A bearing residual life prediction method based on causal double-target regression

Abstract

This invention discloses a bearing remaining life prediction method based on causal bi-objective regression, belonging to the field of mechanical fault prediction and health management technology. This invention enhances causality through exponential smoothing and backward slope to ensure that feature construction relies only on current and historical data; it constructs bi-objective training labels of logarithmic transformation of remaining life and proportion of remaining life, and dynamically weights and fuses them to consider the accuracy of full-life prediction; it introduces a dual-scale trajectory difference regularization term into the training objective to constrain the output rate of change to be consistent with the actual degradation, ensuring the stability of the predicted trajectory; in the inference stage, it uses causal proportion tracking and stability gating correction to suppress instantaneous sudden interference from vibration. The core model is a linear regression structure, which is computationally efficient and highly interpretable. This invention solves the problems of missing causality, predicted trajectory jumps, and weak anti-interference ability in existing methods, and is applicable to the remaining life prediction and condition-based maintenance decision-making of various rotating machinery bearings.

Description

Technical Field

[0001] This invention relates to the field of mechanical failure prediction and health management technology, and in particular to a method for predicting the remaining life of bearings based on causal bi-objective regression. Background Technology

[0002] Rolling bearings are among the most widely used and most vulnerable critical components in rotating machinery. Accurately predicting the remaining usable life (RUL) of bearings is an important technical means to implement condition-based maintenance, avoid sudden downtime accidents, and ensure the safe operation of equipment.

[0003] Existing methods for predicting the remaining life of bearings are mainly divided into physical model-based methods and data-driven methods.

[0004] Physical model-based methods rely on accurate failure mechanism modeling, requiring the establishment of mathematical models of physical processes such as bearing fatigue crack propagation and wear evolution, and the accurate acquisition of a large number of prior parameters such as material properties, load conditions, and lubrication status. However, actual operating conditions are complex and variable, and the bearing degradation process is affected by multiple factors such as load, speed, temperature, and lubrication, making accurate physical modeling extremely difficult and unsuitable for the complex and variable operating conditions in actual engineering.

[0005] Data-driven methods, especially those based on deep neural networks, can automatically learn degradation features from vibration signals, avoiding complex physical modeling processes. However, they generally suffer from problems such as complex network structures, large training sample requirements, difficulties in hyperparameter tuning, and poor interpretability. Currently, using deep networks such as CNN-LSTM and Transformer for bearing RUL prediction has become common practice. However, these networks have a large number of parameters, resulting in high training and deployment costs in industrial applications, and the prediction results lack physical interpretability.

[0006] More importantly, existing data-driven methods still have the following shortcomings in online applications: (1) Non-causal feature construction. Some methods use vibration data or life-cycle label information after the current time step in feature smoothing, normalization, or monotonicity processing, resulting in inflated offline evaluation metrics and significant performance degradation during online deployment. In the bearing RUL prediction scenario, the system can only make inferences based on current and historical sensor data and cannot introduce future time information, otherwise it will lead to serious information leakage and model failure. Causal convolution forces the convolution operation to operate only on the current time step and the time step to its left by applying a one-way mask to the standard convolution kernel. However, many existing methods have already violated the rules by using future information in the feature preprocessing stage. This "non-causal" feature construction method fundamentally violates the physical constraints of online prediction, making it impossible to reproduce the excellent performance in offline experiments in engineering practice.

[0007] (2) Single regression objective. When directly regressing the absolute value of remaining lifetime, the value is large and the scale is sensitive in the early stage of lifetime, making it difficult for the model to give an accurate prediction in the early stage of lifetime; while when regressing the proportion of remaining lifetime, it is affected by the estimation error of the whole lifetime. A single objective is difficult to take into account the prediction accuracy of the whole lifetime. Using a single model for RUL estimation may increase the risk in some scenarios, and existing methods lack collaborative modeling of dual objectives, and cannot take advantage of the complementary advantages of absolute value regression and proportion regression at the same time.

[0008] (3) The predicted trajectory is not smooth. Independent regression at each time step leads to jumps in the predicted values ​​between adjacent time steps, and the predicted curve often exhibits non-physical regeneration, which is inconsistent with the physical fact that the bearing degradation process is monotonically gradual. Existing methods mostly use post-processing smoothing (such as filtering) to mitigate the jumps, but this approach, which separates the learning of degradation patterns from trajectory generation, cannot fundamentally guarantee the physical consistency of the predicted trajectory.

[0009] (4) Weak resistance to sudden interference. Instantaneous impacts and sudden noises in the vibration signal during degradation can cause an instantaneous underestimation of the remaining life, leading to violent fluctuations in the output or even false alarms. Existing methods generally lack a systematic guarantee mechanism for the stability of the predicted trajectory. When instantaneous impact components appear in the vibration signal, the model output often fluctuates violently, resulting in unreliable prediction results and affecting the scientific nature of maintenance decisions. Although some studies have attempted to smooth the post-processing using methods such as particle filtering and Kalman filtering, these methods are mostly used as independent post-processing steps and have failed to form an organic whole with the prediction model. Furthermore, the selection of filtering parameters lacks adaptive capability.

