A voiceprint cross-domain fault diagnosis method based on causal feature alignment

Abstract

The application discloses a voiceprint cross-domain fault diagnosis method based on causal feature alignment, and belongs to the technical field of voiceprint fault diagnosis. The method acquires source domain labeled voiceprint samples and target domain unlabeled voiceprint samples, and constructs a multi-scale recursive graph based on local phase preservation as a voiceprint primary representation. Dynamic time warping is performed on the voiceprint primary representation to acquire an instantaneous frequency fluctuation path as a cross-domain transferable voiceprint structural feature. A causal feature selection criterion is constructed between the source domain and the target domain according to the voiceprint structural feature, and a stable feature subset insensitive to domain changes is screened. The stable feature subset is mapped to a high-dimensional Hilbert space for covariance measurement, the feature mapping direction is adjusted, causal alignment features are obtained, and a classifier is input to output a fault category. The method can extract a cross-domain stable voiceprint structural representation, realize causal driving domain invariant feature alignment, and improve the reliability and precision of cross-domain fault diagnosis.

Description

Technical Field

[0001] This invention relates to the field of voiceprint fault diagnosis technology, specifically to a voiceprint cross-domain fault diagnosis method based on causal feature alignment. Background Technology

[0002] In the field of voiceprint fault diagnosis, the identification of mechanical equipment fault states based on voiceprint signal analysis has been widely applied. However, in actual working conditions, changes in the equipment's operating environment, load conditions, and sensor models can cause shifts in the distribution of collected voiceprint data, leading to cross-domain diagnostic problems. When a diagnostic model trained in the source domain is directly applied to the target domain, the classification accuracy will significantly decrease.

[0003] Existing cross-domain fault diagnosis methods largely rely on domain adaptation techniques based on statistical or deep features. Statistical feature-based methods extract parameters such as mean, variance, and kurtosis from the time and frequency domains, using criteria like maximum mean difference or correlation alignment to approximate the feature distributions of the source and target domains. However, the features extracted by these methods are highly susceptible to noise interference and fail to adequately characterize the phase information and frequency dynamics implicit in the voiceprint signal, resulting in limited domain alignment effectiveness. Deep feature-based methods utilize convolutional neural networks or autoencoders to learn voiceprint representations, employing adversarial training or transfer learning strategies to achieve domain-invariant feature extraction. However, deep learning methods suffer from poor interpretability and are prone to learning non-causal features that are spuriously correlated with fault labels. When the domain shift is large, the model's generalization performance deteriorates sharply. Furthermore, existing feature alignment methods typically perform global distribution matching within the original feature space or a single kernel space, failing to consider the fine-grained differences in the covariance structure between cross-domain features. This results in the inability to eliminate some domain-sensitive spurious correlations, making it difficult to achieve accurate domain-invariant mapping in high-dimensional spaces.

[0004] In cross-domain voiceprint fault diagnosis, the following problems need to be solved: how to extract structured feature representations from non-stationary voiceprint signals that can characterize the instantaneous fluctuation of frequency and remain robust to domain changes; how to establish a feature selection mechanism based on causality to eliminate components that are pseudo-correlated with the domain; and how to achieve fine alignment at the covariance structure level in high-dimensional feature space. Summary of the Invention

[0005] This invention provides a method for cross-domain fault diagnosis based on causal feature alignment. Starting from the phase dynamic characteristics of the voiceprint signal, it extracts the instantaneous frequency fluctuation path features that can be transferred across domains, and achieves accurate fault category determination under the condition of no target domain label by using causal feature selection criteria and high-dimensional space covariance driven alignment.

[0006] To achieve the above objectives, the present invention provides the following technical solution: The present invention provides a cross-domain fault diagnosis method based on causal feature alignment. By extracting cross-domain features with causal invariance from the voiceprint signal, the method significantly reduces the impact of inter-domain distribution differences on the diagnosis results and improves the migration capability and stability of the fault diagnosis model under different operating conditions or equipment conditions.

[0007] After acquiring labeled voiceprint samples from the source domain and unlabeled voiceprint samples from the target domain, a multi-scale recursive graph based on local phase preservation is constructed as the primary representation of the voiceprint, according to the temporal amplitude distribution of each sample. Preferably, the original time-domain signal of each voiceprint sample is processed by framing and normalized to obtain a normalized frame sequence; three basic time-frequency attributes—zero-crossing rate, spectral centroid, and spectral flatness—are extracted from each frame and concatenated into an attribute vector; representative frame attributes are determined based on the Euclidean distance of the attribute vectors under the same fault category, and the frame number corresponding to the representative frame attribute is used as the anchor frame number. A local time frame set is selected with the frame corresponding to the anchor frame number as the center, and a short-time Fourier transform is performed on each frame in the set to obtain the complex spectrum. The phase spectrum is extracted to construct a Hankel matrix; singular value decomposition is performed on the Hankel matrix, and the left and right singular vectors corresponding to the largest singular value are retained to reconstruct the phase-preserving matrix. The diagonal element sequence of this matrix is ​​used as the multi-scale recursive coefficients, thereby obtaining a multi-scale recursive graph while preserving the local phase structure of the voiceprint. This multi-scale recursive graph can fully express the nonlinear dynamic changes of the voiceprint signal and has good robustness to noise interference.

[0008] Dynamic time warping is performed on the primary representation of the voiceprint to obtain the instantaneous frequency fluctuation path of each frequency channel on the time axis, and this instantaneous frequency fluctuation path is used as a cross-domain transferable voiceprint structural feature. Preferably, the cumulative distance matrix between the multi-scale recursive coefficients is calculated using the query sequence and the original amplitude sequence of each frequency channel as the reference sequence. The cumulative distance matrix is ​​then traced back from the lower right corner to the upper left corner, recording the frequency index and time index corresponding to each matrix position traversed by the traversal path and forming a pairing sequence. Differential operations are performed on adjacent pairing points in the pairing sequence to obtain the differential frequency index sequence as the instantaneous frequency fluctuation path. This path reflects the instantaneous frequency curvature of the voiceprint signal in different frequency channels, possessing a natural adaptability to inter-domain variations and facilitating the elimination of temporal distortions between different domains.

[0009] Based on the instantaneous frequency fluctuation path, a causal feature selection criterion is constructed between the source and target domains. This criterion is then used to filter out a stable subset of features from the acoustic signature structural features that are insensitive to domain changes. Preferably, the mutual information value between the instantaneous frequency fluctuation path of each sample in the source domain and the corresponding fault category label is calculated to obtain the source domain mutual information set; the mutual information value between the instantaneous frequency fluctuation path of each sample in the target domain and the target domain sample index is calculated to obtain the target domain mutual information set; the source domain mutual information set and the target domain mutual information set are divided element-wise along the frequency channel dimension to obtain the mutual information ratio for each frequency channel; the acoustic signature structural features corresponding to frequency channels with mutual information ratios greater than a preset ratio threshold are included in the stable feature subset. This process eliminates pseudo-correlation features that are only related to a specific domain, and the retained feature subset maintains a stable causal relationship with the fault category in different domains, effectively improving the generalization performance of cross-domain diagnosis.

