A method for analog circuit fault diagnosis based on wavelet scattering and ensemble learning

Abstract

The application discloses a kind of analog circuit fault diagnosis method based on wavelet scattering and ensemble learning, to solve the problem that analog circuit fault response aliasing leads to difficult fault diagnosis.First, the circuit response is divided into multiple frequency band subsets by wavelet scattering transform, and the fault features of the subsets are enhanced using Fisher discriminant analysis.Second, each frequency band subset is sent to different extreme learning machines under Bagging integration, and the classification accuracy of each fault mode in the frequency band subset is used as the class weight of the extreme learning machine.Then, the output values of each extreme learning machine are weighted to obtain the fused output result, and the fault class is determined accordingly.Finally, two example circuits are simulated, and the simulation results show that the diagnostic accuracy is 100%, indicating that the method is feasible and effective, and can realize fault classification and positioning.

Description

Technical Field

[0001] This invention relates to the field of analog circuit fault diagnosis, specifically to a method for extracting and enhancing frequency band subset features of analog circuit measurement point output signals, and pattern recognition technology, and more specifically to an analog circuit fault diagnosis method based on wavelet scattering and ensemble learning. Background Technology

[0002] In modern electronic systems, the integration level of mixed-signal circuits is increasing. Analog circuits, as an indispensable part of these systems, suffer from complexity and unpredictability in fault diagnosis due to the inherent tolerances of components and external interference. Furthermore, with the increasing integration of circuits, analog circuit diagnosis becomes increasingly difficult, and traditional methods such as fault dictionary methods, probabilistic statistical methods, and component parameter identification methods are no longer sufficient for practical needs. In response to this situation, scholars both domestically and internationally have researched novel intelligent methods, proposing numerous artificial intelligence-based approaches, such as neural networks, support vector machines, wavelet transforms, and mode decomposition.

[0003] Intelligent diagnostic methods mainly include fault feature extraction and diagnostic tool construction. Fault features of analog circuits are typically extracted from the time and frequency domain responses of the circuit under test. Appropriate feature extraction methods can provide inherent and essential information about the signal with minimal overlap. Generally, wavelet packet transform (WPT) and wavelet transform (WT) are used to extract features from the output response, obtaining the decomposition coefficients of each frequency band and the frequency band energy value. This is then combined with dimensionality reduction methods such as principal component analysis to obtain fault features. However, this method neglects the fault identification capabilities of different frequency bands, failing to fully utilize limited fault information. Furthermore, this feature extraction method lacks good coherence with pattern recognition models; the pattern recognition model cannot effectively target the extracted features, resulting in low algorithm-to-analysis matching and a low fault diagnosis rate. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a fault diagnosis method for analog circuits based on wavelet scattering and ensemble learning, thereby solving the problem of low fault diagnosis accuracy in existing technologies.

[0005] This invention addresses the problem of low accuracy in analog circuit fault diagnosis by extracting and classifying features of the output signal based on the phenomenon that slight differences in the output signal are caused by parameter deviations of different components in the circuit. This invention only targets soft faults in resistors and capacitors in the circuit, and each fault occurs only in a single component, excluding the special case where multiple components fail simultaneously. A soft fault is defined as a resistance or capacitance value deviating from its nominal value by ±30%. For example, a resistor with a nominal value of 100kΩ might have a soft fault of 70kΩ or 130kΩ. The circuit being diagnosed is collectively referred to as the circuit under test. If there is only one diagnosable resistor or capacitor in a circuit under test, then the circuit has three fault categories: deviation of 70% of the nominal value, no fault, and deviation of 130% of the nominal value. If there are two diagnosable resistors or capacitors, then the circuit has five fault categories, with no fault also considered a fault category. Whether the resistors and capacitors in the circuit under test can be diagnosed is determined by the sensitivity analysis in the simulation software. For example, if a time-series test signal is input to the input terminal of the circuit under test, and the output response of the component is no different under soft fault conditions and no fault conditions, then the sensitivity of the component in the circuit under test does not meet the basic conditions required for fault diagnosis, and the component cannot be diagnosed. Therefore, the output response of the circuit is the output of the circuit under test under various fault categories when a time-series test signal is input to the input terminal of the circuit under test, and a diagnosable component is identified, and a soft fault is artificially set for the diagnosable component. To ensure the effectiveness of the method of the present invention, the output response is divided into training set response and test set response in a 7:3 ratio. The training set response is used to train the model parameters in the method of the present invention, and the test set response is used to verify the final diagnostic effect of the method of the present invention. The pre-training part of the method of the present invention involves a secondary partitioning of the training set response, which will be described in detail in the specific implementation; the genetic algorithm used to train the model parameters is classic and will not be elaborated in detail.