[0010] Therefore, how to provide a bearing remaining life prediction method that is causal across the entire chain, has a simple structure, provides a stable prediction trajectory, and can suppress instantaneous sudden disturbances is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0011] The purpose of this invention is to provide a bearing remaining life prediction method based on causal biobjective regression, which uses only vibration information at current and historical time points to achieve stable and accurate online prediction of remaining life throughout the entire lifespan.

[0012] To achieve the above objectives, this invention provides a bearing remaining life prediction method based on causal bi-objective regression, comprising the following steps: Step 1: Obtain the vibration acceleration signal during the bearing operation, and extract the basic vibration feature vector at each recording time based on the vibration acceleration signal; Step 2: Perform causal enhancement on the foundation vibration feature vector along the time axis. Causal enhancement includes at least exponential smoothing based on historical time features and backward slope calculation based on the exponential smoothing result. Generate a causal feature vector based on the foundation vibration feature vector, the exponential smoothing result, and the backward slope calculation result. Step 3: Preprocess the causal feature vector. The preprocessing includes scaling based on robust statistics and nonlinear compression transformation to obtain the preprocessed feature vector. Step 4: Construct dual-objective training labels. The dual-objective training labels include the first objective obtained by monotonically compressing the remaining lifetime and the second objective obtained by normalizing and scaling the remaining lifetime. The dual-objective training labels are then sample-weighted and standardized. Step 5: Train the regression model based on the preprocessed feature vector and the weighted standardized dual-objective training labels. The training objective function of the regression model includes a fitting loss term, a regularization term, and a trajectory difference regularization term under at least two lag scales. The trajectory difference regularization term is used to constrain the trend of model output change at different recording times on the same bearing to be consistent with the trend of label change. Step 6: Restore the first output of the regression model to the absolute remaining lifetime, and convert the second output of the regression model into the stage remaining lifetime. Based on the implicit total lifetime corresponding to the absolute remaining lifetime and the stage remaining lifetime, determine the fused remaining lifetime through a dynamic weighted fusion strategy that includes at least consistency gating, schedule gating and maturity gating. Step 7: Determine the current implicit full lifetime based on the fusion remaining lifetime, determine the reference full lifetime based on the implicit full lifetime within the historical window, and when the preset correction conditions are met, pull the current implicit full lifetime back to the reference full lifetime for correction to obtain the corrected remaining lifetime. Step 8: Normalize the remaining lifetime based on the corrected remaining lifetime and the cumulative runtime, and output the normalized remaining lifetime prediction value.

[0013] Preferably, the specific steps of step 1 are as follows: Step 1-1: Collect vibration acceleration signals during the entire life degradation process of the bearing. The vibration acceleration signals contain two sampling sequences in mutually perpendicular directions. The sampling sequences are arranged in chronological order of recording time, and each recording time corresponds to a segment of continuously sampled vibration data. Steps 1-2: For each recording time, the mean of the sampling sequences in two mutually perpendicular directions is removed, and the time domain statistical features and frequency domain shape features are extracted. The correlation coefficient and root mean square value of the two mutually perpendicular sampling sequences are combined to form the basic vibration feature vector for each recording time. Among them, the time-domain statistical features include absolute mean, standard deviation, root mean square value, peak value, peak-to-peak value, skewness, kurtosis, peak index, waveform index, impulse index, and margin index; the frequency-domain shape features include the spectral centroid, spectral dispersion, spectral entropy, and energy proportion of multiple frequency bands calculated from the windowed power spectrum.

[0014] Preferably, in step 2, during the causal enhancement of the foundation vibration characteristic vector along the time axis, the first... Exponential smoothing characteristics at each recording time point satisfy: ,and ; For the first The fundamental vibration feature vector at each recording moment; For smoothing coefficients; No. Backslope characteristics at each recording time point satisfy: ;in, ; For the first EMA smoothing characteristics of records; For the first Smoothing characteristics of records; For about The function represents in and Take the maximum value from the middle. This represents the number of delayed records; Causal eigenvectors for: .

[0015] Preferably, in step 3, the scaling process of the robust statistics is as follows: dimensional scaling is performed using the median of each feature in the training set as the position parameter and the interquartile range as the scale parameter. The interquartile range is the difference between the upper and lower quartiles of the corresponding feature in the training set. When the interquartile range of the corresponding feature is less than a set threshold, the median of the absolute deviation of the feature relative to the median is used as the scale parameter. The nonlinear compression transformation is a hyperbolic arcsine transform.

[0016] Preferably, in the dual-objective training labels of step 4, the first objective is... The second objective is In the formula For the first The remaining lifetime at each recorded moment. This refers to the total lifespan of the bearing.

