual output of the network with the expected output, obtaining the error value, and obtaining the fitness value through the fitness function, selecting the individuals within the preset range of the fitness function to form the parental population; performing genetic operations of selection, crossover and mutation on the parental population to obtain the next generation population; repeating training, individual selection and genetic operations until the number of iterations reaches the maximum number of iterations; after the iteration stops, obtaining the optimal individual, and decoding the optimal individual to obtain the structural parameters.

[0032] In one embodiment, the training and optimization of the weights of the SDAE network based on the genetic algorithm and the BP algorithm specifically include: encoding the weights of the SDAE network using binary encoding; randomly selecting the initial weights of the SDAE network in a preset interval and initializing the population according to the initial weights; training each network using the training sample set, calculating the reconstruction error value, and calculating the reconstruction fitness value according to the reconstruction error value; selecting the individual with the optimal fitness based on the fitness value of the individual; performing genetic operations of selection, crossover, and mutation on the individual with the optimal fitness to obtain the next generation of individuals; determining whether the number of iterations has reached the maximum value. If not, continue training, individual selection, and genetic operations until the number of iterations reaches the maximum value, and output the last generation of individuals as the result; decoding the last generation of individuals to obtain the optimal initial weights and providing them to the BP algorithm to update the weights through the principle of backpropagation.

[0033] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows: By determining the wavelet basis function and the decomposition level, performing wavelet packet decomposition on the initial signal to obtain the target decomposition coefficients, determining the corresponding threshold based on the threshold function, reconstructing the target decomposition coefficients according to the threshold to obtain the reconstructed signal, and extracting the energy contained in different frequency bands of the reconstructed signal to form a feature vector, inputting the feature vector into the SDAE network for learning to extract deep features, so as to improve the signal denoising effect while increasing the retention degree of the effective components in the signal. Performing forward unsupervised pre-training on the SDAE network and fine-tuning, selecting the optimal structural parameters of the SDAE network based on the genetic algorithm, and training and optimizing the weights of the SDAE network based on the genetic algorithm and the BP algorithm. Using the optimized SDAE network to perform fault diagnosis on the deep features improves the feature extraction ability and generalization performance of the SDAE network, and can accurately diagnose the gear faults of the gearbox. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 FIG. is a schematic flowchart of a gearbox fault diagnosis method based on wavelet packet and deep autoencoder in one embodiment;

[0035] Figure 2 is Figure 1 the algorithm flowchart of step S104 in

[0036] Figure 3 FIG. is a comparison chart of the reconstruction errors of the SDAE network before and after optimization. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0037] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below through specific embodiments in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0038] In one embodiment, as Figures 1 to 3 shown, a gearbox fault diagnosis method based on wavelet packet and deep autoencoder is provided, including the following steps:

[0039] Step S101: Determine the wavelet basis function and the decomposition level, perform wavelet packet decomposition on the initial signal to obtain the target decomposition coefficients, determine the corresponding threshold based on the threshold function, and reconstruct the target decomposition coefficients according to the threshold to obtain the reconstructed signal.

[0040] Specifically, when performing wavelet packet decomposition on the initial signal, it is a multi-layer decomposition based on the full frequency. After wavelet packet decomposition, two types of decomposition coefficients will be obtained, namely the target decomposition coefficients and the noise decomposition coefficients. Since the amplitude of the noise decomposition coefficients is smaller than that of the target decomposition coefficients, the method of threshold denoising can be used to filter the noise of the initial signal: by setting an appropriate threshold, the decomposition coefficients smaller than the threshold are identified as the noise part and discarded; the decomposition coefficients greater than the threshold are identified as the target signal part, and this part is retained or shrunk to a certain extent. After the threshold processing is completed, the wavelet packet reconstruction process is performed according to the target decomposition coefficients to obtain the reconstructed signal after filtering the noise.

[0041] In addition, for the gearbox vibration signal under a strong noise background, through the improved wavelet packet threshold denoising method of the present invention, while achieving a good denoising effect, it can retain the characteristic parts in the signal as much as possible, effectively improve the signal-to-noise ratio, reduce the mean square error, and significantly improve the anti-noise performance of the diagnosis method.

[0042] Among them, the threshold function is:

[0043]

[0044]

[0045] Among them, η(x,th,m) is the threshold function, x is the input signal, m is the adjustment coefficient, th is the threshold, and the softness and hardness of the threshold function are adjusted by adjusting the size of m j to adjust the softness and hardness of the threshold function.

