Life prediction method fusing multi-domain degradation characteristics and quantile regression

Abstract

The invention belongs to the field of equipment health state monitoring and fault prediction, and particularly discloses a life prediction method fusing multi-domain degradation characteristics and quantile regression. The method comprises the following steps: extracting time domain, frequency domain and time-frequency domain characteristics of a bearing full-life-cycle vibration signal through a signal collected by a sensor, and screening sensitive characteristics by using comprehensive indexes of monotonicity, correlation and robustness; fusing the sensitive features into multi-domain features by using a stack noise reduction auto-encoder, and constructing health indexes capable of representing a bearing degradation process; and further proposing that health indexes are input through a parallel BiGRU-Transformer model to predict the residual service life of the bearing, and finally quantizing the prediction uncertainty in combination with a quantile regression technology. Experiments on an XJTU-SY data set show that the provided method is obviously superior to a traditional method in point prediction (MAPE is reduced by 12.7%) and interval prediction (PICP is improved to 97%), and a reliable basis is provided for health management of industrial equipment.

Description

Technical Field

[0001] The present invention belongs to the field of equipment health status monitoring and fault prediction, and specifically relates to a life prediction method integrating multi-domain degradation characteristics and quantile regression. Background Art

[0002] In rotating machinery systems, bearings are core transmission components. Any operational anomaly can trigger a chain reaction, decisively impacting the overall safety and reliability of the equipment. These components are highly susceptible to sudden failure or progressive degradation under the combined stresses of variable load fluctuations, temperature gradients, and particulate contamination. Bearing failure not only results in direct economic losses from unplanned equipment downtime, but can also lead to secondary hazards such as resonant fracture of critical components or failure of the lubrication system due to vibration transmission, ultimately resulting in a major safety incident.

[0003] In the intelligent equipment ecosystem of Industry 4.0, smart bearings, integrating embedded sensor arrays with edge computing units, have become the nerve endings and decision-making nodes of rotating machinery systems. They are widely used, ensuring stable operation of wind turbines and reducing downtime losses in wind power generation; facilitating efficient vehicle operation and precise control in automotive manufacturing; and ensuring reliable equipment production in industrial automation production lines. However, smart bearings still face the risk of failure under complex operating conditions, and their health is crucial to the safe and stable operation of rotating machinery systems. As core transmission components, smart bearing failures can easily trigger cascading failures, resulting in not only economic losses from unplanned equipment downtime but also major safety incidents. Therefore, accurately predicting their remaining service life using signals collected by sensors is crucial.

[0004] The core goal of Remaining Useful Life (RUL) prediction is to quantify the remaining service time from the current moment to functional failure by monitoring the equipment's operating status data in real time. As the ultimate goal of a predictive maintenance system, the accuracy of this prediction directly determines the economic efficiency and safety margins of equipment maintenance strategies. With the development of intelligent mechanical systems, traditional bearing life prediction methods are no longer able to meet the real-time perception of equipment status required by Industry 4.0. Modern sensing equipment uses embedded vibration, temperature, and acoustic emission sensor networks, combined with machine learning algorithms, to achieve full-dimensional data collection and dynamic analysis of bearing operating status through the signals collected by sensors.

[0005] Application number CN119646983A discloses a "Bearing Remaining Service Life Estimation Model Design Method Based on Conv-LSTM and CBAM." The paper designs a Conv-LSTM-based network structure for processing time series data such as bearing vibration signals. The CBAM module is introduced to enhance the network's attention mechanism for features, automatically focusing on the signal components most critical for RUL estimation. Separately, application number CN114547795B discloses a "Data-Driven Rolling Bearing Remaining Service Life Prediction Method." This method first utilizes the powerful feature extraction capabilities of CNN to extract low-dimensional degradation features of rolling bearings, and then uses LSTM to further extract high-dimensional degradation features. Finally, a mapping relationship is established between bearing degradation feature information and remaining service life to achieve regression prediction.