[0006] The circuit response is divided into multiple frequency band subsets by wavelet scattering transform of the training set response, and Fisher discriminant analysis is used to enhance the fault characteristics of the frequency band subsets. Next, each frequency band subset is fed into different extreme learning machines under Bagging ensemble. These Bagging ensemble extreme learning machines are mainly divided into pre-trained extreme learning machines and classification extreme learning machines, with one pre-trained extreme learning machine corresponding to each frequency band subset. The classification accuracy of each fault category in the frequency band subset is obtained in the pre-trained extreme learning machine, and this accuracy is used as the category weight for each fault category in the frequency band subset. Then, the output values ​​of each pre-trained extreme learning machine are multiplied and summed with the category weights. The weighted fusion result is fed into the classification extreme learning machine to obtain the diagnostic result, thereby determining the fault category. In this invention, this method combining pre-training and classification is collectively referred to as Bagging subclass extreme learning machine.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] A fault diagnosis method for analog circuits based on wavelet scattering and ensemble learning includes the following steps:

[0009] Simulation data acquisition phase:

[0010] Step 1: Identify the circuit under test and perform sensitivity analysis on the circuit under test in simulation software to identify the diagnosable components in the circuit under test.

[0011] Step 2: Set soft faults for each diagnosable device. Under the conditions of 5% resistance tolerance and 10% capacitance tolerance, perform 100 Monte Carlo analyses for each fault category to obtain 100 simulated samples for each fault category. The simulated samples are used as the output response of the circuit under test, thus obtaining the simulation dataset.

[0012] Frequency band subset extraction stage:

[0013] Step 3: Divide all the collected output responses into training set responses and test set responses in a ratio of 7:3 or 6:4. Perform wavelet scattering transform on each sample in the training set response to obtain the scattering coefficient matrix of each sample. The scattering coefficient matrix is ​​composed of convolution coefficients generated by different scattering channels, and different scattering channels represent the response characteristics within a specific frequency band. When verifying the final diagnostic effect, wavelet scattering transform is also used to obtain the scattering coefficient matrix of each test set response sample.

[0014] Step four: Based on the relationship between the scattering coefficient matrix and the scattering channels, the two-dimensional scattering coefficient matrix obtained by transforming the training set response is split into multiple one-dimensional samples according to the scattering channels. These one-dimensional samples are then recombined into the same number of subsets according to the number of scattering channels. Each subset consists of convolution coefficients generated by the same scattering channel and represents the response characteristics within a specific frequency band. Therefore, they are collectively referred to as frequency band subsets. This completes the division of frequency band subsets. When verifying the final diagnostic effect, the same method is used to divide the scattering coefficient matrix of the test set response into frequency band subsets.

[0015] Fault Feature Enhancement Stage:

[0016] Step 5: Calculate the global scatter matrix, intra-class scatter matrix, and inter-class scatter matrix for each frequency band subset. Using Fisher discriminant analysis, obtain the mapping matrix for each frequency band subset. The mapping matrix is ​​multiplied with the frequency band subset to project the frequency band subset into a multi-dimensional space, so that the mapped samples of the same fault category are clustered as much as possible, and the samples of different fault categories are separated as much as possible, thereby enhancing the fault features of each frequency band subset of the fault.

[0017] Feature fusion and fault diagnosis stage:

[0018] Step 6: The frequency band subsets after fault feature enhancement are fed into the pre-trained extreme learning machine in the Bagging subclass extreme learning machine. During the pre-training stage, the enhanced frequency band subsets are divided into a pre-training set and a pre-test set in a 7:3 ratio. The pre-training set is used to train the pre-trained extreme learning machine in the Bagging subclass extreme learning machine. The pre-test set is used to classify and verify the pre-training results. The verification results consist of the classification accuracy of each fault category. The verification results are used as the class weights of the enhanced frequency band subsets, thus obtaining the class weights of each enhanced frequency band subset.

