Method for predicting deterioration trend of field carbon brush based on current and vibration coupling characteristics

Abstract

The present application belongs to the technical field of power equipment state monitoring, and discloses a method for predicting the deterioration trend of excitation carbon brushes based on current and vibration coupling characteristics; the excitation current, vibration acceleration time series and power scheduling instructions are obtained, and the excitation current is decomposed into a working condition base value component and a working condition internal fluctuation component; a working condition state label is constructed based on the working condition base value component, and a clustering operation data set is formed; within each working condition cluster, the residual projection is performed on the vibration characteristics with the working condition internal fluctuation component as the covariant; a cross-working condition reference manifold is established, and the deterioration sensitive residual vector of each working condition cluster is mapped to a unified state space; the trend fitting is performed on the working condition independent deterioration characteristic sequence, the slope mutation point is identified, and a staged deterioration trajectory is constructed; according to the slope and the duration of the historical deterioration stage, a weighted prediction model is constructed, and a residual life prediction interval is generated. The present application realizes accurate extraction of the degradation characteristics of the excitation carbon brush and life prediction.

Description

Technical Field

[0001] This invention relates to the field of power equipment condition monitoring technology, and more specifically, to a method for predicting the deterioration trend of excitation carbon brushes based on the coupling characteristics of current and vibration. Background Technology

[0002] Existing excitation carbon brush degradation trend prediction technologies are inadequate for generating units facing the flexibility requirements of today's power systems, especially given the increasing importance of ancillary services such as peak shaving and frequency regulation. Traditional prediction methods are mostly based on the assumption of constant operating conditions, ignoring the drastic impact of "variable operating conditions" on monitoring signals in actual power system operation, resulting in a severe "torn" degradation trajectory. The grid dispatch center frequently issues adjustment commands based on the system's reactive power balance needs, forcing the excitation current to adjust in real time according to the grid's reactive power demand, rather than changing smoothly according to a preset path. When units frequently switch between different operating conditions such as full-load, off-peak, and leading-phase operation, the significant differences in the base value of the excitation current directly cause drastic changes in key physical quantities such as electromagnetic force, frictional heat, and contact impedance at the collector ring-carbon brush interface, resulting in discontinuous jumps in vibration characteristics. This operating condition dependence makes it difficult for traditional time-series analysis methods to establish stable degradation assessment indicators, manifesting as multiple separate "feature clusters" on the current-vibration scatter plot, rather than the ideal continuous and smooth degradation trend curve. The constantly changing load rate of generating units during peak shaving introduces complex nonlinear dynamic responses, causing vibration signals to simultaneously contain the superimposed effects of operating condition variations and wear degradation. Current technologies lack effective mechanisms to distinguish between these two sources of change, making it impossible to accurately extract characteristic components reflecting the true degradation state of carbon brushes from the mixed signals. When maintenance personnel attempt to make predictions based on these "torn" degradation trajectories, they often face a dilemma: either ignoring differences in operating conditions and forcibly fitting a single trend leads to severely off-target predictions, or modeling each operating condition separately results in a lack of statistical support due to data sparsity. This technical problem means that carbon brush maintenance for many peak-shaving units remains at the stage of periodic replacement, failing to achieve condition-based precision maintenance and increasing unnecessary downtime losses and maintenance costs.

[0003] In view of this, the present invention proposes a method for predicting the degradation trend of excitation carbon brushes based on the coupling characteristics of current and vibration to solve the above problems. Summary of the Invention

[0004] To overcome the aforementioned deficiencies of the prior art and to achieve the above objectives, the present invention provides the following technical solution: a method for predicting the degradation trend of excitation carbon brushes based on the coupling characteristics of current and vibration, comprising: Obtain the excitation current time series and vibration acceleration time series of the excitation carbon brush during the operating cycle, as well as the corresponding active power and reactive power dispatch command sequences of the unit; Based on the scheduling instruction sequence, the excitation current time series is decomposed into the operating condition base value component and the operating condition fluctuation component, which are denoted as the excitation current dual component pair. For the operating condition base value component in the two-component pair of excitation current, a set of operating condition status labels is constructed, and the operating data is classified into the corresponding operating condition clusters according to the operating condition status labels to form a clustered operating dataset. Within each operating condition cluster, a multidimensional feature vector of the vibration acceleration time series is extracted. Using the fluctuation component within the operating condition as a covariate, the multidimensional feature vector is projected onto the residual within the operating condition to eliminate the linear influence of the current fluctuation within the operating condition on the vibration characteristics and obtain the degradation-sensitive residual vector of each operating condition cluster. Establish a cross-condition benchmark manifold, map the degradation-sensitive residual vectors of each condition cluster to a unified degradation state space, and generate condition-independent degradation feature sequences. Time-series trend fitting is performed on the condition-independent degradation feature sequence, the slope abrupt change points in the trend fitting curve are identified, the segment between adjacent slope abrupt change points is marked as the degradation stage, and a staged degradation trajectory is constructed. Based on the slope and duration of each degradation stage in the phased degradation trajectory, a degradation rate weighted prediction model is constructed, and the remaining life prediction range of the excitation carbon brush is generated by extrapolation.

[0005] The technical effects and advantages of the present invention regarding the method for predicting the degradation trend of excitation carbon brushes based on the coupling characteristics of current and vibration are as follows: This invention effectively separates the apparent characteristic changes caused by operating condition variations from the actual degradation process through an innovative operating condition decoupling mechanism. It establishes an adaptive mathematical mapping for the current-vibration coupling relationship, ensuring consistency and coherence in degradation assessment even under normal grid dispatch conditions such as reactive power regulation and load fluctuations. The application of cross-operating condition mapping expands the effective data available for degradation analysis, overcoming the statistical bottleneck of sparse data under single operating conditions and enhancing the generalization ability and robustness of the prediction model. The phased degradation trajectory identification function of this invention provides a new perspective for the study of degradation mechanisms at different life stages, making the prediction results highly consistent with the physical wear process. The reliable quantification mechanism of the prediction interval provides a risk assessment basis for operation and maintenance decisions, effectively balancing the dual risks of premature maintenance and delayed replacement. This invention improves the carbon brush utilization rate of peak-shaving units, reduces unnecessary preventative replacements and the resulting downtime losses, and also reduces the risk of secondary damage such as slip ring scratches caused by carbon brush failure. Attached Figure Description

[0006] Figure 1 This is a schematic diagram of the excitation carbon brush degradation trend prediction method based on the coupling characteristics of current and vibration according to the present invention. Detailed Implementation

[0007] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0008] This application provides a method for predicting the degradation trend of excitation carbon brushes based on the coupling characteristics of current and vibration. The execution entities of the method include, but are not limited to, generator condition monitoring systems, rotating machinery predictive maintenance platforms, power equipment health management systems, and generator carbon brush life assessment systems, which can be regarded as general computing nodes of this application.

[0009] Please see Figure 1 In this embodiment of the invention, the specific implementation process of the method for predicting the degradation trend of excitation carbon brushes based on the coupling characteristics of current and vibration includes: The excitation current time series and vibration acceleration time series of the excitation carbon brush during its operating cycle, along with the corresponding active and reactive power dispatch command sequences of the unit, are obtained. Multi-source data during the operation of the excitation carbon brush are acquired in real time through a high-precision data acquisition system, including the current signal of the excitation system, the acceleration signal collected by vibration sensors installed near the slip ring, and power command information issued by the power system dispatch center. The excitation current time series reflects the electrical characteristics and load conditions of the excitation system, the vibration acceleration time series contains dynamic characteristics of the carbon brush-slip ring contact interface, and the power dispatch command sequence records changes in the unit's operating conditions. This multi-source heterogeneous data provides comprehensive raw material for subsequent analysis, ensuring the completeness and accuracy of the predictions.

