A Multi-Feature Fusion Fault Diagnosis Method for Vibration Signals of Vehicle Axle Assembly

Abstract

This invention discloses a multi-feature fusion fault diagnosis method for vibration signals of a vehicle axle assembly, belonging to the field of mechanical fault diagnosis technology. The method includes acquiring and preprocessing the raw vibration signals of the vehicle axle assembly. Time-domain, frequency-domain, and time-frequency-domain features are extracted from the preprocessed signals to form a primary feature set. A subset of sensitive features is selected through redundancy analysis and importance ranking. A kernel function is used to map the sensitive features to a high-dimensional space and perform linear reconstruction oriented towards fault categories, resulting in a more discriminative fusion feature vector. This fusion feature is input into a pre-trained probabilistic classification model to calculate the posterior probability of belonging to each fault mode. The fault mode is determined based on the probability, and a diagnostic result is generated. This invention enhances the discriminative ability of fault features through kernel space feature reconstruction and provides a reliability assessment of the diagnostic results using probability output, thereby improving the accuracy of fault diagnosis and the level of decision support.

Description

Technical Field

[0001] This invention belongs to the field of mechanical fault diagnosis technology, specifically a multi-feature fusion fault diagnosis method for vibration signals of a vehicle axle assembly. Background Technology

[0002] In vehicle axle assembly fault diagnosis based on vibration signal analysis, existing technologies generally employ a framework combining multi-domain feature extraction and pattern recognition. Conventional methods extract statistical features in the time and frequency domains from preprocessed signals and directly input them into a classifier. These methods rely on feature selection or linear dimensionality reduction techniques to construct feature vectors, but they struggle to handle complex nonlinear relationships between features. Simple feature concatenation or linear transformation cannot optimize and reorganize the feature structure according to the essential differences in fault categories, resulting in limited discriminative power in the final feature representation and insufficient diagnostic stability under complex operating conditions.

[0003] Existing diagnostic models typically output a single fault category label. This deterministic output pattern fails to provide information on the reliability of diagnostic conclusions. When vibration signal quality is poor or the fault is in its early stages, the deterministic label provided by the model lacks interpretability, making it impossible for users to assess the reliability of the results, thus affecting the timeliness and accuracy of maintenance decisions.

[0004] There is a need for a fault diagnosis method that can automatically construct highly discriminative feature representations from multi-domain features and quantify the reliability of diagnostic results. Summary of the Invention

[0005] This invention aims to solve at least one of the technical problems existing in the prior art; Therefore, this invention proposes a multi-feature fusion fault diagnosis method for vibration signals of axle assemblies, comprising: The original vibration signal of the axle assembly under operating conditions is collected by an accelerometer. The collected original vibration signal is then subjected to noise reduction and standardization preprocessing to obtain preprocessed vibration signal data. From the preprocessed vibration signal data, time-domain statistical features, frequency-domain spectral features, and time-frequency-domain scale features are extracted to form a multi-dimensional primary feature set. Redundancy analysis and importance ranking are performed on the features in the multi-dimensional primary feature set to select a sensitive feature subset for fault characterization; By using kernel functions to map a subset of sensitive features to a high-dimensional feature space, and then linearly reconstructing the fault features of different categories in the high-dimensional feature space, a fusion feature vector with higher discriminative power is obtained. The fused feature vector is input into a pre-trained probability classification model to calculate the posterior probability that the vibration signal belongs to various preset fault modes. Based on the calculated posterior probability, the failure mode of the axle assembly is determined, and a diagnostic result containing the failure mode identifier is generated.

[0006] Furthermore, the noise reduction and standardization preprocessing of the acquired raw vibration signal specifically includes: A moving average filter is applied to the original vibration signal to filter out high-frequency random noise and obtain a preliminarily smoothed vibration signal. The trend term of the initially smoothed vibration signal is eliminated, and the baseline drift of the signal is fitted using the least squares method and then subtracted from the signal. Anomaly detection and correction are performed on the vibration signal after trend term elimination, and the median of the local data distribution is used to replace the abnormal amplitude points that exceed the threshold range; The amplitude of the corrected vibration signal is normalized to scale the amplitude of all data points to a standard distribution with zero mean and unit variance. The amplitude-normalized signal is truncated into fixed-length data segments to ensure that all data segments used for subsequent analysis have the same length, and the output is the preprocessed vibration signal data.

[0007] Furthermore, the extraction of time-domain statistical features, frequency-domain spectral features, and time-frequency-domain scale features respectively constitutes a multi-dimensional primary feature set, specifically including: For the preprocessed vibration signal data, calculate its mean, variance, peak factor, impulse factor and waveform factor to form a time-domain statistical feature set; Fast Fourier Transform is performed on the preprocessed vibration signal data to obtain its spectral distribution. The spectral centroid, frequency variance, and energy proportion within a specific octave band are calculated to form a frequency domain spectral feature group. The preprocessed vibration signal data is subjected to wavelet packet transform, decomposed to a set number of layers, and the energy values ​​of the wavelet packet decomposition coefficients of each node are extracted to form a time-frequency domain scale feature group. The time-domain statistical feature set, the frequency-domain spectral feature set, and the time-frequency domain scale feature set are merged in sequence to form a comprehensive multi-dimensional primary feature set.