[0019] Step 7: Multiply the output of the pre-trained extreme learning machine in the Bagging subclass extreme learning machine with the corresponding class weights to achieve feature fusion. The result of feature fusion is then fed into the classification extreme learning machine in the Bagging subclass extreme learning machine for training. The output Y of the classification extreme learning machine is compared with the label to obtain the diagnostic accuracy. During the training process, a genetic algorithm is used to optimize the parameters of the extreme learning machine. The classification accuracy of the test set response is used as the final diagnostic effect to complete the fault diagnosis.

[0020] This invention proposes innovations based on frequency band information and pattern recognition:

[0021] This invention first extracts a subset of the output response frequency band of the circuit output point, enhances the fault characteristics of the frequency band subset using the Fisher criterion, and then establishes a diagnostic classification model based on the ability to identify different fault modes under different frequency bands, thereby achieving accurate identification of analog circuit faults.

[0022] Effects or advantages of the present invention:

[0023] This invention establishes an analog circuit fault diagnosis model based on the differences in circuit output under different fault modes. Since the simulation is performed under the condition that the resistance tolerance is 5% and the capacitance tolerance is 10% in the circuit under test, it has a certain degree of anti-interference capability. Simulation verification is performed using two example circuits: a Sallen-Key bandpass filter and a quad operational amplifier dual-secondary circuit. The simulation results show a diagnostic accuracy of 100%, indicating that the method is feasible and effective, and can achieve fault classification and location. Attached Figure Description

[0024] Figure 1 This is a diagram of the wavelet scattering network framework.

[0025] Figure 2 A schematic diagram illustrating frequency band subsets and fault feature enhancement;

[0026] Figure 3 This is a diagram of the Extreme Learning Machine (ELM) structure for the Bagging subclass.

[0027] Figure 4 This is a block diagram of the analog circuit fault diagnosis method based on wavelet scattering and ensemble learning in the embodiment.

[0028] Figure 5 Here is the schematic diagram of the Sallen_key bandpass filter circuit.

[0029] Figure 6 This is the schematic diagram of a quad operational amplifier dual second-order circuit. Detailed Implementation

[0030] The invention will be further described below with reference to the accompanying drawings and embodiments, but this is not intended to limit the invention.

[0031] To better understand this invention, the basic principles and related concepts of this invention will be briefly introduced below.

[0032] Wavelet dispersion frequency band characteristics:

[0033] The wavelet scattering network was proposed by Professor Mallet in 2012. This method obtains the corresponding scattering coefficients through complex-valued wavelet transform, modulus operation, and cascaded averaging operation. It has the advantages of reducing data volume and model complexity, as well as automatically extracting relevant compact frameworks. In order to obtain signal features that are both translation-invariant and local deformation stable, the complex-valued Morlet wavelet, i.e., the bandpass filter, is first convolved with the input response, and then modulus operation is used. In order to ensure the stability of high-frequency coefficients, the scattering coefficients are obtained by averaging operation, i.e., convolving the low-pass filter. The above process can ensure local deformation stability, but high-frequency information will be lost, and the discriminative ability of diagnostic features will also be weakened. In order to recover the lost high-frequency information, after obtaining the general features by convolving the low-pass filter, the wavelet modulus of the previous layer is used to convolve the higher-frequency filter to recover the lost high-frequency part. The p-th channel of the wavelet scattering network is shown in Equation (1):

[0034] S[j1,j2,...,jp]x=U[j1,j2,...,jp]x*φ (1)

[0035] Where j represents the scaling coefficient, φ is the low-pass filter, ψ is the high-frequency wavelet, and x is the training set response divided by the circuit output response. The high-frequency part is represented as:

[0036]

[0037] j1<Λ<j p (3)

[0038] Meanwhile, Mallet demonstrated in experiments that the scattering energy reaches over 99% when the wavelet scattering network has three layers. Too many layers increase computational overhead, and redundant scattering coefficients approximate zero, causing feature redundancy. Therefore, this invention employs a three-layer scattering network structure. Each layer contains one or more scattering channels. The filter within each scattering channel convolves the input response, and the output after convolution is the scattering coefficient of that channel. The input response obtains corresponding scattering coefficients for each scattering channel, forming a scattering coefficient matrix. The wavelet scattering network framework is as follows: Figure 1 As shown, since the input response is convolved with high-pass filters of different numbers or scales on different scattering channels, each scattering channel coefficient represents the response characteristics within a specific frequency band.

