A Method and System for Predicting the RUL of Aero-engines Based on Hybrid Attention Fusion and Uncertainty Perception Loss

Abstract

This application provides a method and system for predicting the Relative Limitation (RUL) of aero-engines based on hybrid attention fusion and uncertainty-aware loss, belonging to the field of aero-engine technology. The method includes acquiring time-series data from aero-engine sensor equipment and inputting it into a feature extraction network to obtain initial deep features; inputting these features into a hybrid attention fusion module to compute temporal attention and channel attention in parallel, and then bilinearly fusing them to obtain enhanced features; inputting the enhanced features into a regression prediction head and a variance prediction head respectively, outputting the RUL prediction mean and prediction variance; based on the output results and the actual RUL, calculating the uncertainty-aware loss function, optimizing the parameters of the entire prediction model, inputting the time-series data of the equipment to be predicted into the optimized prediction model, obtaining the RUL prediction mean and variance of the equipment to be predicted, and outputting the final RUL prediction result and its uncertainty assessment result. This application improves the accuracy, reliability, and robustness of RUL prediction.

Description

Technical Field

[0001] This application relates to the field of aero-engine technology, and in particular to an aero-engine RUL prediction method and system based on hybrid attention fusion and uncertainty perception loss. Background Technology

[0002] In safety-critical aero-engine PHM (Prognostics and Health Management), RUL (Remaining Useful Life) prediction not only requires a small average error but also needs to maintain stable output under noise, domain drift, and sensor failures, and provide an auditable confidence interval. Traditional methods often treat robustness as an additional term in preprocessing or loss functions, lacking a closed-loop design of "attention selection—robust training—uncertainty calibration." Under strong disturbances or structured attacks, the prediction curve may exhibit severe fluctuations or critical threshold crossings, directly impacting maintenance decisions. Existing technical solutions have the following shortcomings:

[0003] The feature focusing mechanism is imperfect: Traditional methods often use a single time attention or channel attention, which makes it difficult to synchronously and accurately identify the "critical degradation time period" and "critical degradation associated sensor channel" in multi-sensor time series data. In the stage of noise interference or drastic changes in operating conditions, misfocusing is prone to occur, resulting in the noise being amplified after feature fusion.

[0004] The loss function design is insensitive to uncertainty: the mean squared error or mean absolute error is commonly used as the main loss. Although robust terms such as Huber loss can be introduced, their thresholds are fixed and cannot adapt to different noise levels of different samples. More importantly, most methods do not explicitly learn the uncertainty (variance) of the prediction, and cannot provide confidence intervals that match the residuals, which may lead to overconfidence in the model under noise and a deterioration of the prediction calibration error.

[0005] Lack of stability metrics for engineering decision-making: Traditional evaluation metrics such as root mean square error mainly reflect average accuracy and lack direct measurement of whether the prediction curve fluctuates drastically under disturbances or whether critical decision thresholds are falsely triggered, which is crucial in actual maintenance decisions.

[0006] Therefore, there is an urgent need for a RUL prediction scheme that can jointly optimize prediction accuracy, stability, and uncertainty calibration capabilities. Summary of the Invention

[0007] In view of this, embodiments of this application provide a method and system for predicting the RUL of aero-engines based on hybrid attention fusion and uncertainty perception loss, which at least partially solves the problem that "critical time periods - critical channels" are difficult to be accurately identified simultaneously in multi-sensor degradation data in the prior art.

[0008] In a first aspect, embodiments of this application provide a method for predicting the RUL (Range Limit Indicator) of aero-engines based on hybrid attention fusion and uncertainty perception loss, including:

[0009] The historical operating time-series data of aero-engine sensor equipment from operation to failure is obtained as a training set, and the time-series data is input into a feature extraction network to obtain initial deep features.

[0010] The initial deep features are input into the hybrid attention fusion module, which computes temporal attention and channel attention in parallel, and performs bilinear fusion on the output features of temporal attention and channel attention to obtain enhanced features.

[0011] The enhanced features are input into a regression prediction head consisting of a fully connected layer, and the output is the RUL predicted mean. The enhanced features are input into another independent variance prediction head, and the output is the RUL predicted variance.

[0012] Based on the predicted mean, predicted variance and true RUL, the uncertainty-perceived loss function is calculated, and the parameters of the entire prediction model are optimized through the backpropagation algorithm to obtain the optimized prediction model.

[0013] The time series data of the device to be predicted is input into the optimized prediction model to obtain the mean and variance of the RUL prediction for the device to be predicted.

[0014] Based on the predicted mean and variance of the device to be predicted, a confidence interval at a specified confidence level is constructed, and the final RUL prediction result and its uncertainty assessment result are output.

[0015] According to a specific implementation of an embodiment of this application, the parallel computation of time attention and channel attention includes:

[0016] Calculate temporal attention: Project the initial depth features onto the QKV space, calculate the correlation matrix between all time steps, obtain the temporal attention weights based on the correlation matrix and perform energy normalization, and obtain the temporal attention output features based on the energy-normalized temporal attention weights.

[0017] Calculate channel attention: Perform global average pooling along the sensor channel dimension, then generate channel weights through a feedforward network with a non-linear activation function, and obtain the channel attention output features.

[0018] According to a specific implementation of an embodiment of this application, the formula for calculating temporal attention is:

[0019] ,

[0020] Among them, A t The attention weights for each time step to all other time steps, softmax is the normalization function, and Q is the expression for attention weights at each time step. t For querying the matrix, Let d be the transpose of the key matrix. k Let be the projection dimension of the key matrix. For features after time attention, V t It is a value matrix;

[0021] The formula for calculating the channel weight is:

[0022] ,

[0023] in, σ is the channel weight, δ is the Sigmoid activation function, δ is the ReLU activation function, W1 is the weight matrix of the first fully connected layer, W2 is the weight matrix of the second fully connected layer, and Pool(H) is the global average pooling along the sensor channel dimension.

[0024] According to a specific implementation of an embodiment of this application, the expression for the bilinear fusion is:

[0025] ,

[0026] Where ⊙ represents element-wise multiplication. As the first learnable scalar coefficient, F is the second learnable scalar coefficient. out Enhanced features for the output.