[0006] A common problem with these solutions is that the health indicator construction method focuses solely on the degradation characteristics of a single domain of vibration signals, ignoring nonlinear mapping relationships in other areas. This results in inaccurate health indicators. Bearing RUL predictions are performed using only point predictions, without confidence intervals. This lacks support for actual maintenance decisions, resulting in a lack of quantification of prediction uncertainty and making it difficult to apply to large-scale industrially produced products. Summary of the Invention

[0007] The present invention proposes a life prediction method that integrates multi-domain degradation features and quantile regression to overcome the problems in the existing technology that the multiple features of the acquired signals, including time domain, frequency domain and time-frequency domain, are highly correlated, redundant, and even have information conflicts, while only providing point estimates of the prediction results and lacking quantitative analysis of the prediction confidence interval.

[0008] In order to achieve the purpose of the present invention, the technical solution provided by the present invention is: a life prediction method integrating multi-domain degradation characteristics and quantile regression, comprising the following steps:

[0009] Step 1: Extract the time domain, frequency domain and time-frequency domain degradation features of the vibration signal, and then calculate the correlation, monotonicity and robustness, and calculate the comprehensive index based on the comprehensive evaluation value of the features to screen the sensitive features;

[0010] Step 2: Connect multiple autoencoders (AEs) together to construct a stacked denoising autoencoder (SDAE). Use SDAE to fuse the sensitive features screened in step 1 to construct a health indicator that characterizes the bearing degradation process.

[0011] Step 3: Based on the health indicators constructed in step 2, use the parallel BiGRU-Transformer model based on the quantile regression method to predict the remaining service life of the bearing and provide the confidence interval of the prediction results.

[0012] Furthermore, in step three above, the health indicators are simultaneously input into the Transformer encoder and the BiGRU network for processing. The output tensors of these two are then concatenated into a single tensor along the depth dimension. Finally, this single tensor is input into the fully connected layer, and its output tensor is returned as the final prediction result of the model, that is, the predicted remaining service life of the bearing is obtained.

[0013] Furthermore, in step 3 above, the neural network quantile regression method is used to quantify uncertainty. Specifically, the expected sum of the Pinball loss function of each quantile is used as the loss function of the neural network for training, thereby obtaining the quantile of each quantile τ

[0014] The calculation formula of the loss function is:

[0015]

[0016] Where, ρ τ is the probability density function, Y and are the observed value and the predicted value respectively, X is the characteristic variable, and X=x means under the condition of a given characteristic value X.

[0017] Furthermore, in the above step 1, the correlation calculation formula is as shown in the following equation:

[0018]

[0019] Where Cor represents the Spearman correlation coefficient of the bearing degradation characteristics over time, k is the sampling point, and is the degenerate feature x k and the time series t k Order column.

[0020] Furthermore, in the above step 1, the monotonicity calculation formula is as shown in the following equation:

[0021]

[0022] Where Mon represents the monotonicity coefficient of the bearing degradation characteristic over time, No.ofd / dx>0 is the number of positive derivatives of the degradation characteristic sequence, No.ofd / dx<0 is the number of negative derivatives of the degradation characteristic sequence, and T is the length of the degradation characteristic sequence.

[0023] Furthermore, in the above step 1, the robustness calculation formula is as shown in the following equation:

[0024]

[0025] In the formula, Rob(f) is the robustness evaluation value, which is used to evaluate the stability or anti-interference ability of the function or model under different samples, f (i) is the reference characteristic value or benchmark value, f x(i) is the eigenvalue of the i-th sample.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] 1. This paper proposes a life prediction method that integrates multi-domain degradation features and quantile regression. It uses a stacked denoising autoencoder (SDAE) for feature fusion, extracts sensitive feature information, and constructs health indicators. The BiGRU-Transformer neural network is used to process the signals collected by the sensor to predict the bearing RUL, and the quantile regression method is used to quantify the uncertainty of the prediction results. This provides an effective solution to the difficulties in constructing health indicators and the lack of prediction uncertainty quantification in bearing remaining service life prediction, enhances the stability of the model in complex environments, and provides a more comprehensive reference basis for large-scale engineering applications.