[0039] Enhanced fault characteristics:

[0040] The training set response is transformed by wavelet scattering, and the resulting scattering coefficient matrix consists of p scattering channels, which can be divided into p frequency band subsets. The g-th frequency band subset is denoted as sg, where 1≤g≤p. The discriminable fault features and tolerance interference are distributed in these frequency band information. In order to highlight the discriminable fault features in the frequency band, Fisher discriminant analysis is introduced.

[0041] For the g-th frequency band subset, the mapping matrix w used to enhance fault characteristics is calculated. g This aims to cluster similar samples together as much as possible and separate samples from different classes as much as possible after mapping. The global scatter matrix S is defined as follows. gt Intraclass scatter matrix S gw and the inter-class scatter matrix S gb :

[0042] S gt =(s g -d g )(s g -d g ) T (4)

[0043]

[0044] Where d g Let represent the sample mean of the g-th frequency band subset, l represent the number of fault categories, and s represent the sample mean of the g-th frequency band subset. gi Let d represent the samples belonging to fault category i in the g-th frequency band subset, 1≤i≤l. gi Then, m represents the mean of the samples belonging to fault category i in the p-th frequency band subset. i This represents the number of training samples belonging to fault category i within the frequency band subset. Mapping matrix w g The mapping matrix is ​​constructed by maximizing the closed-form solution of the Fisher criterion function. The frequency band subset is projected into a multidimensional space by multiplying the mapping matrix and the frequency band subset. The Fisher criterion function of the g-th frequency band subset is maximized as shown in equation (7).

[0045]

[0046] Projecting the mapping matrix enhances the fault features of each frequency band subset, suppressing interference distributed across different frequency bands to some extent. This provides high-quality frequency band subsets for subsequent feature fusion and fault diagnosis. The frequency band subsets and fault feature enhancement are as follows: Figure 2 As shown, the projection of the mapping matrix is ​​given by equation (8), where s g ′ represents the enhanced g-th frequency band subset.

[0047] s g ′=w g s g (8).

[0048] Extreme Learning Machine:

[0049] Extreme Learning Machine (ELM) mainly consists of an input layer, hidden layers, and an output layer. Essentially, it is a single-hidden-layer feedforward neural network algorithm. The input layer and hidden layers, as well as the hidden layer and output layer, are fully connected.

[0050] In the Bagging subclass of Extreme Learning Machine, s g ′ corresponds to the g-th pre-trained Extreme Learning Machine (ELM) g m represents the number of training samples, s gm ' represents the m-th training sample, where each sample has n features and the sample label T. g To ensure the lowest possible output deviation, ELM g There are weights a between the input layer and the hidden layer g The hidden layer has a bias b g There is a weight β between the output layer and the hidden layer. g Hidden layer neuron output matrix H g The calculation equation is:

[0051]

[0052] In equation (9), η(·) is the activation function, h is the number of neurons in the hidden layer, and a gh b gh These represent the weights and biases of the h-th neuron in the hidden layer, respectively. ELM g The goal of training is to minimize the training error, such that the error E between the model's output after training and the true output is... g Minimize. Its objective equation is:

[0053]

[0054] In the formula T g The label represents the expected output. The weight β between the output layer and the hidden layer... g This can be obtained by solving the least squares problem:

[0055]

[0056] In equation (11), C is the penalty factor, and ELM g The output is Y g Y g =H g β g The output of the classification extreme learning machine is Y. ELM needs to optimize the parameters of the penalty factor C and the number of hidden layer neurons h. The activation function η() is the Sigmoid function.

[0057] Bagging subclass extreme learning machine:

[0058] To use the frequency band subset with the greatest differences among different faults as the basis for fault feature extraction, and to effectively reduce aliasing in analog circuit fault responses, a Bagging subclassing extreme learning machine that includes feature fusion and fault classification is proposed. The specific steps of fusion and classification are as follows:

[0059] 1. Divide the output response into training set response and test set response in a 7:3 ratio. After frequency band subset extraction and fault feature enhancement, generate an equal number of pre-trained ELMs based on the number p of enhanced frequency band subsets. Then, the inputs of the p ELMs and the corresponding labels of the samples are: Where s g ′ represents the g-th enhanced frequency band subset, which is also the ELM. g The input, T g s g The label corresponding to '.