[0017] Preferably, step 5 consists of the following steps: Step 5-1: Augment the preprocessed feature vectors into basis vectors containing bias terms. The training labels were obtained using a weighted, standardized dual-objective approach. As the training output of the regression model: ; ; ; Step 5-2: Construct the training objective function, which consists of the following three terms summed in a weighted manner: The first term is the sample-weighted fitting loss. This is used to measure the fitting error between the model output and the training labels, where The number of training samples, For the first The bearing balance weights for each sample. Let be the output weight matrix to be solved. For the first The bi-target lifetime labels of the training samples after standardization; The second item is the Ridge Regularity Item. , used to suppress model overfitting, where For ridge regularity coefficients, To output the weight matrix The submatrix after removing the bias rows The square of the Frobenius norm; The third term is the sum of the trajectory difference regularization terms for lag-one-beat and lag-thirty-beat scales. Used to constrain hysteresis on the same bearing The rate of change of the model output between two samples in a record is consistent with the rate of change of the training labels, where For lag Trajectory regularization coefficients at the record scale. and All of these are indexes of the recorded time of the training samples, and This indicates that the time interval on the same bearing is... Pairing samples from two different times in a record. For all sample pairs that meet the above conditions A set; Step 5-3: Solve for the output weight matrix by minimizing the objective function. , is represented as: ; The solution obtained As the output weight matrix of the regression model.

[0018] Preferably, step 6 consists of the following steps: Step 6-1: The first output of the regression model... After exponential restoration and amplitude limiting, the absolute remaining lifetime is obtained. ; Step 6-2: Limit the second output of the regression model to... Postscript , As the upper limit of the limit, for Conduct causal ratio tracking. Among them, causal proportion tracking includes: With initial value Exponential smoothing is used to obtain the current original remaining lifetime ratio. , represented as ; The remaining lifetime percentage is tracked by taking the historical minimum value at each recorded time point. , represented as ,in , The proportional tracking smoothing coefficient; Step 6-3: Set the remaining lifetime proportional tracking value Converted to the first implied lifetime And cut off: ; in, For the first The cumulative runtime at each recorded moment. To minimize the percentage of lifespan already consumed, , A multiple of the maximum lifetime of the training set; For recording periods; The remaining lifetime of the stage is obtained based on the first implicit total lifetime. ; Step 6-4: Based on absolute remaining lifespan Determine the second implicit lifetime , is represented as: Consistency Gating: In the formula, This is the consistency scaling coefficient; Step 6-5: Calculate the progress gating In the formula, To ensure complete trust in the progress; calculate maturity gating. In the formula, This is a maturity ratio coefficient. The median over the entire lifetime of the training set; Step 6-6: Calculate the fusion weights In the formula The maximum stage weight; Steps 6-7, press Dynamic weighted fusion yields the remaining fusion lifetime. .

[0019] Preferably, step 7 consists of the following steps: Step 7-1: Merge remaining lifetime With cumulative runtime Add them together to get the current implied lifetime. ; Step 7-2: Obtain the implicit total lifetime for each recorded moment within the history window, and determine the reference total lifetime based on the median. : ; In the formula The preset number of records per window. For the past The implicit total lifetime of each historical moment; when the number of historical window records is less than the preset minimum number of historical window records, the correction step is skipped; Step 7-3: Determine if the calibration trigger condition is met. The calibration trigger condition is: running progress. Exceeding the preset startup threshold Furthermore, the current implied total lifetime is lower than the reference total lifetime; Step 7-4: If the condition is not met, maintain the current implicit total lifetime unchanged, and set the corrected implicit total lifetime... ; If the correction trigger condition is met, calculate the relative down bias. The correction weights are determined based on Gaussian confidence levels. : ; in, For relative tolerance, The maximum correction weight; Pull the current implicit lifetime back to the reference lifetime to obtain the corrected implicit lifetime. ; The corrected remaining lifetime is obtained from the corrected implicit total lifetime. ; All calculations in steps 7-1 to 7-4 use only the data recorded at the current recording time and previous records, thus satisfying the causality constraint.

[0020] Preferably, in step 8, the normalization formula is: ; In the formula For the first The cumulative runtime at each recorded moment. To correct for remaining lifetime, This is the normalized predicted remaining lifetime.

[0021] Therefore, the bearing remaining life prediction method based on causal biobjective regression of the present invention has the following beneficial effects: (1) Strictly satisfy causality constraints: the exponential smoothing and backward slope calculation in the feature enhancement stage, the causal ratio tracking in the inference stage, and the stability gating correction all rely only on the current recording time and the recorded data before it, without using any vibration signals or tag information from future times, thus eliminating the performance deviation between offline evaluation and online deployment.

[0022] (2) Dual objectives complement each other to improve the accuracy of whole life prediction: the absolute remaining life target ensures the accuracy of numerical scale, while the remaining life ratio target provides the prior of the degradation stage. Through the dynamic weighted fusion of consistency gating, progress gating and maturity gating, the prediction accuracy of the early and late life stages is taken into account, and the advantages of the two objectives are complemented.

[0023] (3) The predicted trajectory is stable and physically consistent: The trajectory difference regularization terms with two scales, one lag and thirty lag, are introduced into the training objective function to directly constrain the rate of change of the model output to be consistent with the rate of change of the real degradation label. This makes the physical law of the monotonous and slow change of the bearing degradation process embedded in the model, and the prediction of adjacent time moments does not jump, effectively avoiding the non-physical life recovery phenomenon.