[0046] Step S102: Extract the energy contained in different frequency bands of the reconstructed signal to form a feature vector, input the feature vector into the SDAE network for learning, and extract deep features.

[0047] Specifically, when there is no fault, the gear will vibrate due to the effects of internal and external excitations. However, when there is a fault, the transmission error will become larger, and the repeated mutual excitation of impact vibration may increase the vibration. When the gear has faults such as broken teeth and cracks, the longer-period components in the vibration amount will be affected; when the gear has faults such as wear and pitting, the short-period components in the fault vibration amount will be affected, and the harmonic amplitude will also change. Therefore, due to different fault types, the vibration signal of the gearbox will cause the energy contained in some frequency bands to increase, while the energy contained in some frequency bands will decrease. Based on this, the energy contained in different frequency bands of the vibration signal can be extracted to form a feature vector, and the feature vector can be input into the SDAE network for learning to extract deep features.

[0048] In this embodiment, the fault information of the signal is enriched by extracting the energy characteristics of different frequency bands of the signal, and the signal processing method is combined with the deep learning method. The deep autoencoder is used to further learn and extract the deep features of the fault, effectively improving the feature abstraction ability of the model.

[0049] Among them, SDAE (stacked denoised autoencoder) is an unsupervised neural network model, also known as a deep autoencoder. The SDAE network is formed by stacking multiple DAEs (denoising autoencoders). The hidden layer of the previous denoising autoencoder is used as the input layer of the next denoising autoencoder. The denoising autoencoders are connected to form a linked list to obtain the SDAE network. The use of a multi-layer network structure such as the SDAE network can improve the learning ability of the model and mine more required feature quantities.

[0050] The specific steps of wavelet packet energy extraction are: decomposing the initial signal by wavelet packet, selecting the wavelet basis function of db8, decomposing 3 layers, and 8 frequency bands in total; calculating the energy corresponding to each self-frequency band, the formula is:

[0051]

[0052] The energy of each sub-band is formed into a vector T:

[0053]

[0054] Normalize the vector T to obtain the eigenvector:

[0055]

[0056] The feature vector is input into the SDAE network for learning and deep features are extracted.

[0057] Specifically, when a gear fails, the energy in each frequency band will change significantly, and the frequency band energy distributions corresponding to different types of failures are also different. Therefore, the energy distribution in different frequency bands can be extracted as a feature vector and input into the SDAE network for learning to obtain deep features, thereby improving the effect of feature extraction.

[0058] Step S103: Perform forward unsupervised pre-training on the SDAE network and fine-tune the trained SDAE network.

[0059] Specifically, performing forward unsupervised pre-training on the SDAE network means training the DAE networks in the SDAE network sequentially. The hidden layer of the last DAE network contains the feature signals of the input signal. Through forward unsupervised pre-training, multiple DAE networks are trained in an unsupervised learning manner to stack and form the SDAE network. When training a single DAE network, in order to enable the hidden layer to reconstruct the input layer as much as possible, the minimum value of the loss function needs to be obtained.

[0060] Among them, the gradient descent method is used to obtain the minimum value of the loss function, and the formula is:

[0061]

[0062] In the formula, is the gradient of the loss function, and the parameter η represents the learning rate; the DAE model is trained based on the minimum value of the loss function and stacked to form the trained SDAE model.

[0063] Specifically, since the loss function is usually a high-dimensional non-linear function, the gradient descent method can be selected for optimization, that is, the minimum value of the loss function is solved along the direction of its gradient descent. In this embodiment, the batch gradient descent algorithm is used, and the full sample is used to update the gradient each time. Compared with the stochastic gradient descent method, the batch gradient descent algorithm can obtain a global optimal solution, but the training time consumed will also be longer.

[0064] After the pre-training is completed, the SDAE network is fine-tuned. Starting from the last layer of the SDAE network, the parameters of the SDAE network are fine-tuned layer by layer backward based on the existing labels using the backpropagation BP algorithm.

[0065] Among them, the specific steps of fine-tuning are: assume that i is a neuron in the corresponding output layer l ni The corresponding residual is:

[0066]

[0067] The expression of the hidden layer residual is:

[0068]

[0069]

[0070] Among them, the parameter i refers to the i-th neuron in the l-th hidden layer, and the parameter j refers to the j-th neuron in the (l + 1)-th hidden layer, and ρ j represents the average activation value; the partial derivatives of the input and the mean squared error function of the input with respect to the weight matrix W and the hidden layer threshold b are calculated respectively:

[0071]

[0072]

[0073] Update the weight parameters:

[0074]

[0075]

[0076] Among them, η represents the learning rate, that is, the rate of weight matrix and threshold update.