[0060] 2. In step 1, the enhanced frequency band subset is divided twice in a 7:3 ratio to create a pre-training set and a pre-test set. The pre-training set and the pre-test set are each used for 0.7s... g ′ and 0.3s g The pre-trained extreme learning machine in the Bagging subclass is trained using a pre-training set. The pre-test set is used to validate the pre-training results, which consist of the classification accuracy for each fault category. These validation results are then used as the class weights for the enhanced frequency band subsets, thus obtaining the class weights z for each enhanced frequency band subset. g .

[0061] 3. Output Y from the pre-trained Extreme Learning Machine output layers of the p Bagging subclass Extreme Learning Machines. g The sum of the products of the corresponding output weights is used as the input X of the classification extreme learning machine in the Bagging subclass extreme learning machine, as shown in Equation (12). Feature fusion is now complete. The output Y of the classification extreme learning machine is compared with the label to obtain the diagnostic result. The structure of the Bagging subclass extreme learning machine is as follows: Figure 3 As shown,

[0062]

[0063] Diagnostic models based on wavelet scattering networks and ensemble learning:

[0064] To improve the fusion diagnostic performance of the Bagging subclass extreme learning machine, this invention employs a classic genetic algorithm (GA) to optimize the parameters of the ELM corresponding to the frequency band subset and the number of hidden layer neurons h and the penalty factor C in the classification ELM. GA is a representative classic method in evolutionary algorithms, mainly including selection, crossover, and mutation. Combined with the Bagging subclass extreme learning machine, the diagnostic accuracy is used as the fitness value of the genetic algorithm; training is complete when the optimal fitness no longer changes.

[0065] The analog circuit fault diagnosis framework proposed in this invention is as follows: Figure 4 As shown, the entire framework is divided into three parts: frequency band subset extraction, fault feature enhancement, and feature fusion and fault diagnosis. In the first part, a wavelet scattering network is used to perform convolution and modulo operations to obtain the scattering coefficient matrix and divide the system into multiple frequency band subsets. In the second part, based on the frequency band subsets, Fisher's discrimination criterion is used to enhance the fault features of each frequency band subset. The enhanced frequency band subsets are then fed into the Bagging subclass extreme learning machine in the third part. The model is trained using GA, and after training, it is fed into a test set to obtain the diagnostic results, thus completing the fault diagnosis.

[0066] Example:

[0067] like Figure 4 As shown, a fault diagnosis method for analog circuits based on wavelet scattering and ensemble learning includes the following steps:

[0068] Simulation data acquisition phase:

[0069] S1. Determine the circuit under test, perform sensitivity analysis on the circuit under test in simulation software, and determine the diagnosable components in the circuit under test under the test signal based on the analysis results.

[0070] S2. Set soft faults for each diagnosable device. Under the conditions of 5% resistance tolerance and 10% capacitance tolerance, perform 100 Monte Carlo analyses for each fault category to obtain 100 simulation samples for each fault category. The simulation samples are used as the output response x of the circuit under test, thus obtaining the simulation dataset.

[0071] Frequency band subset extraction stage:

[0072] S3, the response x obtained in S2 is divided into training set response and test set response in a ratio of 7:3. Each sample in the training set response is subjected to wavelet scattering transformation to obtain the scattering coefficient matrix of each sample.

[0073] S4, the scattering coefficient matrix of each sample in S3 is split into multiple one-dimensional samples. The scattering coefficient matrix consists of p scattering channels, which can be divided into p frequency band subsets. The g-th frequency band subset is represented as s. g 1≤g≤p, to achieve the division of frequency band subsets. When verifying the final diagnostic effect, the scattering coefficient matrix of the test set response is also divided into frequency band subsets using the same method, which can divide into p frequency band subsets.

