A Bayesian-aware SHAP interpretability remaining lifetime prediction method and system based on BA-BiGRU network

Abstract

The application belongs to the field of service life prediction, and discloses a Bayesian-aware SHAP explainability residual useful life prediction method based on a BA-BiGRU network. A selected original data set is divided into a training set, a verification set and a test set, and sensor feature screening, MinMax normalization, PowerTransformer distribution correction, wavelet denoising and RUL label setting are sequentially completed. An RUL prediction model is constructed. The model takes the processed multi-dimensional sensor sequence as input, enhances the expression ability of key input variables through a feature attention mechanism, and extracts bidirectional time sequence dependency in the degradation process by using BiGRU. Monte Carlo random sampling is introduced into the SHAP attribution process. The same sample is randomly forward-inferred for multiple times, and the corresponding SHAP values are calculated, so that the traditional single-deterministic attribution is expanded to the attribution distribution under multiple sampling. The application improves the robustness and stability of the interpretation result under complex working conditions and noise disturbance conditions, thereby providing a more reliable decision basis for complex equipment predictive maintenance.

Description

Technical Field

[0001] This invention belongs to, but is not limited to, the field of remaining useful life prediction, and particularly relates to a Bayesian-aware SHAP interpretable remaining useful life prediction method based on BA-BiGRU networks. Background Technology

[0002] Remaining useful life (RUL) estimation is a key technology in predictive maintenance, enabling the prediction of equipment's remaining uptime based on its operating status, thus providing a basis for fault warning and maintenance decisions. Complex equipment is susceptible to various factors during operation, including changes in operating conditions, load fluctuations, sensor noise, and differences in failure modes, resulting in a degradation process characterized by significant nonlinearity and uncertainty. Traditional physical models, statistical models, and expert-based methods rely on explicit mechanisms and prior assumptions, limiting their adaptability. While deep learning methods have improved prediction accuracy in recent years, the opaque nature of their decision-making processes makes it difficult to explain the key degradation characteristics upon which they are based, leading to insufficient reliability of the prediction results. Therefore, improving the interpretability of RUL prediction models has become a crucial issue in this field.

[0003] To address the issue of insufficient interpretability in RUL prediction models, some scholars have considered using interpretable artificial intelligence methods to explain the model's prediction process. Existing explanation methods typically fall into two categories: global explanation and local explanation. Global explanation primarily reveals the overall decision-making patterns and feature importance distribution of the model, while local explanation focuses on analyzing the reasons for the formation of prediction results for individual samples. Although these methods have achieved some success in improving model transparency, different explanation methods often have different applicability and varying sensitivities to model structure, input data, and noise disturbances. Under complex operating conditions and uncertain degradation conditions, the explanation results may fluctuate, making it difficult to maintain stable and consistent model predictions. Therefore, existing RUL prediction explanation methods still need further improvement in terms of explanation stability and engineering reliability.

[0004] Among existing interpretable artificial intelligence methods, the Shapley Value Analysis (SHAP) method has attracted widespread attention due to its sound theoretical foundation and strong applicability. Compared with interpretive methods relying on local surrogate models, single-feature response analysis methods, and gradient-based saliency analysis methods, SHAP, based on Shapley value theory, can fairly quantify the contribution of different input features to the model's prediction results. Furthermore, SHAP can be used to analyze the predictive basis of a single sample or a certain degradation stage, and can also reveal the key degradation features that the model relies on overall by aggregating the interpretation results of multiple samples.

[0005] In the field of explainable remaining useful life (RUL) prediction, explainable artificial intelligence methods have been used to improve the transparency of data-driven RUL prediction models. Existing explanation methods generally fall into two categories: global explanation and local explanation. The former is used to analyze the overall decision-making patterns of the model, while the latter is used to explain the basis for predictions of individual samples or a certain stage of degradation.

[0006] Among existing ex-post interpretation methods, the SHAP method can quantify the contribution of each input feature to the model's prediction results, possessing both local and global interpretability. Therefore, it is often used for interpreting and analyzing RUL prediction models for complex equipment. This method can identify key degradation features affecting lifetime prediction results by ranking feature contributions, providing some interpretable basis for the model's decision-making process.

[0007] However, existing SHAP interpretation methods still have shortcomings in RUL prediction applications. Ordinary SHAP typically outputs interpretation results in the form of a single attribution or average attribution, mainly focusing on the static ranking of feature importance. When the prediction model includes MCDropout, Bayesian layers, or sampling approximation mechanisms, the model inference process itself has randomness, and ordinary SHAP cannot explicitly reflect the uncertainty of the interpretation results. Furthermore, under conditions of multi-condition variation, sensor noise, and uncertainty in degradation processes, the interpretation results may fluctuate, and relying solely on a single feature importance ranking is insufficient to determine the stability and reliability of the interpretation basis.

[0008] Therefore, the technical problem to be solved in this study is: how to perform interpretable analysis on the feature contribution of the prediction model while ensuring the accuracy of RUL prediction, and further characterize the uncertainty of the interpretation results, so as to improve the robustness and stability of the interpretation results under complex working conditions and noise disturbance conditions, thereby providing a more reliable decision-making basis for predictive maintenance of complex equipment. Summary of the Invention

[0009] To address the aforementioned technical problems, this invention proposes a Bayesian-aware SHAP interpretability remaining lifetime prediction method based on BA-BiGRU networks.

[0010] This invention is implemented as follows: a method for predicting remaining useful life based on Bayesian uncertainty representation, comprising:

[0011] Acquire preprocessed multidimensional sensor time-series data;

[0012] The feature weights corresponding to each sensor feature are determined based on the multidimensional sensor time series data, and the sensor features are weighted according to the feature weights to obtain feature-weighted time series data.

[0013] The feature-weighted time series data is input into a bidirectional time-series dependency extraction mechanism to extract degradation state information propagating forward in time and degradation state information propagating backward in time, respectively. The degradation state information is then correlated to obtain bidirectional time series features characterizing the device degradation process.

[0014] The time weights corresponding to each time step are determined based on the bidirectional time series features, and the bidirectional time series features of different time steps are weighted according to the time weights to obtain lifetime prediction characterization features.

[0015] The remaining useful life prediction feature input adopts a Bayesian output mechanism that uses probability distribution to represent model parameters. The remaining useful life prediction result is generated based on the posterior distribution of the model parameters, and the uncertainty of model parameters in the remaining useful life prediction process is represented by the posterior distribution.

[0016] Furthermore, the preprocessing of the multidimensional sensor time-series data includes:

[0017] Feature filtering is performed on the raw sensor data;

[0018] MinMax normalization is performed on the filtered sensor features based on the minimum and maximum values ​​of each sensor feature in the training set;

[0019] The normalized sensor features were subjected to distribution correction using PowerTransformer based on Yeo-Johnson transform;

[0020] The corresponding noise score is determined based on the relationship between the first-order differential fluctuation of each sensor time series signal and the fluctuation of the sensor time series signal itself. Wavelet denoising is performed on the corresponding sensor time series signal when the noise score exceeds a preset threshold.