[0008] Furthermore, the process of performing redundancy analysis and importance ranking on the features in the multi-dimensional primary feature set to select a subset of sensitive features for fault characterization specifically includes: Calculate the Pearson correlation coefficient between any two features in the multidimensional primary feature set to construct a feature correlation matrix; A correlation threshold is set. If the correlation coefficient between two features is higher than the correlation threshold, they are determined to be redundant feature pairs. The Pearson correlation coefficient between the two features in the redundant feature pair and the fault label is calculated respectively. Features with correlation coefficients lower than the preset label correlation threshold are removed. For the feature set after redundancy removal, a feature importance evaluation method based on decision trees is used to calculate the importance score of each feature in distinguishing different failure modes. All features are sorted in descending order based on their feature importance scores, and the features with the highest ranking and cumulative importance exceeding a preset proportion are selected. The selected feature combinations are determined as a subset of sensitive features for subsequent fault characterization.

[0009] Furthermore, the step of mapping a subset of sensitive features to a high-dimensional feature space using a kernel function, and then linearly reconstructing different categories of fault features in the high-dimensional feature space, specifically includes: By selecting a radial basis kernel function, each sample point in the sensitive feature subset is mapped from the original feature space to a high-dimensional feature space. In the high-dimensional feature space, the feature mean of all sample points belonging to the same fault mode is calculated and used as the feature center of the fault mode. Calculate the Euclidean distance from each sample point to the center of all fault features for each category, forming a distance vector; A new extended feature vector is constructed by concatenating the original sensitive feature subset of the sample point with the distance vector corresponding to the sample point. Principal component analysis was performed on the extended feature vectors of all samples, and the principal component with the largest contribution rate was selected as the final fused feature vector.

[0010] Furthermore, the step of inputting the fused feature vector into a pre-trained probability classification model to calculate the posterior probability of the vibration signal belonging to various preset fault modes specifically includes: The probabilistic classification model employs a Bayesian classifier based on kernel density estimation; For each preset fault mode, the probability density distribution of the fault mode's features in the feature space is fitted using the fused feature vector of its training samples through the kernel density estimation method. When a new fused feature vector is input, the likelihood values ​​of the new fused feature vector under the probability density distributions of various fault modes are calculated respectively. By combining the prior probabilities of various failure modes appearing in historical data, the posterior probability of the new fused feature vector belonging to each failure mode is calculated using Bayes' theorem. Output a probability vector, where each element represents the posterior probability that the vibration signal belongs to the corresponding preset fault mode.

[0011] Furthermore, determining the failure mode of the axle assembly based on the calculated posterior probability specifically includes: Identify the posterior probability with the largest value from the posterior probability vector output by the probabilistic classification model; The posterior probability of the largest value is compared with a preset diagnostic confidence threshold; When the posterior probability of the largest value is greater than or equal to the diagnostic confidence threshold, the preset fault mode corresponding to the posterior probability of the largest value is determined as the fault mode of the axle assembly. When the posterior probability of the largest value is less than the diagnostic confidence threshold, it is determined that the diagnostic confidence is insufficient, and a prompt message indicating that further examination is required is generated.

[0012] Furthermore, the step of performing wavelet packet transform on the preprocessed vibration signal data, decomposing it to a set number of levels, and extracting the energy values ​​of the wavelet packet decomposition coefficients at each node specifically includes: Select appropriate wavelet basis functions and decomposition levels, and perform wavelet packet transform on the preprocessed vibration signal data; After completing the wavelet packet transform, a wavelet packet decomposition node sequence covering the entire frequency band from low frequency to high frequency is obtained; Calculate the sum of squares of the coefficient sequence corresponding to each wavelet packet decomposition node, and use the sum of squares as the energy value of the wavelet packet decomposition node; Arrange the energy values ​​of all wavelet packet decomposition nodes in order of node index to form an energy feature vector; The energy feature vector is normalized so that the sum of all energy values ​​is 1, forming a time-frequency domain scale feature group.

[0013] Furthermore, the step of performing principal component analysis on the extended feature vectors of all samples and selecting the principal component with the largest contribution rate as the final fused feature vector specifically includes: Collect the extended feature vectors of all training samples and samples to be diagnosed, and form an extended feature matrix; The extended feature matrix is ​​centered by subtracting the mean of each feature dimension. Calculate the covariance matrix of the expanded feature matrix after centering; Calculate the eigenvalues ​​and corresponding eigenvectors of the covariance matrix; The feature vectors are arranged in descending order of their eigenvalues. The cumulative contribution rate of the principal components corresponding to the arranged feature vectors is calculated sequentially. All principal components included when the cumulative contribution rate first reaches a set threshold are selected. The extended feature vector of the sample is projected onto all principal components. The resulting low-dimensional projection vector is the final fused feature vector.

[0014] Furthermore, the step of using the fused feature vector of its training samples to fit the probability density distribution of the fault mode's features in the feature space through a kernel density estimation method specifically includes: For the fused feature vector of all training samples of a certain type of fault mode, select a Gaussian kernel function with appropriate smoothing parameters; For each dimension in the feature space, calculate the kernel density contribution of all sample data points in that dimension to a specified location. By combining the kernel density estimation results of all dimensions, the joint probability density distribution function of the corresponding fault mode in the multivariate feature space can be obtained by product or summation. By optimizing the smoothing parameters of the Gaussian kernel function through cross-validation, the estimated probability density distribution is made to be as close as possible to the true distribution.