[0027] According to a specific implementation of an embodiment of this application, the calculation of the uncertainty-aware loss function includes:

[0028] We introduce noise-invariant Huber loss and sample variance learning loss on top of the basic regression error to calculate the uncertainty-aware loss function.

[0029] According to a specific implementation of an embodiment of this application, the expression for the noise-invariant Huber loss is:

[0030] ,

[0031] ,

[0032] Among them, L HuberFor noise-invariant Huber loss, y i Let i be the true remaining useful life of the i-th sample. To predict the mean remaining useful life of the i-th sample using the prediction model, As an adaptive threshold, α is the basic Huber loss threshold. This is a scaling function for input uncertainty based on the prediction variance.

[0033] According to a specific implementation of an embodiment of this application, the calculation of the uncertainty-perceived loss function further includes:

[0034] In the uncertainty-aware loss function, domain adversarial regularization is introduced to force the encoder to produce domain-invariant features, and a time smoothing term is added to constrain the local fluctuations of RUL;

[0035] The expression for the domain adversarial regularity is:

[0036] ,

[0037] Where min is the minimum value, max is the maximum value, G is the feature encoder, D is the domain discriminator, and D(F) is the discriminative output of the domain discriminator on the training domain features F. ’ ) is the domain discriminator's assessment of the test domain features F ’ The discriminant output, This indicates that the distribution P from the training data... train Find the expected value of the sample x. This indicates that the distribution P from the test data... text samples Find the expected value.

[0038] According to a specific implementation of an embodiment of this application, the method further includes:

[0039] Define a set of perturbation sequences with increasing intensity. For a test sample, apply perturbations of different intensities in the perturbation intensity sequence in sequence, and record the RUL prediction value of the optimized prediction model under each perturbation intensity.

[0040] Within this test sample, when the absolute value of the difference between the RUL predicted values ​​under adjacent intensities is greater than a preset threshold, it is recorded as a flip.

[0041] Count the total number of flips for all test samples, and calculate the flip probability based on the total number of flips;

[0042] Risk warning and safety margin setting for aircraft engine maintenance decisions based on rollover probability.

[0043] According to a specific implementation of an embodiment of this application, the step of calculating the uncertainty-aware loss function and optimizing the parameters of the entire prediction model through a backpropagation algorithm includes:

[0044] For each sample in the current training set, an adversarial attack parameter set is independently and randomly selected, which includes an upper limit for the perturbation strength and the number of iterations for projected gradient descent;

[0045] With the goal of maximizing the current loss of the prediction model, the PGD method is used to generate adversarial perturbations for each sample based on the adversarial attack parameters, thus forming adversarial examples;

[0046] The adversarial examples are input into the prediction model to generate the mean and variance of the RUL prediction under adversarial conditions;

[0047] Based on the uncertainty-perceived loss function and the mean and variance of RUL prediction in the adversarial case, the uncertainty-perceived loss of adversarial examples is calculated.

[0048] Based on the original uncertainty perception loss, the adversarial example uncertainty perception loss, and the hard sample consistency regularization loss, the total loss of the fusion adversarial training is calculated.

[0049] Calculate the gradient of the total loss of the fusion adversarial training with respect to all trainable parameters of the prediction model, and update the prediction model parameters through the optimizer.

[0050] Secondly, embodiments of this application also provide an aero-engine RUL prediction system based on hybrid attention fusion and uncertainty perception loss, used to implement the aero-engine RUL prediction method based on hybrid attention fusion and uncertainty perception loss as described in any embodiment of the first aspect, the system comprising:

[0051] The data acquisition module is used to acquire historical time-series data from the operation to failure of aero-engine sensor equipment as a training set, and input the time-series data into the feature extraction network to obtain initial deep features.

[0052] The fusion module is used to input the initial deep features into the hybrid attention fusion module, compute temporal attention and channel attention in parallel, and perform bilinear fusion on the output features of temporal attention and channel attention to obtain enhanced features;

[0053] The prediction module is used to input the enhanced features into a regression prediction head consisting of a fully connected layer and output the RUL prediction mean, and input the enhanced features into another independent variance prediction head and output the RUL prediction variance.

[0054] The optimization module is used to calculate the uncertainty-aware loss function based on the predicted mean, predicted variance and the true RUL, and optimize the parameters of the entire prediction model through the backpropagation algorithm to obtain the optimized prediction model.

[0055] The calculation module is used to input the time series data of the device to be predicted into the optimized prediction model to obtain the mean and variance of the RUL prediction for the device to be predicted.

[0056] The results output module is used to construct a confidence interval at a specified confidence level based on the prediction mean and variance of the device to be predicted, and output the final RUL prediction result and its uncertainty assessment result.

[0057] Beneficial effects:

[0058] The RUL prediction method and system for aero-engines based on hybrid attention fusion and uncertainty-aware loss in this application embodiment, through the parallel processing of key features in time and channel dimensions by the hybrid attention fusion module, can accurately locate "critical degradation time periods" and "critical degradation-related sensor channels" in multi-sensor time-series data, avoiding the misfocusing problem of single attention mechanisms under noise interference or changes in operating conditions. The bilinear fusion method dynamically balances the contribution weights of time and channel features through learnable scalar coefficients, making the enhanced features more closely match the physical characteristics of the aero-engine degradation process. The independent mean and variance prediction head design realizes the probabilistic modeling of RUL prediction results. Combined with the uncertainty-aware loss function, it not only optimizes the prediction accuracy, but also adapts to the noise level of different samples, generating confidence intervals that match the residuals, effectively solving the defects of overconfidence or large calibration errors in traditional methods. This method provides a scientific and reliable quantitative basis for aero-engine maintenance decisions, helping to optimize maintenance resource allocation and reduce operating costs while ensuring flight safety. Attached Figure Description

[0059] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0060] Figure 1 This is a flowchart of an aero-engine RUL prediction method based on hybrid attention fusion and uncertainty perception loss according to an embodiment of the present invention.

[0061] Figure 2 This is a schematic diagram of the spatiotemporal channel attention variation distribution according to an embodiment of the present invention;

[0062] Figure 3This is a schematic diagram illustrating Gaussian robustness according to an embodiment of the present invention. Detailed Implementation

[0063] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0064] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0065] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0066] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0067] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0068] The relevant abbreviations and key terms used in this application are defined as follows:

[0069] HAF (Hybrid Attention Fusion): Hybrid attention fusion couples temporal attention with channel attention and performs bilinear fusion.