[0028] 2. This paper uses SDAE to fuse the filtered sensitive features again, generating a one-dimensional signal as a bearing health indicator. This more accurately models the degradation trend of equipment health, demonstrating greater reliability and accuracy in health indicator construction.

[0029] 3. This paper designs a parallel BiGRU-Transformer network model to capture temporal features and global dependencies to predict the remaining useful life of bearings. Compared with traditional single-model predictions, this model demonstrates higher prediction accuracy in point-by-point prediction tasks and can better predict RUL.

[0030] 4. The present invention introduces quantile regression for interval prediction. This method can not only provide predicted values, but also give a credible range for the prediction. Compared with the traditional focus on the correlation between degradation trend and remaining life, the present invention increases the focus on uncertainty quantification and provides a method that can accurately reflect the full life cycle of the bearing, which can avoid or reduce the decision-making risks that may arise in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 This is an implementation block diagram of the present invention.

[0032] Figure 2 This is the SDAE network structure diagram.

[0033] Figure 3 It is the BiGRU-Transformer structure.

[0034] Figure 4This is a comparison chart of point prediction results of different prediction methods under one working condition.

[0035] Figure 5 This is the interval prediction result graph after adding quantile regression loss to the BiGRU-Transformer structure. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0037] See also Figure 1 The object of this embodiment is bearings: first, the time domain, frequency domain and time-frequency domain features of the bearing vibration signal are extracted through the signals collected by the sensor, and the sensitive features are screened out using the comprehensive indicators of monotonicity, correlation and robustness; second, the sensitive features are fused using a stacked denoising autoencoder to construct a health indicator that can characterize the bearing degradation process; finally, a parallel BiGRU-Transformer model is proposed to capture the time series features and global dependencies to predict the remaining service life of the bearing; and the quantile regression technology is combined to quantify the uncertainty of the prediction.

[0038] Based on the above ideas, the present invention provides a life prediction method that integrates multi-domain degradation characteristics and quantile regression, which specifically includes the following steps:

[0039] Step 1: Extract the time domain, frequency domain and time-frequency domain degradation features of the vibration signal, and then calculate the correlation, monotonicity and robustness, and calculate the comprehensive index based on the comprehensive evaluation value of the features to screen the sensitive features.

[0040] In this example, the XJTU-SY dataset contains rolling bearing failure types, including full lifecycle data for 15 rolling bearings under three operating conditions and various failure types. This step primarily involves collecting signals from sensors, capturing characteristic parameters in the time, frequency, and time-frequency domains of the bearing vibration acceleration signals, and then combining these multiple domains to generate attribute features that can characterize various types of bearings. The specific steps are as follows:

[0041] (1) Extract the time domain, frequency domain and time-frequency domain characteristic parameters of the vibration signal:

[0042] 1.1: Time domain indicator extraction

[0043] Table 1.1 Time domain indicators

[0044]

[0045] 1.2: Frequency domain index extraction

[0046] Table 1.2 Frequency domain indicators

[0047]

[0048] 1.3: Time-frequency domain indicator extraction

[0049] The wavelet packet decomposition method is used to extract time-frequency domain features. The basic process of wavelet packet decomposition can be expressed by the following formula:

[0050]

[0051] Where: W j,n (t) represents the signal of the nth node in the jth layer; W j+1,2n (t) represents the signal of the 2nth node in the j+1th layer after being processed by the low-pass filter; W j+1,2n+1 (t) represents the signal of the 2n+1th node in the j+1th layer after processing by the high-pass filter; h(t-2k) and g(t-2k) represent the responses of the low-pass filter and high-pass filter of the orthogonal filter bank at time t-2k, respectively; k is the sampling point; and t is the time point.

[0052] (2) Calculate the correlation, monotonicity, and robustness, and select sensitive features through comprehensive index calculation:

[0053] When constructing health indicators using bearing characteristic parameters, good degradation characteristics should change over time, be monotonically irreversible, and be resistant to external abnormal shocks. The main steps are as follows:

[0054] 2.1: Calculation of correlation, monotonicity and robustness:

[0055] Correlation calculation:

[0056] The Spearman correlation coefficient is used to evaluate the nonlinear correlation of degradation characteristics over time. The correlation calculation formula is shown in the following equation:

[0057]

[0058] Where Cor represents the Spearman correlation coefficient of the bearing degradation characteristics over time, k is the sampling point, and is the degenerate feature x k and the time series t k Order column.