[0021] Furthermore, based on the equipment operation process, a segmented linear remaining useful life label is set, dividing the equipment operation process into an initial health stage and a degradation stage. In the initial health stage, the remaining useful life label is set to 125. In the degradation stage, the remaining useful life label is linearly decreased according to the equipment operation time, and the remaining useful life label is used as the supervision information of the remaining useful life prediction model.

[0022] Furthermore, a feature attention mechanism is employed to generate feature weights corresponding to the features of each sensor based on multi-dimensional sensor time-series data;

[0023] A BiGRU is used to receive multi-dimensional sensor time-series data weighted by feature weights and output the bidirectional time-series features.

[0024] A time attention mechanism is used to generate time weights for each time step based on the bidirectional temporal features.

[0025] A Bayesian Linear layer is used to receive the time-weighted bidirectional temporal features, and the remaining lifetime prediction results are output based on the posterior distribution of the model parameters.

[0026] Furthermore, during the training of the remaining useful life prediction model, a mean squared error term and a SmoothL1 loss term are determined based on the error between the predicted and actual remaining useful life values. An asymmetric exponential penalty term for the remaining useful life prediction task is determined based on the direction of the prediction error. An L2 regularization term is determined based on the model parameters. A KL divergence term is determined based on the difference between the posterior and prior distributions of the Bayesian Linear layer model parameters. A composite loss constraint is formed based on the mean squared error term, the SmoothL1 loss term, the asymmetric exponential penalty term, the L2 regularization term, and the KL divergence term. The Adam optimization mechanism is then used to update the model parameters based on the composite loss constraint.

[0027] This invention also provides a Bayesian-aware SHAP interpretability analysis method for predicting remaining useful life, comprising:

[0028] Obtain a remaining useful life prediction model with Bayesian stochastic inference capability, multidimensional sensor samples to be explained, and normal operation samples under healthy conditions, and use the normal operation samples as the SHAP attribution baseline;

[0029] While preserving the stochastic inference state of the remaining useful life prediction model, Monte Carlo stochastic forward inference is performed multiple times on the same multidimensional sensor sample to be explained, so that each stochastic forward inference corresponds to a remaining useful life prediction function with the current stochastic parameter state.

[0030] For each random forward inference, SHAP attribution is performed on the remaining useful life prediction function to determine the attribution contribution of each input feature to the remaining useful life prediction result under the corresponding random parameter state, and the attribution contributions obtained by the same input feature in multiple random forward inferences are combined into the SHAP attribution distribution corresponding to the input feature.

[0031] The average contribution strength and attribution fluctuation of the input feature are determined according to the SHAP attribution distribution, and the robust attribution contribution of the input feature is determined according to the relationship between the average contribution strength and the attribution fluctuation, so that the attribution fluctuation forms an uncertainty penalty on the average contribution strength.

[0032] The robust feature ranking is determined based on the robust attribution contribution of each input feature, and the robust feature ranking is compared with the feature ranking formed based on the ordinary SHAP attribution result. The stability of the remaining useful life prediction model interpretation result under stochastic inference conditions is evaluated based on the comparison result.

[0033] Furthermore, during the execution of the Monte Carlo stochastic forward inference, the randomness required by Bayesian inference is maintained and MC Dropout is enabled, so that the same multidimensional sensor sample to be explained corresponds to different model stochastic states in different stochastic forward inferences; the remaining lifetime prediction result is obtained for each model stochastic state, and the prediction function corresponding to the model stochastic state is used as the function to be explained in the current SHAP attribution process.

[0034] Furthermore, for the same input feature, the SHAP attribution contribution of the input feature obtained in multiple Monte Carlo stochastic forward inferences is statistically analyzed, and the average absolute SHAP contribution of the input feature is determined based on the absolute value of each SHAP attribution contribution, so as to characterize the average contribution intensity of the input feature to the remaining useful life prediction result.

[0035] The SHAP attribution standard deviation is determined based on the degree of dispersion of each SHAP attribution contribution relative to the average SHAP attribution result, in order to characterize the degree of attribution fluctuation of the input feature under different model stochastic states.

[0036] Furthermore, robust SHAP contributions are determined based on the mean absolute SHAP contribution and SHAP attribution standard deviation corresponding to the input features. The mean absolute SHAP contribution is used as the base amount of feature contribution, and the SHAP attribution standard deviation is used as the attribution uncertainty. The constraint strength between the base amount of feature contribution and the attribution uncertainty is adjusted by an uncertainty penalty coefficient. The robust SHAP contribution is obtained by subtracting the penalty amount determined by the attribution uncertainty from the base amount of feature contribution. The importance ranking of the input features is determined based on the robust SHAP contributions corresponding to each input feature.

[0037] Furthermore, an evaluation of the interpretability stability of the ordinary SHAP attribution results and the robust SHAP attribution results was performed, including:

[0038] The Spearman rank correlation coefficient is determined based on the difference in the ranking of each input feature in the two interpretation results to characterize the consistency of the overall feature ranking between different interpretation runs.

[0039] The Kendall Tau coefficient is determined based on the number of feature pairs with consistent relative order and the number of pairs with opposite relative order in the two interpretation results, in order to characterize the degree of consistency of the pairwise relative order of features between different interpretation runs;

[0040] The attribution variance is determined based on the degree of dispersion between the attribution contribution of the same input feature in multiple interpretation runs and the average attribution contribution of the input feature, and the average attribution variance is determined based on the attribution variance corresponding to the Top-k input features.

[0041] The reduction in attribution variance is determined by the proportion of the difference between the average attribution variance of ordinary SHAP and the average attribution variance of robust SHAP relative to the average attribution variance of ordinary SHAP. The explanatory stability of the robust SHAP attribution results is evaluated based on the Spearman rank correlation coefficient, Kendall Tau coefficient, average attribution variance, and the reduction in attribution variance.

[0042] This invention also provides a Bayesian-aware SHAP interpretability remaining lifetime prediction method based on BA-BiGRU network, the method comprising:

[0043] S1: Data preprocessing: The selected original dataset is divided into training set, validation set and test set, and sensor feature selection, MinMax normalization, PowerTransformer distribution correction, wavelet denoising and RUL label setting are performed in sequence to reduce the impact of redundant features, dimensional differences, abnormal distribution and noise interference on model training.

[0044] S2: RUL prediction model construction: The model takes the processed multidimensional sensor sequence as input, enhances the expressive power of key input variables through feature attention mechanism, and uses BiGRU to extract the bidirectional temporal dependency in the degradation process; then, a temporal attention mechanism is introduced to further highlight the contribution of different time steps to lifetime prediction, and finally outputs the RUL prediction result through Bayesian Linear layer.

[0045] S3: Bayesian-aware SHAP interpretability analysis: Monte Carlo random sampling is introduced into the SHAP attribution process. Multiple random forward inferences are performed on the same sample, and the corresponding SHAP values ​​are calculated for each sample. This extends the traditional single-sample deterministic attribution to an attribution distribution under multiple sampling. Based on this, Mean|SHAP|, SHAP Std, and Robust|SHAP| are further calculated to characterize the average contribution strength of features, the degree of attribution fluctuation, and the robust contribution level after considering uncertainty penalties, respectively. Finally, the explanatory effectiveness and stability of the proposed method are systematically verified by combining global feature contribution analysis, comparative analysis of Normal SHAP and Robust SHAP, and attribution stability evaluation index.