[0070] UALO (Uncertainty-Aware Loss Optimization): Uncertainty-aware loss optimization, which combines error term, robust term and variance learning.

[0071] ECE (Expected Calibration Error) / CRPS (Continuous Ranked Probability Score): Uncertainty calibration metrics that measure expected calibration error and continuous rank probability score, respectively.

[0072] NASA Score: A commonly used asymmetric cost metric in the field of PHM (Prognostics and Health Management), which imposes different penalties for early / late predictions.

[0073] Domain Adversarial: This type of regularization promotes feature domain invariance through a discriminator.

[0074] PGD ​​(Projected Gradient Descent) / GAP (Generative Adversarial Perturbations): Common structured / generative adversarial perturbation methods used for worst-case robustness verification.

[0075] FP_RUL(τ): RUL flip probability, which measures the proportion of prediction differences exceeding a preset threshold τ under adjacent perturbation intensities.

[0076] SNN (Spiking Neural Network): A neural network that transmits information using discrete impulse events.

[0077] ANN (Artificial Neural Network-only): Artificial Neural Network.

[0078] This application proposes a closed-loop robust optimization framework of HAF+UALO: first, temporal attention and channel attention are computed in parallel on the feature layer (which can be real-valued or impulse embedding), and then fused through bilinear gating; for the training objective, NASAScore / MAE, noise-invariant Huber, sample variance learning, and (optional) domain adversarial regularization are combined, and hierarchical noise injection and adversarial training can be added. See below for reference. Figures 1 to 3 Please provide a detailed explanation.

[0079] Firstly, referring to Figure 1 This application provides a method for predicting the RUL (Range Limiting) of aero-engines based on hybrid attention fusion and uncertainty perception loss, including:

[0080] Step 1: Obtain historical time-series data of the aero-engine sensor equipment from operation to failure as a training set, and input the time-series data into the feature extraction network to obtain initial deep features;

[0081] Step 2: Input the initial deep features into the hybrid attention fusion module, compute temporal attention and channel attention in parallel, and perform bilinear fusion on the output features of temporal attention and channel attention to obtain enhanced features;

[0082] Step 3: Input the enhanced features into a regression prediction head composed of a fully connected layer, and output the RUL prediction mean. Input the enhanced features into another independent variance prediction head, and output the RUL prediction variance.

[0083] Step 4: Based on the predicted mean, predicted variance, and true RUL, calculate the uncertainty-aware loss function, and optimize the parameters of the entire prediction model through the backpropagation algorithm to obtain the optimized prediction model.

[0084] Step 5: Input the time series data of the device to be predicted into the optimized prediction model to obtain the mean and variance of the RUL prediction for the device to be predicted;

[0085] Step 6: Based on the predicted mean and variance of the device to be predicted, construct the confidence interval at the specified confidence level, and output the final RUL prediction result and its uncertainty assessment result.

[0086] In this embodiment, by using a hybrid attention fusion module to compute temporal attention and channel attention in parallel and performing bilinear fusion on the output features of both, the dynamic change features of key time steps in aero-engine time series data and the correlation features between different sensor channels can be fully captured, effectively improving the expressive power of the features. An independent variance prediction head is introduced to output the RUL prediction variance, and combined with the uncertainty-aware loss function to optimize the model, so that the prediction results not only include the mean estimate of RUL, but also provide the corresponding uncertainty assessment, providing a more comprehensive and reliable basis for aero-engine health management and maintenance decisions, and helping to improve the credibility and engineering practicality of the prediction results.

[0087] In specific implementation, the time-series data acquired in step 1 covers various sensor monitoring information of the aero-engine under different operating conditions, such as key parameters like temperature, pressure, and speed. This data can comprehensively reflect the entire process of the engine from normal operation to performance degradation and eventual failure. The feature extraction network can adopt a structure combining multi-layer convolutional neural networks and recurrent neural networks. It captures local feature patterns through convolution operations and mines temporal dependencies using recurrent units, thereby effectively extracting the initial deep features contained in the original data. The hybrid attention fusion module in step 2 uses a time attention mechanism to calculate the importance weights of features at different time steps, highlighting key time stage information that contributes significantly to RUL prediction; the channel attention mechanism assigns weights to features of different sensor channels, strengthening the feature expression of important sensor channels. The bilinear fusion process achieves nonlinear interaction between the two attention features through matrix multiplication, further improving the feature discrimination ability. Step 3 sets up independent mean prediction heads and variance prediction heads, which can simultaneously output the point prediction results and uncertainty quantification information of RUL. The variance prediction head uses a special activation function to ensure that the output variance is non-negative. The uncertainty-perceived loss function in step 4 comprehensively considers the deviation between the predicted mean and the true value, as well as the magnitude of the prediction variance. By dynamically balancing the mean squared error term and the variance regularization term, it guides the model to reasonably estimate its own prediction uncertainty while improving prediction accuracy. In step 5, when predicting the equipment to be predicted, the input time-series data undergoes the same preprocessing operations as in the training phase, including data cleaning, standardization, and sequence length alignment, ensuring the consistency of the model's input format. In step 6, when constructing the confidence interval, based on the predicted mean and variance, and combined with the normal distribution assumption or the Student's t-distribution assumption, the range of RUL values ​​at a specified confidence level (e.g., 95%) is calculated. This confidence interval can intuitively reflect the reliability of the prediction results, providing a more comprehensive basis for condition-based maintenance decisions for aero-engines.

[0088] In one embodiment, the parallel computation of temporal attention and channel attention includes:

[0089] Calculate temporal attention: Project the initial depth features onto the QKV space, calculate the correlation matrix between all time steps, obtain the temporal attention weights based on the correlation matrix and perform energy normalization, and obtain the temporal attention output features based on the energy-normalized temporal attention weights.

[0090] Calculate channel attention: Perform global average pooling along the sensor channel dimension, then generate channel weights through a feedforward network with a non-linear activation function, and obtain the channel attention output features.

