Aircraft bearing fault diagnosis method based on envelope spectrum characteristics and adversarial training
By using envelope spectrum features and adversarial training, the problems of insufficient feature extraction and inadequate model robustness in aircraft bearing fault diagnosis are solved, achieving highly reliable fault diagnosis and improving fault recognition rate and environmental adaptability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-04
- Publication Date
- 2026-04-03
AI Technical Summary
Existing aircraft bearing fault diagnosis methods suffer from insufficient feature extraction and inadequate model robustness, resulting in low diagnostic accuracy and high false alarm rate in complex environments, making it difficult to ensure flight safety.
We employ a method based on envelope spectrum features and adversarial training. By preprocessing data to extract envelope spectrum features, we construct an improved convolutional neural network model and perform enhanced adversarial training to generate adversarial examples to improve the model's robustness.
Significantly improved feature extraction capability and diagnostic accuracy, the model remained stable in noisy and disturbed environments, and the fault identification rate increased from 25.5% to 90.5%, improving the reliability and anti-interference capability of aircraft bearing fault diagnosis.
Smart Images
Figure CN121786673A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for diagnosing aircraft bearing faults based on envelope spectrum features and adversarial training, belonging to the field of aircraft engine condition monitoring and fault diagnosis technology. Background Technology
[0002] Aero engines are the core power units of aircraft, and aircraft bearings, as key components connecting rotating parts to the fuselage, directly determine the reliability of the engine and flight safety. If a bearing malfunctions and is not diagnosed and detected in time, it can lead to engine performance degradation or even engine failure, causing serious accidents. Therefore, accurate and robust fault diagnosis of aircraft bearings is of great importance.
[0003] Currently, bearing fault diagnosis methods can be mainly divided into the following two categories, but each has obvious limitations:
[0004] 1. Traditional diagnostic methods based on expert experience and signal processing primarily rely on analyzing the time-domain and time-frequency domain characteristics of vibration signals (such as peak value, root mean square, spectrum, and envelope spectrum) to identify faults. Their shortcomings include:
[0005] (1) High dependence on expert experience: The accuracy of diagnostic results largely depends on the professional level and subjective judgment of the analysts, making it difficult to achieve automated and standardized deployment;
[0006] (2) Limited noise resistance and generalization ability: In complex field environments such as strong noise and changing working conditions, fault characteristics are easily submerged, resulting in a decrease in diagnostic accuracy, an increase in false alarm rate, and insufficient robustness.
[0007] 2. Data-driven deep learning methods: In recent years, deep learning methods, represented by convolutional neural networks, have been introduced into the field of fault diagnosis. These methods can automatically learn features from large amounts of data, reducing reliance on manual features. However, existing methods still have the following prominent problems in aerospace bearing diagnosis:
[0008] (1) Insufficient feature extraction capability: Bearing fault signals have nonlinear, non-stationary, and time-varying characteristics. Existing network models usually process the original signals or simple time-frequency images directly, making it difficult to fully explore the discriminative features that are sensitive to weak faults and resistant to interference.
[0009] (2) Poor model robustness: The trained model is extremely sensitive to small perturbations in the input data (such as noise, changes in working conditions or artificially constructed adversarial examples), which leads to a serious decline in performance in real complex environments and makes it difficult to guarantee reliability.
[0010] In summary, existing technologies have failed to effectively address the two key issues of insufficient feature extraction and inadequate model robustness, thus hindering the high-reliability application of aerospace bearing fault diagnosis technology in practical engineering. Therefore, developing a diagnostic method capable of automatically extracting highly discriminative features and significantly improving model stability under disturbed environments has become a pressing research direction in this field. Summary of the Invention
[0011] The purpose of this invention is to address the problems of insufficient feature extraction and inadequate model robustness in existing aircraft bearing fault diagnosis methods, and to provide an aircraft bearing fault diagnosis method based on envelope spectrum features and adversarial training.
[0012] The present invention discloses an aircraft bearing fault diagnosis method based on envelope spectrum features and adversarial training, which includes the following steps:
[0013] S1. Data preprocessing and feature extraction: Collect the raw vibration signal of the aircraft bearing, preprocess it and convert it into an envelope spectrum image as the model input;
[0014] S2. Construct and train the improved convolutional neural network model: Based on the bearing signal features, the baseline convolutional neural network model is structurally compressed, and the improved model is trained using the training set samples obtained in S1 to obtain the initial fault diagnosis model.