[0046] Furthermore, S1 specifically includes:

[0047] (1) MinMax Normalization: For features The normalized function formula is shown in formula (1) below:

[0048] (1)

[0049] in, and Let the minimum and maximum values ​​of the j-th feature in the training set be defined. This transformation maps different variables to similar intervals, thereby avoiding the dominance of gradient updates by sensors with larger numerical scales during training.

[0050] (2) PowerTransformer: To address the common problems of skewed distribution, long-tailed distribution, and local extrema in sensor variables, PowerTransformer is used to further correct the feature distribution after MinMax normalization; the specific function formula is shown in formula (2) below:

[0051] (2)

[0052] in, This represents the power transform operator based on the Yeo–Johnson transform;

[0053] (3) Due to the high-frequency noise problem in the sensor channel, a selective wavelet denoising strategy is performed on the sensor. Specifically, the noise score formula for each sensor is as follows (3):

[0054] (3)

[0055] Where S represents the timing signal of a certain sensor, This represents its first-order difference. To prevent extremely small constants with a denominator of zero; if the score exceeds a preset threshold, it is considered that the high-frequency fluctuation of the channel is strong and wavelet denoising is required.

[0056] (4) Dividing the complex degradation process into simple linear stages allows for a more intuitive description of the changes in health status over time, facilitating the establishment of predictive models; therefore, a fragmentary linear degradation model is typically used to set the RUL; generally, in the initial operating stage, the engine is considered healthy, and its RUL value is constant; while in the degradation stage, the engine degrades, and the RUL value decreases linearly; selecting It is 125, regarding The linear function of the tag fragment is shown in the following formula (4):

[0057] (4)

[0058] (5) Root Mean Square Error: Assume that yi and ŷi are the true RUL value and predicted value of the i-th sample, respectively, and N is the total number of samples; the function formula of RMSE is shown in formula (5) below:

[0059] (5)

[0060] (6) Scoring function: The scoring function is widely used as an evaluation index in the field of industrial RUL prediction, as shown in formulas (6) and (7):

[0061] (6)

[0062] (7)

[0063] Where s represents the score. This represents the error between the actual RUL value and the estimated RUL value for the i-th sample. In practical applications, delayed predictions often lead to more severe consequences, so the scoring function penalizes delayed predictions more. For RUL prediction, the lower the values ​​of the two evaluation metrics, the better the performance. This scoring method was also adopted at the International Conference on Predictive and Health Management Data Challenges.

[0064] Furthermore, S2 specifically includes:

[0065] The constructed model mainly consists of three parts: a bidirectional gated recurrent unit network, an attention mechanism, and a Bayesian linear layer. The model takes a multivariate degradation time series as input. First, it uses a feature attention mechanism to adaptively weight key sensor channels to enhance the model's ability to represent important degradation information. Then, it uses BiGRU to model the bidirectional temporal dependency of the sequence, thereby fully extracting the dynamic evolution features in the degradation process. Finally, a Bayesian linear output layer is introduced to predict the remaining lifetime and to characterize the uncertainty of the model parameters to improve the credibility and robustness of the prediction results. During the model training process, the Adam optimizer is used to adaptively update the network parameters, and a composite loss function is introduced to optimize the model to further improve the prediction accuracy and training stability. The loss function is shown in the following formula (8):

[0066] (8)

[0067] in For the mean square error term, For SmoothL1 / Huber loss terms, The asymmetric exponential penalty term designed for PHM tasks is shown in formulas (16) and (17). For the L2 regularization term of the model parameters, This is the KL divergence term between the posterior and prior distributions of the Bayesian layer.

[0068] Furthermore, S3 specifically includes:

[0069] (1) Bayesian Sampling and SHAP Attribution: In the interpretation phase, the randomness required by Bayesian inference is preserved, and MCDropout is enabled. Multiple random forward inferences are used to characterize the variation of model output and interpretation results under uncertainty conditions. Let the model input be x, and the model output under the nth Monte Carlo sampling is denoted as:

[0070] ,

[0071] Where N represents the number of Monte Carlo samplings; in this way, a set of predictions from the model under stochastic inference conditions can be obtained;

[0072] After obtaining the Bayesian sampling output, the SHAP interpretation framework is further combined to perform feature attribution analysis on each sampling. For the RUL prediction task, the normal operating samples in a healthy state are selected as the interpretation baseline to ensure that the attribution results can reveal the influence of each feature from a healthy state to a deteriorating state on lifespan prediction. For the nth sampling, the model prediction results are shown in the following formula (9):

[0073] (9)

[0074] in, This is the baseline output for this sampling. Let M represent the SHAP contribution value of the i-th feature in the nth sampling, where M is the number of input features. By performing SHAP attribution on each sampling, a set of attribution results can be obtained, i.e. ;

[0075] After obtaining the SHAP results from N samplings, the attribution results are further statistically modeled to characterize the average level and fluctuation of the input feature SHAP contribution; specifically, the attribution mean is first calculated, and the specific formula is shown in formula (10) below:

[0076] (10)

[0077] in, The average SHAP attribution result under multiple random inferences is used to characterize the average contribution strength of features to the model output; then the attribution standard deviation is calculated, and the specific formula is shown in formula (11) below:

[0078] (11)

[0079] in, Used to characterize the degree of fluctuation in attribution results across different samples, reflecting the uncertainty of the explanation results; if the SHAP value of a certain feature changes significantly under different samples, then its corresponding The value is also relatively large, indicating that the reliability of the interpretation of this feature is relatively low. Take 50 as an example;

[0080] (2) Robust SHAP Construction: In order to establish a unified metric between average contribution and attribution stability, this invention further introduces an uncertainty penalty mechanism to construct a robust attribution index, the specific formula of which is shown in formula (12) below:

[0081] (12)

[0082] in, This is the uncertainty penalty coefficient, used to adjust the trade-off between average contribution and attribution fluctuation. The basic idea of ​​this formula is: if a feature has a high average contribution but fluctuates significantly under different sampling conditions, then a penalty term is applied. Suppressing unstable interpretations prevents them from interfering with the final feature ranking; while for features that have both high average contributions and remain stable across multiple samplings, their robust attribution values ​​will be preferentially retained; therefore, It can be viewed as an attribution metric that integrates importance and reliability;

[0083] (3) Spearman rank correlation coefficient: used to measure the consistency of the overall ranking of features in two interpretations; it focuses on whether a set of features that ranks high in one Monte Carlo run will still rank high in another run; it reflects the stability of the global ranking; the formula for the Spearman rank correlation coefficient is shown in formula (13) below:

[0084] (13)

[0085] in, Represents the Spearman rank correlation coefficient. The ranking of the i-th feature in the a-th run. This represents the ranking of the i-th feature in the b-th run. represents the difference in rank between the i-th feature in the two runs, and M represents the total number of features participating in the ranking comparison; The value range is [-1, 1]. The closer it is to 1, the more consistent the overall ranking of features under different runs is, and the better the stability is; the closer it is to 0, the weaker the ranking relationship is, and the worse the stability is; if it is close to -1, the ranking is almost the opposite.