[0091] Furthermore, the formula for calculating the time attention is as follows:

[0092] ,

[0093] Among them, A t The attention weights for each time step to all other time steps, softmax is the normalization function, and Q is the expression for attention weights at each time step. t For querying the matrix, Let d be the transpose of the key matrix. k Let be the projection dimension of the key matrix. For features after time attention, V t It is a value matrix;

[0094] The formula for calculating the channel weight is:

[0095] ,

[0096] in, For channel weights, δ is the Sigmoid activation function, W1 is the weight matrix of the first fully connected layer, W2 is the weight matrix of the second fully connected layer, and Pool(H) is the global average pooling along the sensor channel dimension.

[0097] Furthermore, the expression for the bilinear fusion is:

[0098] ,

[0099] Where ⊙ represents element-wise multiplication. As the first learnable scalar coefficient, F is the second learnable scalar coefficient. out Enhanced features for the output.

[0100] This embodiment demonstrates HAF's late-stage fusion of bi-branch features. When there are two features upstream (e.g., a quantized real-value branch and an impulse branch), temporal attention and channel attention can be calculated separately before fusion, and then the output is fused using bilinear gating. The computational cost of this structure mainly comes from lightweight QKV projection and GAP gating, making it suitable for edge deployment.

[0101] In practical implementation, bilinear fusion can also be the element-wise product of temporal attention output and channel attention output, followed by a weighted sum of learnable coefficients, as shown in the following expression:

[0102] F out =η (A t ⊙ w c ⊙ X) + (1-η) X;

[0103] Alternatively, temporal attention and channel attention can be applied to the features separately and then fused, as shown in the following expression:

[0104] F out = γ (A t X) ⊙ (w c X) + (1-γ) X;

[0105] in, This represents matrix multiplication (or attention weighting); X is the input feature; γ is the first fusion coefficient, which can be learned or fixed; η is the second fusion coefficient.

[0106] In this embodiment, during the calculation of temporal attention, the temporal embedding is projected into the QKV (Query-Key-Value) space, and the correlation matrix between time steps is calculated to highlight the degradation inflection point interval. Energy normalization is applied to the attention weights to avoid abnormal spikes in noisy segments. During the calculation of channel attention, global average pooling is performed on the sensor dimension, followed by ReLU and sigmoid gating to generate channel weights. These weights emphasize sensors strongly correlated with degradation (such as the critical temperature / pressure ratio) and suppress weakly correlated or noise-dominated channels. The temporal and channel attention output features obtained through parallel computation are then coupled using bilinear / element-wise multiplication, and combined with learnable coefficients to obtain a hybrid attention feature that integrates important information from both the temporal and channel dimensions. This fusion method achieves the joint selection of "focusing on key channels during critical time periods" without introducing high computational overhead. This fusion approach can simultaneously focus on the dependencies between different time steps and the key features of different sensor channels, effectively improving the richness and specificity of feature representation and providing more discriminative deep feature support for subsequent RUL prediction of aero-engines.

[0107] In one embodiment, calculating the uncertainty-aware loss function includes:

[0108] We introduce noise-invariant Huber loss and sample variance learning loss on top of the basic regression error to calculate the uncertainty-aware loss function.

[0109] Furthermore, the expression for the noise-invariant Huber loss is:

[0110] ,

[0111] ,

[0112] Among them, L HuberFor noise-invariant Huber loss, y i Let i be the true remaining useful life of the i-th sample. To predict the mean remaining useful life of the i-th sample using the prediction model, As an adaptive threshold, α is the basic Huber loss threshold. This is a scaling function for input uncertainty based on the prediction variance.

[0113] In this embodiment, in addition to outputting the mean of the RUL prediction, the network also outputs the variance (or log-variance), which is used to dynamically adjust the residual penalty in the loss and provide a confidence interval during inference. This mechanism can suppress the dominant effect of outlier noise samples on parameter updates, thereby improving calibration and stability.

[0114] Traditional Huber loss has a fixed transition point δ. This embodiment, however, links the noise-invariant Huber loss to the uncertainty of model estimation through its expression. When the model's prediction uncertainty for a sample is high, the transition point δ is automatically relaxed, making the loss function more tolerant of large errors for that sample (closer to MAE behavior). This effectively suppresses the excessive influence of noise or outlier samples on model parameter updates, improving the stability of the training process and the robustness of the model.

[0115] Therefore, the noise-invariant Huber loss in this embodiment adaptively adjusts the loss scale by introducing uncertainty, thereby reducing the loss weight on samples with high noise levels and improving the model's robustness to noise. The uncertainty can be represented by the local standard deviation σ of the quantization window or by the variance head σ explicitly output by the network. 2 Estimate. Transition point. The adaptive scaling makes the transition point of Huber loss adapt to the uncertainty. When the uncertainty is large, the transition point increases, the loss is more tolerant of the error, and the impact of noisy samples is further reduced.

[0116] Furthermore, the calculation of the uncertainty-aware loss function also includes:

[0117] In the uncertainty-aware loss function, domain adversarial regularization is introduced to force the encoder to produce domain-invariant features, and a time smoothing term is added to constrain the local fluctuations of RUL;

[0118] Domain adversarial regularization, through an adversarial training process, forces the feature encoder G to learn and generate "domain-invariant" feature representations. This means that after encoding, the distribution differences between data from different operating domains (such as different flight profiles) are minimized. This directly improves the model's generalization ability and prediction stability under unseen operating conditions or cross-domain conditions. The expression for domain adversarial regularization is:

[0119] ,

[0120] Where min is the minimum value, max is the maximum value, G is the feature encoder, D is the domain discriminator, and D(F) is the discriminative output of the domain discriminator on the training domain features F. ’ ) is the domain discriminator's assessment of the test domain features F ’ The discriminant output, This indicates that the distribution P from the training data... train Find the expected value of the sample x. This indicates that the distribution P from the test data... text samples Find the expected value.