[0010] Based on the scheduling command sequence, the excitation current time series is decomposed into a base value component and an intra-condition fluctuation component, denoted as the excitation current dual-component pair. The excitation current dual-component pair is a key step in separating the influence of operating condition changes from the inherent characteristics of the carbon brush, achieved through time-frequency domain decomposition of the original current signal. The base value component reflects the steady-state response characteristics of the excitation system under different power scheduling conditions, while the intra-condition fluctuation component contains dynamic information about the carbon brush-slip ring contact state under specific operating conditions. This decomposition enables subsequent analysis to distinguish between current changes caused by operating condition switching and current characteristic changes caused by carbon brush degradation, laying the foundation for vibration feature extraction based on operating condition perception.

[0011] For the baseline component of the excitation current dual-component pair, a set of operating condition labels is constructed. Operating data is then categorized into corresponding operating condition clusters according to these labels, forming a clustered operating dataset. The set of operating condition labels is a mathematical representation of typical generator operating states, obtained through statistical analysis and clustering of the baseline components. The clustered operating dataset separates operating data under different operating conditions, ensuring that data within each cluster exhibits similar operating characteristics, facilitating subsequent vibration characteristic analysis for specific operating conditions. This operating condition-aware data organization effectively solves the feature extraction bias problem caused by the mixing of data from different operating conditions in traditional methods.

[0012] Within each operating condition cluster, multidimensional feature vectors of the vibration acceleration time series are extracted. Using the intra-condition fluctuation component as a covariate, intra-condition residual projection is performed on the multidimensional feature vectors to eliminate the linear influence of intra-condition current fluctuations on vibration characteristics, thus obtaining the degradation-sensitive residual vectors for each operating condition cluster. The multidimensional feature vectors comprehensively characterize the time-domain, frequency-domain, and statistical properties of the vibration signal, including key indicators such as root mean square value, peak-to-peak value, kurtosis, waveform factor, and power spectrum characteristics. Intra-condition residual projection is an innovative method for eliminating operating condition fluctuation interference. By establishing a linear regression model between vibration characteristics and current fluctuation components, the regression residuals are extracted as operating condition-insensitive degradation features. The degradation-sensitive residual vectors directly reflect the carbon brush wear state, providing a pure feature basis for subsequent cross-operating condition mapping.

[0013] A cross-condition benchmark manifold is established, mapping the degradation-sensitive residual vectors of each condition cluster to a unified degradation state space, generating a condition-independent degradation feature sequence. The cross-condition benchmark manifold is a key technology for solving the problem of indirect comparison of degradation features under different conditions. It achieves a consistent representation of degradation states through benchmark condition clusters and alignment transformations. The condition-independent degradation feature sequence eliminates the influence of operating condition changes, presents the essential trend of carbon brush degradation, and allows for direct comparison of degradation levels across conditions, providing a continuous and unified feature sequence for subsequent trend analysis.

[0014] A time-series trend fitting method was used to fit the degradation feature sequence independent of operating conditions, identifying abrupt slope changes in the trend fitting curve. The segments between adjacent slope change points were marked as degradation stages, constructing a phased degradation trajectory. Time-series trend fitting is an effective method for extracting long-term trends from noisy data; a smooth degradation trend curve was achieved through a locally weighted regression algorithm. Slope change point identification is a key technology for capturing changes in the degradation rate; second-order difference analysis accurately located the inflection points in the degradation process. The phased degradation trajectory reflects the nonlinear process of carbon brush degradation, decomposing continuous changes into multiple stages with different rate characteristics, providing a more accurate historical reference for remaining life prediction.

[0015] Based on the slope and duration of each degradation stage in the phased degradation trajectory, a degradation rate-weighted prediction model is constructed, which is then extrapolated to generate the remaining life prediction range for the excitation carbon brush. This degradation rate-weighted prediction model is an innovative prediction technique that considers historical degradation patterns. By assigning higher weights to recent degradation stages, it achieves accurate prediction of future degradation trends. The remaining life prediction range not only provides a point estimate of the lifespan but also offers a confidence interval that accounts for prediction uncertainties, providing a reliable basis for maintenance decisions. This prediction method based on phased degradation trajectories overcomes the limitations of traditional single-model predictions, adapts to the nonlinear and phased characteristics of the carbon brush degradation process, and improves prediction accuracy.

[0016] The above steps are executed sequentially through data transfer, forming a complete analysis and processing flow.

[0017] In this embodiment of the invention, the detailed implementation steps of decomposing the excitation current time series into a base value component and an intra-condition fluctuation component based on the scheduling instruction sequence, denoted as the excitation current dual-component pair, include: Using the active and reactive power dispatch command sequences as input, a sliding window median filter is employed to extract the low-frequency trend of the excitation current, denoted as the operating condition following baseline. The sliding window median filter is a robust method for extracting long-term signal trends, effectively suppressing the effects of transient disturbances and outliers. The filtering process uses a time window of length L (typically the number of sampling points corresponding to 5-15 minutes), sliding gradually along the time axis. The median of the current value within each window is calculated, forming a smooth trend curve. Compared to mean filtering, median filtering has a stronger ability to suppress sudden disturbances and can more accurately capture changes in the current baseline caused by power dispatch variations. The operating condition following baseline directly reflects the steady-state response characteristics of the excitation system under different operating conditions, providing a crucial reference for subsequent operating condition analysis and component decomposition.

[0018] The point-by-point difference between the excitation current time series and the operating condition tracking baseline is calculated and denoted as the original fluctuation sequence. The original fluctuation sequence characterizes the dynamic changes in the excitation current deviating from the steady-state value of the operating condition, encompassing the influence of various factors such as carbon brush contact state fluctuations, system disturbances, and measurement noise. The difference calculation employs time-aligned point-by-point subtraction to ensure the consistency of the fluctuation component with the original signal in the time dimension. This step achieves preliminary signal decomposition, separating the long-term trend and dynamic fluctuation characteristics caused by operating condition changes, thus creating conditions for subsequent operating condition switching identification and feature extraction.

[0019] A variance test is performed on the original fluctuation sequence to identify time intervals with significantly increased variance. These intervals are marked as transitional segments for operating condition switching, and their data are removed from subsequent analyses. The variance test is a statistical method for detecting abnormal signal fluctuations. By analyzing the local variance changes in the original fluctuation sequence, non-steady-state regions during operating condition switching can be effectively identified. The test process first calculates the local variance of the fluctuation sequence within a sliding window and then compares it with the background variance level. When the local variance is significantly higher than the background level, the corresponding time interval is marked as a transitional segment for operating condition switching. These transitional segment data typically exhibit high volatility and non-stationary characteristics, making them unsuitable for steady-state degradation analysis. Therefore, they need to be removed from the dataset to improve the accuracy and stability of subsequent feature extraction.