[0015] Compared with the prior art, the beneficial effects of the present invention are: The selected subset of sensitive features is mapped to a high-dimensional regenerated Hilbert space using a kernel function, and then linearly reconstructed for different categories of fault features within this space. Kernel mapping reveals the complex nonlinear separability of the original features, while the linear reconstruction operation for different fault modes essentially constructs the optimal feature combination for a specific fault in the high-dimensional space. This process automatically learns and generates a novel fusion feature vector that maximizes the preservation of discriminative information related to the fault category while suppressing irrelevant individual differences and noise. Compared to traditional feature concatenation or linear dimensionality reduction methods, the generated fusion features exhibit stronger intra-class aggregation and inter-class separability, improving the clarity of the decision boundary for subsequent classifiers under nonlinear sample distributions.

[0016] A probabilistic classification model is used to process the fused feature vectors. The model output is the posterior probability distribution of the vibration signal belonging to various preset fault modes. This method transforms fault diagnosis from a deterministic classification problem into a probabilistic inference problem. The output probability value directly quantifies the model's confidence level for each diagnostic conclusion, providing a continuous measure of reliability. When a sample is diagnosed with a specific fault, its corresponding probability reflects the reliability of the diagnosis; if the probability of a sample is low or evenly distributed across all categories, it suggests that the signal may be in a transitional state, contain unknown faults, or be affected by strong noise. This probabilistic output provides richer and more flexible information support for operation and maintenance decisions, allowing for the setting of multi-level warnings based on confidence thresholds, or triggering more refined secondary diagnoses when probabilities are ambiguous. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the steps of a multi-feature fusion fault diagnosis method for vibration signals of a vehicle axle assembly as described in this invention. Figure 2 The flowchart shows the noise reduction and standardization preprocessing of the original vibration signal. Figure 3A flowchart for extracting primary features from a multi-dimensional set; Figure 4 To expand the feature principal component contribution rate distribution map; Figure 5 This is a graph showing the correlation between feature importance and faults. Detailed Implementation

[0018] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. 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.

[0019] See Figure 1 The system collects raw vibration signals of the axle assembly during operation using an accelerometer. The collected raw vibration signals undergo noise reduction and standardization preprocessing to obtain preprocessed vibration signal data. From the preprocessed vibration signal data, time-domain statistical features, frequency-domain spectral features, and time-frequency-domain scale features are extracted to form a multi-dimensional primary feature set. Redundancy analysis and importance ranking are performed on the features in the multi-dimensional primary feature set to select a subset of sensitive features for fault characterization. A kernel function is used to map the sensitive feature subset to a high-dimensional feature space. In the high-dimensional feature space, different categories of fault features are linearly reconstructed to obtain a fused feature vector with higher discriminative power. The fused feature vector is input into a pre-trained probabilistic classification model to calculate the posterior probability that the vibration signal belongs to each of the preset fault modes. Based on the calculated posterior probabilities, the fault mode of the axle assembly is determined, and a diagnostic result containing a fault mode identifier is generated.

[0020] See Figure 2In one embodiment of the present invention, the acquired raw vibration signal undergoes noise reduction and standardization preprocessing. Specifically, this includes applying a moving average filter to remove high-frequency random noise from the signal, resulting in a preliminarily smoothed vibration signal. For example, in a scenario where the axle assembly operates at a constant speed, the raw vibration signal may contain significant noise fluctuations. After moving average filtering, the signal smoothness is improved, and the waveform exhibits clearer periodic components. In some embodiments, the window length of the moving average filter is set according to the relationship between the signal sampling frequency and the rotation frequency of the axle assembly to effectively suppress high-frequency random noise. Trend term elimination is then performed on the preliminarily smoothed vibration signal. The baseline drift of the signal is fitted using the least squares method and subtracted from the signal. This operation removes low-frequency interference components introduced by sensor zero-point drift or changes in ambient temperature. Comparing the signal data before and after trend term elimination, it can be seen that the signal mean approaches zero while the fluctuation characteristics are more prominent. It can be understood that the trend term elimination process corrects the baseline position of the signal, providing a stable data foundation for subsequent steps.

[0021] In practical implementation, outlier detection and correction are performed on the vibration signal after trend term elimination. The median of the local data distribution is used to replace outlier amplitude points exceeding a threshold range. For example, a sliding window covering 200 data points is set, and the median and standard deviation of the data points within the window are calculated. Points with amplitudes exceeding the median plus or minus four times the standard deviation are identified as outliers and replaced with the median. Comparing the signal data before and after correction, outlier amplitude points are smoothed while the overall signal shape is preserved. Optionally, the threshold range for outlier detection can be adaptively adjusted according to the statistical characteristics of the vibration signal. The corrected vibration signal undergoes amplitude normalization, scaling the amplitude of all data points to a standard distribution with zero mean and unit variance. The formula for amplitude normalization is expressed as:

[0022] in: It is the amplitude of a single data point of the corrected vibration signal. It is the mean of the amplitudes of all data points of the corrected vibration signal. It is the standard deviation of the amplitude of all data points of the corrected vibration signal. This refers to the normalized amplitude of the data points. In some embodiments, amplitude normalization ensures that the amplitude scale of the axle assembly vibration signal is uniform across different test cycles or operating conditions, facilitating numerical comparison in subsequent feature extraction. It can be understood that the signal after amplitude normalization has a distribution characteristic of zero mean and unit variance.