[0077] Specifically, after the fine-tuning is completed, the feature identification of the SDAE network for the gear state can be optimized, so that the model has the ability to diagnose the faults of the gear state.

[0078] Step S104, select the structural parameters of the SDAE network based on the genetic algorithm.

[0079] Specifically, the genetic algorithm can select multiple initial points for parallel computing, thereby improving the computing efficiency, avoiding the problem of local optimum, and the genetic algorithm has self-adaptability. The genetic algorithm uses the principle of probability transformation to solve the optimal value, avoiding the way of brute-force enumeration, with low algorithm complexity and high overall efficiency.

[0080] Such as Figure 2 shown, the specific steps of using the genetic algorithm to select the structural parameters of the SDAE network are: determine the number of nodes in each layer of the hidden layer of the SDAE network and the interval of the sparse parameter, and encode the number of nodes and the sparse parameter in the interval through binary encoding, and decode to obtain the network structure; obtain the initial value, and train the network structure according to the initial value; compare the actual output of the network with the expected output, obtain the error value, and obtain the fitness value through the fitness function, and select the individuals within the preset range of the fitness function to form the parent population; perform genetic operations of selection, crossover and mutation on the parent population to obtain the next generation population; repeat the training, individual selection and genetic operations until the number of iterations reaches the maximum number of iterations; after the iteration stops, obtain the optimal individual, and decode the optimal individual to obtain the structural parameters.

[0081] Specifically, determine the number of nodes and the range of sparse parameters for each layer in the hidden layer of the SDAE network, determine the corresponding interval range, perform binary encoding on the number of nodes and sparse parameters within the interval. After encoding, n chromosomes are generated, and the network structure is obtained through decoding; randomly generate an initial population, obtain the corresponding initial values, and train the network structure with the initial values; during the training process, compare the actual output of the DAE network with the expected output to obtain an error value, input the error value into the fitness function to obtain the corresponding fitness value, and select some individuals with larger fitness values to form a parental population; perform genetic operations such as selection, crossover, and mutation on the parental population to obtain the next generation population from the parental population; repeat the training, individual selection, and genetic operations until the number of iterations reaches the preset maximum number of iterations; after the iteration stops, obtain the last population as the optimal individual, and decode the optimal individual to obtain the optimized SDAE network structure parameters. By adaptively selecting the structure parameters through the genetic algorithm, the computational efficiency is improved, and the problem of local optimality can be avoided.

[0082] Step S105, train and optimize the weights of the SDAE network based on the genetic algorithm and the BP algorithm.

[0083] Specifically, since the traditional BP algorithm cannot solve the global optimal value and the required training time is too long, after the network structure parameters are determined, continue to select the genetic algorithm for global search to optimize the initial connection weights of the network.

[0084] When the BP (Back Propagation) algorithm updates the weights, it is necessary to first find a set of suitable initial weights and update the weights through backpropagation based on the initial weights. Therefore, the genetic algorithm and the BP algorithm can be combined. Before training the network, use the genetic algorithm to optimize the initial weights, provide the value of the obtained optimal individual to the BP algorithm, and then the BP algorithm performs backpropagation to update the initial weights.

[0085] Among them, the specific steps for optimizing the weights of the SDAE network are as follows: encoding the weights of the SDAE network using binary encoding; randomly selecting the initial weights of the SDAE network in a preset interval, and initializing the population according to the initial weights; training each network using the training sample set, calculating the reconstruction error value, and calculating the reconstruction fitness value based on the reconstruction error value; selecting the individual with the optimal fitness based on the fitness value of the individual; performing genetic operations of selection, crossover, and mutation on the individual with the optimal fitness to obtain the next generation of individuals; determining whether the number of iterations has reached the maximum value. If not, continue with training, individual selection, and genetic operations until the number of iterations reaches the maximum value, and output the individuals of the last generation as the result; decoding the individuals of the last generation to obtain the optimal initial weights, and providing them to the BP algorithm to update the weights through the principle of backpropagation.