[0020] The operating condition baseline, excluding the transitional segment between operating conditions, is denoted as the operating condition baseline component, and the corresponding original fluctuation sequence is denoted as the operating condition fluctuation component. Together, they constitute a dual-component pair of excitation current. The operating condition baseline component characterizes the steady-state current level under different operating conditions, reflecting the steady-state characteristics of the generator at each operating point; the operating condition fluctuation component contains the dynamic change characteristics of the current within the steady operating condition, which is closely related to the carbon brush-slip ring contact state. These two components together constitute a dual-component pair of excitation current, realizing a complete decomposition of the current signal in both operating condition response and dynamic characteristics. This signal decomposition method based on operating condition awareness provides a clear data foundation for subsequent operating condition clustering and feature extraction, and is a key preprocessing step for realizing adaptive operating condition analysis.

[0021] In this embodiment of the invention, for the operating condition base value component in the two-component pair of excitation current, a set of operating condition status labels is constructed, and the operating data is classified into the corresponding operating condition cluster according to the operating condition status label to form a clustered operating dataset. The detailed implementation steps include: Kernel density estimation is performed on the amplitudes of the baseline components of the operating condition to identify local maxima in the probability density curve. The current amplitude corresponding to each local maxima is recorded as the representative value of the operating condition. Kernel density estimation is a non-parametric probability density estimation method that can discover the inherent structure and clustering characteristics of the data distribution. The estimation process uses a Gaussian kernel function to smooth the amplitude distribution of the baseline components of the operating condition. The bandwidth parameter of the kernel function is adaptively determined according to the Silverman criterion to ensure a balance between smoothness and accuracy. The estimated probability density curve intuitively reflects the distribution characteristics of the baseline components of the operating condition. The local maxima correspond to the frequently occurring current levels, which usually correspond one-to-one with the typical operating conditions of the generator. The current amplitudes of these local maxima are extracted as representative values ​​of the operating condition, forming the basic reference points for operating condition identification. The formula for kernel density estimation is: ; in, For the estimated probability density function, For the sample size, For bandwidth parameters, For kernel function, For the first One sample point, Points to be estimated.

[0022] Using the arithmetic mean of representative values ​​from adjacent operating conditions as the boundary, the attraction domain of each representative value is delineated, forming a set of operating condition state labels. The attraction domain serves as the decision boundary for operating condition identification, defining the range to which a current value belongs for a specific operating condition. The partitioning process uses the arithmetic mean of representative values ​​from adjacent operating conditions as the boundary point, achieving a complete spatial partition and ensuring that each current value can be uniquely mapped to a specific operating condition. This mean-based boundary delineation method is computationally simple while ensuring the balance and rationality of the decision boundary. The set of operating condition state labels represents a complete decision rule for operating condition identification, containing all representative values ​​of operating conditions and their corresponding attraction domain boundaries, providing a clear classification standard for subsequent data clustering.

[0023] The operating condition baseline component at each moment in the dual-component alignment of the excitation current is compared with the representative values ​​of each operating condition in the operating condition label set. The data at that moment is then assigned to the operating condition cluster corresponding to the closest representative value. Distance comparison is the core step in data clustering. By calculating the distance between the current value and each representative value, the operating condition affiliation of the data point is determined. The comparison process uses Euclidean distance, calculating the absolute difference between the current operating condition baseline component and each representative value, and selecting the representative value with the smallest distance as the operating condition label for that moment. This nearest neighbor classification method is simple and efficient, mathematically equivalent to the previously defined attraction domain boundary, ensuring the consistency and interpretability of the classification results. Through this step, the original time series data is divided into multiple operating condition clusters, with data within each cluster exhibiting similar operating condition characteristics, laying the foundation for subsequent feature analysis targeting specific operating conditions.

[0024] The sample size of each operating condition cluster is counted. Clusters with sample sizes below a preset minimum sample threshold are merged into their nearest neighboring operating condition clusters with the closest current amplitudes, generating a clustered operational dataset. Operating condition cluster merging is a crucial step in optimizing data organization, improving the statistical stability of subsequent analyses by eliminating clusters with sparse samples. The merging process first sets a minimum sample threshold (typically 1%-3% of the total sample size), then identifies operating condition clusters with sample sizes below the threshold and merges them with their nearest neighboring operating condition clusters with the closest current amplitudes. This distance-based merging strategy ensures a natural transition of data and the physical continuity of operating conditions, avoiding potential discontinuities in operating condition characteristics that might result from forced merging. The final clustered operational dataset has a reasonable division of operating conditions and sufficient sample support, providing a high-quality data foundation for subsequent feature extraction and degradation analysis.

[0025] In this embodiment of the invention, within each operating condition cluster, a multidimensional feature vector of the vibration acceleration time series is extracted. Using the fluctuation component within the operating condition as a covariate, the multidimensional feature vector is projected onto the residual within the operating condition to eliminate the linear influence of current fluctuations on vibration characteristics. The detailed implementation steps for obtaining the degradation-sensitive residual vector of each operating condition cluster include: For each operating condition cluster, the root mean square (RMS) value, peak-to-peak value (peak-to-peak value), kurtosis, waveform factor, and 1 / 3 octave band power spectral density vector of the vibration acceleration time series are calculated and concatenated to form a multidimensional feature vector matrix for that cluster. The multidimensional feature vector is a mathematical representation that comprehensively characterizes the vibration signal characteristics. By extracting time-domain, frequency-domain, and statistical properties, it enables multi-faceted analysis of the vibration signal. The feature extraction process is performed independently for the vibration data within each operating condition cluster, ensuring that feature calculations are unaffected by changes in operating conditions. The RMS value reflects the energy level of the vibration, the peak-to-peak value characterizes the amplitude range, the kurtosis describes the impact of the vibration, and the waveform factor characterizes the waveform characteristics. The 1 / 3 octave band power spectral density vector captures the spectral characteristics of the vibration signal through frequency domain decomposition. These features collectively constitute the multidimensional feature vector, providing a comprehensive description of the vibration characteristics for subsequent degradation feature extraction.

[0026] Within this operating condition cluster, using the fluctuation component within the operating condition as the independent variable, a univariate linear regression model is constructed for each dimension of the multidimensional eigenvector matrix, and the regression residuals of each eigenvector component with respect to the fluctuation component within the operating condition are extracted. Univariate linear regression is an effective method for modeling the relationship between vibration characteristics and current fluctuations. By identifying and eliminating the linear influence of current fluctuations on vibration characteristics, the residuals more relevant to the deterioration state are extracted. The regression process is performed independently for each dimension of the multidimensional eigenvector, using the fluctuation component within the operating condition as the independent variable for data within a specific operating condition cluster. The vibration characteristic components are the dependent variables. Fitting a linear model The model fitting uses the least squares method to calculate the optimal parameters. and This minimizes the sum of squared residuals. Regression residuals This represents the portion of the vibration characteristics that cannot be explained by current fluctuations. This portion of the signal is more directly related to the degradation state of the excitation carbon brush, providing a clean data foundation for degradation feature extraction. The parameter estimation formula for the linear regression model is: ; ; in, and The first and second vibration characteristics under the operating conditions are respectively the wave components and vibration characteristics. One sample, and For their respective mean, This represents the number of samples.