[0015] S3. Perform adversarial training to enhance the robustness of the model: Generate adversarial examples and mix them with the original training examples to retrain the initial fault diagnosis model adversarially, thereby obtaining the final highly robust fault diagnosis model.
[0016] S4. Fault Diagnosis Output: Input the vibration signal of the aircraft bearing to be diagnosed into the high robustness fault diagnosis model obtained in S3, and output the corresponding fault category or health status to complete the fault diagnosis.
[0017] Preferably, the specific methods for data preprocessing and feature extraction described in S1 include:
[0018] S1-1. Determine the fault period based on the fault characteristic frequencies of each component of the bearing, and use this period to segment the original vibration signal;
[0019] S1-2. Noise reduction is performed on the segmented signal segments using singular value decomposition.
[0020] S1-3. Perform Hilbert transform on the denoised signal to obtain the analytical signal, and calculate its magnitude to obtain the envelope signal.
[0021] S1-4. Perform Fourier transform on the envelope signal to obtain the envelope spectrum, and then perform normalization processing.
[0022] S1-5, Map the normalized one-dimensional envelope spectrum as A two-dimensional matrix is used to form the two-dimensional feature image.
[0023] Preferably, the specific method described in S1-1 for determining the fault period based on the fault characteristic frequencies of each component of the bearing, and segmenting the original vibration signal using this period, is as follows:
[0024] The original bearing data is sliced into samples according to the bearing failure cycle, and the sample length is greater than or equal to the number of sample points collected in one failure cycle.
[0025] Calculate the number of sample points required to collect from the four main failure sites of the bearing within one failure cycle. The four main failure sites are the outer ring, inner ring, cage, and rolling elements.
[0026] ;
[0027] ;
[0028] ;
[0029] ;
[0030] in, This indicates the number of sample points collected within one fault cycle of the outer ring. This indicates the number of sample points collected within one fault cycle of the inner circle. This indicates the number of sample points collected within one cage failure cycle. This indicates the number of sample points collected within one fault cycle of the rolling element. It is the sampling frequency. It is the sampling factor defined according to the sampling theorem. , , , These represent the failure frequencies of the outer ring, inner ring, cage, and rolling elements, respectively. Indicates the number of rolling elements in the bearing. Indicates shaft frequency. Indicates the diameter of the rolling element. Indicates the pitch diameter. Indicates the initial contact angle of the bearing;
[0031] Minimum number of sample points collected within a fault cycle for:
[0032] .
[0033] Preferably, the specific method for noise reduction of the segmented signal segments using singular value decomposition as described in S1-2 is as follows:
[0034] The expression for singular value decomposition denoising is:
[0035] ;
[0036] in, This represents the denoised signal matrix. Indicates the number of singular values. Indicates the first A singular value, This represents the noise variance estimate. Indicates the weighting coefficient. and Let represent the basis vectors corresponding to the left singular vector and the right singular vector, respectively. express The conjugate transpose of .
[0037] Preferably, the specific method for performing Hilbert transform on the denoised signal to obtain the envelope spectrum and then performing normalization processing as described in S1-3 is as follows:
[0038] Hilbert transform is:
[0039] ;
[0040] in, This represents the original real-valued vibration signal. This represents the Hilbert transform, and the result is an analytic signal. Represents a time variable. The variable representing integration is the time delay. This represents the real part of the analytic signal, i.e., the original signal. , This represents the imaginary part of the analytic signal, i.e. The Hilbert transform result, Represents the imaginary unit;
[0041] The envelope signal is obtained by solving for the modulus of the analytic signal:
[0042] ;
[0043] in, Indicates the envelope signal. Represents the modulus of an analytic signal;
[0044] The envelope spectrum is obtained by performing a Fourier transform on the envelope signal, and then normalized.
[0045] ;
[0046] in, Represents the envelope spectrum. Indicates angular frequency;
[0047] This represents the amplitude of the original envelope spectrum. This represents the normalized amplitude. This represents the maximum amplitude. This represents the minimum value of the amplitude.
[0048] Preferably, the specific method for mapping the normalized one-dimensional envelope spectrum into an N×N two-dimensional matrix as described in S1-5 to form the two-dimensional feature image is as follows:
[0049] Divide the envelope spectrum into a The matrix is filled with color using the envelope spectral line as the threshold. The filling formula is as follows:
[0050]
[0051] in, This represents the side length of a two-dimensional square matrix, i.e., the image resolution. This represents the column index of the matrix, corresponding to the frequency sequence number. This represents the row index of the matrix, corresponding to the amplitude intensity level. This indicates the pixel position of the generated grayscale image. Pixel intensity value at that location Indicates at frequency point The normalized envelope spectrum amplitude is shown at this location.