[0086] Specifically, when encoding the weights of the SDAE network, in order to improve the encoding efficiency, the binary encoding method can be used, which has simple operations and is easy to operate; in the preset interval [-1, 1], select real numbers as the initial weights of the SDAE network for population initialization; train each DAE network using the training sample set, calculate the reconstruction error value, input the reconstruction error value into the fitness function to obtain the reconstruction fitness value; select the individuals within the preset range of the reconstruction fitness value, denoted as the individuals with the optimal fitness; perform genetic operations of selection, crossover, and mutation on the individuals with the optimal fitness to generate the next generation of individuals; determine whether the current number of iterations has reached the maximum value. If not, continue with the above training, individual selection, and genetic operations until the number of iterations reaches the maximum value, and output the individuals of the last generation as the result. Decode the individuals of the last generation to obtain the initial weights that meet the requirements, input the initial weights into the BP algorithm, and use the principle of backpropagation to update the weights, realizing the optimization of the SDAE network, improving the feature extraction ability and generalization performance of the SDAE network, and enhancing the anti-noise ability, and being able to accurately diagnose the gear faults of the gearbox.

[0087] The present invention realizes the adaptive selection of the SDAE network parameters and the training of the training weights through the genetic algorithm, effectively avoiding the drawbacks of selecting network parameters through a large number of experiments and avoiding the local optimal problem of weight training; at the same time, the optimized SDAE network has a smaller reconstruction error, and the feature extraction ability and generalization performance are further enhanced, improving the diagnostic accuracy of the gearbox gears.

[0088] Step S106, using the optimized SDAE network to perform fault diagnosis on the deep features.

[0089] Specifically, after the vibration signal is decomposed by wavelet packet decomposition, the energy distribution of the vibration signal at different scales is obtained. Each component contains information at different scales, with more abundant information than the original signal. Different fault types have different fault frequencies. Therefore, when different types of faults occur, the signals in different frequency bands will also change accordingly. Compared with extracting fault features from the original signal, more effective deep features can be extracted from the signal components in different frequency bands. Moreover, combined with the optimized SDAE network, the diagnosis of gear faults in the gearbox can be realized.

[0090] Based on the gear vibration signal, deep features are extracted. The deep features contain information about whether the gear is faulty and fault information such as broken teeth, cracks, wear, and pitting. Therefore, after obtaining the deep features of the vibration signal, it is possible to identify whether there is a fault in the gear according to the optimized SDAE network, and when there is a fault, which type of fault it is among broken teeth, cracks, wear, and pitting, so as to accurately judge the state of the gearbox gear.

[0091] In this embodiment, by determining the wavelet odd function and the decomposition layer number, the initial signal is decomposed by wavelet packet decomposition to obtain the target decomposition coefficients. Based on the threshold function, the corresponding threshold is determined. According to the threshold, the target decomposition coefficients are reconstructed to obtain the reconstructed signal, and the energy contained in different frequency bands of the reconstructed signal is extracted to form a feature vector. The feature vector is input into the SDAE network for learning to extract deep features, so as to improve the signal denoising effect and the retention degree of effective components in the signal at the same time. The SDAE network is pre-trained forward without supervision and fine-tuned. The optimal structural parameters of the SDAE network are selected based on the genetic algorithm, and the weights of the SDAE network are trained and optimized based on the genetic algorithm and the BP algorithm. The optimized SDAE network is used to diagnose faults in the deep features, improving the feature extraction ability and generalization performance of the SDAE network, and being able to accurately diagnose gear faults in the gearbox.

[0092] Obviously, those skilled in the art should understand that the above-mentioned modules or steps of the present invention can be implemented by a general-purpose computing device. They can be concentrated on a single computing device or distributed on a network composed of multiple computing devices. Optionally, they can be implemented by program codes executable by the computing device, so that they can be stored in a computer storage medium (ROM / RAM, magnetic disk, optical disk) and executed by the computing device. And in some cases, the steps shown or described can be executed in a different order than here, or they can be made into individual integrated circuit modules respectively, or multiple modules or steps among them can be made into a single integrated circuit module to implement. Therefore, the present invention is not limited to any specific combination of hardware and software.