[0086] (4) Kendall-Tau coefficient: used to measure the consistency of the pairwise relative order of features. Unlike Spearman, it focuses on whether the order of two arbitrary features i and j still holds in another round if i is more important than j in one round. Therefore, it reflects the stability of the local order relationship. Its formula is shown in formula (14) below:

[0087] (14)

[0088] Where T represents the Kendall-Tau coefficient. This represents the number of feature pairs that have the same relative order in the two sorting processes. Kendall Tau represents the number of feature pairs whose relative order is reversed in two sortings. In stability analysis, Kendall Tau takes a value in the range of [-1, 1] and the larger the value, the better.

[0089] (5) Attribution Variance is used to measure the degree of fluctuation of the attribution value of the same feature under multiple Monte Carlo runs. It reflects the stability of the attribution value level. Its formula is shown in formula (15) below:

[0090] (15)

[0091] in, If we further analyze the Top-k feature set

[0092] For overall statistics, the average attribution variance is defined as shown in the following formula (16):

[0093] (16)

[0094] This represents the average attribution variance of the Top-k features. This represents the attribution variance of the f-th feature. The attribution contribution value of the f-th feature in the r-th run. This represents the average contribution of the f-th feature across all runs. In stability analysis, a smaller Attribution Variance indicates smaller fluctuations in the attribution value of the same feature across different runs, resulting in a more stable interpretation.

[0095] (6) Reduction is used to quantify the improvement in attribution variance of robust SHAP compared to normal SHAP. Its formula is shown in the following formula (17):

[0096] (17)

[0097] This represents the average attribution variance of a standard SHAP. This represents the average attribution variance of the robust SHAP. If Reduction > 0, it means that the robust SHAP has a smaller variance and improved stability. The larger the Reduction, the more significant the improvement of the robust SHAP compared to the ordinary SHAP.

[0098] In combination with the above technical solutions and the technical problems solved, the significant advancements and unexpected technical effects of the technical solution to be protected by this invention are as follows:

[0099] First, while ensuring the accuracy of RUL prediction, this invention performs interpretable analysis on the feature contributions of the prediction model and further characterizes the uncertainty of the interpretation results, thereby improving the robustness and stability of the interpretation results under complex working conditions and noise disturbance conditions, thus providing a more reliable decision-making basis for predictive maintenance of complex equipment.

[0100] The technical solution protected by this invention is not a simple parallel combination of BiGRU, attention mechanisms, Bayesian inference, and SHAP interpretation methods. Instead, it addresses the technical problems of "insufficient extraction of degradation information, lack of uncertainty representation in prediction results, and insufficient stability of interpretation results due to the influence of model random states" in the remaining useful life prediction process. It establishes a technical mechanism that integrates degradation feature extraction, Bayesian uncertainty modeling, and uncertainty perception attribution analysis. First, it adjusts the participation of different sensor variables in the prediction process by adjusting feature weights. Then, it uses bidirectional temporal dependencies to extract the correlation information between the time states before and after the device degradation process. Furthermore, it weights the contribution of different time steps to the remaining useful life prediction according to the time dimension, allowing important sensor-dimensional information and key degradation information in the time dimension to jointly enter the life prediction stage. Compared to directly encoding the original multivariate time-series data uniformly, this reduces the interference of irrelevant sensor information and non-critical time information on degradation representation. Secondly, this invention employs a Bayesian output mechanism that uses probability distributions to characterize model parameters, so that the remaining useful life prediction no longer corresponds to a single deterministic parameter state, but retains the prediction uncertainty reflected by changes in model parameters, providing a unified source of uncertainty for subsequent credibility analysis of interpretation results.

[0101] This invention does not treat SHAP merely as an additional explanation tool after model training, but rather continuously incorporates Bayesian stochastic inference states into the SHAP attribution process. Prediction and feature attribution are performed on the same sensor sample under multiple stochastic model states, transforming a single deterministic SHAP value into multiple attribution results with statistical distribution characteristics. Based on this, the average contribution strength and attribution volatility of features are simultaneously extracted, and attribution volatility is used to impose uncertainty penalties on the average contribution. This ensures that the determination of feature importance depends not only on the magnitude of its contribution but also on the stability of that contribution under different stochastic model states. This suppresses the abnormal boosting of features with high average contributions but significant attribution volatility in importance ranking, and prioritizes the retention of degenerate features with high contributions that remain stable across stochastic inference states. Furthermore, the consistency and numerical stability of the interpretation results are evaluated using Spearman rank correlation coefficient, Kendall-Tau coefficient, and attribution variance, enabling lifetime prediction results and interpretation results to be validated within the same Bayesian uncertainty framework.

[0102] Therefore, the technical effects achieved by this invention are not only manifested in the effective extraction of equipment degradation features and prediction of remaining service life, but also in the further realization of the transmission and constraint of prediction uncertainty to interpretation uncertainty. Its unexpected technical effect lies in the fact that, without changing the original SHAP basic attribution logic, it can distinguish between sensor features that "contribute significantly but have unstable interpretation" and sensor features that "contribute significantly and have stable interpretation," thus elevating the feature importance results from a simple contribution ranking to a robust ranking that considers both contribution strength and interpretation reliability. This provides a more stable technical basis for the credible analysis of remaining service life prediction results and the identification of key degradation features. Attached Figure Description

[0103] Figure 1 A flowchart of the Bayesian-aware SHAP interpretability remaining lifetime prediction method based on BA-BiGRU network provided in an embodiment of the present invention.

[0104] Figure 2 This provides the overall framework for the Bayesian-aware SHAP method in the embodiments of the present invention.

[0105] Figure 3 The following are the results of Mean|SHAP|, SHAPStd, and Robust|SHAP| for different features in various C-MAPSS datasets provided in this embodiment of the invention;

[0106] Figure 4 A comparison chart of the attribution strength and cross-sampling variability differences of key features in the C-MAPSS dataset provided in this embodiment of the invention;

[0107] Figure 5 A comparison chart of the Top-k feature results of Normal SHAP and Robust SHAP provided in this embodiment of the invention;

[0108] Figure 6 A schematic diagram illustrating the degradation characterization of key features in the time dimension for embodiments of the present invention. Detailed Implementation

[0109] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0110] like Figure 1 , 2 As shown, this embodiment of the invention provides a Bayesian-aware SHAP interpretability remaining lifetime prediction method based on a BA-BiGRU network, the method comprising:

[0111] S1: Data preprocessing: The selected original dataset is divided into training set, validation set and test set, and sensor feature selection, MinMax normalization, PowerTransformer distribution correction, wavelet denoising and RUL label setting are performed in sequence to reduce the impact of redundant features, dimensional differences, abnormal distribution and noise interference on model training.

[0112] S2: RUL prediction model construction: The model takes the processed multidimensional sensor sequence as input, enhances the expressive power of key input variables through feature attention mechanism, and uses BiGRU to extract the bidirectional temporal dependency in the degradation process; then, a temporal attention mechanism is introduced to further highlight the contribution of different time steps to lifetime prediction, and finally outputs the RUL prediction result through Bayesian Linear layer.