[0052] Preferably, in the construction and training of the improved convolutional neural network model described in S2, the improved model is obtained by structural compression of the baseline convolutional neural network model:
[0053] A lightweight network was obtained by reducing the number of convolutional kernels in each convolutional layer to 1 / 4 of the original number, using the AlexNet neural network model as the baseline convolutional neural network model.
[0054] Preferably, the specific method for adversarial training to enhance model robustness as described in S3 includes:
[0055] S3-1. Using the projection gradient descent method based on random perturbation, generate the first set of adversarial examples for the initial fault diagnosis model obtained in S2.
[0056] S3-2. Train an auxiliary network model and generate a general adversarial perturbation based on the DeepFool algorithm. Add the perturbation to the original training images to form a second adversarial sample set.
[0057] S3-3. Mix the first adversarial sample set, the second adversarial sample set, and the original training images to jointly train the initial diagnostic model, thus completing the adversarial training process.
[0058] Preferably, the auxiliary network model described in S3-2 adopts the LeNet-5 model.
[0059] Preferably, the specific method for generating the first adversarial example set based on the projection gradient descent method based on random perturbation in S3-1 is as follows:
[0060] Input the original bearing vibration signal dataset and the initial fault diagnosis model;
[0061] For each sample in the dataset, the perturbation is randomly initialized from a preset uniform distribution, provided that the model's classification results for the original sample and the sample after adding the current perturbation remain consistent.
[0062] Subsequently, the loss gradient of the model under the perturbation is calculated to determine the gradient update direction, and the randomly initialized perturbation is linearly combined with the gradient update direction using a randomly generated weight coefficient to obtain the updated perturbation;
[0063] At the same time, the amplitude of each component of the updated perturbation is constrained within a preset threshold range;
[0064] By iteratively executing the above perturbation generation and constraint process, an adversarial perturbation is generated for each original sample, and the perturbation is added to the original sample to form the first adversarial sample set.
[0065] Advantages of this invention: A fault diagnosis method for aerospace bearings based on envelope spectrum features and adversarial training achieves significant improvements in three key dimensions: feature extraction, diagnostic accuracy, and model robustness, forming a highly reliable and adaptable fault diagnosis solution for aerospace bearings. Specific details are as follows:
[0066] 1. Significantly enhanced feature extraction capability: By using the envelope spectrum as input to the convolutional neural network, key features in bearing fault signals can be effectively separated and aggregated, enhancing the distinction between normal signals and fault features, and laying the foundation for subsequent high-precision diagnosis.
[0067] 2. Significantly improved diagnostic accuracy: The AlexNet neural network model, which is improved for bearing signal characteristics, achieves excellent overall performance while ensuring a lightweight structure. The accuracy of identifying bearing fault types reaches 99.0%, which is higher than other commonly used diagnostic models.
[0068] 3. Significantly Improved Model Robustness: An adversarial training method based on projective gradient descent with random perturbations is introduced, enabling the model to remain stable when facing noise, perturbations, and adversarial attacks. After adversarial training, the model's fault identification rate under attack increases from 25.5% to 90.5%, significantly enhancing its reliability and anti-interference ability in complex real-world environments. Attached Figure Description
[0069] Figure 1 This is a flowchart of the data preprocessing and envelope spectrum feature extraction process of this invention;
[0070] Figure 2 This is a schematic diagram of the structure of the improved AlexNet neural network model in this invention;
[0071] Figure 3 This is an overall flowchart of the adversarial training and robustness verification of the present invention;
[0072] Figure 4 This is a schematic diagram of a general adversarial perturbation generated based on the DeepFool algorithm. Detailed Implementation
[0073] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0074] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.
[0075] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.
[0076] Example 1:
[0077] The following is combined with Figures 1-4 This embodiment describes an aircraft bearing fault diagnosis method based on envelope spectrum features and adversarial training, which includes the following steps:
[0078] S1. Data preprocessing and feature extraction: Collect the raw vibration signal of the aircraft bearing, preprocess it and convert it into an envelope spectrum image as the model input;
[0079] S2. Construct and train the improved convolutional neural network model: Based on the bearing signal features, the baseline convolutional neural network model is structurally compressed, and the improved model is trained using the training set samples obtained in S1 to obtain the initial fault diagnosis model.