[0010] The stable feature subsets are mapped to a high-dimensional Hilbert space, and the covariance of the distributions in the source and target domains is measured in the high-dimensional Hilbert space. The feature mapping direction is adjusted based on the covariance measurement. Preferably, a Gaussian radial basis function is selected as the kernel function, and the kernel width parameter is determined based on the mean vector and covariance matrix of the stable feature subsets in the source domain. The embedding matrices of the stable feature subsets in the source and target domains are calculated using this parameter and centered. The source domain covariance operator is obtained by multiplying the centered matrix of the source domain with its transpose, and the target domain covariance operator is obtained by multiplying the centered matrix of the target domain with its transpose. The product matrix of the inverse matrix of the source domain covariance operator and the target domain covariance operator is calculated, and the eigenvalue sequence of the product matrix is ​​extracted. The square root of the sum of squares of all eigenvalues ​​is used as the covariance measure. A preset allowable deviation threshold is used. If the covariance metric is greater than this threshold, the current feature mapping basis vector is rotated in the direction that reduces the Fréchet distance between the source domain covariance operator and the target domain covariance operator. If the covariance metric is less than or equal to the threshold, the current feature mapping basis vector remains unchanged and is used as the adjusted feature mapping direction. This mapping direction adaptively reduces the difference in second-order statistics between the source and target domains in the reproducing kernel Hilbert space, enabling the distributions of different domains to achieve high-order moment alignment along this mapping direction.

[0011] The stable feature subset is converted into causal-aligned features using the adjusted feature mapping direction, and these causal-aligned features are then input into the classifier to output the fault category. Preferably, each sample vector in the stable feature subset is multiplied by the adjusted feature mapping direction to obtain a projection scalar. The projection scalars of all sample vectors are then arranged in the original sample order to form a projection vector sequence. This projection vector sequence is then zero-mean and unit-variance processed to obtain the causal-aligned features. The decision boundary of the classifier is initialized as the bisecting hyperplane between the means of the causal-aligned features of each fault category in the source domain. After inputting the causal-aligned features, the signed distance to each bisecting hyperplane is calculated, and the fault category corresponding to the maximum signed distance is selected as the diagnostic result. This process allows the classifier to make decisions directly in the domain-invariant feature space, significantly improving the accuracy and stability of cross-domain voiceprint fault diagnosis.

[0012] The technical effects and advantages provided by the present invention in the above technical solution are as follows: By combining local phase-preserving multi-scale recursive graphs with dynamic time warping, cross-domain transferable acoustic signature structural features are constructed from acoustic signature signals. After constructing the Hankel matrix and performing singular value decomposition on the phase spectrum of the short-time Fourier transform, the reconstructed phase-preserving matrix captures the recursive behavior of the signal across multiple time scales, preserving the nonlinear phase dynamics inherently related to the fault state. Based on this, dynamic time warping is performed to calculate the cumulative distance between the multi-scale recursive coefficients and the amplitude sequences of each frequency channel, extracting the frequency index change sequence in the backtracking path to obtain the instantaneous frequency fluctuation path. This path directly reflects the microscopic fluctuation law of frequency change over time, is insensitive to domain variations such as acquisition conditions and environmental noise, and can form a consistent feature expression across different domains, avoiding distortion of statistical features or ordinary spectral features under domain shifts.

[0013] A causal feature selection criterion is constructed using instantaneous frequency fluctuation paths, and the feature mapping direction is adjusted in conjunction with a covariance metric in a high-dimensional Hilbert space to achieve causally driven, domain-invariant feature alignment. The mutual information between the instantaneous frequency fluctuation paths of the source domain and the fault labels is calculated, along with the mutual information between the target domain features and the sample index. The mutual information ratio is calculated element-wise for each frequency channel, and components with ratios higher than a preset threshold are selected to form a stable feature subset. This ratio suppresses channels that are strongly correlated with the domain distribution but weakly causally correlated with the fault category, retaining only frequency components with stable causal explanatory power for the fault labels and eliminating interference from cross-domain spurious correlations. After mapping to a high-dimensional Hilbert space, a covariance metric is constructed using the eigenvalues ​​of the product matrix of the source and target domain covariance operators. By comparing this metric with an allowable deviation threshold, the feature mapping basis vector is rotated along the direction of decreasing Friesian distance, achieving fine alignment of the source and target domains in terms of second-order statistical properties, rather than merely matching distributions at the mean level. The resulting causal alignment features exhibit high invariance to domain shifts, significantly reducing the cross-domain diagnostic error rate when input into a classifier. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0015] Figure 1 This is a flowchart of a cross-domain fault diagnosis method based on causal feature alignment; Figure 2 This is a flowchart of the process for obtaining instantaneous frequency fluctuation paths based on dynamic time warping; Figure 3 These are Euclidean distance sorting curves of anchor frame attribute vectors for different fault categories; Figure 4 These are differential frequency index curves representing the instantaneous frequency fluctuation paths of different frequency channels; Figure 5 It is the distribution of the mutual information ratio between the source and target domains and the results of stable channel selection; Figure 6 It is the curve showing the iterative change of the covariance metric as the feature map is adjusted. Figure 7 This is a schematic diagram of the projection distribution of samples of different fault categories and the classification decision boundary in the causal alignment feature space. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0017] See Figure 1 This invention provides a method for cross-domain fault diagnosis based on causal feature alignment, which includes the following overall implementation scheme: After acquiring labeled voiceprint samples from the source domain and unlabeled voiceprint samples from the target domain, a multi-scale recursive graph based on local phase preservation is constructed as the primary voiceprint representation according to the temporal amplitude distribution of each sample. Dynamic time warping is performed on the primary voiceprint representation to obtain the instantaneous frequency fluctuation path of each frequency channel on the time axis, and this instantaneous frequency fluctuation path is used as a cross-domain transferable voiceprint structural feature. Based on the instantaneous frequency fluctuation path, a causal feature selection criterion is constructed between the source and target domains. This criterion is used to select a stable feature subset from the voiceprint structural features that is insensitive to domain changes. The stable feature subset is mapped to a high-dimensional Hilbert space, and the covariance of the distributions in the source and target domains is measured in the high-dimensional Hilbert space. The feature mapping direction is adjusted based on the covariance measurement. The adjusted feature mapping direction is used to convert the stable feature subset into causal aligned features, which are then input into a classifier to output the fault category.

