A method for predicting the remaining useful life of an aeroengine operating condition

Abstract

The application discloses a kind of aviation engine operating condition's remaining useful life prediction method, including the monitoring data of aviation engine is carried out step S1 data preprocessing, the step S1 data preprocessing after still includes: step S2: the one-dimensional time series after preprocessing is converted into time domain sequence and time-frequency scale diagram;Step S3: extract the evolution characteristics of time domain and the energy characteristics of frequency domain;Step S4: construct time domain guide frequency domain path and frequency domain guide time domain path;Step S5: prediction;The fusion feature vector output by step S4 is input into multilayer perception machine prediction network, and the remaining useful life prediction value y of aviation engine is output ^. Gradient guide consistency loss (GGCL) is introduced, the consistency of model attention weight and feature real contribution degree is constrained, the problem of "attention not loyal" and poor interpretability of deep learning model is solved.

Description

Technical Field

[0001] This invention relates to the field of aero-engine operation technology, and in particular to a method for predicting the remaining service life of an aero-engine under operating conditions. Background Technology

[0002] Predictive and Health Management (PHM) technology is a core enabling technology for ensuring the safe, reliable, and efficient operation of complex and critical industrial assets such as aero-engines and industrial gas turbines. With the advancement of Industry 4.0 and intelligent manufacturing, PHM has become a key means of shifting from traditional "post-failure maintenance" or "scheduled maintenance" to a more scientific "condition-based maintenance." As the holy grail of PHM, Remaining Useful Life (RUL) prediction aims to utilize multi-source sensor monitoring data to assess the current health status of equipment in real time and accurately estimate its remaining operating time before complete failure. High-precision RUL prediction can not only effectively prevent catastrophic failures and ensure flight and production safety, but also significantly optimize spare parts inventory management, reduce unnecessary downtime maintenance, and thus substantially reduce the overall lifecycle maintenance costs. Early prediction methods were mainly based on physical failure mechanisms, but constructing accurate and universal physical models is extremely challenging when facing the increasingly complex system structure and coupled degradation mechanisms of modern aero-engines. With the development of the Industrial Internet of Things (IIoT) and sensor technology, data-driven methods, represented by Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and their variant Transformer, have gradually become the dominant research paradigm in the field of RUL prediction due to their powerful nonlinear feature extraction capabilities. In particular, the Transformer architecture, because of its ability to capture long-range dependencies, has achieved significant improvements in prediction accuracy on multiple publicly available benchmark datasets.

[0003] However, despite the significant achievements of existing deep learning models, they still face the following serious challenges in practical industrial applications:

[0004] First, existing methods lack sufficient generalization ability when facing complex and ever-changing operating conditions, exhibiting a "distribution offset" problem. Aero engines typically switch operating points frequently under different flight envelopes (e.g., changes in altitude, Mach number, and throttle lever angle). Mainstream data preprocessing workflows often employ Z-score normalization based on global statistics, which ignores the statistical distribution differences in sensor data under different operating conditions. This makes the model highly susceptible to confusing normal signal jumps caused by operating condition switching with performance degradation caused by component damage, making convergence difficult when facing unfamiliar or complex combinations of operating conditions, and significantly increasing prediction errors.

[0005] Second, existing feature fusion strategies are relatively shallow and struggle to construct robust health indicators in noisy environments. To overcome the limitation of single time-domain sensor readings failing to capture subtle signs of degradation under strong background noise, some studies have attempted to introduce frequency domain or time-frequency domain information (such as continuous wavelet transform, CWT). However, most current fusion strategies remain at the level of simple vector concatenation or shallow weighting. This approach ignores the deep semantic correlation between time trends and spectral patterns, creating a "semantic gap" between different modal features. This makes it difficult for the model to fully utilize multi-domain complementary information, limiting its prediction upper limit in complex noisy environments. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for predicting the remaining service life of an aero-engine under operating conditions.

[0007] The technical solution adopted by this invention to solve the above-mentioned technical problem is: a method for predicting the remaining service life of an aero-engine under operating conditions, including step S1 data preprocessing of monitoring data of the aero-engine, and step S1 data preprocessing followed by:

[0008] Step S2: Convert the preprocessed one-dimensional time series into a time-domain series and a time-frequency scale map;

[0009] Step S3: Extract the evolution features in the time domain and the energy features in the frequency domain;

[0010] Step S4: Construct time-domain guided frequency-domain paths and frequency-domain guided time-domain paths, generate cross-modal attention maps, obtain fused features through residual fusion, extract the feature vector of the last time step in the fused sequence, and input it into the subsequent prediction network;

[0011] Step S5: Prediction; Input the fused feature vector output from step S4 into the multilayer perceptron prediction network to output the predicted remaining service life of the aero-engine. .