[0080] S3. Perform adversarial training to enhance the robustness of the model: Generate adversarial examples and mix them with the original training examples to retrain the initial fault diagnosis model adversarially, thereby obtaining the final highly robust fault diagnosis model.
[0081] S4. Fault Diagnosis Output: Input the vibration signal of the aircraft bearing to be diagnosed into the high robustness fault diagnosis model obtained in S3, and output the corresponding fault category or health status to complete the fault diagnosis.
[0082] Furthermore, the specific methods for data preprocessing and feature extraction described in S1 include:
[0083] S1-1. Determine the fault period based on the fault characteristic frequencies of each component of the bearing, and use this period to segment the original vibration signal;
[0084] S1-2. Noise reduction is performed on the segmented signal segments using singular value decomposition.
[0085] S1-3. Perform Hilbert transform on the denoised signal to obtain the analytical signal, and calculate its magnitude to obtain the envelope signal.
[0086] S1-4. Perform Fourier transform on the envelope signal to obtain the envelope spectrum, and then perform normalization processing.
[0087] S1-5, Map the normalized one-dimensional envelope spectrum as A two-dimensional matrix is used to form the two-dimensional feature image.
[0088] Furthermore, the specific method described in S1-1 for determining the fault period based on the fault characteristic frequencies of each component of the bearing, and segmenting the original vibration signal using this period, is as follows:
[0089] The original bearing data is sliced into samples according to the bearing failure cycle, and the sample length is greater than or equal to the number of sample points collected in one failure cycle.
[0090] Calculate the number of sample points required to collect from the four main failure sites of the bearing within one failure cycle. The four main failure sites are the outer ring, inner ring, cage, and rolling elements.
[0091] ;
[0092] ;
[0093] ;
[0094] ;
[0095] in, This indicates the number of sample points collected within one fault cycle of the outer ring. This indicates the number of sample points collected within one fault cycle of the inner circle. This indicates the number of sample points collected within one cage failure cycle. This indicates the number of sample points collected within one fault cycle of the rolling element. It is the sampling frequency. It is the sampling factor defined according to the sampling theorem. , , , These represent the failure frequencies of the outer ring, inner ring, cage, and rolling elements, respectively. Indicates the number of rolling elements in the bearing. Indicates shaft frequency. Indicates the diameter of the rolling element. Indicates the pitch diameter. Indicates the initial contact angle of the bearing;
[0096] Minimum number of sample points collected within a fault cycle for:
[0097] .
[0098] Furthermore, the specific method for noise reduction of the segmented signal segments using singular value decomposition, as described in S1-2, is as follows:
[0099] The expression for singular value decomposition denoising is:
[0100] ;
[0101] in, This represents the denoised signal matrix. Indicates the number of singular values. Indicates the first A singular value, This represents the noise variance estimate. Indicates the weighting coefficient. and Let represent the basis vectors corresponding to the left singular vector and the right singular vector, respectively. express The conjugate transpose of .
[0102] Furthermore, the specific method described in S1-3 for performing Hilbert transform on the denoised signal to obtain the envelope spectrum and then performing normalization processing is as follows:
[0103] Hilbert transform is:
[0104] ;
[0105] in, This represents the original real-valued vibration signal. This represents the Hilbert transform, and the result is an analytic signal. Represents a time variable. The variable representing integration is the time delay. This represents the real part of the analytic signal, i.e., the original signal. , This represents the imaginary part of the analytic signal, i.e. The Hilbert transform result, Represents the imaginary unit;
[0106] The envelope signal is obtained by solving for the modulus of the analytic signal:
[0107] ;
[0108] in, Indicates the envelope signal. Represents the modulus of an analytic signal;
[0109] The envelope spectrum is obtained by performing a Fourier transform on the envelope signal, and then normalized.
[0110] ;
[0111] in, Represents the envelope spectrum. Indicates angular frequency;
[0112] This represents the amplitude of the original envelope spectrum. This represents the normalized amplitude. This represents the maximum amplitude. This represents the minimum value of the amplitude.
[0113] Furthermore, the specific method described in S1-5 for mapping the normalized one-dimensional envelope spectrum into an N×N two-dimensional matrix to form the two-dimensional feature image is as follows:
[0114] Divide the envelope spectrum into a The matrix is filled with color using the envelope spectral line as the threshold. The filling formula is as follows:
[0115]
[0116] in, This represents the side length of a two-dimensional square matrix, i.e., the image resolution. This represents the column index of the matrix, corresponding to the frequency sequence number. This represents the row index of the matrix, corresponding to the amplitude intensity level. This indicates the pixel position of the generated grayscale image. Pixel intensity value at that location Indicates at frequency point The normalized envelope spectrum amplitude is shown at this location.