[0024] (4) Resistant to sudden interference and simple and efficient structure: Causal ratio tracking takes the historical minimum value record by record to ensure that the lifetime ratio is monotonically non-rising. Stable gating uses the gradual change prior of the whole lifetime to perform unilateral pull-back correction, effectively suppressing the prediction jump caused by the instantaneous sudden vibration. The core model is a linear regression based on causal enhancement features, which does not require complex deep networks and a large number of hyperparameter tuning. The training and inference are efficient, the decision path is clear and interpretable, and it is easy to deploy in industry.

[0025] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0026] Figure 1 This is the overall flowchart of the bearing remaining life prediction method based on causal bi-objective regression of the present invention; Figure 2 This is a schematic diagram illustrating the enhancement of causal features in the bearing remaining life prediction method based on causal bi-objective regression of the present invention; Figure 3 This is a schematic diagram of gated dynamic dual-target fusion and causal life-long stable gating correction in Embodiment 1 of the present invention. Detailed Implementation

[0027] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0028] 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 some embodiments of the present invention, but not all embodiments.

[0029] This invention provides a method for predicting the remaining life of bearings based on causal biobjective regression, such as... Figure 1 As shown, it includes the following steps: Step S1: Acquisition of vibration signals throughout the bearing's lifespan.

[0030] During accelerated life testing or actual service of bearings, vibration acceleration signals are collected from the bearing throughout its entire lifespan degradation process using two mutually perpendicular accelerometers mounted on the bearing housing, and recorded at fixed intervals. Record vibration data. Each recording moment corresponds to a segment of continuously sampled vibration data. All recording moments are arranged in chronological order to form the full life recording sequence of the bearing.

[0031] The vibration acceleration signal contains two sampling sequences in mutually perpendicular directions (e.g., horizontal and vertical directions), and the sampling sequences are arranged in chronological order of recording time.

[0032] Step S2: Extract fundamental features in the time-frequency domain to obtain the fundamental vibration feature vectors for each recorded time.

[0033] For each recording time, the mean of the two mutually perpendicular sampling sequences is removed, and the mean-removed sampling sequence is denoted as . N is the number of sampling points. The time-domain statistical features extracted are: mean and absolute value. Root mean square value Peak With mean square amplitude They are respectively: ; ; ; .

[0034] Skewness With kurtosis They are respectively: ; ; Peak Indicator Waveform Indicators Pulse Indicators With margin indicators They are respectively: ; ; ; ; A Hanning window is applied to the mean-reduced sampled sequence, followed by a Fast Fourier Transform, and the one-sided power spectrum is obtained. , , For the first The frequency corresponding to each frequency point, spectral probability With the spectral centroid for: ; ; in, Indicates the first Power spectrum values ​​corresponding to each frequency point; This represents the total number of frequency points. Spectral Dispersion With spectral entropy for: , ; In the formula It is the natural logarithm. For Nyquist frequency; by frequency band Statistical band power ratio ; ; The spectral centroid and spectral dispersion are normalized by dividing by the Nyquist frequency and then used as frequency domain features. Each directional channel yields 18-dimensional features. The features of two directional channels are concatenated with the correlation coefficient and root mean square value of the two directional sampling sequences to form the first... 38-dimensional fundamental vibration feature vector at each recording time point .

[0035] Step S3: As Figure 2 As shown, the foundation vibration eigenvector is subjected to exponential smoothing and backward slope causal enhancement.

[0036] For the fundamental vibration eigenvector During causal reinforcement along the timeline, the first... Exponential smoothing characteristics at each recording time point satisfy: ,and ;in, For the first The fundamental vibration feature vector at each recording moment; For smoothing coefficients; No. Backslope characteristics at each recording time point satisfy: ;in, ; For the first EMA smoothing characteristics of records; For the first Smoothing characteristics of records; It is about The function represents in and Take the maximum value from the middle. This represents the number of delayed records; Basic vibration characteristics Exponential smoothing characteristics Back slope characteristics By concatenating the vectors, we obtain the causal feature vectors. : .

[0037] Exponential smoothing and backward slope only utilize current and previous records. Appending future records to the record sequence does not change the causal feature vector at any point in time that has been generated, that is, the causal feature vector satisfies prefix invariance.

[0038] Step S4: Perform robust preprocessing of the causal feature vectors using median and interquartile range.

[0039] The median of each feature in the training set Position parameters, interquartile range The scaling parameter is applied dimension-wise, where the interquartile range (IMR) is the difference between the upper and lower quartiles of the corresponding feature in the training set. When the IMR of a corresponding feature is less than a set threshold, the median of the absolute deviation of that feature from the median is used as the scaling parameter. The vector is then compressed using a hyperbolic arcsine transform to obtain the preprocessed feature vector. : .

[0040] In the formula The feature dimension number; It is a hyperbolic arcsine function; when the scale parameter of a certain feature is less than the set threshold, it is replaced by the median of the absolute deviation of that feature relative to the median. If it is still less than the threshold, it is taken as 1 to avoid division by zero; the position parameter and scale parameter are estimated only on the training set and are frozen for use during the inference stage.