[0121] In this embodiment, noise-invariant Huber, sample variance learning, and domain adversarial regularization are introduced on top of the basic regression error to ensure that the model maintains consistent error-confidence levels under strong noise and cross-domain conditions. To enhance cross-operating condition generalization, domain adversarial regularization is introduced, forcing the encoder to generate domain-invariant features. Through adversarial training between the domain discriminator and the encoder, the model can stably extract key degradation features on data from different operating conditions, reducing the interference of operating condition differences on feature expression. The time smoothing term effectively suppresses local drastic fluctuations in the prediction results by penalizing the RUL prediction values ​​of adjacent time steps, ensuring that the output RUL change trend conforms to the gradual law of aero-engine performance degradation. Specifically, the time smoothing term can be in the form of the sum of the squared differences of adjacent prediction means. By adjusting the weight coefficients, the smoothing intensity is controlled, allowing the model to capture long-term degradation trends while avoiding short-term prediction oscillations caused by local noise. This multi-component collaborative uncertainty-aware loss function design constrains and optimizes the model from multiple dimensions such as noise robustness, uncertainty quantification, cross-domain generalization, and prediction smoothness, ultimately achieving high-precision prediction and reliable uncertainty assessment of aero-engine RUL.

[0122] In practical implementation, the total loss can be expressed as:

[0123] L total = L error +λ1 L Huber +λ2 L var +λ3 L da +λ4 L smooth ,

[0124] Among them, L total For the total loss, L errorIt is the basic regression error (such as MSE (Mean Squared Error) or MAE (Mean Absolute Error)) that ensures prediction accuracy; L Huber To improve robustness by using Huber loss with invariant noise; L var It is a variance learning term (such as negative log-likelihood) that enables the model to learn reasonable estimates of uncertainty; L da It is a domain-adversarial regularization that improves cross-domain generalization; L smooth λ1 is the time smoothing term, which constrains the smoothing of the prediction curve; λ2, λ3 and λ4 are the weighting coefficients corresponding to each loss. By adjusting the weighting coefficients, the performance focus of the model can be customized for different application needs, and finally a RUL prediction model that achieves a balance between accuracy, robustness, calibration and generalization can be obtained.

[0125] In this embodiment, the total loss is jointly optimized to improve prediction error, robustness, uncertainty calibration, and cross-domain generalization, enabling the model to maintain high accuracy and reliability under complex conditions.

[0126] The spatiotemporal channel attention variation distribution of this application is as follows: Figure 2 As shown, the Gaussian robustness results refer to Figure 3 As shown, branching ablation is demonstrated, which studies the specific contribution of different branching architectures to model robustness by systematically controlling the types of branches included in the model (ANN, SNN, or both) and testing their performance under Gaussian noise interference.

[0127] In one embodiment, to measure "stability" rather than just averaging error, this embodiment proposes the reversal probability of the regression scenario: at adjacent perturbation intensities (such as the j-th standard deviation) →The (j+1)th standard deviation or the j-th disturbance amplitude → The (j+1)th disturbance amplitude Under this metric, if the difference in predictions for the same sample exceeds a preset threshold τ (or triggers a critical threshold crossing), it is counted as a flip, and the overall proportion is statistically analyzed. This indicator directly corresponds to the risk of "false / missed triggering of maintenance thresholds" in engineering decisions.

[0128] Specifically, the method further includes:

[0129] Define a set of perturbation sequences with increasing intensity. For a test sample, apply perturbations of different intensities in the perturbation intensity sequence in sequence, and record the RUL prediction value of the optimized prediction model under each perturbation intensity.

[0130] Within this test sample, when the absolute value of the difference between the RUL predicted values ​​under adjacent intensities is greater than a preset threshold, it is recorded as a flip.

[0131] Count the total number of flips for all test samples, and calculate the flip probability based on the total number of flips;

[0132] Risk warning and safety margin setting for aircraft engine maintenance decisions based on rollover probability.

[0133] The method of this embodiment is illustrated below with a specific example, as shown in the following steps:

[0134] 1. Define the perturbation intensity sequence: First, define a perturbation sequence from weak to strong, for example, the noise standard deviation: [σ1=0.01, σ2=0.05, σ3=0.1, σ4=0.2]. There are n=4 intensity levels, forming 3 pairs of "adjacent perturbation intensity pairs": (σ1, σ2), (σ2, σ3), (σ3, σ4).

[0135] 2. Calculate the prediction sequence for each sample: For a given test sample (such as a segment of vibration data from an engine):

[0136] First, obtain its baseline prediction RUL (baseline) under undisturbed conditions;

[0137] Then, perturbations σ1 to σ4 are applied sequentially to obtain the predicted values: RUL(σ1), RUL(σ2), RUL(σ3), RUL(σ4);

[0138] 3. Detect the number of "flips" for this sample: For this sample, examine the change in predicted value under each pair of adjacent perturbation intensities:

[0139] Calculate |RUL(σ1)-RUL(σ2)|. If it is greater than τ, then count one flip. τ is a preset threshold, such as 10 flight cycles.

[0140] Calculate |RUL(σ2)-RUL(σ3)|, and if it is greater than τ, count 1 flip;

[0141] Calculate |RUL(σ3)-RUL(σ4)|, and if it is greater than τ, count 1 flip;

[0142] This sample may be flipped up to 3 times;

[0143] 4. Summarize all samples and calculate the global probability:

[0144] Molecular (total number of flips): The sum of the number of flips generated by each of the test samples;

[0145] Denominator (total number of comparisons): Total number of test samples Logarithm of adjacent disturbance strength (in this case, the total number of samples) 3);

[0146] Then, the flip probability (FP_RUL(τ)) = the total number of flips for all samples / (total number of test samples × logarithm of adjacent perturbation strengths).

[0147] FP_RUL(τ) measures the average probability that the model's RUL prediction value will "jump" (exceed the preset threshold τ) when the input data encounters a disturbance of gradually increasing intensity. It directly reflects the smoothness and anti-interference resilience of the model output. This indicator can directly correspond to the risk of "false triggering / missed triggering of maintenance threshold" in engineering decision-making. The preset threshold τ can be associated with the key threshold in actual maintenance decision-making.

[0148] In practical implementation, the risk warning and safety margin setting based on the rollover probability for aircraft engine maintenance decision-making can be illustrated through the following example:

[0149] 1. Model robustness assessment and selection:

[0150] During the model development phase, the same test set and preset perturbation chains (such as [σ1, σ2, σ3, σ4]) and decision-related threshold τ (such as τ=10 cycles) were used to calculate the flip probability FP_RUL_A(10) of candidate model A (HAF+UALO of this application) and the flip probability FP_RUL_B(10) of candidate model B (traditional model).

[0151] Assuming the results are: FP_RUL_A(10) = 5%, FP_RUL_B(10) = 30%.