[0018] Example 1

[0019] In practice, the process of obtaining labeled voiceprint samples from the source domain and unlabeled voiceprint samples from the target domain includes the following steps.

[0020] The original time-domain signal of each voiceprint sample is divided into frames. The frame length is set to 2048 sampling points, and the frame shift is set to 1024 sampling points. After framing, multiple frame signals are obtained. Normalization is performed on each frame signal as follows: the mean of all sampling points within the frame signal is calculated, and the value of each sampling point in the frame signal is subtracted from the calculated mean to obtain the mean-reduced frame signal; the standard deviation of the mean-reduced frame signal is calculated, and the value of each sampling point in the mean-reduced frame signal is divided by the calculated standard deviation to obtain the normalized frame. All normalized frames constitute a normalized frame sequence.

[0021] For each frame in the normalized frame sequence, three fundamental time-frequency attributes are extracted: zero-crossing rate, spectral centroid, and spectral flatness. The zero-crossing rate is the number of times the signal in that frame crosses the zero-amplitude point on the time-domain waveform. The spectral centroid is the amplitude-weighted average frequency of the signal's spectrum in that frame, reflecting the centroid of the spectral energy distribution. Spectral flatness is the ratio of the geometric mean to the arithmetic mean of the signal's spectrum in that frame, reflecting the flatness of the spectrum. The extracted zero-crossing rate, spectral centroid, and spectral flatness values ​​are concatenated into a three-dimensional vector, which serves as the attribute vector for the corresponding frame.

[0022] For each fault category in the labeled voiceprint samples of the source domain, an anchor frame number determination process is performed. The determination process is as follows: Collect the attribute vectors of all frames belonging to the same fault category. For each frame, calculate the Euclidean distance between its attribute vector and the attribute vectors of all other frames in the same fault category, and calculate the average of all Euclidean distances. Use this average as the distance metric for that frame. Sort all frames within the fault category according to their distance metric values ​​in ascending order. If the total number of frames after sorting is odd, select the frame in the middle as the representative frame; if the total number of frames after sorting is even, select the frame with the smaller distance metric value between the two middle frames as the representative frame. Use the attribute vector corresponding to the representative frame as the representative frame attribute, and use the frame number of the representative frame in the normalized frame sequence as the anchor frame number.

[0023] For unlabeled voiceprint samples in the target domain, although there are no fault category labels, a normalized frame sequence is obtained using the same frame processing method as the source domain. Based on the representative frame attributes determined for each fault category in the source domain, the frame with the smallest Euclidean distance to the representative frame attributes is found in the normalized frame sequence of the target domain. The frame number of this frame is used as the simulated anchor frame number under the corresponding fault category in the target domain, or the temporal offset relationship corresponding to the anchor frame number in the source domain is directly used to determine the local time period of the target domain.

[0024] In practice, the process of constructing a multi-scale recursive graph based on local phase preservation includes the following steps.

[0025] Centered on the frame indicated by the anchor frame number, a preset first number of frames are taken forward and a preset second number of frames are taken backward from the normalized frame sequence, forming a local time period frame set together with the center frame. The first and second number of frames are both positive integers, which can be set according to the duration of the voiceprint sample and the required local time period length.

[0026] A short-time Fourier transform (SFT) is performed on each frame in the local time frame set. The SFT uses a Hanning window with a window length equal to the frame length (2048 sampling points), and the number of Fourier transform points is set to 2048. The complex spectrum corresponding to each frame is obtained after the SFT. Phase information is extracted from the complex spectrum to obtain the phase spectrum corresponding to each frame. The phase spectrum is a vector with a length half the number of Fourier transform points plus one, where each element represents the phase angle of the corresponding frequency channel.

[0027] A Hankel matrix is ​​constructed using the phase spectrum of a specific frame within a local time frame set. The construction method is as follows: the phase spectrum vector is denoted as... The vector length is Set the embedding dimension Then the number of rows in the Hankel matrix is The number of columns is The first of the Hankel matrix Line number The column element takes the value of the phase spectrum vector. The Middle The values ​​of the elements, where The value is to , The value is to , The value is usually less than Integers.

[0028] Singular value decomposition (SVD) is performed on the constructed Hankel matrix. SVD represents the Hankel matrix as a product of three matrices: the Hankel matrix equals the transpose of the left singular vector matrix, the singular value diagonal matrix, and the right singular vector matrix. The largest singular value is extracted from the singular value diagonal matrix, and the corresponding left and right singular vectors are extracted. The left singular vector is the column in the left singular vector matrix corresponding to the largest singular value, and the right singular vector is the column in the right singular vector matrix corresponding to the largest singular value.

[0029] The phase-preserving matrix is ​​reconstructed using the extracted maximum singular value, left singular vector, and right singular vector. The reconstruction formula is as follows:

[0030] in, Represents the phase-preserving matrix. Represents the maximum singular value. The left singular vector corresponding to the maximum singular value is represented by a column vector. This represents the right singular vector corresponding to the maximum singular value, and is also in column vector form. This represents the transpose of the right singular vector. The phase-preserving matrix has the same number of rows as the left singular vector and the same number of columns as the right singular vector.

[0031] The diagonal elements of the phase-preserving matrix are extracted and arranged in order to form a sequence, which is the multi-scale recursive coefficient of the corresponding frame. The above Hankel matrix construction, singular value decomposition, and phase-preserving matrix reconstruction operations are performed on each frame in the local time frame set to obtain the multi-scale recursive coefficient of each frame. The multi-scale recursive coefficients of all frames together constitute the multi-scale recursive coefficients of the local time frame, which serve as the primary representation of the voiceprint.

[0032] See Figure 3 In the graph, the horizontal axis represents the sorting frame number, ranging from 0 to 600, and the vertical axis represents the distance metric value, ranging from 0 to 1.0. The legend indicates the distance metric trend curves for fault categories 1, 2, and 3. Each curve uses a different line type and symbol: solid dot for fault category 1, dashed square for fault category 2, and dashed triangle for fault category 3.

[0033] Overall, the three curves show a highly consistent and overlapping trend in distance metric values. Furthermore, as the sorted frame number increases, the distance metric value exhibits a steady, monotonic increase, demonstrating a positive correlation between the distance metric value and the frame number. This trend aligns with the processing steps in Example 1, which involve calculating the Euclidean distance between the attribute vector of each frame in the source domain's labeled voiceprint samples and the attribute vectors of similar frames, and then sorting them. The increasing distance metric value reflects a gradual decrease in the similarity between the frame's attribute vector and other frames in the fault category.

[0034] Regarding the key numerical range, in the interval where the sorted frame number is around 300, the representative frame (anchor frame) is marked with a black cross in the figure. The distance metric value of this frame is at the median level of the distance metric value of the entire sequence, which conforms to the principle in Example 1 that if the total number of sorted frames is even, the frame with the smaller distance metric value among the two middle frames is taken as the representative frame. The determination of the representative frame provides the anchor frame sequence number as a basis for the subsequent construction of a multi-scale recursive graph based on local phase preservation.