[0027] The regression residuals of each feature component are subjected to variance normalization to eliminate differences in the dimensions of different features and obtain a normalized residual matrix. Variance normalization is a standard procedure for unifying feature scales. By eliminating dimensional differences, features of different dimensions can be fairly compared and comprehensively analyzed. The process first calculates the standard deviation of the regression residuals for each feature dimension, and then uses this as a divisor to standardize the original residuals, converting them into standardized residuals with zero mean and unit variance. This normalization ensures the equal contribution of each feature dimension in subsequent principal component analysis, avoiding the problem of features with large dimensions dominating the analysis results. For feature components with extremely small standard deviations, it indicates that their response to fluctuations within the operating condition is very weak or completely explained by fluctuations within the operating condition. These features are not very indicative of the deterioration state, so they are set to zero during the normalization process and removed from subsequent analysis to improve the signal-to-noise ratio and analysis efficiency.

[0028] Principal component analysis (PCA) is performed on the normalized residual matrix. Principal components whose cumulative variance contribution rate exceeds a preset threshold are retained, forming the degradation-sensitive residual vector for this operating condition cluster. PCA is a dimensionality reduction technique that extracts the main change directions of high-dimensional data. Through linear transformation, relevant features are combined into mutually orthogonal principal components, achieving compact data representation and noise filtering. The analysis process first calculates the covariance matrix of the normalized residual matrix, then solves for the eigenvalues ​​and eigenvectors, and sorts the principal components according to the eigenvalue magnitude. The top k principal components with a cumulative variance contribution rate exceeding a preset threshold (usually 85%-95%) are selected to form the dimensionality-reduced degradation-sensitive residual vector. These principal components capture the main change patterns in the vibration residuals, filtering out random noise and minor changes, making the extracted features more stable and effective. The formula for calculating the variance contribution rate in PCA is: ; in, For the front The cumulative variance contribution rate of each principal component For the first 1 eigenvalue, The total number of features.

[0029] In this embodiment of the invention, the detailed implementation steps for establishing a cross-condition reference manifold, mapping the degradation-sensitive residual vectors of each condition cluster to a unified degradation state space, and generating condition-independent degradation feature sequences include: The operating condition cluster with the largest sample size is selected as the baseline operating condition cluster, and the distribution of its degradation-sensitive residual vector is used as the baseline manifold. The baseline operating condition cluster serves as the reference system for cross-operating condition mapping. By selecting the operating condition cluster with the richest sample size as the baseline, the statistical stability and representational completeness of the reference system are ensured. The baseline selection process first counts the sample size of each operating condition cluster, selecting the cluster with the largest sample size as the baseline. The distribution space of its degradation-sensitive residual vector is defined as the baseline manifold. This selection is based on the principle of maximum data support, ensuring that the baseline manifold has sufficient sample coverage and statistical representativeness, and can comprehensively reflect the changing characteristics of equipment degradation status. As a unified representation space for degradation status, the baseline manifold provides a stable target domain for the feature mapping of other operating conditions, and is a key foundation for achieving cross-operating condition consistency analysis.

[0030] For each non-baseline operating condition cluster, the overlapping operating segments between this cluster and the baseline operating condition cluster on the time axis are identified. These overlapping operating segments serve as bridging data for cross-operating condition mapping. By identifying the correspondence between different operating condition clusters at the same point in time, a practical basis for feature space alignment is provided. The identification process first sorts the data of each operating condition cluster by timestamp, and then uses set intersection operations to find the overlapping intervals between the non-baseline and baseline operating condition clusters in the time dimension. The data in these overlapping periods contain the characteristic manifestations of the same degradation state under different operating conditions, and are key samples for establishing cross-operating condition mapping relationships. The identification of overlapping periods fully utilizes the operating condition switching characteristics of the generator during operation, cleverly capturing the characteristic correspondences of the same degradation state under different operating conditions, providing reliable pairing data for subsequent alignment transformation.

[0031] During the overlapping operating period, the mean vectors of the degradation-sensitive residual vectors of the two operating condition clusters are extracted respectively, and the offset vector between them is calculated, denoted as the cross-operating condition alignment offset. The cross-operating condition alignment offset is a transformation parameter for realizing feature space mapping. By calculating the difference in feature mean values ​​during the overlapping period, the feature distribution deviation between different operating condition clusters is quantified. The calculation process first extracts the mean vectors of the degradation-sensitive residual vectors of the reference and non-reference operating condition clusters during the overlapping period, and then calculates the offset of the non-reference operating condition mean vector relative to the reference operating condition mean vector. This mean alignment-based method assumes that the degradation state of the two operating condition clusters is the same during the overlapping period, and the difference in their feature distribution mainly comes from operating condition factors rather than the degree of degradation. By eliminating this systematic bias, consistent expression of degradation features under different operating conditions can be achieved.

[0032] Cross-condition alignment is achieved by subtracting the corresponding cross-condition alignment offset from all degradation-sensitive residual vectors of each non-baseline operating condition cluster. Cross-condition alignment is a key step in mapping features under different operating conditions to a unified space. By applying the previously calculated offset vectors, a spatial transformation of the feature distribution is realized. The alignment process performs a translation transformation on each degradation-sensitive residual vector of the non-baseline operating condition cluster, subtracting the corresponding cross-condition alignment offset, so that its distribution characteristics are aligned with the baseline operating condition cluster. This simple translation-based transformation preserves the local structure and relative relationships of the original feature space, while achieving consistent alignment of the global distribution. It is a computationally efficient and physically interpretable mapping method. After alignment, degradation features under different operating conditions are transformed into a unified feature space, making cross-condition comparison and comprehensive analysis of degradation states possible.

[0033] The degradation-sensitive residual vectors of the baseline operating condition cluster and all aligned non-baseline operating condition clusters are merged and arranged in chronological order to generate an operating condition-independent degradation feature sequence. This sequence is a pure degradation feature time series after eliminating the influence of operating conditions. By merging the features of each aligned operating condition cluster, continuous monitoring of degradation status is achieved. The merging process first sorts the feature vectors of the baseline operating condition cluster and all aligned non-baseline operating condition clusters by timestamp, forming a time-continuous sequence. For overlapping time regions, a weighted average method is used to fuse the feature values ​​of multiple operating conditions. The weights are proportional to the sample size of each operating condition cluster to ensure statistical stability. This process generates an operating condition-independent degradation feature sequence that covers the entire operating cycle of the equipment, is unaffected by changes in operating conditions, and directly reflects the temporal evolution of degradation status, providing a high-quality feature sequence for subsequent trend analysis and life prediction.

[0034] In this embodiment of the invention, the detailed implementation steps for performing time-series trend fitting on the condition-independent degradation feature sequence, identifying abrupt slope changes in the trend fitting curve, marking the segments between adjacent abrupt slope changes as degradation stages, and constructing a staged degradation trajectory include:

[0035] The Mahalanobis distance norm is calculated for multidimensional vectors in the condition-independent degradation feature sequence, compressing them into a one-dimensional degradation index time series. The Mahalanobis distance norm is an effective measure of comprehensive multidimensional feature information. By considering the correlation between features, it achieves an effective mapping from multidimensional feature vectors to a one-dimensional degradation index. The calculation process first estimates the covariance matrix Σ of the condition-independent degradation feature sequence, and then calculates the Mahalanobis distance of the feature vector xt at each time point t relative to the feature mean μ. Compared with Euclidean distance, Mahalanobis distance considers the correlation structure between features, inherently balances redundant information of correlated features, and provides a more reasonable comprehensive measure. The one-dimensional degradation index intuitively reflects the comprehensive level of equipment degradation, providing a simplified and effective feature expression for subsequent trend analysis. The formula for calculating the Mahalanobis distance is: ; in, For time points Mahalanobis distance value, This is the feature vector at that time point. The feature mean vector, Let be the characteristic covariance matrix.