[0023] In practice, the amplitude-normalized signal is truncated into fixed-length data segments to ensure that all data segments used for subsequent analysis have the same length. The output is pre-processed vibration signal data, for example, a fixed length of 2048 data points, corresponding to the vibration sequence of multiple rotation cycles of the axle assembly. Comparing the signal data before and after truncation, the data segment lengths are consistent and contain complete vibration cycle information. Optionally, the data segment length can be selected as an integer multiple of the sampling frequency according to the analysis requirements to ensure the integrity of the frequency domain transformation.

[0024] See Figure 2 In one embodiment of the present invention, time-domain statistical features, frequency-domain spectral features, and time-frequency-domain scale features are extracted from the preprocessed vibration signal data to form a multi-dimensional primary feature set. Specifically, this includes calculating the mean, variance, peak factor, impulse factor, and waveform factor of the preprocessed vibration signal data to form a time-domain statistical feature set. For example, in an example scenario where the axle assembly operates at a constant speed and there is slight bearing wear, the calculated waveform factor will show a quantifiable difference compared to the data under normal conditions. In some embodiments, the formula for calculating the waveform factor is:

[0025] in: It is the root mean square value of the preprocessed vibration signal data. It is the absolute average value of the preprocessed vibration signal data. This refers to the calculated waveform factor. A Fast Fourier Transform (FFT) is performed on the preprocessed vibration signal data to obtain its spectral distribution. The spectral centroid, frequency variance, and energy proportion within a specific octave band are calculated, forming a set of frequency domain spectral features. For example, in the presence of a gear meshing fault, sidebands will appear in the signal spectrum at the meshing frequency and its octaves, causing a change in the energy proportion within a specific octave band. Comparing the spectral data of normal and fault states allows observation of the energy distribution shift. In essence, the FFT transforms the time-domain vibration signal to the frequency domain, revealing the frequency composition information of the signal.

[0026] In practical implementation, wavelet packet transform is performed on the preprocessed vibration signal data. A suitable wavelet basis function and decomposition level are selected, for example, the 'db4' wavelet basis function is chosen and the decomposition level is set to 4 levels. The vibration signal of the axle assembly under impact load is analyzed. After wavelet packet transform, a wavelet packet decomposition node sequence covering the entire frequency band from low to high frequency is obtained. The sum of squares of the coefficient sequence corresponding to each wavelet packet decomposition node is calculated, and this sum of squares is used as the energy value of the wavelet packet decomposition node. The energy values ​​of all wavelet packet decomposition nodes are arranged in node index order to form an energy feature vector. For example, for a 4-level wavelet packet decomposition, the energy feature vector contains 16 elements, corresponding to the energy values ​​of the 16 wavelet packet decomposition nodes. The energy feature vector is normalized so that the sum of all energy values ​​is 1, forming a time-frequency domain scale feature group. After normalization, the energy feature vectors of different samples are comparable. Optionally, wavelet packet transform can capture the time-frequency localization characteristics of transient impact components in non-stationary vibration signals. In some embodiments, the time-domain statistical feature set, the frequency-domain spectral feature set, and the time-frequency domain scale feature set are merged in sequence to form a comprehensive multi-dimensional primary feature set, which simultaneously contains the statistical and energy information of the signal in the time domain, frequency domain, and time-frequency domain.

[0027] Understandably, the multi-dimensional primary feature set provides a multi-faceted characterization of the vibration state of the axle assembly. Optionally, the time-domain statistical feature set reflects the overall amplitude level and fluctuation shape of the signal, the frequency-domain spectral feature set reveals the frequency distribution characteristics of the signal, and the time-frequency domain scaling feature set describes the distribution of signal energy across different frequency bands over time. The merged multi-dimensional primary feature set provides comprehensive raw feature data for subsequent feature selection and fusion.

[0028] In one embodiment of the present invention, redundancy analysis and importance ranking are performed on the features in the multi-dimensional primary feature set to select a subset of sensitive features for fault characterization. Specifically, this includes calculating the Pearson correlation coefficient between any two features in the multi-dimensional primary feature set to construct a feature correlation matrix. The calculation formula is:

[0029] in: and These represent two different features in a multi-dimensional primary feature set. and It is a feature and characteristics In the The values ​​taken on each sample and It is a feature and characteristics The mean over all samples, This refers to the total number of samples. For example, in a scenario where gear pitting failure exists in an axle assembly, the feature correlation matrix reveals a moderate negative correlation between the time-domain peak factor and the frequency-domain spectral centroid characteristics. In some embodiments, the feature correlation matrix is ​​stored in the form of a symmetric square matrix, with matrix elements... The Pearson correlation coefficient between the i-th feature and the j-th feature is defined. A correlation threshold is set. If the correlation coefficient between two features is higher than the threshold, they are considered a redundant feature pair. The Pearson correlation coefficients between the two features in the redundant feature pair and the fault label are calculated separately. Features with correlation coefficients lower than the preset label correlation threshold are removed. For example, if the correlation threshold is set to 0.8, when the correlation coefficient between the features "waveform factor" and "pulse factor" is 0.88, they are considered a redundant feature pair. The correlation coefficient between the features "waveform factor" and the fault label is calculated to be 0.72, while the correlation coefficient between the features "pulse factor" and the fault label is 0.68. The preset label correlation threshold is 0.70, so the feature "pulse factor" is removed. Optionally, the correlation threshold can be dynamically set according to the feature type. The thresholds between time-domain features and between time-frequency domain features can be different. For example, the correlation threshold between time-domain features can be set to 0.85, while the correlation threshold between time-frequency domain features can be set to 0.75.