[0035] Furthermore, the distance metric curves for the three fault categories exhibit a high degree of consistency in shape and value, indicating that the frame attribute vector distance metric method used for different fault categories in this embodiment has good stability and consistency, which is beneficial for subsequent construction of local time frame sets and extraction of multi-scale recursive coefficients based on anchor frames.

[0036] Example 2

[0037] In specific implementation, please refer to Figure 2The process involves performing dynamic time warping on the primary voiceprint representation to obtain the instantaneous frequency fluctuation path of each frequency channel on the time axis, which involves the following processing steps.

[0038] A multi-scale recursive coefficient sequence is extracted from the primary voiceprint representation. This multi-scale recursive coefficient sequence is a sequence constructed on a local time frame set. The order of the elements in the sequence corresponds to the order of the frequency channels. The sequence length is equal to the total number of frequency channels obtained after the short-time Fourier transform.

[0039] For each frequency channel, the original amplitude sequence corresponding to that frequency channel is extracted from the time spectrum of the original voiceprint sample. The original amplitude sequence is formed by arranging the amplitude of that frequency channel in each time frame in chronological order, and the sequence length is equal to the total number of time frames.

[0040] Let the multi-scale recursive coefficient sequence be the query sequence, and let the total length of the query sequence be U. Let the original amplitude sequence of the current frequency channel be the reference sequence, and let the total length of the reference sequence be V.

[0041] Calculate the local distance between each element in the query sequence and each element in the reference sequence. The local distance uses the Euclidean distance metric, which is calculated by subtracting the square root of the square of the value of the v-th element in the reference sequence from the value of the u-th element in the query sequence, where u is an integer from 1 to U, and v is an integer from 1 to V. All local distances form a local distance matrix of size U rows and V columns.

[0042] Construct the cumulative distance matrix based on the local distance matrix. The element in the u-th row and v-th column of the cumulative distance matrix is ​​denoted as... , The value of is determined by both the local distance and the cumulative distance of adjacent calculated neighbors. The specific calculation formula is as follows:

[0043] in, This represents the element in the u-th row and v-th column of the cumulative distance matrix. This represents the local distance between the u-th element of the query sequence and the v-th element of the reference sequence; This represents the value of the element in the (u-1)th row and (v-1)th column of the cumulative distance matrix; This represents the value of the element in the (u-1)th row and vth column of the cumulative distance matrix; This represents the value of the element in the u-th row and v-1-th column of the cumulative distance matrix. When u-1 or v-1 is 0, the cumulative distance at the corresponding position is considered to be infinite, and the minimum value is selected from the remaining finite values. The starting point for the recursive calculation is... .

[0044] After filling all elements of the cumulative distance matrix, the path backtracks from the bottom right corner (row U, column V) towards the top left. During backtracking, each matrix position traversed by the backtracking path is recorded. Each matrix position corresponds to a row index and a column index. The row index is the sequence number of the element in the query sequence (frequency index), and the column index is the sequence number of the element in the reference sequence (time index). All frequency and time indices corresponding to the backtracking positions are grouped into pairs and arranged in the order of backtracking to form a paired sequence.

[0045] The generated pairing sequence undergoes a difference operation between adjacent pairing points. The difference operation is performed as follows: starting from the first pairing point in the pairing sequence, the frequency index of each pairing point is extracted sequentially to form a frequency index sequence; the difference is obtained by subtracting the previous frequency index from the next frequency index in the frequency index sequence, and this difference is used as the differential frequency index; the differential frequency indices calculated from all adjacent pairing points are arranged in order to form a differential frequency index sequence. This differential frequency index sequence represents the instantaneous frequency fluctuation path of the current frequency channel on the time axis.

[0046] By performing the above-mentioned cumulative distance matrix construction, path backtracking, paired sequence generation, and differential frequency index sequence calculation on the original amplitude sequence of each frequency channel, the instantaneous frequency fluctuation path of each frequency channel can be obtained.

[0047] See Figure 4 In the figure, the horizontal axis represents the time index, ranging from 0 to 600, and the vertical axis represents the differential frequency index, ranging from -20 to 80. The figure depicts the instantaneous frequency fluctuation paths of three frequency channels (frequency channel 50, frequency channel 150, and frequency channel 300) on the time axis, distinguished by different colors and markings: frequency channel 50 is represented by a solid blue line and a diamond mark, frequency channel 150 by an orange dashed line and a square mark, and frequency channel 300 by a green dotted line and a triangle mark.

[0048] Observing the instantaneous frequency fluctuation path of frequency channel 50 in the figure, in its initial stage (time index 0 to 100), the fluctuation amplitude is small and mostly negative, indicating that the frequency fluctuation of this frequency channel is relatively stable and tends to be negatively offset during this period. Subsequently, in the time index range of 100 to 400, the fluctuation value gradually rises and shows alternating positive and negative changes, with relatively small fluctuation amplitude, which is a slight adjustment of local frequency fluctuation. In the time index range of 400 to 600, the fluctuation amplitude further decreases and tends to be negative, showing a relatively gentle fluctuation trend overall.

[0049] The instantaneous frequency fluctuation path of frequency channel 150 fluctuates slightly in the time index range of 0 to 150, but generally remains around 0. Then, a significant upward trend appears in the time index range of 150 to 300, with the fluctuation amplitude gradually increasing and reaching a peak of about 40, indicating that the frequency fluctuation of this frequency channel is significantly enhanced in this time period. Then, in the time index range of 300 to 600, the fluctuation value remains at a high level and shows some oscillation, but the overall trend is still upward, with the maximum value close to 80, showing that the instantaneous frequency fluctuation path of this frequency channel is continuously strengthening.

[0050] The instantaneous frequency fluctuation path of frequency channel 300 shows a relatively stable change in the time index range of 0 to 200, with the fluctuation amplitude remaining between 0 and 20. Subsequently, it rises significantly in the time index range of 200 to 320, with the fluctuation amplitude rapidly increasing to about 40. In the time index range of 320 to 600, the fluctuation amplitude remains at a relatively high level, reaching a maximum of about 60, showing a similar strengthening trend as frequency channel 150, but the fluctuation amplitude is slightly lower than that of frequency channel 150, indicating that the frequency fluctuation of this channel has strong dynamic change characteristics in local time periods.

[0051] Example 3

[0052] In practice, a causal feature selection criterion is constructed between the source and target domains based on the instantaneous frequency fluctuation path. This causal feature selection criterion is then used to select a stable subset of features from the voiceprint structure features that are insensitive to domain changes. The following processing steps are involved.