[0012] Preferably, step S5 includes:

[0013] S5-1: Predicted Output:

[0014] The fused feature vector output from step S4 is input into a multilayer perceptron prediction network. The multilayer perceptron uses two fully connected layers with ReLU activation function, and the output layer is a single-neuron linear layer. The final output is the predicted value of the remaining service life of the aero-engine. ;

[0015] S5-2: Constructing a Teacher Distribution Model

[0016] During the backpropagation process of the model, the predicted values ​​are calculated. Gradient relative to the attention map The absolute value is taken to obtain the feature sensitivity map; a temperature coefficient is applied to the sensitivity map. The Softmax function is used for normalization to construct a teacher distribution model T that reflects the true contribution of features;

[0017] S5-3: Calculate the consistency loss:

[0018] The original attention weight distribution model generated during the forward propagation process is compared with the teacher distribution model T constructed in S5-2, and the KL divergence between the two is calculated. This KL divergence is defined as the consistency loss. The formula is:

[0019] ;

[0020] in This is a gradient sensitivity map. Attention weights;

[0021] S5-4: Joint Optimization

[0022] Construct a multi-objective joint loss function, the formula of which is:

[0023] ;

[0024] Explanation of each loss item:

[0025] Mean squared error loss, which is the predicted value. Mean square error compared to the true RUL label y(t);

[0026] Weighted consistency loss This is the consistency loss weighting coefficient;

[0027] Weighted regularization loss This represents the regularization loss weight coefficient.

[0028] Preferably, the data preprocessing in step S1 further includes the following steps:

[0029] S1-1: Feature Optimization: Monitoring data is collected from multiple sensor monitoring channels to form an original dataset. Variance analysis is performed on the full life cycle data in the original dataset. If the data monitored by some sensors are constant in value or the variance approaches 0 throughout the entire operating cycle, the feature information corresponding to the data monitored by those sensors is removed. The set of feature information corresponding to the remaining data monitored by the sensors is used as the retained sensor sequence.

[0030] S1-2: Exponentially weighted moving average noise reduction:

[0031] The retained sensor sequences were smoothed using an exponentially weighted moving average and used as the training set.

[0032] The smoothing process is as follows: for the observation value of the i-th sensor at time t... its smoothed value The calculation formula is as follows:

[0033] ; in, For smoothing coefficients;

[0034] S1-3: Anti-condition normalization based on K-Means clustering:

[0035] Using the three operation settings channels of height, Mach number, and throttle resolution angle as the feature space, the K-Means algorithm is used to divide the samples into K clusters on the training set, with each cluster representing an operation mode;

[0036] Calculate the mean vector of sensor data within each cluster. and standard deviation vector ;

[0037] For samples belonging to the k-th cluster Standardization is performed, and the formula is:

[0038] .

[0039] Preferably, during the testing phase, the test samples are first assigned to the training set cluster center with the closest Euclidean distance based on their operational settings, and then the corresponding training set statistics are used. Perform the normalization process in steps S1-3.

[0040] Preferably, the data preprocessing in step S1 further includes the following steps:

[0041] S1-4: Piecewise linear RUL tag construction;

[0042] A piecewise linear function is used to truncate the true RUL, specifically as follows: when the true RUL is greater than a set threshold, the label is set to the set threshold; otherwise, the true value is retained; the formula is as follows:

[0043] .

[0044] Preferably, step S2 includes the following:

[0045] S2-1: Random noise injection based on manifold smoothing:

[0046] Preprocessed input data during training Implement dynamic Gaussian noise injection; by superimposing zero mean and standard deviation Gaussian noise, smoothing the decision manifold in the feature space; the calculation formula is:

[0047] ;

[0048] S2-2: CWT Time-Frequency Feature Extraction:

[0049] The frequency domain energy distribution is explored using continuous wavelet transform, and complex Morlet wavelet is selected as the basis function.