[0113] S3: Bayesian-aware SHAP interpretability analysis: Monte Carlo random sampling is introduced into the SHAP attribution process. Multiple random forward inferences are performed on the same sample, and the corresponding SHAP values ​​are calculated for each sample. This extends the traditional single-sample deterministic attribution to an attribution distribution under multiple sampling. Based on this, Mean|SHAP|, SHAP Std, and Robust|SHAP| are further calculated to characterize the average contribution strength of features, the degree of attribution fluctuation, and the robust contribution level after considering uncertainty penalties, respectively. Finally, the explanatory effectiveness and stability of the proposed method are systematically verified by combining global feature contribution analysis, comparative analysis of Normal SHAP and Robust SHAP, and attribution stability evaluation index.

[0114] Furthermore, S1 specifically includes:

[0115] (1) MinMax Normalization: For features The normalized function formula is shown in formula (1) below:

[0116] (1)

[0117] in, and Let the minimum and maximum values ​​of the j-th feature in the training set be defined. This transformation maps different variables to similar intervals, thereby avoiding the dominance of gradient updates by sensors with larger numerical scales during training.

[0118] (2) PowerTransformer: To address the common problems of skewed distribution, long-tailed distribution, and local extrema in sensor variables, PowerTransformer is used to further correct the feature distribution after MinMax normalization; the specific function formula is shown in formula (2) below:

[0119] (2)

[0120] in, This represents the power transform operator based on the Yeo–Johnson transform;

[0121] (3) Due to the high-frequency noise problem in the sensor channel, a selective wavelet denoising strategy is performed on the sensor. Specifically, the noise score formula for each sensor is as follows (3):

[0122] (3)

[0123] Where S represents the time-series signal of a certain sensor, This represents its first-order difference. To prevent extremely small constants with a denominator of zero; if the score exceeds a preset threshold, it is considered that the high-frequency fluctuation of the channel is strong and wavelet denoising is required.

[0124] (4) Dividing the complex degradation process into simple linear stages allows for a more intuitive description of the changes in health status over time, facilitating the establishment of predictive models; therefore, a fragmentary linear degradation model is typically used to set the RUL; generally, in the initial operating stage, the engine is considered healthy, and its RUL value is constant; while in the degradation stage, the engine degrades, and the RUL value decreases linearly; selecting It is 125, regarding The linear function of the tag fragment is shown in the following formula (4):

[0125] (4)

[0126] (5) Root Mean Square Error: Assume that yi and ŷi are the true RUL value and predicted value of the i-th sample, respectively, and N is the total number of samples; the function formula of RMSE is shown in formula (5) below:

[0127] (5)

[0128] (6) Scoring function: The scoring function is widely used as an evaluation index in the field of industrial RUL prediction, as shown in formulas (6) and (7):

[0129] (6)

[0130] (7)

[0131] Where s represents the score. This represents the error between the actual RUL value and the estimated RUL value for the i-th sample. In practical applications, delayed predictions often lead to more severe consequences, so the scoring function penalizes delayed predictions more. For RUL prediction, the lower the values ​​of the two evaluation metrics, the better the performance. This scoring method was also adopted at the International Conference on Predictive and Health Management Data Challenges.

[0132] Furthermore, S2 specifically includes:

[0133] The constructed model mainly consists of three parts: a bidirectional gated recurrent unit network, an attention mechanism, and a Bayesian linear layer. The model takes a multivariate degradation time series as input. First, it uses a feature attention mechanism to adaptively weight key sensor channels to enhance the model's ability to represent important degradation information. Then, it uses BiGRU to model the bidirectional temporal dependency of the sequence, thereby fully extracting the dynamic evolution features in the degradation process. Finally, a Bayesian linear output layer is introduced to predict the remaining lifetime and to characterize the uncertainty of the model parameters to improve the credibility and robustness of the prediction results. During the model training process, the Adam optimizer is used to adaptively update the network parameters, and a composite loss function is introduced to optimize the model to further improve the prediction accuracy and training stability. The loss function is shown in the following formula (8):

[0134] (8)

[0135] in For the mean square error term, For SmoothL1 / Huber loss terms, The asymmetric exponential penalty term designed for PHM tasks is shown in formulas (16) and (17). For the L2 regularization term of the model parameters, This is the KL divergence term between the posterior and prior distributions of the Bayesian layer.

[0136] Table 1 Model hyperparameter settings

[0137]

[0138] Furthermore, S3 specifically includes:

[0139] (1) Bayesian Sampling and SHAP Attribution: In the interpretation phase, the randomness required by Bayesian inference is preserved, and MCDropout is enabled. Multiple random forward inferences are used to characterize the variation of model output and interpretation results under uncertainty conditions. Let the model input be x, and the model output under the nth Monte Carlo sampling is denoted as:

[0140] ,

[0141] Where N represents the number of Monte Carlo samplings; in this way, a set of predictions from the model under stochastic inference conditions can be obtained;

[0142] After obtaining the Bayesian sampling output, the SHAP interpretation framework is further combined to perform feature attribution analysis on each sampling. For the RUL prediction task, the normal operating samples in a healthy state are selected as the interpretation baseline to ensure that the attribution results can reveal the influence of each feature from a healthy state to a deteriorating state on lifespan prediction. For the nth sampling, the model prediction results are shown in the following formula (9):

[0143] (9)

[0144] in, This is the baseline output for this sampling. Let M represent the SHAP contribution value of the i-th feature in the nth sampling, where M is the number of input features. By performing SHAP attribution on each sampling, a set of attribution results can be obtained, i.e. ;

[0145] After obtaining the SHAP results from N samplings, the attribution results are further statistically modeled to characterize the average level and fluctuation of the input feature SHAP contribution; specifically, the attribution mean is first calculated, and the specific formula is shown in formula (10) below:

[0146] (10)

[0147] in, The average SHAP attribution result under multiple random inferences is used to characterize the average contribution strength of features to the model output; then the attribution standard deviation is calculated, and the specific formula is shown in formula (11) below:

[0148] (11)

[0149] in, Used to characterize the degree of fluctuation in attribution results across different samples, reflecting the uncertainty of the explanation results; if the SHAP value of a certain feature changes significantly under different samples, then its corresponding The value is also relatively large, indicating that the reliability of the interpretation of this feature is relatively low. Take 50 as an example;

[0150] (2) Robust SHAP Construction: In order to establish a unified metric between average contribution and attribution stability, this invention further introduces an uncertainty penalty mechanism to construct a robust attribution index, the specific formula of which is shown in formula (12) below:

[0151] (12)

[0152] in, This is the uncertainty penalty coefficient, used to adjust the trade-off between average contribution and attribution fluctuation. The basic idea of ​​this formula is: if a feature has a high average contribution but fluctuates significantly under different sampling conditions, then a penalty term is applied. Suppressing unstable interpretations prevents them from interfering with the final feature ranking; while for features that have both high average contributions and remain stable across multiple samplings, their robust attribution values ​​will be preferentially retained; therefore, It can be viewed as an attribution metric that integrates importance and reliability;

[0153] (3) Spearman rank correlation coefficient: used to measure the consistency of the overall ranking of features in two interpretations; it focuses on whether a set of features that ranks high in one Monte Carlo run will still rank high in another run; it reflects the stability of the global ranking; the formula for the Spearman rank correlation coefficient is shown in formula (13) below:

[0154] (13)

[0155] in, Represents the Spearman rank correlation coefficient. The ranking of the i-th feature in the a-th run. This represents the ranking of the i-th feature in the b-th run. represents the difference in rank between the i-th feature in the two runs, and M represents the total number of features participating in the ranking comparison; The value range is [-1, 1]. The closer it is to 1, the more consistent the overall ranking of features under different runs is, and the better the stability is; the closer it is to 0, the weaker the ranking relationship is, and the worse the stability is; if it is close to -1, the ranking is almost the opposite.