[0053] The calculation process of the source domain mutual information set is as follows: The source domain contains several labeled voiceprint samples, each labeled voiceprint sample corresponding to a specific fault category label and an extracted instantaneous frequency fluctuation path. For each frequency channel, the instantaneous frequency fluctuation path values ​​of all samples in the source domain on that frequency channel are collected and arranged into a source domain sample feature vector; simultaneously, the fault category labels corresponding to all samples in the source domain are collected and arranged into a source domain label vector. The source domain sample feature vector is used as a first observation realization of the first random variable, and the source domain label vector is used as a first observation realization of the second random variable. The mutual information value between the first random variable and the second random variable is calculated. The calculation of the mutual information value adopts a probability density estimation method based on histograms, specifically: the value range of the source domain sample feature vector is divided into... A series of equal-width intervals, The value is the square root of the total number of samples in the source domain, rounded up. The set of values ​​for the source domain label vector is naturally divided into discrete intervals equal to the number of fault categories. The number of samples where the first random variable falls into each equal-width interval is counted, and divided by the total number of samples in the source domain to obtain the marginal probability distribution estimate of the first random variable. The number of samples where the second random variable falls into each discrete interval is counted, and divided by the total number of samples in the source domain to obtain the marginal probability distribution estimate of the second random variable. The number of samples where the first and second random variables simultaneously fall into each combination of two-dimensional intervals is counted, and divided by the total number of samples in the source domain to obtain the joint probability distribution estimate of the first and second random variables. Based on the above marginal probability distribution estimates and joint probability distribution estimates, the mutual information value between the first and second random variables is calculated. The formula for calculating the mutual information value is:

[0054] in, Indicates the first in the source domain Mutual information values ​​corresponding to each frequency channel; This represents the index of the range of values ​​for the first random variable, where the range is [value range missing]. to integers, The value is the square root of the total number of samples in the source domain, rounded up. This represents the index of the range of values ​​for the second random variable, where the range is... to integers, This represents the total number of fault categories in the source domain; This indicates that the first random variable falls into the first... The second random variable falls within the interval of equal width. Joint probability estimates for discrete intervals; This indicates that the first random variable falls into the first... Marginal probability estimates for equal-width intervals; This indicates that the second random variable falls into the first... Marginal probability estimates for each discrete interval; Represented by natural constant The natural logarithm operation is performed with base 0. The mutual information value calculation is performed on all frequency channels to obtain the source domain mutual information set composed of the mutual information values ​​of each frequency channel.

[0055] The calculation process of the mutual information set of the target domain is as follows: The target domain contains several unlabeled voiceprint samples, each corresponding to an extracted instantaneous frequency fluctuation path, but without a fault category label. For each frequency channel, the instantaneous frequency fluctuation path values ​​of all samples in the target domain on that frequency channel are collected and arranged into a target domain sample feature vector; simultaneously, a unique sample index is assigned to each target domain sample, which is a natural number. The sample indices of all samples in the target domain are arranged into a target domain index vector. The target domain sample feature vector is used as a first observation realization of the third random variable, and the target domain index vector is used as a first observation realization of the fourth random variable. The mutual information value between the third and fourth random variables is calculated. The calculation of the mutual information value also adopts the probability density estimation method based on histograms, specifically: the value range of the target domain sample feature vector is divided into... A series of equal-width intervals, The value of is the square root of the total number of samples in the target domain, rounded up. The range of values ​​for the target domain index vector is divided into the same number of discrete intervals as the total number of samples in the target domain, with each discrete interval corresponding to a unique sample index value. Following the same probability estimation and mutual information calculation method as the source domain mutual information calculation, the mutual information value between the third and fourth random variables is calculated to obtain the value of the first random variable in the target domain. The mutual information values ​​corresponding to each frequency channel are calculated. This mutual information value calculation is performed on all frequency channels to obtain the target domain mutual information set composed of the mutual information values ​​of each frequency channel.

[0056] The construction of the causal feature selection criterion and the screening process of the stable feature subset are as follows: Each mutual information value in the source domain mutual information set is divided element-wise with the mutual information value of the corresponding frequency channel in the target domain mutual information set. Specifically, for the ... For each frequency channel, extract the mutual information value of that frequency channel from the source domain mutual information set. Extract the mutual information value of the frequency channel from the mutual information set of the target domain. Calculate the ratio of the two. This ratio is taken as the first The mutual information ratio of each frequency channel.

[0057] A pre-defined ratio threshold is used to define whether a frequency channel is a stable channel that is insensitive to domain changes. The ratio threshold is determined by: sorting all frequency channels from largest to smallest mutual information ratios, and taking the mutual information ratios in the top 50% of the sorted values ​​as the ratio threshold; or setting the ratio threshold to a fixed value, such as 1.0, indicating that a frequency channel is considered domain-stable when the correlation strength between a frequency channel and the fault category in the source domain is greater than or equal to the correlation strength between the frequency channel and the sample index in the target domain. For each frequency channel, the calculated mutual information ratio is compared with the pre-defined ratio threshold. When the mutual information ratio is greater than the pre-defined ratio threshold, the frequency channel is marked as a stable channel; when the mutual information ratio is less than or equal to the pre-defined ratio threshold, the frequency channel is marked as an unstable channel.

[0058] The voiceprint structure features are composed of the instantaneous frequency fluctuation paths of all frequency channels, with each frequency channel corresponding to a set of voiceprint structure features. The voiceprint structure features corresponding to the frequency channels marked as stable channels are extracted, and all extracted voiceprint structure features together form a stable feature subset. Each feature element in the stable feature subset corresponds to the instantaneous frequency fluctuation path value of a stable frequency channel across all samples.

[0059] See Figure 5 In the figure, the horizontal axis represents the frequency channel index, ranging from 0 to 1000, and the vertical axis represents the mutual information ratio, spanning approximately 0 to 6. Green dots indicate the mutual information ratio of stable channels, and red dots indicate the mutual information ratio of unstable channels. The black dashed line represents the preset ratio threshold, located at approximately 1.35. The green dots are mainly distributed in the higher regions of the vertical axis, showing a characteristic significantly higher than the threshold. Furthermore, there are locally concentrated peak intervals with high mutual information ratios at frequency channel indices of approximately 80, 400, and 670, with peak values ​​approaching the maximum of 6. This indicates that the mutual information ratios of these frequency channels are significantly greater than the threshold, suggesting stable correlation strength between the source and target domains and insensitivity to domain changes. The red dots are mostly distributed below the threshold line, concentrated in the range where the mutual information ratio is less than 1.35, and the overall trend is relatively flat, indicating that these channels have low mutual information correlation between the source and target domains and belong to unstable channels.

[0060] Example 4

[0061] In practice, the process of mapping a stable subset of features to a high-dimensional Hilbert space is as follows.