[0117] Furthermore, in the construction and training of the improved convolutional neural network model described in S2, the baseline convolutional neural network model is structurally compressed, and the resulting improved model is as follows:
[0118] A lightweight network was obtained by reducing the number of convolutional kernels in each convolutional layer to 1 / 4 of the original number, using the AlexNet neural network model as the baseline convolutional neural network model.
[0119] Furthermore, the specific methods for adversarial training to enhance model robustness described in S3 include:
[0120] S3-1. Using the projection gradient descent method based on random perturbation, generate the first set of adversarial examples for the initial fault diagnosis model obtained in S2.
[0121] S3-2. Train an auxiliary network model and generate a general adversarial perturbation based on the DeepFool algorithm. Add the perturbation to the original training images to form a second adversarial sample set.
[0122] S3-3. Mix the first adversarial sample set, the second adversarial sample set, and the original training images to jointly train the initial diagnostic model, thus completing the adversarial training process.
[0123] Furthermore, the auxiliary network model described in S3-2 adopts the LeNet-5 model.
[0124] Furthermore, the specific method described in S3-1 for generating the first adversarial example set based on the projection gradient descent method with random perturbation for the initial fault diagnosis model obtained in S2 is as follows:
[0125] Input the original bearing vibration signal dataset and the initial fault diagnosis model;
[0126] For each sample in the dataset, the perturbation is randomly initialized from a preset uniform distribution, provided that the model's classification results for the original sample and the sample after adding the current perturbation remain consistent.
[0127] Subsequently, the loss gradient of the model under the perturbation is calculated to determine the gradient update direction, and the randomly initialized perturbation is linearly combined with the gradient update direction using a randomly generated weight coefficient to obtain the updated perturbation;
[0128] At the same time, the amplitude of each component of the updated perturbation is constrained within a preset threshold range;
[0129] By iteratively executing the above perturbation generation and constraint process, an adversarial perturbation is generated for each original sample, and the perturbation is added to the original sample to form the first adversarial sample set.
[0130] In this invention, the publicly available Case Western Reserve University bearing dataset is used for method verification. The specific implementation steps are as follows:
[0131] like Figure 1 The image shows step one: data preprocessing and envelope spectrum feature extraction.
[0132] Signal segmentation: Based on the bearing geometric parameters (rolling element diameter, pitch diameter, contact angle, etc.), shaft frequency, and the theoretical fault characteristic frequencies of each component, the minimum number of sampling points corresponding to the fault cycles of the outer ring, inner ring, cage, and rolling elements is calculated respectively. The maximum value is taken as the uniform sampling length, and the original continuous vibration signal is sliced into equal-length slices to form the initial samples.
[0133] Signal denoising: Construct a Hankel matrix for each sample signal and perform singular value decomposition. By setting a reasonable noise variance threshold, use formula (6) to perform weighted shrinkage of the singular values and reconstruct the signal to achieve noise reduction.
[0134] Envelope extraction and transformation: The denoised signal is subjected to Hilbert transform to obtain the analytic signal, and its magnitude is calculated according to formula (8) to obtain the envelope signal. Then, the envelope signal is subjected to fast Fourier transform to obtain the envelope spectrum.
[0135] Generating a feature image: After normalizing the one-dimensional envelope spectrum amplitude sequence, it is filled into a two-dimensional matrix of a preset size (e.g., 64×64) according to the rules of formula (10) to generate a grayscale image. In this image, the brightness distribution directly reflects the amplitude contour of the envelope spectrum, thereby visualizing the fault characteristics.
[0136] Step 1.1: Slice the raw bearing data from Case Western Reserve University into samples based on the bearing failure cycle. The sample length should be greater than or at least equal to the number of sample points collected within one failure cycle. The number of sample points collected within one failure cycle corresponds to the four main failure sites of the bearing: outer ring, inner ring, cage, and rolling elements. , , , The sample length is determined by formulas (1)-(4) respectively. To ensure that the sample length is greater than or at least equal to the number of sample points collected within a fault cycle under all fault conditions, the minimum number of sample points collected within a fault cycle is... It is determined by formula (5).