[0030] In practical implementation, for the feature set after redundancy removal, a feature importance evaluation method based on decision trees is adopted. This method calculates the importance score of each feature in distinguishing different failure modes. The method involves constructing a decision tree classifier and fitting it to the training data. The sum of the Gini impurity reduction resulting from splitting at all nodes of the tree for each feature is calculated and normalized to obtain the feature importance score. Optionally, the feature importance score can also be calculated based on the information gain or variance reduction resulting from splitting. For example, in the scenario of bearing inner race failure in an axle assembly, the energy feature of a wavelet packet node in the time-frequency domain scale feature group may exhibit high information gain. All features are sorted in descending order according to their importance scores. Features with the highest ranking and a cumulative importance exceeding a preset proportion (e.g., 90%) are selected. The score is accumulated starting with the feature with the highest importance score, and selection stops when the cumulative importance reaches 90%. The resulting feature set may contain the top 8 features with the highest importance scores. Comparing the feature lists before and after sorting, time-domain variance features and frequency-domain spectral centroid features typically rank higher. The selected feature combinations were determined as the sensitive feature subset for subsequent fault characterization. Comparing the feature sets before and after screening, the multi-dimensional primary feature set contained 25 features while the sensitive feature subset contained 8 features, significantly reducing the data dimensionality.

[0031] In one embodiment of the present invention, a kernel function is used to map a subset of sensitive features to a high-dimensional feature space, and linear reconstruction is performed on different categories of fault features in the high-dimensional feature space. Specifically, this process includes selecting a radial basis function (RBF) kernel function to map each sample point in the subset of sensitive features from the original feature space to the high-dimensional feature space. The RBF kernel function has the following form:

[0032] in: and These represent two sample feature vectors within the sensitive feature subset. Representing vectors with vector The Euclidean distance between them The width parameter of the radial basis function (RBF) controls the function's scope. This kernel function calculates the similarity between samples and implicitly maps to a higher-dimensional space. In some embodiments, the width parameter... The value of is determined through cross-validation. In the high-dimensional feature space, the feature mean of all sample points belonging to the same fault mode is calculated, which serves as the feature center of the fault mode. For example, the feature center vector of the "bearing inner ring fault" mode is calculated based on the training data. .

[0033] Calculate the Euclidean distance from each sample point to the feature centers of all fault categories, forming a distance vector. Assuming there are four preset fault modes: "normal," "bearing inner race fault," "bearing outer race fault," and "gear pitting," the distance vector for a sample point contains four elements, representing the Euclidean distances from the sample point to the feature centers of the normal mode, the bearing inner race fault mode, the bearing outer race fault mode, and the gear pitting mode, respectively. The distance vector intuitively reflects the relative proximity of the sample to each fault mode in the feature space. For example, a real bearing inner race fault sample is usually much closer to the bearing inner race fault mode feature center than to the feature centers of other categories. It can be understood that the distance vector supplements the geometric information of the sample's relationship to the overall distribution of each category. Concatenate the original sensitive feature subset of the sample point with the corresponding distance vector to construct a new extended feature vector. If the original sensitive feature subset has a dimension of 8 and there are 4 fault modes, the dimension of the extended feature vector is 12 (see Table 1).

[0034] Table 1: Euclidean Distances from Different Sample Points to Feature Centers of the Four Fault Modes Sample identification Distance to the center of the normal pattern feature Distance to the center of the bearing inner ring fault feature Distance to the center of the bearing outer ring fault feature Distance to the center of gear pitting feature Sample A 5.21 1.37 6.84 4.92 Sample B 1.89 7.45 6.12 5.78 Sample C 4.05 3.98 1.26 6.33 In practice, the extended feature vectors of all training samples and samples to be diagnosed are collected to form an extended feature matrix. The rows of the extended feature matrix correspond to the samples, and the columns correspond to the dimensions of the extended feature vectors. The extended feature matrix is ​​centered by subtracting the mean of each feature dimension, making the mean of each feature dimension zero. The covariance matrix of the centered extended feature matrix is ​​calculated, reflecting the linear correlation between the dimensions of the extended features. The eigenvalues ​​of the covariance matrix and their corresponding eigenvectors are calculated; the magnitude of the eigenvalue represents the magnitude of the variance contribution in the direction of the corresponding feature vector. The feature vectors are arranged in descending order of eigenvalues. The cumulative contribution rate of the principal components corresponding to the arranged feature vectors is calculated sequentially. All principal components included when the cumulative contribution rate first reaches a set threshold are selected. For example, if the threshold is set to 95%, these k principal components are selected when the cumulative contribution rate of the current k principal components first reaches or exceeds 95%. The extended feature vectors of the samples are projected onto all the principal components, and the resulting low-dimensional projection vector is the final fused feature vector. The fused feature vector is a linear representation of the original extended feature vector along a few principal directions. For example, a 12-dimensional extended feature vector is projected onto the first three principal components to obtain a 3-dimensional fused feature vector. In some embodiments, the cumulative contribution rate threshold of the principal components is set to a value between 90% and 99%, such as 95% in axle assembly fault diagnosis. Optionally, principal component analysis reduces data dimensionality while preserving the variation information in the extended feature matrix to the greatest extent possible.