[0062] The Gaussian radial basis function is chosen as the kernel function. The expression for the Gaussian radial basis function is: ,in and Represents two input vectors, Indicates the kernel width parameter. This represents the Euclidean norm of a vector.

[0063] kernel width parameter The method for determining the stable feature subsets is as follows: collect the stable feature subset vectors of all samples in the source domain, and calculate the mean vector and covariance matrix of the stable feature subsets of the source domain. The mean vector consists of the arithmetic mean of the values ​​of all samples in the source domain for each feature dimension, and the mean vector is the arithmetic mean of the values ​​of the samples in the source domain for each feature dimension. Line number The element of the column is the first The first feature dimension and the first feature dimension The covariance of each feature dimension in the source domain samples. Calculate the sum of the diagonal elements of the covariance matrix; this sum is the trace of the covariance matrix. Then, apply the kernel width parameter... Set to the square root of the trace of the covariance matrix. If the trace of the covariance matrix is ​​zero, then set the kernel width parameter. Set as .

[0064] Using the determined kernel width parameter Calculate the source domain embedding matrix of the stable feature subset of the source domain in a high-dimensional Hilbert space. Each row of the source domain embedding matrix corresponds to the embedding representation of a source domain sample in the high-dimensional Hilbert space, and each column corresponds to an implicit dimension in the Hilbert space. The source domain embedding matrix is... Line number The column values ​​are ,in Indicates the first Stable feature subset vectors of samples from the source domain Indicates the first A stable feature subset vector of a source domain sample. and The range of values ​​is Total number of samples to the source domain.

[0065] Using the same core width parameter Calculate the target domain embedding matrix in a high-dimensional Hilbert space for the stable feature subset of the target domain. Each row of the target domain embedding matrix corresponds to the embedding representation of a target domain sample in the high-dimensional Hilbert space. The target domain embedding matrix... Line number The column values ​​are ,in Indicates the first Stable feature subset vectors of samples in the target domain Indicates the first Stable feature subset vectors of samples in the target domain and The range of values ​​is Total number of samples in the target domain.

[0066] The source domain embedding matrix is ​​centered to obtain the source domain centered matrix. The centered matrix is ​​obtained by calculating the average value of each column vector of the source domain embedding matrix, subtracting the average value of the column from each element of the source domain embedding matrix, and then using all the centered elements to form the source domain centered matrix.

[0067] The target domain embedding matrix is ​​centered to obtain the target domain centered matrix. The centered matrix is ​​centered in the same way as the source domain: the average value of each column vector in the target domain embedding matrix is ​​calculated, and the average value of the column in which each element of the target domain embedding matrix is ​​subtracted to obtain the target domain centered matrix.

[0068] In practice, the process of measuring the covariance of the source and target domains in a high-dimensional Hilbert space is as follows.

[0069] Multiplying the source domain centered matrix by its transpose yields the source domain covariance operator. The source domain covariance operator is a matrix whose number of rows and columns equals the total number of samples in the source domain. The source domain covariance operator's... Line number The column elements are the source domain centered matrix. Row vectors and source domain centered matrix The inner product of row vectors.

[0070] Multiplying the target domain centered matrix by its transpose yields the target domain covariance operator. The target domain covariance operator is a matrix whose number of rows and columns equals the total number of samples in the target domain. Line number The column elements are the target domain centered matrix. Row vectors and the target domain centering matrix The inner product of row vectors.

[0071] Calculate the inverse matrix of the source domain covariance operator. The inverse matrix of the source domain covariance operator is obtained by solving for the inverse of the source domain covariance operator matrix. If the source domain covariance operator is not invertible, a regularization constant is added to the diagonal elements of the source domain covariance operator matrix before inverting. The regularization constant is set to... .

[0072] Multiplying the inverse matrix of the source domain covariance operator with the target domain covariance operator yields a product matrix. The number of rows in the product matrix equals the total number of samples in the source domain, and the number of columns equals the total number of samples in the target domain.

[0073] The eigenvalue sequence of the product matrix is ​​extracted by performing eigenvalue decomposition on the product matrix to obtain each eigenvalue of the product matrix, and arranging all eigenvalues ​​into a sequence according to their numerical value. The length of the sequence is equal to the smaller of the number of rows and columns of the product matrix.

[0074] The covariance measure is calculated using the following formula:

[0075] in, Represents the covariance measure; This represents the eigenvalue index in the eigenvalue sequence, with a value range of 1. to Integers; Indicates the total length of the eigenvalue sequence; Represents the eigenvalue sequence of the eigenvalue sequence. The values ​​of each feature.

[0076] In practice, the process of adjusting the feature mapping direction based on the covariance metric is as follows.

[0077] A preset allowable deviation threshold is established. This threshold is used to determine whether the difference in covariance between the source and target domain distributions in Hilbert space under the current feature mapping direction is within an acceptable range. The allowable deviation threshold is set as follows: an initial covariance metric is calculated under the initial feature mapping direction, and the allowable deviation threshold is set to five percent of the initial covariance metric.

[0078] Compare the calculated covariance values The size of the allowable deviation threshold.

[0079] When the covariance metric exceeds the allowable deviation threshold, a rotation operation is applied to the current feature map basis vector. The rotation operation proceeds in the direction that reduces the Fréchet distance between the source and target domain covariance operators. The direction of decreasing Fréchet distance is calculated as follows: the gradient directions of the source and target domain covariance operators under the current feature map basis vector are calculated. The gradient direction is obtained by solving for the partial derivative of the trace of the difference between the two covariance operator matrices with respect to the feature map basis vector. The feature map basis vector is then updated in the opposite direction of the gradient, with an update step size set to... After updating, the rotated feature map basis vector is obtained. The current feature map basis vector is replaced with the rotated feature map basis vector, and the calculation and comparison of the covariance metric are re-executed.

[0080] When the covariance metric is less than or equal to the allowable deviation threshold, the adjustment stops, the current feature mapping basis vector remains unchanged, and the current feature mapping basis vector is used as the adjusted feature mapping direction. The adjusted feature mapping direction is a set of multiple basis vectors, which is used to subsequently project the stable feature subset into causal aligned features.

[0081] See Figure 6 In the graph, the vertical axis represents the covariance metric, and the horizontal axis represents the number of adjustment iterations. The blue solid line represents the curve of covariance metric change, and the red dashed line represents the allowable deviation threshold. As the number of adjustment iterations increases, the covariance metric shows a gradual decreasing trend. In the initial stage, the covariance metric is relatively large, above 10. After about 360 iterations, the covariance metric stabilizes and decreases to about 0.5, close to the allowable deviation threshold, and remains below this threshold in subsequent iterations.

[0082] Example 5

[0083] In practice, the process of converting stable feature subsets into causal aligned features is as follows.