[0041] Step S5: Construction and weighted standardization of dual-target labels.

[0042] For each bearing in the training set Record the number of times it is recorded as , No. The cumulative runtime of each recorded moment , This is the serial number recorded within the bearing, representing the bearing's total lifespan. , No. Remaining lifetime at each recording moment .

[0043] Constructing dual-objective training labels: First goal ; Second objective ; The training labels for the two objectives are weighted and standardized according to the balanced sample weights of the bearings: ; In the formula For the first The training sample of the th training sample One target value, Choose 1 or 2; For the first The training sample, the first The standardized label values ​​of each target. Choose 1 or 2; weighted mean Weighted standard deviation They are respectively: ; ; In the formula, The sample weights are represented as: ; To train the number of bearings, For the first Each sample belongs to a specific bearing; sample weights ensure that each training bearing contributes equally to the total parameter estimation, preventing bearings with a large number of records from dominating the training.

[0044] Step S6: Trajectory regularization bi-objective regression training.

[0045] The preprocessed feature vectors are augmented into basis vectors containing bias terms. superscript Transpose; use weighted standardized bi-objective training labels As the training output of the regression model, the training output weight matrix The formulas involved are as follows: ; .

[0046] Construct a training objective function, which is a weighted sum of the following three terms: The first term is the sample-weighted fitting loss. This is used to measure the fitting error between the model output and the training labels, where The number of training samples, For the first The bearing balance weights for each sample. Here is the output weight matrix to be solved; For the first The bi-target lifetime labels of the training samples after standardization; The second item is the Ridge Regularity Item. , used to suppress model overfitting, where For ridge regularity coefficients, To output the weight matrix The submatrix after removing the bias rows The square of the Frobenius norm; The third term is the sum of the trajectory difference regularization terms for lag-one-beat and lag-thirty-beat scales. Used to constrain hysteresis on the same bearing The rate of change of the model output between two samples in a record is consistent with the rate of change of the training labels, where For lag Trajectory regularization coefficients at the record scale. and All of these are indexes of the recorded time of the training samples, and This indicates that the time interval on the same bearing is... Pairing samples from two different times in a record. For all sample pairs that meet the above conditions A set of.

[0047] The output weight matrix is ​​obtained by minimizing the objective function. , is represented as: ; The solution obtained As the output weight matrix of the regression model.

[0048] Furthermore, the objective function is quadratic with respect to W and has an analytical solution: ; In the formula For the reason A matrix formed by arranging rows. R is a ridge canonical diagonal matrix. To standardize the dual-target label matrix, , , , .

[0049] Step S7: Gated dynamic dual-target fusion.

[0050] 1) During the inference phase, the model output is obtained through inverse standardization. The absolute remaining lifetime is obtained by exponentially restoring the first output. ; 2) Limit the second output of the regression model to Postscript , As the upper limit of the limit, for Perform causal proportion tracking, which includes: using initial values The current original remaining lifetime ratio is obtained by performing exponential smoothing. , The minimum historical value is used as the remaining lifespan percentage tracking value for each recorded moment. , represented as ,in , To track the smoothing coefficient; During this process, the remaining lifetime proportion tracking value The record takes the historical minimum, which does not rise over time, consistent with the degradation pattern of the remaining lifespan ratio remaining monotonically unchanged; 3) Track the remaining lifetime percentage value Converted to the first implied lifetime And cut off: ; in, For cumulative runtime, To minimize the percentage of lifespan already consumed, , A multiple of the maximum lifetime of the training set; The remaining lifetime of the stage is obtained based on the first implicit total lifetime. ; 4) Based on absolute remaining lifespan Determine the second implicit lifetime , is represented as: .

[0051] Consistency gating compares the logarithmic deviation of two outputs in the implicit lifetime space and calculates the consistency gating: In the formula, This is the consistency scaling coefficient; 5) Progress gating increases with the proportion of spent life, while maturity gating saturates linearly with runtime.

[0052] Among them, progress gating , To fully trust the progress; Maturity Gating ; This is a maturity ratio coefficient. The median over the entire lifetime of the training set; 6) Calculate the fusion weights In the formula The maximum stage weight; 7) Press Dynamic weighted fusion yields the remaining fusion lifetime. .

[0053] In this step, consistency gating makes the two outputs corroborate each other, while progress gating and maturity gating make the remaining lifetime of the stage conservative in the early stages of the lifetime and gradually open up as the degradation process progresses.

[0054] Step S8: Causal lifecycle stable gating correction.

[0055] Will merge remaining lifespan With cumulative runtime Add them together to get the current implied lifetime. ; Obtain the implicit total lifetime for each recorded moment within the historical window, and determine the reference total lifetime based on the median. : ; In the formula The preset number of records per window. For the past The implicit total lifetime of each historical moment; when the number of historical window records is less than the preset minimum number of historical window records, the correction step is skipped; The bearing's total lifespan is a slowly varying latent variable; as the operating progresses... Exceeding the preset startup threshold Furthermore, the current implied total lifetime is lower than the reference total lifetime ( When calculating the relative downward bias, The correction weights are determined based on the Gaussian confidence level, as follows: ; ; For relative tolerance, The maximum correction weight is determined by the relative underbias; the larger the relative underbias, the greater the correction weight. The current implicit lifetime is pulled back to the reference lifetime to obtain the corrected remaining lifetime. , is represented as: ; ; This is the implied full lifetime after correction.