[0036] Locally weighted regression (LOESS) was used to smooth the time series of degradation indices, yielding a smoothed degradation trend curve. LOESS is a nonparametric regression technique that extracts underlying trends from noisy data, achieving adaptive smoothing of time series data through local fitting. The process employed the LOESS algorithm, applying weighted least squares fitting within a local window around each time point. The weights decreased with increasing distance, typically calculated using a cubic kernel. The smoothing parameter (window size) was adaptively set based on the data length and noise level, typically covering 5%-15% of the data points. This local fitting method effectively captures nonlinear trends while suppressing random fluctuations and measurement noise. The resulting smoothed degradation trend curve retains key characteristics of the degradation process, laying the foundation for subsequent slope analysis.

[0037] The first-order difference is calculated point-by-point on the smoothed degradation trend curve to obtain the slope sequence. The slope sequence is a direct measure of the rate of trend change; through first-order differencing, the trend curve is transformed into a time function of the rate of change. The calculation process employs the central difference method on the smoothed degradation trend curve. Calculate the average rate of change of the left and right neighboring points at each time point, using the formula: ,in The sampling time interval is defined as . This central difference method offers better numerical stability and accuracy than one-sided difference, accurately capturing local slope changes in the trend curve. The slope sequence directly reflects the temporal evolution characteristics of the degradation rate and is a key indicator for identifying transition points in the degradation stage.

[0038] The slope sequence is subjected to second-order differencing. Time points where the absolute value of the second-order differencing exceeds a preset mutation detection threshold are identified and recorded as candidate slope mutation points. Second-order differencing is an effective means of detecting slope changes; by calculating the rate of change of the slope, the time points where significant slope changes can be accurately located. The calculation process also uses the central difference method for the slope sequence. Calculate the second difference The mutation detection threshold is typically set to the mean of the absolute values ​​of the second-order differences plus twice the standard deviation, ensuring that only significant slope changes are marked as mutation points. These slope mutation candidate points usually correspond to turning points in the degradation process, such as the end of the initial break-in period, the beginning of the stable wear period, and the arrival of the accelerated degradation period, and are the basic markers for constructing a phased degradation trajectory.

[0039] The time interval between two adjacent candidate points for slope abrupt changes is examined. If the interval is less than the preset minimum stage duration, the two candidate points are merged into a single slope abrupt change point. Candidate point merging is a crucial step in optimizing stage division. By eliminating adjacent abrupt change points with excessively short time intervals, it avoids over-segmentation and false stage identification caused by noise. The merging process first sets a minimum stage duration threshold (typically 5%-10% of the total monitoring time), then checks the time interval between adjacent candidate abrupt change points. When the interval is less than the threshold, the two points are merged into a single abrupt change point, with the position calculated as a weighted average of the two, the weights being proportional to the absolute value of the second-order difference. This merging strategy ensures that each identified degradation stage has sufficient duration and data support, improving the reliability and stability of stage division.

[0040] A staged degradation trajectory is constructed by recording the degradation index segments and their corresponding slope values ​​between adjacent slope abrupt change points. This staged degradation trajectory is a piecewise linear representation of the degradation process. By recording the start and end points, duration, and average slope of each stage, a structured description of the complex degradation process is achieved. The recording process first determines the temporal location of each slope abrupt change point, using them as the boundary points between adjacent stages; then, the average slope of the degradation index within each stage is calculated as the degradation rate characteristic of that stage; finally, the time range, degradation index interval, and average slope of each stage are organized into structured data to form a complete staged degradation trajectory. This piecewise representation method not only simplifies the complex nonlinear degradation process, facilitating understanding and analysis, but also provides a direct reference for lifetime prediction based on historical degradation patterns.

[0041] In this embodiment of the invention, the detailed implementation steps for constructing a degradation rate-weighted prediction model based on the slope and duration of each degradation stage in the phased degradation trajectory, and extrapolating to generate the remaining life prediction range of the excitation carbon brush, include: The average slope and duration of each degradation stage in the phased degradation trajectory are extracted to construct slope-duration sequence pairs. These slope-duration sequence pairs are the core feature representation of the degradation pattern, capturing the evolutionary pattern of the degradation process by recording the degradation rate and duration of historical stages. The extraction process first reads the average slope and duration of each stage from the phased degradation trajectory, then organizes them into sequence pairs in chronological order to form a temporal representation of the degradation pattern. This sequence representation retains the phased characteristics of the degradation process while quantifying the key parameters of each stage, providing direct historical evidence for subsequent prediction models. The slope-duration sequence pairs serve as a bridge connecting historical observations and future predictions. By analyzing the patterns and trends within them, the degradation characteristics of the next stage can be reasonably inferred, enabling scientific predictions of future developments.

[0042] In slope-duration series pairs, the closer the degradation stage is to the current time, the greater the time decay weight is assigned. The time decay weight is a key mechanism for considering the impact of timeliness; by differentially weighting historical data, it highlights the predictive value of recent observations. The weighting process uses an exponential decay model, where the weight decreases exponentially with increasing time distance, as shown in the formula: ,in For stage index, For the current stage index, The decay parameter λ controls the rate at which the weights decay. The decay parameter λ is typically set between 0.5 and 1.5 and can be dynamically adjusted based on the stability of historical data and the magnitude of recent trend changes. This time-weighted strategy reflects the practical principle that "recent experience is more valuable," emphasizing the greater influence of recent observations on future predictions while preserving long-term trend information, thus improving the model's sensitivity and adaptability to changes in deteriorating trends.

[0043] Using the average slope of each degradation stage as a feature and its duration as the objective, a weighted linear extrapolation model is fitted with time decay weights to predict the slope and duration of the next degradation stage. Weighted linear extrapolation is the core algorithm for predicting future characteristics based on historical patterns. By analyzing the historical relationship between slope and duration, it predicts the key parameters of the next stage. The fitting process uses a weighted linear regression method, taking the average slope of the previous i stages as the starting point. Duration (as an independent variable) As the dependent variable, the weight is... Fitting a linear model The model parameters are solved using weighted least squares, with the goal of minimizing the weighted sum of squared residuals. The fitted model is used to predict the duration of the next stage, and the average slope of the next stage is predicted through time series analysis of the slope sequence. This extrapolation prediction based on historical degradation patterns fully utilizes the inherent regularity and continuity of the equipment degradation process, and can reasonably predict the key characteristics of future stages, providing a reliable basis for remaining life calculation.

[0044] The nominal remaining life is calculated based on the difference between the current degradation index and the preset failure threshold, combined with the predicted slope. Nominal remaining life is the central estimate of lifespan prediction, calculating the time required for the equipment to reach failure by considering the current state, the failure threshold, and the predicted slope. The calculation process first determines the current degradation index and the preset failure threshold; the difference between the two represents the amount of degradation required to progress from the current state to failure. Then, this degradation amount is divided by the predicted average slope of the next stage to obtain the time required to reach failure at the current rate. Finally, the predicted duration of the next stage is combined to determine the nominal remaining life. The preset failure threshold is typically set based on historical failure case analysis or expert experience, representing the critical degree of degradation at which the equipment cannot operate safely. This lifespan calculation method based on the current state and the predicted rate is intuitive and practical, providing a clear time reference for maintenance decisions.