[0156] (4) Kendall-Tau coefficient: used to measure the consistency of the pairwise relative order of features. Unlike Spearman, it focuses on whether the order of two arbitrary features i and j still holds in another round if i is more important than j in one round. Therefore, it reflects the stability of the local order relationship. Its formula is shown in formula (14) below:

[0157] (14)

[0158] Where T represents the Kendall-Tau coefficient. This represents the number of feature pairs that have the same relative order in the two sorting processes. Kendall Tau represents the number of feature pairs whose relative order is reversed in two sortings. In stability analysis, Kendall Tau takes a value in the range of [-1, 1], and a larger value is better.

[0159] (5) Attribution Variance is used to measure the degree of fluctuation of the attribution value of the same feature under multiple Monte Carlo runs. It reflects the stability of the attribution value level. Its formula is shown in formula (15) below:

[0160] (15)

[0161] in, If we further analyze the Top-k feature set For overall statistics, the average attribution variance is defined as shown in the following formula (16):

[0162] (16)

[0163] This represents the average attribution variance of the Top-k features. This represents the attribution variance of the f-th feature. The attribution contribution value of the f-th feature in the r-th run. This represents the average contribution of the f-th feature across all runs. In stability analysis, a smaller Attribution Variance indicates smaller fluctuations in the attribution value of the same feature across different runs, resulting in a more stable interpretation.

[0164] (6) Reduction is used to quantify the improvement in attribution variance of robust SHAP compared to normal SHAP. Its formula is shown in the following formula (17):

[0165] (17)

[0166] This represents the average attribution variance of a standard SHAP. This represents the average attribution variance of the robust SHAP. If Reduction > 0, it means that the robust SHAP has a smaller variance and improved stability. The larger the Reduction, the more significant the improvement of the robust SHAP compared to the ordinary SHAP.

[0167] This invention uses the CMAPSS dataset as an example for verification. This dataset was generated using NASA's C-MAPSS simulation model, and the engine sensor distribution and structure are as follows. Figure 2As shown in Table 2, the dataset is divided into four subsets (FD001, FD002, FD003, and FD004), each representing different operating conditions and failure modes. These data include various sensor measurements crucial for understanding engine health and performance, including sensor observations (temperature, pressure, speed, etc.) and operating margins, as shown in Table 3. During unit operation, the parameters shown in Table 3 demonstrate the diversity of operating conditions and failure modes across the different subsets.

[0168] Table 2 C-MPASS Output Measurement Data

[0169]

[0170] Table 3. Description of the C MAPSS dataset

[0171]

[0172] This invention uses the aforementioned methods to predict RUL for four subsets of C-MAPSS, and the specific results are shown in Table 4. The model of this invention can effectively track the RUL change trend of the engine on all four C-MAPSS subsets (FD001, FD002, FD003, and FD004). The prediction results maintain a high degree of consistency with the actual values, and the error of most samples is near zero, indicating that the model has strong degradation feature modeling ability and good prediction stability. Quantitative indicators show that the RMSE of the model on FD001, FD002, FD003, and FD004 are 12.69, 15.44, 13.92, and 13.96, respectively, with overall prediction errors at a low level. FD001 has the lowest RMSE, indicating that the model has higher accuracy under relatively simple operating conditions; FD003 has the lowest score, only 282.17, indicating that its overall prediction performance is the best. In comparison, FD002 and FD004 have scores of 1065.55 and 1331.58, respectively. Although the RMSE remains within an acceptable range, there are still some samples with large biases under complex operating conditions and multiple failure modes. Overall, the model of this invention demonstrates good RUL prediction ability on all four datasets and shows good generalization ability under different complexity scenarios.

[0173] Table 4 Model Results Analysis

[0174]

[0175] To further verify the superiority of the proposed method, this invention was compared with several other advanced RUL prediction methods, and the specific results are shown in Table 5. Compared with traditional machine learning methods SVM and MLP, the proposed method significantly improves the prediction performance on all four datasets, with a substantial reduction in RMSE and Score. This indicates that the constructed model can more effectively mine the nonlinear temporal features in the engine degradation process and significantly enhance the accuracy of RUL estimation. Compared with deep learning models such as CNN_GRU, BiLSTM, and BiGRU, the proposed method also shows stronger overall competitiveness, especially on multi-condition and complex fault mode datasets such as FD002 and FD004, where the RMSE reaches 15.44 and 13.96 respectively, and the Score is reduced to 1065.55 and 1331.58 respectively, both better than other comparative methods. This shows that the proposed model has better feature representation and generalization capabilities in complex scenarios. Furthermore, compared with BiGRU models such as BiGRU_AS and BiGRU_TSAM, the results of the method of this invention on FD001 and FD003 are slightly lower than the optimal values, but the overall difference is small. However, it achieves better results on FD002 and FD004, indicating that the improved mechanism introduced in this invention not only maintains high prediction accuracy but also exhibits stronger stability and robustness under complex operating conditions. Overall, these comparative results fully demonstrate that the method of this invention has better effectiveness and superiority than traditional methods and existing improved models, and is particularly suitable for predicting engine remaining service life under complex conditions.

[0176] Table 5 Comparison with traditional methods

[0177]

[0178] To further analyze which input features the model mainly relies on globally. Figure 3The results of Mean|SHAP|, SHAP Std, and Robust|SHAP| for different features in various C-MAPSS datasets are presented. Mean|SHAP| represents the average absolute value of the SHAP attribution results under multiple Monte Carlo samplings, which can be considered as the average contribution strength of Normal SHAP in this invention. SHAP Std represents the fluctuation of the feature attribution result under multiple samplings, used to characterize the uncertainty of SHAP explanation. Robust|SHAP| represents the robust attribution strength obtained after introducing uncertainty penalty. The results show that there are significant differences in the feature contribution patterns of different datasets. In FD001, the model mainly relies on key features such as S8, S13, S11, and S4, and the order of Mean|SHAP| and Robust|SHAP| is basically consistent, indicating that the contribution of the main features is relatively stable. In FD002, S15 contributes significantly more than other variables, demonstrating strong single-major feature-driven characteristics, while S11, S13, and S4 play auxiliary roles. In FD003, S8, S13, and S17 are the main contributing features, with relatively small differences in overall ranking, indicating that the explanatory results also have good stability. In FD004, except for S11, multiple features such as S4, S9, S13, S15, S14, and S17 all have high contributions, indicating that the model relies more on multi-feature collaborative discrimination under complex conditions. Overall, from the perspective of global contribution, the main input dependencies of the model on different C-MAPSS datasets are revealed; in addition, Robust SHAP, while preserving the main explanatory structure, can reduce the interference of high-fluctuation attribution on feature ranking, making the global feature importance results more robust.