[0152] The results show that the flip probability of model A is much lower than that of model B. This means that when the data faces the same level of noise or interference, the risk of model A's predictions fluctuating drastically for more than 10 cycles is only 5%, while that of model B is as high as 30%. From the perspective of system stability and decision reliability, model A should be the preferred choice for deployment.

[0153] 2. Risk warning and safety margin setting for maintenance decisions:

[0154] During the online monitoring phase, the system provides the mean RUL prediction μ = 50 cycles for the current state of a certain engine and outputs the uncertainty σ = 5 cycles (or obtains stability information from the flip probability).

[0155] The decision system not only looks at the predicted mean μ=50, but also retrieves the model’s FP_RUL(τ) performance during the validation phase (e.g., FP_RUL=8% when τ=8 cycles).

[0156] This indicates that the model has approximately an 8% probability of predicting a sudden change in value exceeding 8 cycles under minor disturbances. Therefore, when developing a maintenance plan, maintenance should not be simply scheduled at the 50th cycle, but rather a safety margin should be set. For example, considering the 8% "skip" risk, the maintenance window can be moved forward to 50 - (τ + k) cycles. σ) = 50 - (8 + 2) 5) Check approximately every 32 cycles to greatly reduce the risk of failures occurring before the plan due to predicted mutations.

[0157] Risk can be flagged, such as explicitly stating in a maintenance recommendation report: "The current predicted value is 50 cycles, but due to an approximately 8% stability risk (meaning the predicted value may experience a sudden change of more than 8 cycles), preventative checks are recommended within the 32-40 cycle range." This shifts decision-making from single-point prediction to risk-range-based management.

[0158] 3. Guiding data collection and model iteration:

[0159] Analyzing the specific samples that caused "flips" in the tests (i.e., cases of unstable predictions) reveals that these samples mostly come from certain rare flight maneuvers (such as emergency climbs), indicating that the current model is not robust enough to this condition. Based on this, data on such rare conditions can be collected specifically and added to the next round of training, thereby improving the overall stability and generalization ability of the model in a targeted manner.

[0160] Through the above steps, FP_RUL(τ) is transformed from an evaluation metric into a key tool for connectivity model development, online decision-making, and system iteration.

[0161] In one embodiment, under worst-case perturbations such as PGD (Projected Gradient Descent), hybrid adversarial training (MPAdvT) with multiple perturbation amplitudes and multiple step sizes is employed. The perturbation intensity and iteration step are randomly sampled within a batch to cover different attack intensities. Furthermore, a "hard sample consistency regularization" (MAAdvT) can be introduced to strengthen the consistency constraint of the prediction distribution for samples with large residuals, avoiding the trade-off of robustness through excessive smoothing. Specifically, the calculation of the uncertainty-aware loss function and the optimization of the entire prediction model parameters through backpropagation include:

[0162] For each sample in the current training set, an adversarial attack parameter set is independently and randomly selected, which includes an upper limit for the perturbation strength and the number of iterations for projected gradient descent;

[0163] With the goal of maximizing the current loss of the prediction model, the PGD method is used to generate adversarial perturbations for each sample based on the adversarial attack parameters, thus forming adversarial examples;

[0164] The adversarial examples are input into the prediction model to generate the mean and variance of the RUL prediction under adversarial conditions;

[0165] Based on the uncertainty-perceived loss function and the mean and variance of RUL prediction in the adversarial case, the uncertainty-perceived loss of adversarial examples is calculated.

[0166] Based on the original uncertainty perception loss, the adversarial example uncertainty perception loss, and the hard sample consistency regularization loss, the total loss of the fusion adversarial training is calculated.

[0167] Calculate the gradient of the total loss of the fusion adversarial training with respect to all trainable parameters of the prediction model, and update the prediction model parameters through the optimizer.

[0168] The method of this embodiment will be described in detail below with a specific example, including:

[0169] 1. For each sample in the current batch, independently and randomly select a set of adversarial attack parameters, including: upper limit of perturbation strength ε, randomly sampled from a preset range; number of iteration steps K for projected gradient descent, randomly sampled from a preset set;

[0170] 2. To maximize the model's current loss (such as negative log-likelihood loss), the PGD method is used to generate adversarial perturbations for each sample;

[0171] 3. Generate the adversarial example X adv Input the same prediction model to obtain the mean μ of RUL predictions in adversarial scenarios. adv Sum of logarithmic variance ;

[0172] 4. Calculate the total loss of the fusion adversarial training: It consists of the original sample loss, the adversarial sample loss, and the consistency constraint between the two, as expressed below:

[0173] L ’ total =L ualo (X clean )+λ adv L ualo (X adv )+λ consist L consist ,

[0174] Among them, L ’ totalThe total loss in fusion adversarial training; L ualo (X clean The loss represents the perceived uncertainty of the original samples, i.e., the loss of the original input data X in the current batch. clean The input prediction model is processed sequentially through the feature extractor, HAF module, regression prediction head, and variance prediction head to obtain the baseline RUL predicted mean μ. clean Sum of logarithmic variance , will μ clean and Substitute the total loss L total The calculation formula for L is obtained ualo (X clean );

[0175] L ualo (X adv To combat sample uncertainty perception loss, the same total loss L is used. total The calculation formula is given, but the μ value of the adversarial example output is used in the calculation. adv Sum of logarithmic variance And the same real label y, this item L ualo (X adv The forced model must make accurate and uncertainty-calibrated predictions even in the face of malicious perturbations, with an adversarial sample uncertainty-perceived loss coefficient λ. adv Used to control the intensity of adversarial training;

[0176] λ consist Difficulty in determining the sample consistency regularization loss coefficient, L consist The hard sample consistency regularization loss is used to prevent the model from simply satisfying the adversarial loss by "collapsed" the prediction distribution, thereby maintaining the ability to discriminate hard samples (adversarial samples). It is defined as a measure of the difference between the original prediction distribution and the adversarial prediction distribution. This loss encourages the model to maintain consistency in the probability distribution of its predictions (including mean and uncertainty) of the original sample and its adversarial variants, thereby improving robustness without compromising the model's expressive power and calibration characteristics.

[0177] 5. Calculate the total loss L in fusion adversarial training. ’ total The gradients of all trainable parameters of the network (including feature extractors, HAF modules, prediction heads, etc.) are used to update the prediction model weights through an optimizer (such as Adam).