[0137] (1)
[0138] (2)
[0139] (3)
[0140] (4)
[0141] (5)
[0142] in Indicates the number of rolling elements in the bearing. Indicates shaft frequency. Indicates the diameter of the rolling element. Indicates the pitch diameter. Indicates the initial contact angle of the bearing. , , , These represent the failure frequencies of the outer ring, inner ring, cage, and rolling elements, respectively. It is the sampling frequency. It is the sampling factor defined according to the sampling theorem.
[0143] Step 1.2: Denoising the sample signal using Singular Value Decomposition (SVD). SVD is a subspace-based algorithm, and its denoising expression is as follows:
[0144] (6)
[0145] Step 1.3: Obtain the analytic signal, a real-valued function, from the denoised sample signal using the Hilbert transform. Its Hilbert transform is:
[0146] (7)
[0147] The envelope signal is obtained by solving for the modulus of the analytic signal:
[0148] (8)
[0149] The envelope spectrum is obtained by performing a Fourier transform on the envelope signal, and then normalized.
[0150] (9)
[0151] Step 1.4: To highlight the feature information contained in the envelope spectrum, this invention divides the envelope spectrum into a... The matrix is filled with color using the envelope spectral line as the threshold. The filling formula is as follows:
[0152] (10)
[0153] in The corresponding value for the envelope spectral line. The pixel intensity of the image.
[0154] like Figure 2 The image shows step two: building and training an improved lightweight diagnostic model.
[0155] Model Improvement: Based on the classic AlexNet network, in order to adapt to the characteristics of bearing signals and reduce the amount of computation, the number of convolutional kernels in all convolutional layers was reduced to 1 / 4 of the original design, forming an improved lightweight network.
[0156] Model Training: The envelope spectrum images generated in Step 1 are divided into training and test sets proportionally. The improved AlexNet model is trained under supervision using the training set, with cross-entropy as the loss function and the Adam optimizer used for parameter updates.
[0157] Performance Validation: The performance of the trained model was evaluated using a test set. In this embodiment, the model achieved an average diagnostic accuracy of 99.0% for normal bearing conditions and various fault types, demonstrating its excellent initial diagnostic capabilities.
[0158] Step 2 includes the following steps:
[0159] Step 2.1: As Figure 2 As shown, the AlexNet neural network model is improved based on the characteristics of bearing signals, and the number of convolutional kernels in each layer is reduced to 1 / 4 of the original network.
[0160] Step 2.2: Train the improved AlexNet neural network model using the training set generated in Step 1.3.
[0161] Step 2.3: Use the test set generated in Step 1.3 to verify the accuracy of the neural network model trained in Step 2.2 in identifying bearing faults.
[0162] like Figure 3 As shown, this is step three: performing adversarial training to enhance model robustness.
[0163] Generate diverse adversarial examples: Algorithm 1 (projective gradient descent based on random perturbation) is used to attack the initial model trained in step two. By randomly initializing the perturbation and combining it with the gradient direction in a weighted manner, a set of synthetic adversarial examples is generated from the original training samples, denoted as the first adversarial example set.
[0164] Generate transferable adversarial examples: An additional LeNet-5 model with a different architecture is trained as an auxiliary model. A general adversarial perturbation is generated for this auxiliary model based on the DeepFool algorithm. This perturbation is added to the original test set samples to form a second set of adversarial examples, used to simulate cross-model transfer attacks.
[0165] Perform adversarial training: Mix the first set of adversarial examples with the original training set and retrain the initial model obtained in step two. This process forces the model to learn to maintain a stable decision boundary under perturbations.
[0166] Robustness verification: The models before and after adversarial training were tested using a second set of adversarial examples (transfer attack examples). The results show that the recognition rate of the untrained model plummeted to 25.5% under attack, while the recognition rate of the trained model significantly improved to 90.5%. This fully demonstrates that the method proposed in this invention can effectively enhance the model's ability to resist unknown perturbations and greatly improve its reliability in real-world complex environments.