[0059] Monotonicity calculation:

[0060] The sensitive original characteristics of rolling bearings during machine degradation should have a good monotonic degradation trend. The monotonicity calculation formula is shown in the following equation:

[0061]

[0062] Where Mon represents the monotonicity coefficient of the bearing degradation characteristic over time, No.ofd / dx>0 is the number of positive derivatives of the degradation characteristic sequence, No.ofd / dx<0 is the number of negative derivatives of the degradation characteristic sequence, and T is the length of the degradation characteristic sequence.

[0063] Robustness calculation:

[0064] In the process of feature screening and HI construction, the present invention takes robustness as one of the design principles to reflect whether it has a strong ability to reflect the degradation process. The robustness calculation formula is shown in the following equation:

[0065]

[0066] In the formula, Rob(f) is the robustness evaluation value, which is used to evaluate the stability or anti-interference ability of the function or model under different samples, f (i) is the reference characteristic value or benchmark value, f x(i) is the eigenvalue of the i-th sample.

[0067] 2.2: Calculate the comprehensive evaluation value of features and screen out sensitive features:

[0068] Correlation, monotonicity, and robustness are all important metrics for evaluating the quality of bearing performance degradation characteristics. The present invention uses the linear combination of these three evaluation criteria as the feature comprehensive evaluation value to screen features. The feature comprehensive evaluation value calculation formula is shown in the following equation:

[0069] Ce=Mon+Cor+Rob(f)(5)

[0070] Where Ce is the comprehensive evaluation value of the feature, Mon is the monotonicity evaluation value, Cor is the correlation evaluation value, and Rob(f) is the robustness evaluation value.

[0071] Step 2: See Figure 2 , multiple autoencoders (AEs) are connected together to construct a stacked denoising autoencoder (SDAE). SDAE is further used to fuse sensitive features to construct a health indicator that characterizes the bearing degradation process:

[0072] SDAE constructs a deep neural network structure by connecting multiple autoencoders together. The hidden layer of each autoencoder serves as the input layer of the next autoencoder, and the layers are stacked one on top of the other. This stacking method allows each autoencoder to learn a higher-level representation of data features. The specific steps are as follows:

[0073] (1) Building a stacked denoising autoencoder:

[0074] 1.1: Training the Autoencoder

[0075] First, the input layer data of AE will reach the hidden layer after linear transformation and activation function. The formula of this encoding process is shown in the following equation:

[0076] h=σ1(W1x+b1) (6)

[0077] Where x is the input layer data, h is the hidden layer representation of the input data, W1 and b1 represent the weight and bias of the encoder respectively, and σ1 is the activation function of the encoder.

[0078] Secondly, the hidden layer data will reach the output layer after linear transformation and activation function reconstruction. The formula for this decoding process is shown in the following equation:

[0079] x'=σ2(W2h+b2)(7)

[0080] Where x′ is the reconstructed output layer data, W2 and b2 represent the weight and bias of the decoder respectively, and σ2 is the activation function of the decoder.

[0081] 1.2: Training the Denoising Autoencoder

[0082] 1.3: Training a stacked denoising autoencoder

[0083] (2) Using SDAE to fuse sensitive features and construct health indicators that characterize the bearing degradation process:

[0084] The trained SDAE fuses the sensitive features given in step 1 to construct a health index. Tests show that the comprehensive evaluation feature index constructed by this embodiment is higher than that constructed by other feature fusion methods under all data of the three working conditions, showing higher reliability and accuracy in the health index construction task. As shown in the following table:

[0085] Table 2.1 Comprehensive rating indicators of different feature fusion methods

[0086]

[0087] Further analysis of the quantitative results in Table 2.1 shows that the Ce of the SDAE method is the highest on all datasets.