[0179] Furthermore, Figure 4This study demonstrates the attribution strength and cross-sampling variability differences of key features in the C-MAPSS dataset. In FD001, features S7, S17, S12, S11, and S4 contribute significantly and have a relatively concentrated box distribution, indicating that these features not only have strong degenerate characterization capabilities but also relatively stable attribution results. In FD002, the attribution strength of S9 is significantly higher than other variables, showing a clear single-principal feature dominance, while variables such as S7, S21, S3, and Op1 mainly play a supporting role. In FD003, S12, S7, and S9 are the main contributing features, and their box distribution is relatively concentrated, indicating that the model's explanation results on this dataset have good consistency and mainly rely on a few core variables to complete the RUL discrimination. In FD004, besides S3 contributing the most, the attribution strengths of several features such as S14, S2, S20, S8, S21, and Op2 are relatively similar, indicating that the model relies more on the synergistic effect of multiple features. Meanwhile, the distribution of some feature boxes and outliers suggests an increase in explanatory volatility. Overall, under relatively simple operating conditions, the model's explanatory results are more likely to be dominated by a few key features; however, under complex operating conditions and multiple failure modes, the model's joint dependence on multiple sensor variables and operating condition variables increases, and the explanatory structure exhibits a more pronounced multi-feature synergistic characteristic.

[0180] To quantitatively evaluate the stability of different interpretation methods under multiple Monte Carlo runs, this invention calculated four indicators—Spearman Rank Correlation, Kendall Tau Coefficient, Attribution Variance, and Reduction—for the Top-k (rankings of the top 5, 10, and 14 features) of different feature stability rankings on the C-MAPSS datasets FD001, FD002, FD003, and FD004. The specific results are shown in Table 6. As shown in Table 5, compared to ordinary SHAP, robust SHAP consistently demonstrates improved interpretability across all four datasets. First, considering Spearman Rank Correlation and Kendall Tau Correlation, robust SHAP's values ​​on FD001, FD002, FD003, and FD004 are all higher than those of ordinary SHAP, indicating that the overall feature ranking and pairwise relative order exhibit higher consistency under multiple Monte Carlo runs. Secondly, from the perspective of the Attribution Variance (Mean) metric, the attribution variance of robust SHAP is significantly lower than that of ordinary SHAP for Top-5, Top-10, and Top-14 datasets, indicating that its feature contribution values ​​fluctuate less across different runs and the interpretation results are more stable. Furthermore, the Reduction metric quantitatively illustrates the extent of this improvement, with variance reductions of approximately 36%–38% for FD001, 45%–47% for FD002, 37%–42% for FD003, and reaching 49%–55% for FD004. This demonstrates that the method of this invention has a more significant effect on suppressing attribution fluctuations on more complex datasets. Overall, these results collectively demonstrate that the robust SHAP method proposed in this invention not only maintains the consistency of the feature ranking structure but also significantly reduces the cross-sampling fluctuations of attribution values, thus making the interpretation results more stable and reliable than ordinary SHAP; its advantages are particularly prominent on complex work condition datasets such as FD004.

[0181] Table 6 Model Results Analysis

[0182]

[0183] Furthermore, Table 5 shows the ranking of feature stability under different Top-K conditions on different datasets. As shown in Table 7, within the same dataset, as k expands from 5 to 10 and 14, core features that appeared more frequently in the early stages usually remain in a larger set of stable features, indicating that these variables have strong ranking stability over multiple runs. The composition of stable features in ordinary SHAP and robust SHAP is generally very similar, with only minor adjustments in a few feature positions. This indicates that robust SHAP does not change the overall structure of the model in identifying key variables, but rather performs a more robust correction to the feature ranking based on the original explanation. Finally, cross-dataset comparisons show that the stable feature sets are not the same for each dataset, indicating that the key explanatory variables relied upon by the model under different operating conditions and degradation modes have significant dataset specificity. However, at the same time, each dataset contains a set of recurring core features, indicating that these variables are the most stable and reliable lifetime determination criteria for the corresponding dataset. Overall, this table demonstrates that the method of this invention can stably select a representative set of key features from multiple random inferences while preserving the main explanatory structure, providing a reliable foundation for feature mechanism analysis and credible explanation.

[0184] Table 7. Ranking of feature stability under different Top-K values

[0185]

[0186] at the same time, Figure 5 The Top-k feature results of Normal SHAP and Robust SHAP were compared from a stability perspective. As shown in the figure, Robust |SHAP| and Normal |SHAP| maintain overall consistency in the ranking of major features, indicating that the proposed method does not alter the original main feature contribution structure of the model. Meanwhile, for some features with relatively high SHAP Std, Robust |SHAP| shows a certain degree of reduction compared to Normal |SHAP|, indicating that the method moderately corrects unstable feature contributions by introducing attribution fluctuation penalties, thereby reducing the impact of high-fluctuation attribution on feature importance judgment. Combined with the aforementioned stability evaluation metrics, it can be concluded that the proposed method can improve the stability and reliability of feature attribution results while preserving the main explanatory structure.

[0187] at last, Figure 6The figure illustrates the degradation characteristics of key features over time. Several key features in FD001 showed high responses at both the beginning and end of the sequence, indicating that their degradation information remained effective over a longer period. FD002 exhibited a more pronounced late-stage enhancement, particularly with a few core features showing a rapid increase in contribution towards the end of the lifetime, suggesting that the model relies more on late-stage degradation signals for discrimination under complex operating conditions. FD003 showed a relatively smooth temporal distribution, but some dominant features continued to show an enhancing trend in the middle and later stages. In FD004, several key features showed significantly high responses in the latter half, especially towards the end, indicating that the model primarily relies on stronger late-stage degradation characteristics for lifetime estimation under complex multi-condition conditions. Overall, this figure demonstrates that the stable key features selected in this invention are not only statistically reliable but also exhibit clear stage-specific patterns in temporal evolution, further validating the good temporal consistency between the model's interpretation results and the actual degradation process.

[0188] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0189] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting remaining useful life based on Bayesian uncertainty representation, characterized in that, include: Acquire preprocessed multidimensional sensor time-series data; The feature weights corresponding to each sensor feature are determined based on the multidimensional sensor time series data, and the sensor features are weighted according to the feature weights to obtain feature-weighted time series data. The feature-weighted time series data is input into a bidirectional time-series dependency extraction mechanism to extract degradation state information propagating forward in time and degradation state information propagating backward in time, respectively. The degradation state information is then correlated to obtain bidirectional time series features characterizing the device degradation process. The time weights corresponding to each time step are determined based on the bidirectional time series features, and the bidirectional time series features of different time steps are weighted according to the time weights to obtain lifetime prediction characterization features. The remaining useful life prediction feature input adopts a Bayesian output mechanism that uses probability distribution to represent model parameters. The remaining useful life prediction result is generated based on the posterior distribution of the model parameters, and the uncertainty of model parameters in the remaining useful life prediction process is represented by the posterior distribution.