[0167] Step 3.1: Generate adversarial examples using projective gradient descent based on random perturbation. Assuming the initial perturbation follows a uniform distribution, the perturbation is first randomly initialized, and then the gradient value after perturbation is calculated. The final gradient value is obtained by combining the initial perturbation and the resulting gradient value with different weights, and the maximum value of the perturbation is limited. This method can enrich the diversity of adversarial examples. The algorithm for generating adversarial examples using projective gradient descent based on random perturbation is as follows:
[0168] Algorithm 1: Generate adversarial examples using projective gradient descent based on random perturbations
[0169] enter: For bearing datasets; For classifiers; This represents the number of iterations. This is the step size parameter; For the threshold; For hyperparameters; For disturbance;
[0170] Output: Bearing adversarial sample dataset
[0171] ;
[0172] for do
[0173] for do
[0174] if then
[0175]
[0176]
[0177]
[0178]
[0179] Else
[0180] Break
[0181] end
[0182]
[0183] end
[0184] return
[0185] Step 3.2: Train a LeNet-5 model using the original bearing training set generated in Step 1.4. Based on this model and the DeepFool algorithm, generate the general perturbation DeepFool-UAP, as shown below. Figure 4 As shown, this perturbation is then added to the original sample to form an adversarial sample.
[0186] Step 3.3: Use the adversarial examples generated in Step 3.2 to transfer attacks on the improved AlexNet model of this invention. The fault identification rate of the improved AlexNet model after being attacked is 25.5%.
[0187] Step 3.4: Train the improved AlexNet neural network model using the adversarial examples generated in Step 3.1 and the examples generated in Step 1.4.
[0188] Step 3.5: Use the adversarial examples generated in Step 3.2 to transfer attack the improved AlexNet model of this invention again. The fault identification rate of the improved AlexNet model of this invention after adversarial training with randomly perturbed projective gradient descent is improved to 90.5%, which proves that the robustness of the model is enhanced after training with adversarial examples.
[0189] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.
Claims
1. A method for diagnosing aircraft bearing faults based on envelope spectrum features and adversarial training, characterized in that, It includes the following steps: S1. Data preprocessing and feature extraction: Collect the raw vibration signal of the aircraft bearing, preprocess it and convert it into an envelope spectrum image as the model input; S2. Construct and train the improved convolutional neural network model: Based on the bearing signal features, the baseline convolutional neural network model is structurally compressed, and the improved model is trained using the training set samples obtained in S1 to obtain the initial fault diagnosis model. S3. Perform adversarial training to enhance the robustness of the model: Generate adversarial samples and mix them with the original training samples to retrain the initial fault diagnosis model adversarially, thereby obtaining the final highly robust fault diagnosis model. S4. Fault Diagnosis Output: Input the vibration signal of the aircraft bearing to be diagnosed into the high robustness fault diagnosis model obtained in S3, and output the corresponding fault category or health status to complete the fault diagnosis.
2. The method for diagnosing aircraft bearing faults based on envelope spectrum features and adversarial training according to claim 1, characterized in that, The specific methods for data preprocessing and feature extraction described in S1 include: S1-1. Determine the fault period based on the fault characteristic frequencies of each component of the bearing, and use this period to segment the original vibration signal; S1-2. Noise reduction is performed on the segmented signal segments using singular value decomposition. S1-3. Perform Hilbert transform on the denoised signal to obtain the analytical signal, and calculate its magnitude to obtain the envelope signal. S1-4. Perform Fourier transform on the envelope signal to obtain the envelope spectrum, and then perform normalization processing. S1-5, Map the normalized one-dimensional envelope spectrum as A two-dimensional matrix is used to form the two-dimensional feature image.
3. The method for diagnosing aircraft bearing faults based on envelope spectrum features and adversarial training according to claim 2, characterized in that, The specific method described in S1-1 for determining the fault period based on the fault characteristic frequencies of each component of the bearing, and for segmenting the original vibration signal using this period, is as follows: The original bearing data is sliced into samples according to the bearing failure cycle, and the sample length is greater than or equal to the number of sample points collected in one failure cycle. Calculate the number of sample points required to collect from the four main failure sites of the bearing within one failure cycle. The four main failure sites are the outer ring, inner ring, cage, and rolling elements. ； ； ； ； in, This indicates the number of sample points collected within one fault cycle of the outer ring. This indicates the number of sample points collected within one fault cycle of the inner circle. This indicates the number of sample points collected within one cage failure cycle. This indicates the number of sample points collected within one fault cycle of the rolling element. It is the sampling frequency. It is the sampling factor defined according to the sampling theorem. , , , These represent the failure frequencies of the outer ring, inner ring, cage, and rolling elements, respectively. Indicates the number of rolling elements in the bearing. Indicates shaft frequency. Indicates the diameter of the rolling element. Indicates the pitch diameter. Indicates the initial contact angle of the bearing; Minimum number of sample points collected within a fault cycle for: 。 4. The method for diagnosing aircraft bearing faults based on envelope spectrum features and adversarial training according to claim 2, characterized in that, The specific method for noise reduction of the segmented signal segments using singular value decomposition, as described in S1-2, is as follows: The expression for singular value decomposition denoising is: ； in, This represents the denoised signal matrix. Indicates the number of singular values. Indicates the first A singular value, This represents the noise variance estimate. Indicates the weighting coefficient. and Let represent the basis vectors corresponding to the left singular vector and the right singular vector, respectively. express The conjugate transpose of .