[0056] No correction is made when the implied lifetime is not less than the reference lifetime; that is, the stability gating only suppresses downward drops without suppressing upward changes, thus avoiding the introduction of hysteresis bias. The current implied lifetime is maintained unchanged, that is, the corrected implied lifetime is set to remain unchanged. .

[0057] All calculations in the above steps utilize only the data recorded at the current recording time and previous records, thus satisfying the causality constraint.

[0058] Step S9: Normalize the remaining lifetime output.

[0059] Normalization is performed based on the corrected remaining lifetime and cumulative runtime: ; In the formula For the first The cumulative runtime at each recorded moment. To correct for remaining lifetime, This is the normalized predicted remaining lifetime. It characterizes the proportion of remaining life to the predicted total life, facilitating comparisons and threshold alarms between bearings at different life scales.

[0060] Example 1 This embodiment uses steps S1 to S9 of the above-described bearing remaining life prediction method.

[0061] This embodiment uses publicly available accelerated life test data for rolling bearings (IEEE PHM 2012 bearing dataset): two mutually perpendicular accelerometers (horizontal and vertical) are mounted on the bearing housing, with a sampling frequency of 25.6 kHz and a recording period of... For each recording time point, N=2560 points were continuously sampled. The full lifespan data of two bearings of the same model were used as the training set, totaling 3674 recording times; the full lifespan data of another bearing under the same operating conditions was used as the test set. During the training phase, only the training set was used to estimate all learnable parameters, and the model hyperparameters were fixed. During the testing phase, the model was frozen and only forward inference was performed.

[0062] In step S2, a Hanning window is applied to the mean-removed sampled sequence, and the window coefficient is... After fast Fourier transform, the one-sided power spectrum is obtained, with M=1281 frequency points; the four frequency bands are the Nyquist frequencies. of , , , The interval; for each directional channel, the absolute value of the mean, standard deviation, root mean square value, peak value, peak-to-peak value, skewness, kurtosis, peak index, waveform index, impulse index, margin index, spectral centroid, spectral dispersion, spectral entropy and the energy ratio of the four frequency bands are extracted, totaling 18 features; the 36 features of the two directional channels are concatenated with the correlation coefficient between channels and the root mean square value of the vector to obtain a 38-dimensional basic vibration feature vector.

[0063] In step S3, the smoothing coefficient The number of lag records h=6, corresponding to a 60-second backward slope window; after causal enhancement, the causal feature vector of each recording moment is 114-dimensional, that is, the splicing of 38-dimensional basic vibration features, 38-dimensional exponential smoothing features and 38-dimensional backward slope features.

[0064] In step S6, the basis vector dimension is 115, and the output weight matrix W is... The preferred hyperparameter values ​​for this embodiment are shown in Table 1.

[0065] Table 1: Optimal Hyperparameter Values

[0066] In step S7, refer to Figure 3 The model's two outputs are processed by the exponential reduction branch and the causal proportional tracking branch to obtain the absolute remaining lifetime and the stage remaining lifetime, respectively. The gating weight calculation module outputs consistency gating, progress gating and maturity gating. The dynamic weighted fusion module weights and fuses the outputs of the two branches according to the fusion weight.

[0067] In step S8, refer to Figure 3 Causal lifetime stability gating performs unilateral correction on the fusion result in the implicit lifetime space; no correction is performed at the first recording time.

[0068] In step S9, the normalized remaining lifetime is calculated according to... Calculation: When the cumulative runtime is zero and the corrected remaining lifetime is positive, the normalized output is set to 1.

[0069] To further verify the effectiveness of the method protected by this invention, four other existing model methods were selected for comparison, specifically: 1) LSTM: Long Short-Term Memory Network 2) CNN: Convolutional Neural Network 3) Transformer: Transformer 4) Pathformer–TCLSTM: A temporal convolutional long short-term memory network based on the Pathways architecture and an adaptive multi-scale Transformer.

[0070] Predictive performance is achieved using normalized mean absolute error. With root mean square error Evaluation, in the formula To achieve true normalized remaining lifespan, The number of test records is shown in Table 2. The average of the predicted results for all bearings is shown in Table 2.

[0071] Table 2: Prediction Results

[0072] Experimental results show that among the three baseline models (LSTM, CNN, and Transformer), LSTM performs best in the comparison. Further introduction of Pathformer-TCLSTM further reduces the error. Among the four comparison models, Pathformer-TCLSTM performs best. In contrast, the model proposed in this paper achieves the best performance, with MAE and RMSE reaching 0.017791 and 0.024081, respectively. Compared to the second-best Pathformer-TCLSTM, MAE is reduced by approximately 43.2% and RMSE by approximately 42.5%, fully validating the significant superiority of the method protected by this invention in terms of prediction accuracy and stability.