[0084] Obtain the adjusted feature map direction, which is a set of basis vectors, the number of which is the same as the dimension of a single sample vector in the stable feature subset. Collect stable feature subset vectors for all samples from the source and target domains, and perform a projection operation on each sample vector. The projection operation is performed by taking a dot product between the sample vector and each basis vector in the adjusted feature map direction. The result of the dot product is a real value, called the projection scalar. After taking the dot product of a sample vector with all basis vectors, a projection scalar string of the same length as the number of basis vectors is obtained. Use this projection scalar string as the projection scalar vector of the sample vector.

[0085] The same projection operation is performed on each sample vector in both the source and target domains. The projected scalar vectors of all sample vectors are arranged sequentially according to the order of the samples in the original set, forming a sequence of projected vectors. Each element in the sequence is a projected scalar vector, and the length of the sequence is equal to the sum of the total number of samples in the source domain and the total number of samples in the target domain.

[0086] The projected vector sequence is then zero-mean normalized. This is done by calculating the arithmetic mean of all projected scalars along each feature dimension of the sequence, and then subtracting this arithmetic mean from the value of each projected scalar along that feature dimension to obtain the zero-mean normalized projected scalar value. After performing this operation on all feature dimensions, the projected vector sequence is transformed into a zero-mean normalized projected vector sequence.

[0087] The zero-mean projected vector sequence is then subjected to unit variance transformation. This transformation is performed as follows: for each feature dimension in the zero-mean projected vector sequence, the standard deviation of all zero-mean projected scalars along that feature dimension is calculated. Then, the value of each zero-mean projected scalar along that feature dimension is divided by the calculated standard deviation. If the standard deviation of a feature dimension is zero, no division is performed, and the zero-mean projected scalar for that feature dimension remains unchanged. After performing this operation on all feature dimensions, the zero-mean projected vector sequence is transformed into a unit variance projected vector sequence. This unit variance projected vector sequence is used as a causal alignment feature, where each element is a projected scalar vector that has undergone zero-mean and unit variance transformation.

[0088] In practice, the decision boundary initialization process of the classifier is as follows.

[0089] The classifier employs a multi-class classification architecture based on the nearest mean distance. The number of classes in the classifier is equal to the total number of fault categories in the source domain, denoted as the total number of categories G. For each fault category in the source domain, the causal alignment feature vector corresponding to all samples under that fault category is extracted. The causal alignment feature vector is the portion of the unit variance projected vector sequence corresponding to the samples of that fault category. The mean vector of all causal alignment feature vectors under that fault category is calculated, where the value of each feature dimension in the mean vector is the arithmetic mean of the values ​​of all causal alignment feature vectors under that fault category along that dimension. Each fault category corresponds to one mean vector, resulting in a total of G mean vectors.

[0090] For any two distinct fault categories, compute the bisecting hyperplane between their mean vectors. The bisecting hyperplane is a hyperplane in the high-dimensional feature space that is equidistant from the two mean vectors and perpendicular to the line connecting them. The analytic representation of the bisecting hyperplane is a normal vector and a bias term. The normal vector is obtained by normalizing the difference vector between the two mean vectors, and the bias term is the negative projection of the midpoint vector of the two mean vectors onto the normal vector. By iterating through all pairwise combinations of fault categories, a total of G times (G minus one) divided by half a bisecting hyperplane is obtained. The set of all computed bisecting hyperplanes is used as the initial decision boundary for the classifier.

[0091] In practice, the process of inputting causal alignment features into the classifier and outputting the fault category is as follows.

[0092] For each target domain sample to be classified, the causal alignment feature vector corresponding to that causal alignment feature vector is calculated to each bisecting hyperplane. The formula for calculating the signed distance is:

[0093] in, This represents the signed distance, which is a real value. The normal vector that bisects the hyperplane is in column vector form, and its dimension is the same as that of the causal alignment feature vector. The transpose of the normal vector is represented as a row vector. The causal alignment feature vector to be classified is in column vector form. The bias term, representing the bisection of the hyperplane, is a real value. Signed distance. The sign of the causal alignment feature vector indicates which side of the bisector of the hyperplane it is located on, and its absolute value indicates how close or far it is from the bisector of the hyperplane.

[0094] For each causal alignment feature vector to be classified, the signed distances to all bisecting hyperplanes are calculated, and the bisecting hyperplane corresponding to the maximum value among these signed distances is selected. This bisecting hyperplane is determined by the mean vectors of two specific fault categories, with each side corresponding to one of these two fault categories. The sign of the signed distance determines which of the two fault categories the causal alignment feature vector to be classified belongs to. Specifically, when the signed distance is positive, the classification result is the fault category corresponding to the side pointed to by the normal vector; when the signed distance is negative, the classification result is the fault category corresponding to the side opposite to the normal vector. The determined fault category is then output as the fault category of the target domain sample.

[0095] See Figure 7 In the figure, the horizontal axis represents projection scalar 1, and the vertical axis represents projection scalar 2. The distribution of the causal alignment features of the three types of fault samples in the two-dimensional projection space is shown in the figure. The legend identifies the three fault categories, represented by blue dots, orange squares, and green triangles, respectively. The sample points of each category show a clear clustering trend in the projection space, and the distribution ranges of the three types of samples are basically separated from each other, indicating that the projection operation on the stable feature subset based on the adjusted feature mapping direction in Example 5 can effectively distinguish between fault categories.

[0096] In the diagram, multiple bisecting hyperplanes, marked with black dashed lines, serve as the decision boundaries for the classifier. Each bisecting hyperplane intersects the origin of the two-dimensional coordinate axes, dividing the different category regions in the projection space. Samples of fault category 1 are mainly clustered between the positive directions of projection scalar 1 and projection scalar 2; samples of fault category 2 are mainly distributed between the negative directions of projection scalar 1 and projection scalar 2; and samples of fault category 3 are mainly located in the negative direction of projection scalar 2. The relatively concentrated sample points across categories, coupled with the well-defined classification boundaries, ensure good differentiation between the three categories in two-dimensional space.

[0097] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for cross-domain fault diagnosis based on causal feature alignment, characterized in that, include: After obtaining labeled voiceprint samples from the source domain and unlabeled voiceprint samples from the target domain, a multi-scale recursive graph based on local phase preservation is constructed as the primary representation of the voiceprint according to the temporal amplitude distribution of each sample. Dynamic time warping is performed on the primary voiceprint representation to obtain the instantaneous frequency fluctuation path of each frequency channel on the time axis, and the instantaneous frequency fluctuation path is used as a cross-domain transferable voiceprint structural feature. Based on the instantaneous frequency fluctuation path, a causal feature selection criterion is constructed between the source domain and the target domain. The causal feature selection criterion is used to select a stable feature subset that is insensitive to domain changes from the voiceprint structural features. The stable feature subset is mapped to a high-dimensional Hilbert space, and the covariance of the distribution of the source and target domains is measured in the high-dimensional Hilbert space. The feature mapping direction is adjusted according to the covariance measurement. The stable feature subset is converted into causal aligned features using the adjusted feature mapping direction, and the causal aligned features are input into the classifier to output the fault category.