[0050] The wavelet transform formula is:

[0051] ;

[0052] in, As a scale factor, The translation factor is... Let be the complex conjugate of the complex Morlet wavelet. The mathematical form of the complex conjugate of the complex Morlet wavelet is: ;

[0053] Convert the N sensor signals within each time window into a time-frequency tensor of size (N, H, L). ， Time-frequency tensor As input to the frequency domain encoder.

[0054] Preferably, step S3 includes the following:

[0055] S3-1: Noise-resistant hybrid timing coding;

[0056] Local feature extraction: Two stacked one-dimensional convolutional layers are used. The first layer captures high-frequency noise and transient impacts, and the second layer aggregates local degradation patterns.

[0057] Global dependency modeling: Accessing a gated loop unit containing hidden units to capture long-distance temporal dependencies;

[0058] S3-2: Asymmetric time-frequency coding, processing time-frequency tensors :

[0059] Asymmetric max pooling: Asymmetric max pooling is applied after each convolutional block to reduce dimensionality and keep the time step constant.

[0060] Channel recalibration: At the end of frequency domain feature extraction, the SE-Block channel attention module is applied to learn the weights of the frequency domain feature channels, enhance the feature response of key engine fault frequency bands, suppress invalid frequency band interference, and finally output frequency domain feature codes. .

[0061] Preferably, step S4 includes:

[0062] Two independent cross-modal attention interaction paths are constructed to achieve bidirectional guidance of temporal and frequency domain features:

[0063] Time-domain guided frequency-domain path: encoding with time-domain features For the query vector, encoded using frequency domain features These are the key vector and the value vector.

[0064] Frequency-domain to time-domain path: Encoding with frequency domain features The query vector is encoded using time-domain features. These are the key vector and the value vector.

[0065] Preferably, in step S4, the fusion feature sequences of the two paths are aggregated at time steps, and only the feature vector of the last time step in the fusion feature sequence is extracted, and this vector is used as the input feature of the subsequent prediction network.

[0066] Step S3-1, following global dependency modeling, also includes adaptive feature recalibration. This adaptive feature recalibration includes: 1) Squeezing operation: For the temporal features output by the GRU, global average pooling is used to aggregate feature information along the time dimension, eliminating changes in the time dimension and generating a channel-level global descriptor reflecting the global response of the sensor channels; 2) Activation operation: A two-layer multilayer perceptron with a bottleneck structure is used to process the global descriptor, learning the nonlinear dependencies between different sensor channels, and generating feature importance weight coefficients s between 0 and 1 using an activation function; 3) Recalibration and mapping: Based on the generated weight coefficients s, the original feature channels are reorganized element-wise to enhance the feature weights of channels containing significantly degraded information, suppress channel interference containing high-frequency noise or irrelevant information, and map the weighted features to a unified latent space dimension through a fully connected layer with L2 regularization. The final output is the temporal feature code. .

[0067] The beneficial effects of this invention are as follows: Through data preprocessing in step S1, targeting the characteristics of high-dimensionality, non-stationarity, and multiple operating conditions of aero-engine monitoring data, the original data is cleaned and standardized through four sub-steps: feature optimization, noise reduction, anti-operating condition normalization, and RUL label construction, providing a high-quality dataset for subsequent model training. In response to the data distribution shift problem caused by the multi-operating condition operation of aero-engines, the traditional global Z-score normalization method is abandoned, and a hierarchical anti-operating condition normalization strategy based on K-Means clustering is adopted to avoid the model confusing "operating condition jump" with "performance degradation".

[0068] Two parallel neural network branches, a time-domain coding branch and a frequency-domain coding branch, are constructed to extract features from the noise-resistant time-domain sequence and time-frequency tensor obtained by S2, respectively, to mine time-domain evolution features and frequency-domain energy features. In order to bridge the "semantic gap" between time-domain and frequency-domain features, a bidirectional cross-modal attention fusion mechanism is designed to establish a deep interaction relationship between time-domain and frequency-domain features, realize the complementary fusion of multimodal features, and at the same time ensure the causality of fused features.