[0073] The method protected by this invention outputs a normalized remaining life trajectory with a reasonable degradation trend throughout the entire lifespan of the tested bearing. The sudden drop interference caused by instantaneous vibration is effectively suppressed. Furthermore, adding future records to the recording sequence does not change the already output prediction results, thus verifying the causality, stability, and accuracy of the method of this invention.

[0074] Therefore, this invention relates to a bearing remaining life prediction method based on causal bi-objective regression. It ensures strict causality in feature construction through exponential smoothing and causal enhancement of the backward slope; it constructs a bi-objective model of absolute remaining life and remaining life ratio, achieving full-life accuracy through three-gated dynamic fusion; it introduces a dual-scale trajectory difference regularization term into the training objective to constrain the output rate of change, ensuring stable and physically consistent predicted trajectory; and it effectively suppresses instantaneous sudden disturbances through causal ratio tracking and stability gating correction during the inference stage. The core model is a linear regression structure, offering high computational efficiency and strong interpretability. This invention provides a reliable and efficient engineering solution for condition-based maintenance and health management of rotating machinery bearings.

[0075] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting the remaining life of bearings based on causal bi-objective regression, characterized in that, Includes the following steps: Step 1: Obtain the vibration acceleration signal during the bearing operation, and extract the basic vibration feature vector at each recording time based on the vibration acceleration signal; Step 2: Perform causal enhancement on the foundation vibration feature vector along the time axis. Causal enhancement includes at least exponential smoothing based on historical time features and backward slope calculation based on the exponential smoothing result. Generate a causal feature vector based on the foundation vibration feature vector, the exponential smoothing result, and the backward slope calculation result. Step 3: Preprocess the causal feature vectors. The preprocessing includes scaling based on robust statistics and nonlinear compression transformation to obtain preprocessed feature vectors. Step 4: Construct dual-objective training labels. The dual-objective training labels include the first objective obtained by monotonically compressing the remaining lifetime and the second objective obtained by normalizing and scaling the remaining lifetime. The dual-objective training labels are then sample-weighted and standardized. Step 5: Train the regression model based on the preprocessed feature vector and the weighted and standardized samples with dual objectives. The training objective function of the regression model includes a fitting loss term, a regularization term, and a trajectory difference regularization term under at least two lag scales. The trajectory difference regularization term is used to constrain the trend of model output change at different recording times on the same bearing to be consistent with the trend of label change. Step 6: Restore the first output of the regression model to the absolute remaining lifetime, and convert the second output of the regression model into the stage remaining lifetime. Based on the implicit total lifetime corresponding to the absolute remaining lifetime and the stage remaining lifetime, determine the fused remaining lifetime through a dynamic weighted fusion strategy that includes at least consistency gating, schedule gating and maturity gating. Step 7: Determine the current implicit full lifetime based on the fusion remaining lifetime, determine the reference full lifetime based on the implicit full lifetime within the historical window, and when the preset correction conditions are met, pull the current implicit full lifetime back to the reference full lifetime for correction to obtain the corrected remaining lifetime. Step 8: Normalize the remaining lifetime based on the corrected remaining lifetime and the cumulative runtime, and output the normalized remaining lifetime prediction value.

2. The bearing remaining life prediction method based on causal biobjective regression according to claim 1, characterized in that, The specific steps of step 1 are as follows: Step 1-1: Collect vibration acceleration signals during the entire life degradation process of the bearing. The vibration acceleration signals contain two sampling sequences in mutually perpendicular directions. The sampling sequences are arranged in chronological order of recording time, and each recording time corresponds to a segment of continuously sampled vibration data. Steps 1-2: For each recording time, the mean of the sampling sequences in two mutually perpendicular directions is removed, and the time domain statistical features and frequency domain shape features are extracted. The correlation coefficient and root mean square value of the two mutually perpendicular sampling sequences are combined to form the basic vibration feature vector for each recording time. Among them, the time-domain statistical features include absolute mean, standard deviation, root mean square value, peak value, peak-to-peak value, skewness, kurtosis, peak index, waveform index, impulse index, and margin index; the frequency-domain shape features include the spectral centroid, spectral dispersion, spectral entropy, and energy proportion of multiple frequency bands calculated from the windowed power spectrum.

3. The bearing remaining life prediction method based on causal biobjective regression according to claim 1, characterized in that: In step 2, during the causal enhancement of the foundation vibration eigenvector along the time axis, the first... Exponential smoothing characteristics of each recording time point satisfy: ,and ; For the first The fundamental vibration feature vector at each recording moment; For smoothing coefficients; No. Backslope characteristics at each recording time point satisfy: ;in, ; For the first EMA smoothing characteristics of records; For the first Smoothing characteristics of records; For about The function represents in and Take the maximum value from the middle. This represents the number of delayed records. Causal eigenvectors for: .