[0178] In this embodiment, robust optimization of the closed loop is achieved by seamlessly integrating MPAdvT and MAAdvT into the UALO loss framework. In each training round, the model not only learns how to minimize prediction errors and uncertainties on the original data, but also actively exposes itself to a series of worst-case perturbations of random strength, and is forced to maintain prediction accuracy and calibration (through L) in such "stress tests." ualo (X adv )) and consistency (through L consist The robustness of the ultimately trained model is not achieved through excessive smoothing or sacrificing performance, but rather is inherent in its strong feature representation and uncertainty perception capabilities.

[0179] Furthermore, the method also includes: engineering indicators and comprehensive evaluation, in addition to RMSE (Root Mean Square Error) / MAE, NASA Score, ECE / CRPS and FP_RUL(τ) can be reported, forming a three-dimensional evaluation of "error-stability-calibration".

[0180] It should be noted that in the above embodiments, temporal attention can be replaced by local window attention / multi-scale attention; channel attention can be replaced by ECA (Efficient Channel Attention) or Gated Multi-Layer Perceptron (GLP), but the fusion idea of ​​coupling the two is still retained. Bilinear fusion can be replaced by additive fusion, gated weighted summation, or low-rank tensor fusion to adapt to different computing budgets. Uncertainty replacement: variance learning can be replaced by quantile regression, ensemble models, or Monte Carlo to output confidence intervals. Robust training replacement: adversarial training can be replaced by stochastic smoothing, noise consistency regularization, or Distributively Robust Optimization (DRO). Domain generalization replacement: domain adversarial can be replaced by MMD (Maximum Mean Discrepancy), CORAL (Correlation Alignment), or domain alignment based on contrastive learning.

[0181] Secondly, embodiments of this application also provide an aero-engine RUL prediction system based on hybrid attention fusion and uncertainty perception loss, used to implement the aero-engine RUL prediction method based on hybrid attention fusion and uncertainty perception loss as described in any embodiment of the first aspect, the system comprising:

[0182] The data acquisition module is used to acquire historical time-series data from the operation to failure of aero-engine sensor equipment as a training set, and input the time-series data into the feature extraction network to obtain initial deep features.

[0183] The fusion module is used to input the initial deep features into the hybrid attention fusion module, compute temporal attention and channel attention in parallel, and perform bilinear fusion on the output features of temporal attention and channel attention to obtain enhanced features;

[0184] The prediction module is used to input the enhanced features into a regression prediction head consisting of a fully connected layer and output the RUL prediction mean, and input the enhanced features into another independent variance prediction head and output the RUL prediction variance.

[0185] The optimization module is used to calculate the uncertainty-aware loss function based on the predicted mean, predicted variance and the true RUL, and optimize the parameters of the entire prediction model through the backpropagation algorithm to obtain the optimized prediction model.

[0186] The calculation module is used to input the time series data of the device to be predicted into the optimized prediction model to obtain the mean and variance of the RUL prediction for the device to be predicted.

[0187] The results output module is used to construct a confidence interval at a specified confidence level based on the prediction mean and variance of the device to be predicted, and output the final RUL prediction result and its uncertainty assessment result.

[0188] The embodiments provided by the present invention have the following advantages:

[0189] Joint selection is more robust: HAF couples time attention with channel attention, reducing the risk of misfocusing caused by "only focusing on time / only focusing on channels", and suppressing noisy segments and weakly correlated channels at the same time;

[0190] Auditable confidence: UALO uses variance learning and noise adaptive Huber to make the prediction interval consistent with the residual, improving the performance of calibration metrics such as ECE / CRPS;

[0191] Cross-domain generalization: Domain adversarial regularization keeps the feature domain unchanged, reduces the distribution differences between different flight profiles, and improves the stability of cross-condition prediction;

[0192] Engineering stability: FP_RUL(τ) provides a stability metric directly related to the maintenance threshold, helping to verify the reliability of the model's decision-making under noise and attacks;

[0193] Easy to deploy: Both HAF and UALO are lightweight differentiable modules that can be embedded into existing RUL networks without significantly increasing inference overhead.

[0194] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for predicting the RUL (Range Limit Indicator) of aero-engines based on hybrid attention fusion and uncertainty perception loss, characterized in that, include: The historical operating time-series data of aero-engine sensor equipment from operation to failure is obtained as a training set, and the time-series data is input into a feature extraction network to obtain initial deep features. The initial deep features are input into the hybrid attention fusion module, which computes temporal attention and channel attention in parallel, and performs bilinear fusion on the output features of temporal attention and channel attention to obtain enhanced features. The enhanced features are input into a regression prediction head consisting of a fully connected layer, and the output is the RUL predicted mean. The enhanced features are input into another independent variance prediction head, and the output is the RUL predicted variance. Based on the predicted mean, predicted variance and true RUL, the uncertainty-perceived loss function is calculated, and the parameters of the entire prediction model are optimized through the backpropagation algorithm to obtain the optimized prediction model. The time series data of the device to be predicted is input into the optimized prediction model to obtain the mean and variance of the RUL prediction for the device to be predicted. Based on the predicted mean and variance of the device to be predicted, a confidence interval at a specified confidence level is constructed, and the final RUL prediction result and its uncertainty assessment result are output. The parallel computation of temporal attention and channel attention includes: Calculate temporal attention: Project the initial depth features onto the QKV space, calculate the correlation matrix between all time steps, obtain the temporal attention weights based on the correlation matrix and perform energy normalization, and obtain the temporal attention output features based on the energy-normalized temporal attention weights; Calculate channel attention: Perform global average pooling along the sensor channel dimension, and then generate channel weights through a feedforward network with a non-linear activation function to obtain the channel attention output features. The formula for calculating the time attention is: ， Among them, A t The attention weights for each time step to all other time steps, softmax is the normalization function, and Q is the expression for attention weights at each time step. t For querying the matrix, Let d be the transpose of the key matrix. k Let be the projection dimension of the key matrix. For features after time attention, V t It is a value matrix; The formula for calculating the channel weight is: ， in, σ is the channel weight, δ is the Sigmoid activation function, δ is the ReLU activation function, W1 is the weight matrix of the first fully connected layer, W2 is the weight matrix of the second fully connected layer, and Pool(H) is the global average pooling along the sensor channel dimension. The expression for the bilinear fusion is: ， Where ⊙ represents element-wise multiplication. As the first learnable scalar coefficient, F is the second learnable scalar coefficient. out Enhanced features for the output.