2. The method for predicting remaining useful life based on Bayesian uncertainty characterization according to claim 1, characterized in that, The preprocessing of the multidimensional sensor time-series data includes: Feature filtering is performed on the raw sensor data; MinMax normalization is performed on the filtered sensor features based on the minimum and maximum values ​​of each sensor feature in the training set; The normalized sensor features were subjected to distribution correction using PowerTransformer based on Yeo-Johnson transform; The corresponding noise score is determined based on the relationship between the first-order differential fluctuation of each sensor time series signal and the fluctuation of the sensor time series signal itself. Wavelet denoising is performed on the corresponding sensor time series signal when the noise score exceeds a preset threshold.

3. The method for predicting remaining useful life based on Bayesian uncertainty characterization according to claim 2, characterized in that, Based on the equipment operation process, a segmented linear remaining useful life label is set, dividing the equipment operation process into an initial health stage and a degradation stage. In the initial health stage, the remaining useful life label is set to 125. In the degradation stage, the remaining useful life label is linearly decreased according to the equipment operation time, and the remaining useful life label is used as the supervision information of the remaining useful life prediction model.

4. The method for predicting remaining useful life based on Bayesian uncertainty characterization according to claim 1, characterized in that, A feature attention mechanism is used to generate feature weights corresponding to the features of each sensor based on multi-dimensional sensor time-series data; A BiGRU is used to receive multi-dimensional sensor time-series data weighted by feature weights and output the bidirectional time-series features. A time attention mechanism is used to generate time weights for each time step based on the bidirectional temporal features. A Bayesian Linear layer is used to receive the time-weighted bidirectional temporal features, and the remaining lifetime prediction results are output based on the posterior distribution of the model parameters.

5. The method for predicting remaining useful life based on Bayesian uncertainty characterization according to claim 4, characterized in that, During the training of the remaining useful life prediction model, a mean squared error term and a SmoothL1 loss term are determined based on the error between the predicted and actual remaining useful life values. An asymmetric exponential penalty term for the remaining useful life prediction task is determined based on the direction of the prediction error. An L2 regularization term is determined based on the model parameters. A KL divergence term is determined based on the difference between the posterior and prior distributions of the Bayesian Linear layer model parameters. A composite loss constraint is formed based on the mean squared error term, SmoothL1 loss term, asymmetric exponential penalty term, L2 regularization term, and KL divergence term. The Adam optimization mechanism is then used to update the model parameters based on the composite loss constraint.

6. A Bayesian-aware SHAP interpretability analysis method for predicting remaining useful life, characterized in that, include: Obtain a remaining useful life prediction model with Bayesian stochastic inference capability, multidimensional sensor samples to be explained, and normal operation samples under healthy conditions, and use the normal operation samples as the SHAP attribution baseline; While preserving the stochastic inference state of the remaining useful life prediction model, Monte Carlo stochastic forward inference is performed multiple times on the same multidimensional sensor sample to be explained, so that each stochastic forward inference corresponds to a remaining useful life prediction function with the current stochastic parameter state. For each random forward inference, SHAP attribution is performed on the remaining useful life prediction function to determine the attribution contribution of each input feature to the remaining useful life prediction result under the corresponding random parameter state, and the attribution contributions obtained by the same input feature in multiple random forward inferences are combined into the SHAP attribution distribution corresponding to the input feature. The average contribution strength and attribution fluctuation of the input feature are determined according to the SHAP attribution distribution, and the robust attribution contribution of the input feature is determined according to the relationship between the average contribution strength and the attribution fluctuation, so that the attribution fluctuation forms an uncertainty penalty on the average contribution strength. The robust feature ranking is determined based on the robust attribution contribution of each input feature, and the robust feature ranking is compared with the feature ranking formed based on the ordinary SHAP attribution result. The stability of the remaining useful life prediction model interpretation result under stochastic inference conditions is evaluated based on the comparison result.

7. The Bayesian-aware SHAP interpretability analysis method for predicting remaining useful life according to claim 6, characterized in that, When performing the Monte Carlo stochastic forward inference, the randomness required by Bayesian inference is maintained and MC Dropout is enabled so that the same multidimensional sensor sample to be explained corresponds to different model stochastic states in different stochastic forward inferences; the remaining lifetime prediction result is obtained for each model stochastic state, and the prediction function corresponding to the model stochastic state is used as the function to be explained in the current SHAP attribution process.

8. The Bayesian-aware SHAP interpretability analysis method for predicting remaining useful life according to claim 6, characterized in that, For the same input feature, the SHAP attribution contribution of the input feature obtained in multiple Monte Carlo stochastic forward inferences is statistically analyzed. The average absolute SHAP contribution of the input feature is determined based on the absolute value of each SHAP attribution contribution, so as to characterize the average contribution intensity of the input feature to the remaining useful life prediction result. The SHAP attribution standard deviation is determined based on the degree of dispersion of each SHAP attribution contribution relative to the average SHAP attribution result, in order to characterize the degree of attribution fluctuation of the input feature under different model stochastic states.

9. The Bayesian-aware SHAP interpretability analysis method for predicting remaining useful life according to claim 8, characterized in that, Robust SHAP contribution is determined based on the mean absolute SHAP contribution and SHAP attribution standard deviation corresponding to the input features. The mean absolute SHAP contribution is used as the base amount of feature contribution, and the SHAP attribution standard deviation is used as the attribution uncertainty. The constraint strength between the base amount of feature contribution and the attribution uncertainty is adjusted by an uncertainty penalty coefficient. The robust SHAP contribution is obtained by subtracting the penalty amount determined by the attribution uncertainty from the base amount of feature contribution. The importance ranking of the input features is determined based on the robust SHAP contribution corresponding to each input feature.

10. The Bayesian-aware SHAP interpretability analysis method for predicting remaining useful life according to claim 9, characterized in that, An evaluation of the interpretability stability of ordinary SHAP attribution results and robust SHAP attribution results was performed, where: The Spearman rank correlation coefficient is determined based on the difference in the ranking of each input feature in the two interpretation results to characterize the consistency of the overall feature ranking between different interpretation runs. The Kendall-Tau coefficient is determined based on the number of feature pairs with consistent relative order and the number of pairs with opposite relative order in the two interpretation results, in order to characterize the degree of consistency of the pairwise relative order of features between different interpretation runs; The attribution variance is determined based on the degree of dispersion between the attribution contribution of the same input feature in multiple interpretation runs and the average attribution contribution of the input feature, and the average attribution variance is determined based on the attribution variance corresponding to the Top-k input features. The reduction in attribution variance is determined by the proportion of the difference between the average attribution variance of ordinary SHAP and the average attribution variance of robust SHAP relative to the average attribution variance of ordinary SHAP. The explanatory stability of the robust SHAP attribution results is evaluated based on the Spearman rank correlation coefficient, Kendall Tau coefficient, average attribution variance, and the reduction in attribution variance.

Images