[0035] It is understandable that the dimensions of the fused feature vector obtained through principal component analysis are linearly uncorrelated. Optionally, the fused feature vector, as input to a subsequent probabilistic classification model, benefits from reduced dimensionality, which improves the model's computational efficiency and generalization ability. In some embodiments, the projection transformation matrix from the extended feature vector to the fused feature vector is calculated based on the training sample data and is also applied to the sample to be diagnosed. Comparing the features before and after fusion, the fused feature vector is a comprehensive expression of the original sensitive features and class distance information after linear reconstruction and dimensionality reduction.

[0036] See Figure 4This is a distribution chart of the contribution rates of principal components in the extended feature matrix, showcasing the results of principal component analysis. It is a crucial visualization in the feature fusion stage of vehicle axle fault diagnosis. The contribution rate of a single principal component is highest at approximately 47% for the first principal component, decreasing rapidly with increasing principal component number. The contribution rates of the sixth principal component and subsequent components are almost zero, indicating that the first few principal components already contain most of the variation information of the extended features. The cumulative contribution rate of the first two principal components exceeds 75%, reaching approximately 90% for the third principal component, and reaching 100% for the fifth principal component, far exceeding the 95% threshold. The original 12-dimensional extended features can be effectively reduced to 3-dimensional fusion features, significantly reducing the computational complexity of subsequent classification models.

[0037] In one embodiment of the present invention, the fused feature vector is input into a pre-trained probabilistic classification model to calculate the posterior probability of the vibration signal belonging to various preset fault modes. The probabilistic classification model employs a Bayesian classifier based on kernel density estimation. For each preset fault mode, the probability density distribution of the fault mode's features in the feature space is fitted using the fused feature vector of its training samples through a kernel density estimation method. For the fused feature vector of all training samples of a certain fault mode, a Gaussian kernel function with a suitable smoothing parameter is selected. The form of the Gaussian kernel function is:

[0038] in: It is any point in the feature space where the probability density needs to be estimated. It is the first The fused feature vector of each training sample It is the smoothing parameter or bandwidth of the Gaussian kernel function. It is the dimension of the fused feature vector. Point With point The Euclidean distance between them. For each dimension in the feature space, calculate the kernel density contribution of all sample data points in that dimension to a specified location. Combine the kernel density estimates of all dimensions and obtain the joint probability density distribution function of the corresponding fault mode in the multivariate feature space by product or summation. For example, assuming that the feature dimensions are independent, the joint probability density distribution function is the product of the probability density estimates of each dimension.

[0039] In practical implementation, the smoothing parameter of the Gaussian kernel function is optimized through cross-validation to make the estimated probability density distribution closest to the true distribution. For example, the training samples of a certain fault mode are divided into 5 folds, and a candidate set of smoothing parameters is traversed. The smoothing parameter value that maximizes the average log-likelihood is selected as the final parameter. When a new fused feature vector is input, the likelihood value of the new fused feature vector under the probability density distribution of each fault mode is calculated. The likelihood value is the function value of the new fused feature vector in the joint probability density distribution function of each fault mode. Combining the prior probabilities of each fault mode appearing in historical data, Bayes' theorem is used to calculate the posterior probability of the new fused feature vector belonging to each fault mode. For example, in the example scenario of bearing outer race failure in axle assembly, a fused feature vector representing an unknown state is input, and its likelihood value is calculated under four modes: "normal", "bearing inner race failure", "bearing outer race failure", and "gear pitting". Combining the prior probabilities obtained from historical statistics, the posterior probability values ​​are calculated using Bayes' formula as 0.02, 0.07, 0.01, and 0.90, respectively. Output a probability vector, where each element represents the posterior probability that the vibration signal belongs to the corresponding preset fault mode, and the sum of all elements of the probability vector is 1.

[0040] In specific implementation, the failure mode of the axle assembly is determined based on the calculated posterior probability. The largest posterior probability is identified from the posterior probability vector output by the probabilistic classification model; for example, the largest posterior probability value is identified as 0.90 from the probability vector [0.02, 0.07, 0.01, 0.90]. This largest posterior probability is compared with a preset diagnostic confidence threshold, for example, 0.85. When the largest posterior probability is greater than or equal to the diagnostic confidence threshold, the preset failure mode corresponding to the largest posterior probability is determined as the failure mode of the axle assembly. In this example, 0.90 is greater than 0.85, therefore the "gear pitting" failure mode corresponding to 0.90 is determined as the diagnostic result. In some embodiments, the diagnostic confidence threshold is set to a fixed value between 0.8 and 0.95, for example, 0.85. It can be understood that setting the diagnostic confidence threshold balances the reliability and sensitivity of the diagnosis. When the posterior probability of the largest value is less than the diagnostic confidence threshold, the system determines that the diagnostic confidence is insufficient and generates a prompt message indicating that further investigation is needed. For example, when the probability vector is [0.35, 0.32, 0.18, 0.15], the maximum posterior probability of 0.35 is less than the threshold of 0.85, and the system outputs the message "Insufficient diagnostic confidence; further analysis using other detection methods is recommended." Optionally, the generated prompt message may include the currently calculated posterior probability vector for maintenance personnel to reference. It is understood that setting a diagnostic confidence threshold can effectively avoid giving incorrect definitive conclusions when the model's judgment is ambiguous.