[0088] Step 3: Input the health indicators obtained in step 2 into the parallel BiGRU-Transformer model to predict the remaining service life of the bearing. The uncertainty of the prediction results is analyzed and quantified based on quantile regression. The neural network is trained to perform uncertainty prediction:

[0089] In order to more accurately predict the bearing degradation trend, the present invention proposes a parallel BiGRU-Transformer model, see Figure 3. Specifically, the input sequence is first sent to the two parallel modules of BiGRU and Transformer at the same time. BiGRU can capture the local temporal features of the sequence through the bidirectional processing of forward and reverse GRU. Its output is merged through the splicing layer and passed to the fully connected layer to form a refined representation of the local context. At the same time, the Transformer encoder gives temporal information to the input sequence through the position encoding layer, and uses the multi-head self-attention mechanism to model the global dependency. Its linearly transformed output also has the ability to comprehensively represent global information. The outputs of the two modules are finally cascaded in the feature fusion layer, and the final prediction or classification task is completed through the fully connected layer. The specific steps are as follows:

[0090] This step simultaneously inputs the health indicators into the Transformer encoder and BiGRU network for processing, then concatenates the output tensors of the two into a single tensor along the depth dimension. Finally, this single tensor is input into the fully connected layer, and its output tensor is returned as the final prediction result of the model, that is, the predicted remaining bearing service life.

[0091] The health indicator is input into the BiGRU network. The output of BiGRU is affected by both the forward state and the backward state. Compared with the unidirectional GRU, which propagates from forward to backward, it can better reflect the impact of past and future moments on the current state, enabling the model to better mine the information of time series and process the hidden relationships in time series, thereby further improving the prediction accuracy. Figure 5 , in the figure: x t-1 、x t 、x t+1 Respectively represent the input at time t-1, time t, and time t+1; y t-1 、y t 、y t+1 Represent the output at time t-1, time t, and time t+1 respectively.

[0092] The health indicators are input into the Transformer encoder. The attention mechanism in the Transformer achieves better sequence modeling capabilities by weighting different positions in the sequence. It allows the model to focus on certain important information of the input features, and can also integrate the information contained in the input sequence and pay attention to information from different performance subspaces at different positions.

[0093] Three comparative experiments were conducted using the GRU, Transformer, and BiGRU-Transformer models across all datasets for the three working conditions. In the deterministic prediction task, the BiGRU-Transformer model demonstrated significant superiority in both MAPE and RMS metrics. Compared to the GRU and Transformer models, the BiGRU-Transformer model achieved significantly lower prediction errors, as shown in the table below.

[0094] Table 3.1 Comparison of deterministic prediction results

[0095]

[0096]

[0097] As shown in Table 3.1, in the deterministic prediction task, the BiGRU-Transformer model showed significant superiority over the GRU and Transformer models in terms of both MAPE and RMS indicators.

[0098] like Figure 4 As can be seen, for Bearing1_2, the actual failure point occurs at 153 minutes, corresponding to an actual remaining useful life of 30 minutes. In the point prediction results, the GRU model predicts a RUL value of 11 minutes, the Transformer model predicts a value of 17 minutes, and the BiGRU-Transformer model predicts a value of 26 minutes. In terms of accuracy, the BiGRU-Transformer model's prediction results are closest to the true value, and its health indicator curve also better fits the actual change trend near the failure point, demonstrating the model's strong performance in point prediction tasks.

[0099] In an unknown environment, cognitive uncertainty increases, and uncertainty needs to be quantified to improve RUL prediction confidence, model generalization ability, and maintenance decision reliability. This paper uses a neural network quantile regression method to quantify uncertainty. The specific steps are as follows:

[0100] 3.2: Neural Network Quantile Regression Method

[0101] The neural network quantile regression method specifically uses the expected sum of the Pinball loss function of each quantile as the loss function of the neural network for training, thereby obtaining the quantile of each quantile τ The specific loss function calculation formula is:

[0102]

[0103] Where, ρ τis the probability density function, Y and are the observed value and the predicted value respectively, X is the characteristic variable, and X=x means under the condition of a given characteristic value X.