[0093] The above content is a further detailed description of the present invention in combination with specific implementation manners. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A gearbox fault diagnosis method based on wavelet packet and deep autoencoder, characterized in that It includes the following steps: Determine the wavelet basis function and the decomposition level, perform wavelet packet decomposition on the initial signal to obtain the target decomposition coefficients, set a preset threshold, adjust the corresponding preset threshold based on the threshold function, and reconstruct the target decomposition coefficients according to the preset threshold to obtain a reconstructed signal, where the threshold function is: ； ； Among them, is a threshold function, is an input signal, is an adjustment coefficient, is a preset threshold; Extract the energies contained in different frequency bands of the reconstructed signal to form a feature vector, input the feature vector into the SDAE network for learning, and extract deep features; Perform forward unsupervised pre-training on the SDAE network, and fine-tune the trained SDAE network; Select the structural parameters of the SDAE network based on the genetic algorithm; Train and optimize the weights of the SDAE network based on the genetic algorithm and the BP algorithm; Use the optimized SDAE network to perform fault diagnosis on the deep features.

2. The gearbox fault diagnosis method based on wavelet packet and deep autoencoder according to claim 1, characterized in that The extracting the energies contained in different frequency bands of the reconstructed signal to form a feature vector, inputting the feature vector into the SDAE network for learning, and extracting deep features specifically includes: Perform wavelet packet decomposition on the initial signal, select the wavelet basis function of db8, and the decomposition level is 3 layers, with a total of 8 frequency bands; Calculate the energy corresponding to each self-frequency band, and the formula is: ； Form a vector T with the energies of each sub-frequency band: ； Perform normalization processing on the vector T to obtain a feature vector: ； Input the feature vector into the SDAE network for learning to extract deep features.

3. A gearbox fault diagnosis method based on wavelet packet and deep autoencoder according to claim 1, characterized in that, The performing forward unsupervised pre-training on the SDAE network specifically includes: Use the gradient descent method to obtain the minimum value of the loss function, and the formula is: ； In the formula, is the loss function gradient, and the parameter represents the learning rate; Train the DAE model based on the minimum value of the loss function, and stack to form a trained SDAE model.

4. A gearbox fault diagnosis method based on wavelet packet and deep autoencoder according to claim 1, characterized in that, The fine-tuning the trained SDAE network specifically includes: Assume that i is a neuron corresponding to the output layer and the corresponding residual is: ； The expression of the hidden layer residual is: ； ； Among them, the parameter i refers to the i-th neuron in the -th hidden layer, and the parameter j refers to the j-th neuron in the -th hidden layer. represents the average activation value; Take the partial derivatives of the mean square error function of the input and the input with respect to the weight matrix W and the hidden layer threshold b respectively: ； ； Update the weight parameters: ； ； Among them, represents the learning rate, that is, the rate at which the weight matrix and the threshold are updated.

5. A gearbox fault diagnosis method based on wavelet packet and deep autoencoder according to claim 1, characterized in that, The selecting the structural parameters of the SDAE network based on the genetic algorithm specifically includes: Determine the number of nodes in each layer of the hidden layer of the SDAE network and the interval of the sparse parameters, and encode the number of nodes and the sparse parameters in the interval through binary coding, and decode to obtain the network structure; Obtain the initial value, and train the network structure according to the initial value; Compare the actual output of the network with the expected output to obtain an error value, and obtain a fitness value through the fitness function, and select the individuals within the preset range of the fitness function to form a parental population; Perform genetic operations of selection, crossover and mutation on the parental population to obtain the next generation population; Repeat the training, individual selection and genetic operations until the number of iterations reaches the maximum number of iterations; After the iteration stops, obtain the optimal individual, and decode the optimal individual to obtain the structural parameters.

6. The method for diagnosing gearbox faults based on wavelet packet and deep autoencoder according to claim 1, characterized in that The training and optimizing the weights of the SDAE network based on the genetic algorithm and the BP algorithm specifically includes: Encode the weights of the SDAE network using binary coding; Randomly select the initial weights of the SDAE network in the preset interval, and initialize the population according to the initial weights; Each network is trained using a training sample set, the reconstruction error value is calculated, and the reconstruction fitness value is calculated based on the reconstruction error value; Based on the fitness values of the individuals, the individual with the optimal fitness is selected; Genetic operations of selection, crossover, and mutation are performed on the individual with the optimal fitness to obtain the next generation of individuals; It is judged whether the number of iterations has reached the maximum value. If not, continue with training, individual selection, and genetic operations until the number of iterations reaches the maximum value, and the individuals of the last generation are output as the result; The individuals of the last generation are decoded to obtain the optimal initial weights, which are provided to the BP algorithm, and the weights are updated through the principle of backpropagation.

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