5. The method for diagnosing aircraft bearing faults based on envelope spectrum features and adversarial training according to claim 2, characterized in that, The specific method described in S1-3 for performing Hilbert transform on the denoised signal to obtain the envelope spectrum and then performing normalization is as follows: Hilbert transform is: ； in, This represents the original real-valued vibration signal. This represents the Hilbert transform, and the result is an analytic signal. Represents a time variable. The variable representing integration is the time delay. This represents the real part of the analytic signal, i.e., the original signal. , This represents the imaginary part of the analytic signal, i.e. The Hilbert transform result, Represents the imaginary unit; The envelope signal is obtained by solving for the modulus of the analytic signal: ； in, Indicates the envelope signal. Represents the modulus of an analytic signal; The envelope spectrum is obtained by performing a Fourier transform on the envelope signal, and then normalized. ； in, Represents the envelope spectrum. Indicates angular frequency; This represents the amplitude of the original envelope spectrum. This represents the normalized amplitude. This represents the maximum amplitude. This represents the minimum value of the amplitude.
6. The method for diagnosing aircraft bearing faults based on envelope spectrum features and adversarial training according to claim 2, characterized in that, The specific method described in S1-5 for mapping the normalized one-dimensional envelope spectrum into an N×N two-dimensional matrix to form the two-dimensional feature image is as follows: Divide the envelope spectrum into a The matrix is filled with color using the envelope spectral line as the threshold. The filling formula is as follows: in, This represents the side length of a two-dimensional square matrix, i.e., the image resolution. This represents the column index of the matrix, corresponding to the frequency sequence number. This represents the row index of the matrix, corresponding to the amplitude intensity level. This indicates the pixel position of the generated grayscale image. Pixel intensity value at that location, Indicates at frequency point The normalized envelope spectrum amplitude is shown at this location.
7. The method for diagnosing aircraft bearing faults based on envelope spectrum features and adversarial training according to claim 1, characterized in that, In the construction and training of the improved convolutional neural network model described in S2, the improved model is obtained by structural compression of the baseline convolutional neural network model: A lightweight network was obtained by reducing the number of convolutional kernels in each convolutional layer to 1 / 4 of the original number, using the AlexNet neural network model as the baseline convolutional neural network model.
8. The method for diagnosing aircraft bearing faults based on envelope spectrum features and adversarial training according to claim 1, characterized in that, The specific methods for adversarial training to enhance model robustness, as described in S3, include: S3-1. Using the projection gradient descent method based on random perturbation, generate the first set of adversarial examples for the initial fault diagnosis model obtained in S2. S3-2. Train an auxiliary network model and generate a general adversarial perturbation based on the DeepFool algorithm. Add the perturbation to the original training images to form a second adversarial sample set. S3-3. Mix the first adversarial sample set, the second adversarial sample set, and the original training images to jointly train the initial diagnostic model, thus completing the adversarial training process.
9. The method for diagnosing aircraft bearing faults based on envelope spectrum features and adversarial training according to claim 1, characterized in that, The auxiliary network model described in S3-2 adopts the LeNet-5 model.
10. The method for diagnosing aircraft bearing faults based on envelope spectrum features and adversarial training according to claim 1, characterized in that, The specific method described in S3-1 for generating the first adversarial example set based on the projection gradient descent method with random perturbation for the initial fault diagnosis model obtained in S2 is as follows: Input the original bearing vibration signal dataset and the initial fault diagnosis model; For each sample in the dataset, the perturbation is randomly initialized from a preset uniform distribution, provided that the model's classification results for the original sample and the sample after adding the current perturbation remain consistent. Subsequently, the loss gradient of the model under the perturbation is calculated to determine the gradient update direction, and the randomly initialized perturbation is linearly combined with the gradient update direction using a randomly generated weight coefficient to obtain the updated perturbation; At the same time, the amplitude of each component of the updated perturbation is constrained within a preset threshold range; By iteratively executing the above perturbation generation and constraint process, an adversarial perturbation is generated for each original sample, and the perturbation is added to the original sample to form the first adversarial sample set.