[0069] Gradient-guided consistency loss (GGCL) is introduced to constrain the consistency between the model's attention weights and the true contribution of features, thus solving the problems of "attention fidelity" and poor interpretability in deep learning models. Attached Figure Description

[0070] Figure 1 This is a model structure diagram of the S3-1 noise-resistant hybrid timing coding in this invention;

[0071] Figure 2 This is a model structure diagram of the S3-2 asymmetric time-frequency coding in this invention;

[0072] Figure 3 This is an overall framework diagram of the prediction method of the present invention. Detailed Implementation

[0073] The present invention will now be described in further detail with reference to the accompanying drawings and preferred embodiments. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0074] The proposed method for predicting the remaining service life (RUL) of aero-engines addresses issues such as distribution shift, semantic gap in feature fusion, and poor model interpretability in RUL prediction under complex operating conditions of aero-engines through five core steps: data preprocessing, multimodal input construction, parallel encoding of dual-stream features, bidirectional cross-modal attention fusion, and gradient-guided consistency training and prediction. This achieves high-precision, robust, and interpretable RUL prediction. This embodiment uses the aero-engine C-MAPSS dataset (FD002 / FD004 multi-condition dataset) as the experimental object. This dataset contains 21 sensor monitoring channels and 3 operation setting channels (altitude, Mach number, and throttle resolution angle), covering the entire lifecycle of the engine. The specific implementation details of each step are as follows.

[0075] Step S1: Data Preprocessing

[0076] This step addresses the high-dimensional, non-stationary, and multi-condition characteristics of aero-engine monitoring data. It employs four sub-steps—feature optimization, noise reduction, condition-resistant normalization, and RUL label construction—to clean and standardize the raw data, providing a high-quality dataset for subsequent model training. The specific implementation is as follows:

[0077] S1-1: Feature Optimization

[0078] Analysis of variance (ANOVA) was performed on the full lifecycle data of the C-MAPSS dataset to analyze the numerical fluctuation characteristics of 21 sensor monitoring channels throughout the engine's operating cycle. The results showed that the monitoring data of sensors 1, 5, 6, 10, 16, 18, and 19 had constant values ​​or variances close to 0 during the operating cycle, indicating no effective degradation information; these were considered redundant and were removed. The monitoring data of the remaining 14 degradation-sensitive sensor channels (i.e., sensors 2, 3, 4, 7, 8, 9, 11, 12, 13, 14, 15, 17, 20, and 21) were retained, forming a preserved sensor sequence as the basis for subsequent processing. Degradation-sensitive sensor channels refer to those whose monitoring data are not constant during the operating cycle.

[0079] S1-2: Exponentially Weighted Moving Average Noise Reduction

[0080] To suppress high-frequency electromagnetic noise while preserving the signal degradation trend, an exponentially weighted moving average (EWMA) is used to smooth the sensor sequence obtained in S1-1. The processed data is used as the model training set. For the observation value of the i-th sensor at time t... its smoothed value The calculation formula is as follows:

[0081] ;in, The smoothing coefficient. In this embodiment, the smoothing coefficient... Setting it to 0.1 can effectively filter out random fluctuations in the data, while avoiding time lag in degradation trends caused by over-smoothing, thus ensuring the integrity of the time-series characteristics of the data.

[0082] S1-3: Anti-condition normalization based on K-Means clustering

[0083] To address the data distribution shift issue caused by multi-condition operation of aero-engines, the traditional global Z-score normalization method is abandoned. Instead, a hierarchical anti-condition normalization strategy based on K-Means clustering is adopted to avoid the model confusing "condition jumps" with "performance degradation." Specific operations are as follows:

[0084] Feature space construction and clustering: Using altitude, Mach number and throttle resolution angle as the three operation settings channels as the feature space, the K-Means clustering algorithm is used on the training set obtained in S1-2 to divide the training set samples into K=6 clusters, each cluster representing an aero-engine operation mode;

[0085] Statistical calculation: Statistical analysis is performed on the sensor data within each cluster, and the mean vector of each cluster is calculated. and standard deviation vector (k=1,2,⋅⋅⋅,6).

[0086] Intra-cluster standardization: For a sample x belonging to the k-th cluster, perform standardization using the following formula: ;in This is a minimum value correction term to avoid calculation anomalies where the denominator is 0;

[0087] Test set normalization: To prevent data leakage, test set statistics are not used during the testing phase. First, channel data is set based on the three operations of the test sample, and the Euclidean distance between the sample and the centers of the six clusters in the training set is calculated. The test sample is then assigned to the cluster with the closest Euclidean distance, and the mean vector of the training set corresponding to that cluster is used. and standard deviation vector Then perform the standardization process described above.