[0104] To verify the GRU-Transformer's superiority in interval prediction, we conducted an uncertainty prediction experiment using the same setup as the deterministic prediction experiment. The remaining useful life of equipment often involves uncertainty, and relying solely on point predictions may not fully reflect the reliability of the prediction. Therefore, interval prediction further improves the practicality and robustness of the prediction. The following table compares the uncertainty prediction results of the three models:

[0105] Table 3.6 Comparison of uncertainty prediction results

[0106]

[0107] As shown in Table 3.6, the BiGRU-Transformer model not only has higher prediction accuracy than the GRU and Transformer models, but also can significantly reduce the uncertainty of the prediction.

[0108] like Figure 5 It can be seen that, taking Bearing1_2 as an example, the interval prediction results after adding quantile regression loss to the parallel BiGRU-Transformer show that the addition of the quantile loss function provides a 95% confidence interval for the prediction results without affecting the prediction accuracy.

[0109] The above description is an explanation of the specific implementation of the present invention, rather than a limitation of the present invention. Those skilled in the relevant technical field can also make various equivalent technical solutions without departing from the scope of the present invention, so all equivalent technical solutions should be included in the scope of protection of the present invention.

Claims

1. A lifespan prediction method integrating multi-domain degradation features and quantile regression, characterized by: The steps include: Step 1: Extract the time domain, frequency domain and time-frequency domain degradation features of the vibration signal, and then calculate the correlation, monotonicity and robustness, and calculate the comprehensive index based on the comprehensive evaluation value of the features to screen the sensitive features; Step 2: Connect multiple autoencoders (AEs) together to construct a stacked denoising autoencoder (SDAE). Use SDAE to fuse the sensitive features screened in step 1 to construct a health indicator that characterizes the bearing degradation process. Step 3: Based on the health indicators constructed in step 2, use the parallel BiGRU-Transformer model based on the quantile regression method to predict the remaining service life of the bearing and provide the confidence interval of the prediction results.

2. The lifespan prediction method integrating multi-domain degradation features and quantile regression according to claim 1 is characterized by: In step three, the health indicators are simultaneously input into the Transformer encoder and BiGRU network for processing, and then the output tensors of the two are spliced ​​into a single tensor along the depth dimension. Finally, this single tensor is input into the fully connected layer, and its output tensor is returned as the final prediction result of the model, that is, the predicted remaining service life of the bearing is obtained.

3. The lifespan prediction method integrating multi-domain degradation features and quantile regression according to claim 2 is characterized by: In step 3, the neural network quantile regression method is used to quantify uncertainty. Specifically, the expected sum of the Pinball loss function of each quantile is used as the loss function of the neural network for training, so as to obtain the quantile of each quantile τ. The calculation formula of the loss function is: Where, ρ τ is the probability density function, Y and are the observed value and the predicted value respectively, X is the characteristic variable, and X=x means under the condition of a given characteristic value X.

4. The lifespan prediction method integrating multi-domain degradation features and quantile regression according to claim 3 is characterized by: In step 1, the correlation calculation formula is as shown in the following equation: Where Cor represents the Spearman correlation coefficient of the bearing degradation characteristics over time, k is the sampling point, and is the degenerate feature x k and the time series t k Order column.

5. The lifespan prediction method integrating multi-domain degradation features and quantile regression according to claim 4 is characterized by: In step 1, the monotonicity calculation formula is as shown in the following equation: Where Mon represents the monotonicity coefficient of the bearing degradation characteristic over time, No.ofd / dx>0 is the number of positive derivatives of the degradation characteristic sequence, No.ofd / dx<0 is the number of negative derivatives of the degradation characteristic sequence, and T is the length of the degradation characteristic sequence.

6. The lifespan prediction method integrating multi-domain degradation features and quantile regression according to claim 5 is characterized by: In step 1, the robustness calculation formula is as shown in the following equation: In the formula, Rob(f) is the robustness evaluation value, which is used to evaluate the stability or anti-interference ability of the function or model under different samples, f (i) is the reference characteristic value or benchmark value, f x(i) is the eigenvalue of the i-th sample.

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