[0074] Fault Feature Enhancement Stage:

[0075] S5, for s in S4 g Define the global scatter matrix S respectively. gt Intraclass scatter matrix S gw And the inter-class scatter matrix Sgb:

[0076] S gt =(s g -d g )(s g -d g ) T (13)

[0077]

[0078] Where d g Let represent the sample mean of the g-th frequency band subset, l represent the number of fault categories, and s represent the sample mean of the g-th frequency band subset. gi Let d represent the samples belonging to fault category i in the g-th frequency band subset, 1≤i≤l. gi Then, m represents the mean of the samples belonging to fault category i in the p-th frequency band subset. i The mapping matrix w represents the number of training samples belonging to fault category i within the frequency band subset. g The closed-form solution of maximizing the Fisher criterion function is constructed. The maximization of the Fisher criterion function for the g-th frequency band subset is shown in equation (16).

[0079]

[0080] Equation (17)s g ′ represents the enhanced g-th frequency band subset.

[0081] s g ′=w g s g (17)

[0082] Feature fusion and fault diagnosis stage:

[0083] S6, the frequency band subset s of S5 after fault feature enhancement. gThe enhanced frequency band subsets are fed into the pre-training extreme learning machine of the Bagging subclass extreme learning machine. During the pre-training phase, the subsets are divided into a pre-training set and a pre-test set in a 7:3 ratio. The pre-training set and the pre-test set are then processed using 0.7s... g ′ and 0.3s g ′ indicates that the pre-test set is used to classify and validate the pre-training results. The validation results consist of the classification accuracy of each fault category, and the validation results are used as the class weights of the enhanced frequency band subsets, thus obtaining the class weights z of each enhanced frequency band subset. g ;

[0084] S7 outputs Y from each frequency band subset of ELM in S6. g With weight z g The products are multiplied and the results are added to complete feature fusion. The fused result is then sent to the diagnostic ELM to obtain the final result, as shown in Equation (18). The number of hidden layer neurons h and the penalty factor C in the ELM are optimized by a genetic algorithm. This completes the fault diagnosis.

[0085]

[0086] Sallen-Key Circuit Fault Diagnosis and Analysis:

[0087] Taking the Sallen-Key bandpass filter circuit fault diagnosis model as an example, this paper details how the proposed method achieves fault location and fault diagnosis. After establishing the model, further experiments were conducted to verify its correctness.

[0088] The simulation experiment was conducted on a personal computer using an Intel(R) Core(TM) i5-4210M CPU. PSPICE 16.6 was used for simulation analysis and dataset acquisition, and MATLAB 2022a was used for data processing. First, the test signal source was set up for the simulation circuit. For the Sallen-key experiment, a square wave signal source with a frequency of 5kHz, a duty cycle of 50%, and an amplitude of 1V was selected. The transient analysis duration was 0.4ms, and the sampling rate was 250kHz. The resistor tolerance in the circuit was 5%, and the capacitor tolerance was 10%. A component was considered faulty when its actual value deviated from its nominal value by 30%. The Sallen-key circuit was as follows: Figure 5 As shown.

[0089] The simulation experiment is conducted as follows:

[0090] 1) After drawing the circuit diagram in OrCAD Pspice, sensitivity analysis shows that R2, R3, R4, R5, C1, and C2 in the Sallen-key filter circuit easily affect the circuit output. These components are set as diagnostic devices, and soft faults are configured. The fault settings are shown in Table 1, where NF indicates no fault in the circuit under test.

[0091] Table 1. Fault Modes of the Sallen-key Circuit

[0092]

[0093] 2) Simulation parameter settings and dataset partitioning:

[0094] A total of 1300 raw data samples, i.e., circuit output responses, were generated by performing 100 Monte Carlo analyses on each fault category in Table 1. Of these, 910 samples were assigned as training set responses and the remaining 390 samples were assigned as test set responses.

[0095] 3) Wavelet scattering transform:

[0096] The training set responses are processed by a wavelet scattering network to obtain wavelet scattering coefficient matrices for three scattering layers. Each scattering coefficient matrix consists of six scattering channels, with each channel containing 32 scattering coefficients. The three scattering layers contain channels 1, 2-4, and 5-6, respectively. Each channel represents a frequency band coefficient with a bandwidth of 34.064 kHz.

[0097] 4) Frequency band subset partitioning:

[0098] The wavelet scattering coefficient matrix of all samples is divided according to the scattering channel. The scattering coefficient matrix consists of 6 scattering channels, and therefore is divided into 6 frequency band subsets.