[0045] Based on the historical standard deviation of the slope at each degradation stage, the uncertainty range of the predicted slope is estimated, and the upper and lower confidence boundaries of the nominal remaining lifetime together constitute the remaining lifetime prediction interval. The remaining lifetime prediction interval is a complete lifetime expression considering prediction uncertainty, defining the possible range of lifetime prediction through the upper and lower confidence boundaries. The calculation process first analyzes the variability of the slope at historical degradation stages and calculates the sample standard deviation of the slope; then, based on the central limit theorem, a confidence interval for the slope prediction is constructed; finally, the uncertainty of the slope is transferred to lifetime prediction, and the upper and lower confidence boundaries of lifetime are calculated. The confidence level is typically set to 95%, corresponding to a slope interval of the predicted value ± 1.96 times the standard error. This interval expression not only provides a point estimate of lifetime but also quantifies the level of prediction uncertainty, providing more comprehensive information support for risk assessment and maintenance decisions, and enhancing the practicality and reliability of the prediction results.

[0046] In this embodiment of the invention, the detailed implementation steps for performing variance testing on the original fluctuation sequence, identifying time intervals with significantly increased variance, and marking them as transitional segments for operating condition switching include: The local variance time series is obtained by progressively calculating the local variance of the original fluctuation sequence using a preset sliding window length. Local variance is a statistical measure of the degree of signal fluctuation. Calculation using a sliding window enables dynamic tracking of signal fluctuation characteristics. The calculation process employs a fixed-length sliding window (typically the number of sampling points corresponding to 30-120 seconds), which moves progressively along the time axis. The sample variance is calculated for the original fluctuation sequence within each window, forming a continuous variance time series. The choice of window length balances temporal resolution and statistical stability; a window that is too short leads to unstable variance estimation, while a window that is too long reduces the sensitivity to abrupt changes. The local variance time series visually reflects the fluctuation intensity of the original fluctuation sequence at different time periods, providing a key indicator for subsequent identification of abnormal segments.

[0047] The global median and interquartile range (IQR) of the local variance time series are calculated. Time windows where the local variance exceeds the global median plus three times the IQR are marked as transitional candidate windows. The IQR is a robust statistical measure of dispersion; by calculating the difference between the upper and lower quartiles, it is unaffected by extreme values ​​and can stably characterize the dispersion of data. The detection process first calculates the global median Med and the IQR of the local variance time series, then sets a threshold Th = Med + 3 × IQR, and time windows where the local variance exceeds the threshold are marked as transitional candidate windows. This anomaly detection method based on the median and IQR is more robust than methods based on the mean and standard deviation, less susceptible to extreme values, and can reliably identify regions where the local variance deviates significantly from the normal level. These transitional candidate windows typically correspond to operating condition changes, load variations, or disturbance events, representing non-stationary regions of the system state.

[0048] Adjacent transition candidate windows are merged. If the time interval between two candidate windows is less than a preset merging interval threshold, both windows and the interval between them are uniformly marked as a single operating condition switching transition segment. Candidate window merging is a key step in optimizing detection results. By connecting temporally adjacent abnormal segments, the complete operating condition switching process is identified. The merging process first sets a merging interval threshold (usually 1-3 times the window length), then checks the time interval between adjacent transition candidate windows. When the interval is less than the threshold, the two windows and the segment between them are merged and marked as a single operating condition switching transition segment. This merging strategy is based on the actual characteristic that operating condition switching is usually a continuous process, which can avoid incorrectly dividing a single switching process into multiple independent events, improving the coherence and physical rationality of the detection results. The finally marked operating condition switching transition segments comprehensively cover the entire transition process of the system from one stable operating condition to another, providing accurate non-steady-state region division for subsequent analysis.

[0049] In this embodiment of the invention, the detailed implementation steps of performing kernel density estimation on the amplitude of the operating condition base value component, identifying local maxima points in the probability density curve, and recording the current amplitude corresponding to each local maxima point as the representative value of the operating condition include: A Gaussian kernel function is used to estimate the kernel density of the amplitude distribution of the baseline load condition components, with the bandwidth parameter adaptively determined using the Silverman criterion. The Gaussian kernel function is the most commonly used kernel function in kernel density estimation, possessing good smoothness and theoretical properties, making it suitable for nonparametric estimation of continuous data distributions. The estimation process uses amplitude samples of the baseline load condition components as input, generating a continuous probability density function through convolution operations with the Gaussian kernel function. The bandwidth parameter h is a key parameter controlling the smoothness of the estimation; too small a bandwidth leads to overfitting, revealing excessive local fluctuations; too large a bandwidth leads to underfitting, masking important distribution characteristics. The Silverman criterion adaptively calculates the optimal bandwidth based on the sample standard deviation and sample size, using the following formula: ,in The standard deviation of the sample is 1. Interquartile range, The sample size is [value missing]. This adaptive bandwidth selection method balances the smoothness and accuracy of the estimation, and the generated probability density curve can accurately reflect the multi-peak distribution characteristics of the baseline components of the operating conditions, providing an intuitive visual reference and data foundation for subsequent operating condition identification.

[0050] Taking the first derivative of the kernel density estimation curve, we identify the zero-crossing points where the first derivative changes from positive to negative, and record the current amplitudes corresponding to each zero-crossing point as candidate local maxima. The zero-crossing point of the first derivative is a calculus method for finding extreme points on the density curve. By analyzing the rate of change of the density function, we accurately locate the inflection points of the curve. The calculation process first involves taking the first derivative of the kernel density estimation function... By performing numerical differentiation, the first derivative function is obtained. Then, the sign change of the derivative function is detected. When a value changes from positive to negative, the corresponding x-value is marked as a candidate local maximum. This derivative-based extremum detection method is more accurate and stable than directly comparing adjacent values, and can accurately locate the extrema of continuous functions, working reliably even in the presence of noise and small fluctuations. Candidate local maximums represent high-probability regions in the distribution of basic operating condition components, typically corresponding to the generator's typical steady-state operating conditions, and serve as initial reference points for operating condition identification.

[0051] The ratio of the probability density valley to the peak value between two adjacent candidate local maxima is calculated and denoted as the peak-valley ratio. The peak-valley ratio is an effective indicator for evaluating the separation of distribution peaks; by comparing the relative heights of peaks and valleys, it quantifies the discriminative power between adjacent peaks. The calculation process first identifies two adjacent candidate local maxima. and Corresponding density value and Then in the interval Find the minimum value of the density function within the valley, and denote it as the valley value. Finally, the ratio of the trough value to the smaller peak value is calculated using the following formula: The peak-to-valley ratio ranges from [0,1]. A value closer to 0 indicates a more pronounced separation between peaks, while a value closer to 1 indicates a less pronounced separation. This indicator intuitively reflects the significance of the multimodal structure in the distribution, providing a quantitative basis for peak merging decisions.

[0052] When the peak-to-valley ratio is less than the preset peak-to-valley separation threshold, two candidate points are retained as independent representative values ​​for each operating condition. When the peak-to-valley ratio is greater than or equal to the peak-to-valley separation threshold, the two candidate points are merged and their average is taken as a single representative value for the operating condition. The peak-to-valley separation threshold is a key parameter for peak merging decisions. By setting an appropriate threshold, the distinction between small fluctuations and true multi-peak structures in the distribution is achieved. The decision-making process first sets the peak-to-valley separation threshold (usually 0.3-0.6), then compares the calculated peak-to-valley ratio with the threshold, and decides whether to retain independent peaks or merge them into a single peak based on the comparison result. When the peak-to-valley ratio is less than the threshold, it indicates that the separation between the two peaks is significant and they should be retained as independent representative values ​​for the operating condition. When the peak-to-valley ratio is greater than or equal to the threshold, it indicates that the separation between the two peaks is not obvious and may be random fluctuations of the same operating condition. They should be merged into a single representative value for the operating condition, and the position is taken as the arithmetic mean of the two peaks. This adaptive merging strategy based on the peak-to-valley ratio effectively balances the detail and stability of operating condition identification, avoids the problems of over-segmentation or over-merging, and produces a set of representative values ​​for operating conditions that correspond well to the actual operating conditions.