2. The air-to-air engine RUL prediction method based on hybrid attention fusion and uncertainty perception loss according to claim 1, characterized in that, The calculation of the uncertainty-aware loss function includes: We introduce noise-invariant Huber loss and sample variance learning loss on top of the basic regression error to calculate the uncertainty-aware loss function.

3. The aero-engine RUL prediction method based on hybrid attention fusion and uncertainty perception loss according to claim 2, characterized in that, The expression for the noise-invariant Huber loss is: ， ， Among them, L Huber For noise-invariant Huber loss, y i Let i be the true remaining useful life of the i-th sample. To predict the mean remaining useful life of the i-th sample using the prediction model, As an adaptive threshold, α is the basic Huber loss threshold. This is a scaling function for input uncertainty based on the prediction variance.

4. The aero-engine RUL prediction method based on hybrid attention fusion and uncertainty perception loss according to claim 3, characterized in that, The calculation of the uncertainty-aware loss function also includes: In the uncertainty-aware loss function, domain adversarial regularization is introduced to force the encoder to produce domain-invariant features, and a time smoothing term is added to constrain the local fluctuations of RUL; The expression for the domain adversarial regularity is: ， Where min is the minimum value, max is the maximum value, G is the feature encoder, D is the domain discriminator, and D(F) is the discriminative output of the domain discriminator on the training domain features F. ’ ) is the domain discriminator's assessment of the test domain features F ’ The discriminant output, This indicates that the distribution P from the training data... train Find the expected value of the sample x. This indicates that the distribution P from the test data... text samples Find the expected value.

5. The aero-engine RUL prediction method based on hybrid attention fusion and uncertainty perception loss according to claim 1, characterized in that, The method further includes: Define a set of perturbation sequences with increasing intensity. For a test sample, apply perturbations of different intensities in the perturbation intensity sequence in sequence, and record the RUL prediction value of the optimized prediction model under each perturbation intensity. Within this test sample, when the absolute value of the difference between the RUL predicted values ​​under adjacent intensities is greater than a preset threshold, it is recorded as a flip. Count the total number of flips for all test samples, and calculate the flip probability based on the total number of flips; Risk warning and safety margin setting for aircraft engine maintenance decisions based on rollover probability.

6. The aero-engine RUL prediction method based on hybrid attention fusion and uncertainty perception loss according to claim 4, characterized in that, The calculation of the uncertainty-aware loss function and the optimization of the entire prediction model parameters through the backpropagation algorithm include: For each sample in the current training set, an adversarial attack parameter set is independently and randomly selected, which includes an upper limit for the perturbation strength and the number of iterations for projected gradient descent; With the goal of maximizing the current loss of the prediction model, the PGD method is used to generate adversarial perturbations for each sample based on the adversarial attack parameters, thus forming adversarial examples; The adversarial examples are input into the prediction model to generate the mean and variance of the RUL prediction under adversarial conditions; Based on the uncertainty-perceived loss function and the mean and variance of RUL prediction in the adversarial case, the uncertainty-perceived loss of adversarial examples is calculated. Based on the original uncertainty perception loss, the adversarial example uncertainty perception loss, and the hard sample consistency regularization loss, the total loss of the fusion adversarial training is calculated. Calculate the gradient of the total loss of the fusion adversarial training with respect to all trainable parameters of the prediction model, and update the prediction model parameters through the optimizer.

7. A wind power limit (RUL) prediction system for aero-engines based on hybrid attention fusion and uncertainty perception loss, used to implement the wind power limit (RUL) prediction method for aero-engines based on hybrid attention fusion and uncertainty perception loss as described in any one of claims 1-6, characterized in that, The system includes: The data acquisition module is used to acquire historical time-series data from the operation to failure of aero-engine sensor equipment as a training set, and input the time-series data into the feature extraction network to obtain initial deep features. The fusion module is used to input the initial deep features into the hybrid attention fusion module, compute temporal attention and channel attention in parallel, and perform bilinear fusion on the output features of temporal attention and channel attention to obtain enhanced features; The prediction module is used to input the enhanced features into a regression prediction head consisting of a fully connected layer and output the RUL prediction mean, and input the enhanced features into another independent variance prediction head and output the RUL prediction variance. The optimization module is used to calculate the uncertainty-aware loss function based on the predicted mean, predicted variance and the true RUL, and optimize the parameters of the entire prediction model through the backpropagation algorithm to obtain the optimized prediction model. The calculation module is used to input the time series data of the device to be predicted into the optimized prediction model to obtain the mean and variance of the RUL prediction for the device to be predicted. The results output module is used to construct a confidence interval at a specified confidence level based on the prediction mean and variance of the device to be predicted, and output the final RUL prediction result and its uncertainty assessment result. The parallel computation of temporal attention and channel attention includes: Calculate temporal attention: Project the initial depth features onto the QKV space, calculate the correlation matrix between all time steps, obtain the temporal attention weights based on the correlation matrix and perform energy normalization, and obtain the temporal attention output features based on the energy-normalized temporal attention weights; Calculate channel attention: Perform global average pooling along the sensor channel dimension, and then generate channel weights through a feedforward network with a non-linear activation function to obtain the channel attention output features. The formula for calculating the time attention is: ， Among them, A t The attention weights for each time step to all other time steps, softmax is the normalization function, and Q is the expression for attention weights at each time step. t For querying the matrix, Let d be the transpose of the key matrix. k Let be the projection dimension of the key matrix. For features after time attention, V t It is a value matrix; The formula for calculating the channel weight is: ， in, σ is the channel weight, δ is the Sigmoid activation function, δ is the ReLU activation function, W1 is the weight matrix of the first fully connected layer, W2 is the weight matrix of the second fully connected layer, and Pool(H) is the global average pooling along the sensor channel dimension. The expression for the bilinear fusion is: ， Where ⊙ represents element-wise multiplication. As the first learnable scalar coefficient, F is the second learnable scalar coefficient. out Enhanced features for the output.

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