[0088] S1-4: Piecewise Linear RUL Tag Construction

[0089] Considering the stable health state of an aero-engine during its initial operational phase, meaningless fluctuations in its Realized Limiting Rank (RUL) can lead to model training bias. Therefore, a piecewise linear function is used to truncate the true RUL, constructing a robust RUL label. In this embodiment, a RUL threshold is set. =125 running cycles, the tag construction formula is: That is, when the engine's actual remaining service life... When the number of execution cycles exceeds 125, set the label value to 125; when... For 125 or fewer running cycles, the true value remains unchanged. This processing allows the model to focus more on feature learning during the engine degradation phase, improving prediction accuracy.

[0090] Step S2: Multimodal Input Construction

[0091] The one-dimensional time series data preprocessed by S1 is transformed into two modal data: a noise-resistant time-domain sequence and a time-frequency scale map. These are used as the time-domain and frequency-domain inputs of the subsequent two-stream network, respectively, to achieve preliminary extraction of multimodal features. Specific implementation details are as follows:

[0092] S2-1: Random noise injection based on manifold smoothing

[0093] To enhance the model's robustness to real sensor drift and noise interference during the testing phase, preprocessed input data is used during model training. Dynamic Gaussian noise injection is implemented, and the decision manifold of the feature space is smoothed by superimposing noise, forcing the model to learn an engine-natured degradation mode with translation invariance. The noise injection calculation formula is as follows: ;in With zero mean and standard deviation of Gaussian noise, in this embodiment The value is set to 0.05, which ensures the noise-injected training effect without masking the degradation features in the data. The time-domain sequence after noise injection is used as the input to the time-domain coding branch in the two-stream network.

[0094] S2-2: Time-Frequency Feature Extraction in CWT

[0095] To extract the frequency domain energy distribution characteristics from sensor data, continuous wavelet transform (CWT) is used to extract time-frequency features from the preprocessed one-dimensional time series, transforming the one-dimensional data into a two-dimensional time-frequency tensor. The specific steps are as follows:

[0096] Basis function selection: Complex Morlet wavelets are chosen as the basis functions for continuous wavelet transform. This basis function can simultaneously capture the amplitude and phase information of the signal, adapting to the non-stationary characteristics of aero-engine monitoring signals. Its conjugate complex form is as follows:

[0097] ;

[0098] in For bandwidth parameters, The center frequency parameter.

[0099] Wavelet transform execution: The formula for continuous wavelet transform is:

[0100] ;

[0101] in, As a scale factor, The translation factor is... The complex conjugate of the complex Morlet wavelet (i.e. ).

[0102] Time-frequency tensor generation: In this embodiment, the frequency scale H=16 and the time step L=30 are set, and the 14 sensor signals in each time window are converted into a time-frequency tensor of size (14,16,30). This time-frequency tensor serves as the input to the frequency domain coding branch in the two-stream network.

[0103] Step S3: Parallel encoding of dual-stream features

[0104] Two parallel neural network branches, a time-domain coding branch and a frequency-domain coding branch, are constructed to extract features from the noise-resistant time-domain sequence and the time-frequency tensor obtained from S2, respectively, to mine time-domain evolution features and frequency-domain energy features. The two branches encode independently and have matched feature dimensions, laying the foundation for subsequent cross-modal fusion. Specific implementation details are as follows:

[0105] S3-1: Noise-resistant hybrid timing coding (time-domain branching), such as Figure 1 As shown,

[0106] The temporal branch employs a hybrid architecture of 1D-CNN+GRU+SE-Attention to process noise-resistant temporal sequences, achieving local degradation feature extraction, global temporal dependency modeling, and feature channel recalibration. Specific operations include:

[0107] Local feature extraction: Two stacked one-dimensional convolutional layers (1D-CNN) are used, each containing 16 filters, with a kernel size of 3, an activation function of ReLU, and a Batch Normalization layer; the first convolutional layer captures high-frequency noise and transient impacts in the data, and the second convolutional layer aggregates the local degradation patterns of the engine to output local temporal features.

[0108] Global dependency modeling: A gated recurrent unit (GRU) with 16 hidden units is connected after the 1D-CNN to capture long-distance temporal dependencies in the engine degradation process. The output layer of the GRU is normalized using Layer Normalization to eliminate feature scale differences.