[0053] In this embodiment of the invention, the detailed implementation steps for normalizing the variance of the regression residuals of each feature component to eliminate differences in the dimensions of different features and obtain the normalized residual matrix include: Calculate the standard deviation of the regression residual sequence for each feature component, denoted as the residual standard deviation for that feature dimension. The residual standard deviation is a statistical measure of feature variability; by calculating the dispersion of the regression residuals, it reflects the inherent volatility level of the feature after eliminating the influence of operating condition fluctuations. The calculation process is performed on the regression residual sequence { for each feature component i}. Perform the calculation separately, using the formula: ,in Let be the mean of the residual sequence. The sample size is represented by the standard deviation of the residuals. The standard deviation directly reflects the remaining variation of this feature after responding to fluctuations within the operating condition; a larger value indicates richer potential degradation information contained in the feature, and a greater contribution to subsequent analysis. This step provides a statistical basis for assessing the importance of each feature dimension and is a prerequisite for feature selection and normalization.

[0054] When the residual standard deviation exceeds a preset minimum standard deviation threshold, the regression residual sequence of that feature is divided by the residual standard deviation to complete normalization. Normalization is a standard transformation to unify the feature scale. By scaling the standard deviation, features with different dimensions are converted into standardized variables of the same scale. The process first sets a minimum standard deviation threshold (usually 1%-3% of the overall residual standard deviation), then performs Z-score standardization on features whose residual standard deviation exceeds the threshold, dividing the original residual sequence by its standard deviation to convert it into standardized residuals with a mean of 0 and a standard deviation of 1. This standard deviation-based normalization method preserves the relative variation pattern of the original residual sequence while eliminating dimensional differences and scale imbalances, ensuring that different features have the same statistical weight in subsequent analyses and avoiding the problem of large-scale features dominating the analysis results.

[0055] When the residual standard deviation is less than or equal to a preset minimum standard deviation threshold, the feature dimension is determined to have an extremely weak response to the fluctuation components within the operating condition. The regression residual sequence of this feature is then set to zero and removed from subsequent principal component analysis. Feature removal is a crucial step in improving the signal-to-noise ratio. By identifying and removing features with extremely low variability, the quality and effectiveness of the feature set are optimized. The removal decision is based on a comparison of the residual standard deviation with the minimum threshold. When the standard deviation is below the threshold, it indicates that the feature is either almost entirely explained by the fluctuations within the operating condition or has extremely low variability, offering limited indicative value for deterioration. These features are marked as invalid features, their residual sequences are set to zero, and they are excluded from subsequent principal component analysis. This feature selection strategy effectively reduces data dimensionality, eliminates interference from low-information features, and improves the efficiency and accuracy of subsequent analysis. Especially for high-dimensional feature sets, it can significantly improve the quality and computational performance of principal component analysis.

[0056] The retained normalized residual sequences of each dimension are concatenated column-wise to form a normalized residual matrix. The normalized residual matrix is ​​a data structure that integrates multi-dimensional features. Through columnar organization, the standardized residuals of each feature dimension are systematically integrated into a unified matrix form. The concatenation process uses the retained normalized residual sequences of each feature dimension as column vectors of the matrix, forming a two-dimensional matrix structure of sample number × feature dimension. Each row in the matrix corresponds to a multi-dimensional feature residual vector at a given time point, and each column corresponds to the residual sequence of a feature component across all time points. This matrix organization not only facilitates subsequent matrix operations such as principal component analysis but also preserves the temporal structure and feature relationships of the data, providing a standardized input format for multivariate statistical analysis. The normalized residual matrix is ​​a pure feature expression after eliminating the influence of operating conditions, directly reflecting the multi-dimensional feature patterns of equipment degradation, laying a solid data foundation for principal component analysis and degradation feature extraction.

[0057] This invention achieves accurate prediction of the degradation trend of excitation carbon brushes under different operating conditions through dual-component decomposition of excitation current, residual projection within operating conditions, cross-operating condition mapping, and construction of staged degradation trajectories. The operating condition adaptive feature extraction and multi-stage degradation modeling methods of this invention can effectively eliminate the influence of operating condition fluctuations and accurately identify the transition points of degradation stages.

[0058] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0059] It should be noted that all formulas in this manual are calculated by removing dimensions and taking their numerical values. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters and thresholds in the formulas are set by those skilled in the art according to the actual situation.

[0060] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for predicting the degradation trend of excitation carbon brushes based on the coupling characteristics of current and vibration, characterized in that, include: Obtain the excitation current time series and vibration acceleration time series of the excitation carbon brush during the operating cycle, as well as the corresponding active power and reactive power dispatch command sequences of the unit; Based on the scheduling instruction sequence, the excitation current time series is decomposed into a base value component and an intra-condition fluctuation component, which are denoted as a dual-component pair of excitation current. For the operating condition base value component in the excitation current dual-component pair, a set of operating condition status labels is constructed, and the operating data is classified into the corresponding operating condition cluster according to the operating condition status label to form a clustered operating dataset. Within each of the operating condition clusters, a multidimensional feature vector of the vibration acceleration time series is extracted, and the wave component within the operating condition is used as a covariate to perform residual projection within the operating condition on the multidimensional feature vector to obtain the degradation-sensitive residual vector of each operating condition cluster. A cross-condition baseline manifold is established, and the degradation-sensitive residual vectors of each condition cluster are mapped to a unified degradation state space to generate a condition-independent degradation feature sequence. The working condition-independent degradation feature sequence is fitted with a time-series trend, the slope abrupt change points in the trend fitting curve are identified, the segments between adjacent slope abrupt change points are marked as degradation stages, and a staged degradation trajectory is constructed. Based on the slope and duration of each degradation stage in the phased degradation trajectory, a degradation rate weighted prediction model is constructed, and the remaining life prediction range of the excitation carbon brush is generated by extrapolation.

2. The method according to claim 1, characterized in that, Based on the scheduling instruction sequence, the excitation current time series is decomposed into a base value component and an intra-condition fluctuation component, denoted as an excitation current dual-component pair, including: Using the active power and reactive power scheduling command sequence as input, the low-frequency trend of the excitation current is extracted by the sliding window mid-range filter and denoted as the operating condition following baseline. Calculate the point-by-point difference between the excitation current time series and the operating condition following baseline, and record it as the original fluctuation series; A variance test is performed on the original fluctuation sequence to identify time intervals with significantly increased variance, which are marked as operating condition switching transition segments, and the data of the operating condition switching transition segments are removed from subsequent analysis; The operating condition following baseline after removing the operating condition switching transition segment is recorded as the operating condition base value component, and the corresponding original fluctuation sequence is recorded as the operating condition fluctuation component, which together constitute the excitation current dual component pair.