4. The bearing remaining life prediction method based on causal biobjective regression according to claim 1, characterized in that: In step 3, the scaling of robust statistics is performed as follows: the median of each feature in the training set is used as the position parameter and the interquartile range is used as the scale parameter for dimension-wise scaling. The interquartile range is the difference between the upper and lower quartiles of the corresponding feature in the training set. When the interquartile range of the corresponding feature is less than a set threshold, the median of the absolute deviation of the feature relative to the median is used as the scale parameter. The nonlinear compression transformation is a hyperbolic arcsine transform.

5. The bearing remaining life prediction method based on causal biobjective regression according to claim 4, characterized in that: In step 4, the dual-objective training labels, the first objective is... The second objective is In the formula For the first The remaining lifetime at each recorded moment. This refers to the total lifespan of the bearing.

6. The bearing remaining life prediction method based on causal bi-objective regression according to claim 5, characterized in that, The specific steps of step 5 are as follows: Step 5-1: Augment the preprocessed feature vectors into basis vectors containing bias terms. The training labels were obtained using a weighted, standardized dual-objective approach. As the training output of the regression model: ； ； ； Step 5-2: Construct the training objective function, which consists of the following three terms summed in a weighted manner: The first term is the sample-weighted fitting loss. This is used to measure the fitting error between the model output and the training labels, where The number of training samples, For the first The bearing balance weights for each sample. Let be the output weight matrix to be solved. For the first The bi-target lifetime labels of the training samples after standardization; The second item is the Ridge Regularity Item. , used to suppress model overfitting, where For ridge regularity coefficients, To output the weight matrix The submatrix after removing the bias rows The square of the Frobenius norm; The third term is the sum of the trajectory difference regularization terms for lag-one-beat and lag-thirty-beat scales. Used to constrain hysteresis on the same bearing The rate of change of the model output between two samples in a record is consistent with the rate of change of the training labels, where Lagging Trajectory regularization coefficients at the record scale. and All of these are indexes of the recorded time of the training samples, and This indicates that the time interval on the same bearing is... Pairing samples from two different times in a record. For all sample pairs that meet the above conditions A set; Step 5-3: Solve for the output weight matrix by minimizing the objective function. , is represented as: ； The solution obtained As the output weight matrix of the regression model.

7. The bearing remaining life prediction method based on causal bi-objective regression according to claim 6, characterized in that, The specific steps of step 6 are as follows: Step 6-1: The first output of the regression model After exponential restoration and amplitude limiting, the absolute remaining lifetime is obtained. ; Step 6-2: Limit the second output of the regression model to... Postscript , As the upper limit of the limit, for Causal proportion tracking is performed, which includes: With initial value Exponential smoothing is used to obtain the current original remaining lifetime ratio. , represented as ; The remaining lifetime percentage is tracked by taking the historical minimum value at each recorded time point. , represented as ,in , This is the proportional tracking smoothing coefficient; Step 6-3: Track the remaining lifetime percentage value Converted to the first implied lifetime And cut off: ； in, For the first The cumulative runtime at each recorded moment. To minimize the percentage of lifespan already consumed, , A multiple of the maximum lifetime of the training set; The preset recording period; The remaining lifetime of the stage is obtained based on the first implicit total lifetime. ; Step 6-4: Based on absolute remaining lifespan Determine the second implicit lifetime , is represented as: Consistency Gating: In the formula, This is the consistency scaling coefficient; Step 6-5: Calculate the progress gating In the formula, To ensure complete trust in the progress; calculate maturity gating. In the formula, This is a maturity ratio coefficient. The median over the entire lifetime of the training set; Step 6-6: Calculate the fusion weights In the formula The maximum stage weight; Steps 6-7, press Dynamic weighted fusion yields the remaining fusion lifetime. .

8. The bearing remaining life prediction method based on causal bi-objective regression according to claim 7, characterized in that, The specific steps for step 7 are as follows: Step 7-1: Merge remaining lifetime With cumulative runtime Add them together to get the current implied lifetime. ; Step 7-2: Obtain the implicit total lifetime for each recorded moment within the history window, and determine the reference total lifetime based on the median. : ； In the formula The preset number of records per window. For the past The implicit total lifetime of each historical moment; when the number of historical window records is less than the preset minimum number of historical window records, the correction step is skipped; Step 7-3: Determine if the calibration trigger condition is met. The calibration trigger condition is: running progress. Exceeding the preset startup threshold Furthermore, the current implied total lifetime is lower than the reference total lifetime; Step 7-4: If the condition is not met, maintain the current implicit total lifetime unchanged, and set the corrected implicit total lifetime... ; If the correction trigger condition is met, calculate the relative down bias. The correction weights are determined based on Gaussian confidence levels. : ； in, For relative tolerance, The maximum correction weight; Pull the current implicit lifetime back to the reference lifetime to obtain the corrected implicit lifetime. ; The corrected remaining lifetime is obtained from the corrected implicit total lifetime. ; All calculations in steps 7-1 to 7-4 use only the data recorded at the current recording time and previous records, thus satisfying the causality constraint.

9. The bearing remaining life prediction method based on causal bi-objective regression according to claim 8, characterized in that, In step 8, the normalization formula is: ； In the formula For the first The cumulative runtime at each recorded moment. To correct for remaining lifetime, This is the normalized predicted remaining lifetime.

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