2. The method for cross-domain fault diagnosis of voiceprints based on causal feature alignment according to claim 1, characterized in that, Acquire labeled voiceprint samples from the source domain and unlabeled voiceprint samples from the target domain, including: The original time-domain signal of each voiceprint sample is divided into frames with a frame length of 2048 sampling points and a frame shift of 1024 sampling points. The mean of the frame signal is subtracted from each frame signal after framing and then divided by the standard deviation of the frame signal to obtain the normalized frame sequence. For each frame in the normalized frame sequence, three time-frequency basic attributes of the frame are extracted: zero-crossing rate, spectral centroid, and spectral flatness. The zero-crossing rate, spectral centroid, and spectral flatness are then concatenated to form the attribute vector of the frame. Based on the Euclidean distance of the attribute vectors, all frames under the same fault category are sorted, and the attribute vector of the frame in the middle position after sorting is taken as the representative frame attribute of the fault category. The frame number corresponding to the representative frame attribute is taken as the anchor frame number.

3. The method for cross-domain fault diagnosis of voiceprints based on causal feature alignment according to claim 2, characterized in that, Constructing a multi-scale recurrent graph based on local phase preservation, including: Taking the frame corresponding to the anchor frame number as the center, take a first number of frames forward and a second number of frames backward to form a local time frame set; Perform a short-time Fourier transform on each frame in the local time frame set to obtain the complex spectrum corresponding to each frame, extract the phase spectrum of the complex spectrum, and construct a Hankel matrix using the phase spectrum as elements; The Hankel matrix is ​​subjected to singular value decomposition, and the left and right singular vectors corresponding to the largest singular values ​​are retained. The phase-preserving matrix is ​​reconstructed using the left and right singular vectors, and the diagonal element sequence of the phase-preserving matrix is ​​used as the multi-scale recursive coefficients for the local time period.

4. The method for cross-domain fault diagnosis of voiceprints based on causal feature alignment according to claim 3, characterized in that, Performing dynamic time warping on the primary voiceprint representation includes: Using the multi-scale recursive coefficients as the query sequence and the original amplitude sequence of each frequency channel as the reference sequence, calculate the cumulative distance matrix between the query sequence and the reference sequence; In the cumulative distance matrix, backtracking from the lower right corner to the upper left corner, the frequency index and time index corresponding to each matrix position traversed by the backtracking path are recorded, and the frequency index and time index are combined into a pair sequence. Differential operation is performed on adjacent paired points in the pairing sequence to obtain a differential frequency index sequence, which is then used as the instantaneous frequency fluctuation path.

5. The method for cross-domain fault diagnosis of voiceprints based on causal feature alignment according to claim 4, characterized in that, Based on the instantaneous frequency fluctuation path, a causal feature selection criterion is constructed between the source and target domains, including: Calculate the mutual information value between the instantaneous frequency fluctuation path of each sample in the source domain and the corresponding fault category label to obtain the source domain mutual information set; Calculate the mutual information value between the instantaneous frequency fluctuation path of each sample in the target domain and the sample index in the target domain to obtain the mutual information set of the target domain; The source domain mutual information set and the target domain mutual information set are divided element by element along the frequency channel dimension to obtain the mutual information ratio of each frequency channel. The voiceprint structure features corresponding to the frequency channels whose mutual information ratio is greater than a preset ratio threshold are included in the stable feature subset.

6. The method for cross-domain fault diagnosis of voiceprints based on causal feature alignment according to claim 5, characterized in that, Mapping the stable feature subset to a high-dimensional Hilbert space includes: A Gaussian radial basis function is selected as the kernel function, and the kernel width parameter of the Gaussian radial basis function is determined based on the mean vector and covariance matrix of the stable feature subset in the source domain. The source domain embedding matrix of the source domain stable feature subset in the high-dimensional Hilbert space is calculated using the kernel width parameter, and the target domain embedding matrix of the target domain stable feature subset in the high-dimensional Hilbert space is also calculated. The source domain embedding matrix is ​​centered to obtain a source domain centered matrix, and the target domain embedding matrix is ​​centered to obtain a target domain centered matrix.

7. The method for cross-domain fault diagnosis of voiceprints based on causal feature alignment according to claim 6, characterized in that, The covariance measurement of the distributions of the source and target domains in the high-dimensional Hilbert space includes: Multiply the source domain centering matrix by its transpose to obtain the source domain covariance operator; Multiply the target domain centering matrix by its transpose to obtain the target domain covariance operator; Calculate the product matrix of the inverse matrix of the source domain covariance operator and the target domain covariance operator, extract the eigenvalue sequence of the product matrix, and take the square root of the sum of squares of all eigenvalues ​​in the eigenvalue sequence as the covariance metric.

8. The method for cross-domain fault diagnosis of voiceprints based on causal feature alignment according to claim 7, characterized in that, Adjusting the feature mapping direction based on the covariance metric includes: A preset allowable deviation threshold is used to compare the covariance metric with the allowable deviation threshold. When the covariance metric is greater than the allowable deviation threshold, the current feature mapping basis vector is rotated in the direction that reduces the Fréchet distance between the source domain covariance operator and the target domain covariance operator; When the covariance metric is less than or equal to the allowable deviation threshold, the current feature mapping basis vector remains unchanged, and the current feature mapping basis vector is used as the adjusted feature mapping direction.

9. The method for cross-domain fault diagnosis of voiceprints based on causal feature alignment according to claim 8, characterized in that, Converting the stable feature subset into causal aligned features includes: Perform a dot product operation between each sample vector in the stable feature subset and the adjusted feature mapping direction to obtain the projection scalar of the sample vector in the adjusted feature mapping direction; Arrange the projection scalars of all sample vectors in the original sample order to form a sequence of projection vectors; The projection vector sequence is subjected to zero-mean and unit variance processing, and the resulting vector sequence is used as the causal alignment feature.

10. The method for cross-domain fault diagnosis of voiceprints based on causal feature alignment according to claim 9, characterized in that, Before inputting the causal alignment features into the classifier, the decision boundary of the classifier is initialized. The decision boundary of the classifier is initialized as the bisecting hyperplane between the mean values ​​of the causal alignment features of each fault category in the source domain. The causal alignment features are input into the initialized classifier, and the signed distance from the causal alignment features to each of the bisecting hyperplanes is calculated. The fault category corresponding to the maximum value in the signed distance is selected as the fault category output.

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