3. The method according to claim 1, characterized in that, For the operating condition base value component in the dual-component pair of excitation current, a set of operating condition status labels is constructed, and the operating data is classified into corresponding operating condition clusters according to the operating condition status labels to form a clustered operating dataset, including: Kernel density estimation is performed on the amplitude of the base value component of the operating condition, local maxima are identified in the probability density curve, and the current amplitude corresponding to each local maxima is recorded as the representative value of the operating condition. Using the arithmetic mean of the representative values ​​of adjacent working conditions as the boundary, the attraction domain of each representative value of working condition is defined to form a set of working condition status labels; The operating condition base value component at each moment in the dual-component pair of excitation current is compared with the distance of each operating condition representative value in the operating condition status label set, and the moment is assigned to the operating condition cluster corresponding to the nearest operating condition representative value. The number of samples in each operating condition cluster is counted. For operating condition clusters with a sample number lower than a preset minimum sample threshold, a merging operation is performed, merging them into the adjacent operating condition cluster with the closest current amplitude, and generating the clustered operation dataset.

4. The method according to claim 1, characterized in that, Within each of the operating condition clusters, a multidimensional feature vector of the vibration acceleration time series is extracted, and the operating condition residual projection is performed on the multidimensional feature vector using the fluctuation component within the operating condition as a covariate to obtain the degradation-sensitive residual vector of each operating condition cluster, including: For each working condition cluster, the root mean square value, peak-to-peak value, kurtosis, waveform factor, and 1 / 3 octave band power spectral density vector of the vibration acceleration time series are calculated and concatenated to form the multidimensional feature vector matrix of that working condition cluster. Within this operating condition cluster, using the fluctuation component within the operating condition as the independent variable, a univariate linear regression model is constructed for each dimension of the multidimensional feature vector matrix, and the regression residuals of each dimension of the feature component on the fluctuation component within the operating condition are extracted. The variance of the regression residuals of each feature component is normalized to obtain the normalized residual matrix; Principal component analysis is performed on the normalized residual matrix, and the principal components whose cumulative variance contribution rate exceeds the preset contribution rate threshold are retained to form the degradation-sensitive residual vector of the operating condition cluster.

5. The method according to claim 1, characterized in that, The establishment of a cross-condition baseline manifold, mapping the degradation-sensitive residual vectors of each condition cluster to a unified degradation state space, and generating a condition-independent degradation feature sequence includes: The operating condition cluster with the largest number of samples is selected as the benchmark operating condition cluster, and the degradation-sensitive residual vector distribution of this operating condition cluster is used as the benchmark manifold. For each non-baseline operating condition cluster, identify the overlapping running segments of the operating condition cluster and the baseline operating condition cluster on the time axis; During the overlapping runtime, the mean vector of the degradation-sensitive residual vectors of the two operating condition clusters is extracted respectively, and the offset vector between them is calculated, which is denoted as the cross-operating condition alignment offset. Subtract the corresponding cross-condition alignment offset from all the degradation-sensitive residual vectors of each non-baseline condition cluster to complete the cross-condition alignment. The degradation-sensitive residual vectors of the baseline operating condition cluster and all aligned non-baseline operating condition clusters are merged and arranged in chronological order to generate the operating condition-independent degradation feature sequence.

6. The method according to claim 1, characterized in that, The process of performing time-series trend fitting on the condition-independent degradation feature sequence, identifying abrupt slope changes in the trend fitting curve, marking the segments between adjacent abrupt slope changes as degradation stages, and constructing a staged degradation trajectory includes: The Mahalanobis distance norm is calculated for the multidimensional vectors in the condition-independent degradation feature sequence, and then compressed into a one-dimensional degradation exponential time series. Local weighted regression is used to smooth the time series of the degradation index to obtain a smoothed degradation trend curve. Calculate the first-order difference point by point on the smoothed degradation trend curve to obtain the slope sequence; The slope sequence is subjected to second-order difference, and the time nodes in which the absolute value of the second-order difference exceeds the preset mutation detection threshold are identified and recorded as slope mutation candidate points. The time interval between two adjacent candidate points of slope change is examined. If the interval is less than the preset minimum stage duration, the two candidate points are merged into a single slope change point. The degradation index segments between adjacent slope abrupt change points and their corresponding slope values ​​are recorded together to construct the phased degradation trajectory.

7. The method according to claim 1, characterized in that, The step involves constructing a degradation rate-weighted prediction model based on the slope and duration of each degradation stage in the phased degradation trajectory, and extrapolating this model to generate a prediction range for the remaining life of the excitation carbon brush, including: Extract the average slope and duration of each degradation stage in the phased degradation trajectory, and construct slope-duration sequence pairs; The slope-duration sequence pair assigns a greater time decay weight to the deterioration stage that is closer to the current time. Using the average slope of each degradation stage as a feature and the duration as an objective, a weighted linear extrapolation model is fitted according to the time decay weight to predict the slope and duration of the next degradation stage. The nominal remaining lifetime is calculated based on the difference between the current degradation index value and the preset failure threshold, combined with the predicted slope. Based on the historical standard deviation of the slope at each degradation stage, the uncertainty range of the predicted slope is estimated, and the upper and lower confidence boundaries of the nominal remaining lifetime are used together to form the remaining lifetime prediction interval.

8. The method according to claim 2, characterized in that, The step of performing a variance test on the original fluctuation sequence to identify time intervals with significantly increased variance, and marking them as transitional periods for changing operating conditions, includes: The local variance of the original fluctuation sequence is calculated step by step using a preset sliding window length to obtain the local variance time series. Calculate the global median and interquartile range of the local variance time series, and mark the time windows in which the local variance exceeds the global median plus three times the interquartile range as transitional candidate windows; Adjacent transition candidate windows are merged. If the time interval between two candidate windows is less than the preset merging interval threshold, both windows and their interval segment are uniformly marked as a single working condition switching transition segment.

9. The method according to claim 3, characterized in that, The step of performing kernel density estimation on the amplitude of the baseline component of the operating condition, identifying local maxima in the probability density curve, and recording the current amplitude corresponding to each local maxima as the representative value of the operating condition includes: The amplitude distribution of the baseline components under the operating conditions is estimated using a Gaussian kernel function; Take the first derivative of the kernel density estimation curve, identify the zero-crossing points where the first derivative changes from positive to negative, and record the current amplitude corresponding to each zero-crossing point as a candidate point of local maximum. The ratio of the valley value to the peak value of the probability density between two adjacent candidate points of local maxima is denoted as the peak-valley ratio. When the peak-to-valley ratio is less than the preset peak-to-valley separation threshold, two candidate points are retained as independent operating condition representative values; when the peak-to-valley ratio is greater than or equal to the peak-to-valley separation threshold, the two candidate points are merged and the average value is taken as a single operating condition representative value.

10. The method according to claim 4, characterized in that, The step of normalizing the variance of the regression residuals of each feature component to obtain the normalized residual matrix includes: Calculate the standard deviation of the regression residual sequence for each feature component, and denote it as the residual standard deviation of that feature. When the residual standard deviation is greater than the preset minimum standard deviation threshold, the regression residual sequence of this feature is divided by the residual standard deviation to complete the normalization. When the residual standard deviation is less than or equal to the preset minimum standard deviation threshold, it is determined that the response of this feature to the fluctuation component within the working condition is extremely weak, and the regression residual sequence of this feature is set to zero and removed from the subsequent principal component analysis. The retained normalized residual sequences of each dimension are concatenated column by column to form the normalized residual matrix.

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