[0041] See Figure 5 This is a feature importance and fault correlation analysis chart, demonstrating the selection criteria for multi-dimensional primary features in vehicle axle fault diagnosis. It represents a crucial step from the primary feature set to the sensitive feature subset. Feature importance is evaluated using a decision tree model, reflecting the contribution of features to distinguishing different fault modes. The correlation with fault labels uses the Pearson correlation coefficient to measure the strength of the linear association between features and fault types. Features such as spectral centroid, peak factor, and wavelet energy 1 perform exceptionally well in both metrics and are core sensitive features for fault diagnosis. Features such as mean and waveform factor either contribute little to fault differentiation or have a weak correlation with fault labels and can be eliminated as redundant features. The selected sensitive feature subset retains the most discriminative information for fault modes while eliminating redundant noise.

[0042] The above embodiments are only used to illustrate the technical methods of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical methods of the present invention without departing from the spirit and scope of the technical methods of the present invention.

Claims

1. A method for fault diagnosis of axle assembly vibration signals by multi-feature fusion, characterized in that, Includes the following steps: The original vibration signal of the axle assembly under operating conditions is collected by an accelerometer. The collected original vibration signal is then subjected to noise reduction and standardization preprocessing to obtain preprocessed vibration signal data. From the preprocessed vibration signal data, time-domain statistical features, frequency-domain spectral features, and time-frequency-domain scale features are extracted to form a multi-dimensional primary feature set. Redundancy analysis and importance ranking are performed on the features in the multi-dimensional primary feature set to select a sensitive feature subset for fault characterization; By using kernel functions to map a subset of sensitive features to a high-dimensional feature space, and then linearly reconstructing the fault features of different categories in the high-dimensional feature space, a fusion feature vector with higher discriminative power is obtained. The fused feature vector is input into a pre-trained probability classification model to calculate the posterior probability that the vibration signal belongs to various preset fault modes. Based on the calculated posterior probability, the failure mode of the axle assembly is determined, and a diagnostic result containing the failure mode identifier is generated.

2. The method for multi-feature fusion fault diagnosis of vibration signals in a vehicle axle assembly according to claim 1, characterized in that, The noise reduction and standardization preprocessing of the acquired raw vibration signals specifically includes: A moving average filter is applied to the original vibration signal to filter out high-frequency random noise and obtain a preliminarily smoothed vibration signal. The trend term of the initially smoothed vibration signal is eliminated, and the baseline drift of the signal is fitted using the least squares method and then subtracted from the signal. Anomaly detection and correction are performed on the vibration signal after trend term elimination, and the median of the local data distribution is used to replace the abnormal amplitude points that exceed the threshold range; The amplitude of the corrected vibration signal is normalized to scale the amplitude of all data points to a standard distribution with zero mean and unit variance. The amplitude-normalized signal is truncated into fixed-length data segments to ensure that all data segments used for subsequent analysis have the same length, and the output is the preprocessed vibration signal data.

3. The method for multi-feature fusion fault diagnosis of vibration signals in a vehicle axle assembly according to claim 2, characterized in that, The extraction of time-domain statistical features, frequency-domain spectral line features, and time-frequency-domain scale features respectively constitutes a multi-dimensional primary feature set, specifically including: For the preprocessed vibration signal data, calculate its mean, variance, peak factor, impulse factor and waveform factor to form a time-domain statistical feature set; Fast Fourier Transform is performed on the preprocessed vibration signal data to obtain its spectral distribution. The spectral centroid, frequency variance, and energy proportion within a specific octave band are calculated to form a frequency domain spectral feature group. The preprocessed vibration signal data is subjected to wavelet packet transform, decomposed to a set number of layers, and the energy values ​​of the wavelet packet decomposition coefficients of each node are extracted to form a time-frequency domain scale feature group. The time-domain statistical feature set, the frequency-domain spectral feature set, and the time-frequency domain scale feature set are merged in sequence to form a comprehensive multi-dimensional primary feature set.

4. The method for multi-feature fusion fault diagnosis of vibration signals in a vehicle axle assembly according to claim 3, characterized in that, The process of performing redundancy analysis and importance ranking on the features in the multi-dimensional primary feature set to select a sensitive feature subset for fault characterization specifically includes: Calculate the Pearson correlation coefficient between any two features in the multidimensional primary feature set to construct a feature correlation matrix; A correlation threshold is set. If the correlation coefficient between two features is higher than the correlation threshold, they are determined to be redundant feature pairs. The Pearson correlation coefficient between the two features in the redundant feature pair and the fault label is calculated respectively. Features with correlation coefficients lower than the preset label correlation threshold are removed. For the feature set after redundancy removal, a feature importance evaluation method based on decision trees is used to calculate the importance score of each feature in distinguishing different failure modes. All features are sorted in descending order based on their feature importance scores, and the features with the highest ranking and cumulative importance exceeding a preset proportion are selected. The selected feature combinations are determined as a subset of sensitive features for subsequent fault characterization.