[0099] 5) Enhanced fault characteristics:

[0100] Based on Fisher's discrimination criterion, the mapping matrix is ​​obtained by maximizing the criterion function, which increases the similarity of samples of the same fault category after mapping and increases the difference between different categories, thereby achieving the effect of enhancing fault features.

[0101] 6) Feature fusion:

[0102] Based on p enhanced frequency band subsets, a 30% pre-test set is divided, and the remaining training set is used as the pre-training set. The classification accuracy of p ELMs for each fault category is obtained through pre-training and used as their respective class weights. The outputs of p ELMs are multiplied by the corresponding class weights and summed. The sum of the products is used as the input of the classification ELM. In order to compare the effect of fault feature enhancement, the class weights of each frequency band subset before and after enhancement are compared. The results before and after enhancement are shown in Tables 2 and 3. For easy observation, the mean weight of each fault category under the frequency band subset (class mean), the mean weight of each frequency band subset under the fault category (subset mean), and the overall mean (at the bottom right corner of the table) are added to the table.

[0103] Table 2 Enhanced Front Band Subset Category Weights

[0104]

[0105] Table 3. Enhanced Frequency Band Subset Category Weights

[0106]

[0107] 7) Fault diagnosis:

[0108] The fused results are fed into the classification ELM, and the model is optimized using a classic genetic algorithm to find the number of hidden layer neurons and the penalty factor, and finally the diagnostic results are obtained.

[0109] Fault diagnosis and analysis of a four-op-amp dual-secondary circuit:

[0110] The quad op-amp dual secondary circuit uses a 2kHz square wave signal source with a 50% duty cycle and an amplitude of 1V. The fault offset and parameter tolerance settings are the same as those of the Sallen-key circuit. The quad op-amp dual secondary circuit is as follows: Figure 6 As shown in Table 4, the fault settings are as follows.

[0111] Table 4 Fault Modes of Quad Op-Amp Dual Secondary Circuit

[0112]

[0113] The experimental results of this method are compared with those of other methods, as shown in Table 5.

[0114] Table 5 Comparison of Diagnostic Results

[0115]

[0116] This method utilizes wavelet scattering networks to extract response features from the time-frequency domain and fully leverages the effective features within each frequency band through the fusion processing of multiple frequency band subsets, resulting in diagnostic results superior to other methods in the literature. The fault feature enhancement process has been described above; after enhancing the fault features, the overall accuracy improved by 2.82% and 2.56%, respectively, demonstrating a significant enhancement effect.

[0117] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A fault diagnosis method for analog circuits based on wavelet scattering and ensemble learning, characterized in that, Includes the following steps: Simulation data acquisition phase: Step 1: Identify the circuit under test and perform sensitivity analysis on the circuit under test in simulation software to identify the diagnosable components in the circuit under test. Step 2: Set soft faults for each diagnosable device. Under the conditions of 5% resistance tolerance and 10% capacitance tolerance, perform 100 Monte Carlo analyses for each fault category to obtain 100 simulated samples for each fault category. The simulated samples are used as the output response of the circuit under test, thus obtaining the simulation dataset. Frequency band subset extraction stage: Step 3: Divide all the collected output responses into training set responses and test set responses in a ratio of 7:3 or 6:

4. Perform wavelet scattering transform on each sample in the training set response to obtain the scattering coefficient matrix of each sample. When verifying the final diagnostic effect, the test set response is also transformed using wavelet scattering transform to obtain the scattering coefficient matrix of each test set response sample. Step 4: Split the scattering coefficient matrix of each sample in the training set response into multiple one-dimensional samples, and recombine these one-dimensional samples into the same number of subsets according to the number of scattering channels. Each subset consists of convolution coefficients generated by the same scattering channels. When verifying the final diagnostic effect, the scattering coefficient matrix of the test set response is also divided into frequency band subsets using the same method. Fault Feature Enhancement Stage: Step 5: Calculate the global scatter matrix, intra-class scatter matrix, and inter-class scatter matrix for each frequency band subset. Maximize these matrices according to the Fisher criterion to obtain the mapping matrix for each frequency band subset. Multiply the mapping matrix with the frequency band subset to project the frequency band subset into a multi-dimensional space, so that the mapped samples of the same fault category are clustered as much as possible, and samples of different fault categories are separated as much as possible, thereby enhancing the fault features of each frequency band subset of the fault. Feature fusion and fault diagnosis stage: Step 6: Divide the enhanced frequency band sub-classes into a pre-training set and a pre-test set. Train the pre-trained extreme learning machine in the Bagging subclass extreme learning machine using the pre-training set. Use the pre-test set to classify and verify the pre-training results. The verification results consist of the classification accuracy of each fault category. Use the verification results as the category weights of the enhanced frequency band subsets to obtain the category weights of each enhanced frequency band subset. Step 7: Multiply the output of the pre-trained extreme learning machine output layer in the Bagging subclass extreme learning machine with the corresponding class weight to achieve feature fusion. Feed the fused feature result into the classification extreme learning machine in the Bagging subclass extreme learning machine for training. During the training process, a genetic algorithm is used to optimize the parameters of the extreme learning machine. The classification accuracy of the test set response is used as the final diagnostic effect to complete the fault diagnosis.

2. The analog circuit fault diagnosis method based on wavelet scattering and ensemble learning according to claim 1, characterized in that, In step two, the components selected in step one are limited to resistors and capacitors, and the output response differs between fault conditions and fault-free conditions.

3. The analog circuit fault diagnosis method based on wavelet scattering and ensemble learning according to claim 1, characterized in that, In step three, wavelet scattering transform is performed on the training set responses divided from the circuit output responses to obtain the scattering coefficient matrix of each training set response sample. The scattering coefficient matrix is ​​composed of the convolution results of the scattering channels. The p-th channel of the wavelet scattering network is shown in equation (19). （19） Where j represents the scaling factor. It is a low-pass filter. For high-frequency wavelets, x represents the training set response divided from the circuit output response. The high-frequency part is represented as: （20） （21）。 4. The analog circuit fault diagnosis method based on wavelet scattering and ensemble learning according to claim 1, characterized in that, In step four, the scattering coefficient matrix obtained in the previous step is split into multiple one-dimensional samples. The scattering coefficient matrix consists of p scattering channels and can be divided into p frequency band subsets. The g-th frequency band subset is represented as... , This enables the partitioning of frequency band subsets.

5. The analog circuit fault diagnosis method based on wavelet scattering and ensemble learning according to claim 4, characterized in that, In step five, the global scatter matrix of each frequency band subset is calculated. Intra-class scatter matrix and inter-class scatter matrix The calculation is as follows: （22） （23） （24） in Let represent the sample mean of the g-th frequency band subset, and l represent the number of fault categories. This represents the samples in the g-th frequency band subset that belong to fault category i. , This represents the mean of the samples belonging to fault category i in the g-th frequency band subset. The mapping matrix represents the number of training samples belonging to fault category i within the frequency band subset. The mapping matrix is ​​constructed by maximizing the closed-form solution of the Fisher criterion function. The frequency band subset is projected into a multidimensional space by multiplying the mapping matrix and the frequency band subset. The Fisher criterion function of the g-th frequency band subset is maximized as shown in equation (25). The enhanced g-th frequency band subset is then used... express, , （25）。 6. The analog circuit fault diagnosis method based on wavelet scattering and ensemble learning according to claim 5, characterized in that, In step six, During the pre-training phase, the pre-training set and the pre-test set are partitioned twice in a 7:3 ratio. The pre-test set is used to classify and validate the pre-training results. The validation results consist of the classification accuracy of each fault category, and these validation results are used as the class weights of the enhanced frequency band subsets. This process yields the class weights of each enhanced frequency band subset. .

7. The analog circuit fault diagnosis method based on wavelet scattering and ensemble learning according to claim 6, characterized in that, In step seven, the output layer of the pre-trained extreme learning machine is output. The sum of the products of the corresponding output weights is used as the input X of the classification extreme learning machine in the Bagging subclass extreme learning machine, as shown in Equation (26). Feature fusion is now complete. Finally, the final diagnosis is completed according to the principle of ELM. （26）。 8. The analog circuit fault diagnosis method based on wavelet scattering and ensemble learning as described in any one of claims 1-7 is used for fault diagnosis of Sallen_Key bandpass filters or quad op-amp dual-secondary circuits.

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