5. The method for multi-feature fusion fault diagnosis of vibration signals in a vehicle axle assembly according to claim 4, characterized in that, The process of mapping a subset of sensitive features to a high-dimensional feature space using a kernel function, and then linearly reconstructing different categories of fault features in the high-dimensional feature space, specifically includes: By selecting a radial basis kernel function, each sample point in the sensitive feature subset is mapped from the original feature space to a high-dimensional feature space. In the high-dimensional feature space, the feature mean of all sample points belonging to the same fault mode is calculated and used as the feature center of the fault mode. Calculate the Euclidean distance from each sample point to the center of all fault features for each category, forming a distance vector; A new extended feature vector is constructed by concatenating the original sensitive feature subset of the sample point with the distance vector corresponding to the sample point. Principal component analysis was performed on the extended feature vectors of all samples, and the principal component with the largest contribution rate was selected as the final fused feature vector.

6. The method for multi-feature fusion fault diagnosis of vibration signals in a vehicle axle assembly according to claim 5, characterized in that, The step of inputting the fused feature vector into a pre-trained probability classification model to calculate the posterior probability of the vibration signal belonging to various preset fault modes specifically includes: The probabilistic classification model employs a Bayesian classifier based on kernel density estimation; For each preset fault mode, the probability density distribution of the fault mode's features in the feature space is fitted using the fused feature vector of its training samples through the kernel density estimation method. When a new fused feature vector is input, the likelihood values ​​of the new fused feature vector under the probability density distributions of various fault modes are calculated respectively. By combining the prior probabilities of various failure modes appearing in historical data, the posterior probability of the new fused feature vector belonging to each failure mode is calculated using Bayes' theorem. Output a probability vector, where each element represents the posterior probability that the vibration signal belongs to the corresponding preset fault mode.

7. The method for multi-feature fusion fault diagnosis of vibration signals in a vehicle axle assembly according to claim 6, characterized in that, The step of determining the failure mode of the axle assembly based on the calculated posterior probability specifically includes: Identify the posterior probability with the largest value from the posterior probability vector output by the probabilistic classification model; The posterior probability of the largest value is compared with a preset diagnostic confidence threshold; When the posterior probability of the largest value is greater than or equal to the diagnostic confidence threshold, the preset fault mode corresponding to the posterior probability of the largest value is determined as the fault mode of the axle assembly. When the posterior probability of the largest value is less than the diagnostic confidence threshold, it is determined that the diagnostic confidence is insufficient, and a prompt message indicating that further examination is required is generated.

8. The method for multi-feature fusion fault diagnosis of vibration signals in a vehicle axle assembly according to claim 7, characterized in that, The process of performing wavelet packet transform on the preprocessed vibration signal data, decomposing it to a set number of levels, and extracting the energy values ​​of the wavelet packet decomposition coefficients at each node specifically includes: Select appropriate wavelet basis functions and decomposition levels, and perform wavelet packet transform on the preprocessed vibration signal data; After completing the wavelet packet transform, a wavelet packet decomposition node sequence covering the entire frequency band from low frequency to high frequency is obtained; Calculate the sum of squares of the coefficient sequence corresponding to each wavelet packet decomposition node, and use the sum of squares as the energy value of the wavelet packet decomposition node; Arrange the energy values ​​of all wavelet packet decomposition nodes in order of node index to form an energy feature vector; The energy feature vector is normalized so that the sum of all energy values ​​is 1, forming a time-frequency domain scale feature group.

9. The method for multi-feature fusion fault diagnosis of vibration signals in a vehicle axle assembly according to claim 8, characterized in that, The step of performing principal component analysis on the extended feature vectors of all samples and selecting the principal component with the largest contribution rate as the final fused feature vector specifically includes: Collect the extended feature vectors of all training samples and samples to be diagnosed, and form an extended feature matrix; The extended feature matrix is ​​centered by subtracting the mean of each feature dimension. Calculate the covariance matrix of the expanded feature matrix after centering; Calculate the eigenvalues ​​and corresponding eigenvectors of the covariance matrix; The feature vectors are arranged in descending order of their eigenvalues. The cumulative contribution rate of the principal components corresponding to the arranged feature vectors is calculated sequentially. All principal components included when the cumulative contribution rate first reaches a set threshold are selected. The extended feature vector of the sample is projected onto all principal components. The resulting low-dimensional projection vector is the final fused feature vector.

10. The method for multi-feature fusion fault diagnosis of vibration signals in a vehicle axle assembly according to claim 9, characterized in that, The step of using the fused feature vector of its training samples to fit the probability density distribution of the fault mode's features in the feature space through a kernel density estimation method specifically includes: For the fused feature vector of all training samples of a certain type of fault mode, select a Gaussian kernel function with appropriate smoothing parameters; For each dimension in the feature space, calculate the kernel density contribution of all sample data points in that dimension to a specified location. By combining the kernel density estimation results of all dimensions, the joint probability density distribution function of the corresponding fault mode in the multivariate feature space can be obtained by product or summation. By optimizing the smoothing parameters of the Gaussian kernel function through cross-validation, the estimated probability density distribution is made to be as close as possible to the true distribution.

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