[0109] Adaptive Feature Recalibration: Considering the significant differences in the response of different sensor channels to equipment failures and the potential for misleading noise in some channels, an SE-Attention (Squeeze-and-Excitation) channel attention mechanism is introduced to dynamically weight the features output by the GRU, giving the model an adaptive "feature selection" capability. Specifically, this includes the following three sub-processes: 1) Squeeze Operation: For the temporal features output by the GRU, global average pooling is used to aggregate feature information in the time dimension, eliminating changes in the time dimension and generating a channel-level global descriptor reflecting the global response of 14 sensor channels; 2) Activation Operation: A two-layer multilayer perceptron (MLP) with a bottleneck structure is used to process the above global descriptor, learning the nonlinear dependencies between different sensor channels, and generating feature importance weight coefficients s between 0 and 1 through an activation function; 3) Recalibration and Mapping: Based on the generated weight coefficients s, the original feature channels are re-weighted element-wise (i.e., soft thresholding), automatically enhancing the feature weights of channels containing significant degradation information (such as the EGT temperature channel), while suppressing channel interference containing high-frequency noise or irrelevant information. Finally, the weighted features are passed through a fully connected layer with L2 regularization to map to a unified latent space dimension. The final output is the temporal feature code. .

[0110] S3-2: Asymmetric time-frequency coding (frequency domain branching), such as Figure 2 As shown,

[0111] The frequency domain branch employs a 2D-CNN + asymmetric max pooling + SE-Block architecture to process the time-frequency tensor I. cwt This achieves deep feature extraction in the frequency domain, dimensionality compression, and enhancement of key fault frequency bands. Specific operations include:

[0112] Deep mapping: Two-dimensional convolutional layers (2D-CNN) are used to extract deep features from the time-frequency tensor. The first layer contains 32 filters and the second layer contains 64 filters. The convolutional kernels are all (3,3), which gradually mine the fault energy distribution features in the frequency domain.

[0113] Asymmetric max pooling: After each 2D-CNN convolutional block, an asymmetric max pooling operation of size (2,1) is applied, where the "2" of the pooling kernel acts on the frequency dimension to achieve dimensionality reduction and compression of frequency domain features, and the "1" acts on the time dimension to keep the time step constant at 30. This design reduces the number of model parameters and ensures that the frequency domain feature sequence and the time domain feature sequence are strictly aligned on the time axis, providing a foundation for cross-modal fusion.

[0114] Channel recalibration: At the end of frequency domain feature extraction, the SE-Block channel attention module is applied to learn the weights of the frequency domain feature channels, enhance the feature response of key engine fault frequency bands, suppress invalid frequency band interference, and finally output frequency domain feature codes. .

[0115] The specific structural parameters of SE-Block are: MLP is 128→64 neurons, ReLU activation, and global average pooling window is 1×1.

[0116] Step S4: Bidirectional cross-modal attention fusion

[0117] To bridge the semantic gap between time-domain and frequency-domain features, a bidirectional cross-modal attention fusion mechanism is designed to establish a deep interaction relationship between time-domain and frequency-domain features, achieving complementary fusion of multimodal features while ensuring the causality of the fused features. Specific implementation details are as follows:

[0118] S4-1: Constructing a bidirectional interaction path

[0119] Two independent cross-modal attention interaction paths are constructed to achieve bidirectional guidance of temporal and frequency domain features:

[0120] Time-domain guided frequency-domain path: encoding with time-domain features The query vector is encoded using frequency domain features. It consists of a key vector and a value vector.

[0121] Frequency-domain to time-domain path: Encoding with frequency domain features The query vector is encoded using time-domain features. It consists of a key vector and a value vector.

[0122] S4-2: Attention Calculation and Retrieval

[0123] Taking time-domain guided frequency-domain path as an example, the dot product similarity between the query and the key is calculated, and then normalized by Softmax to generate a cross-modal attention map. This reflects the correlation between the time-domain state and frequency-domain characteristics at each moment, and the calculation formula is:

[0124] ;

[0125] in To avoid the vanishing of the Softmax gradient due to excessive dot product similarity, a scaling factor is used; the cross-modal attention map for frequency-domain guided time-domain paths is calculated in the same manner as described above. , .

[0126] S4-3: Residual Fusion

[0127] By using cross-modal attention maps to perform weighted summation on the corresponding Value vectors, complementary feature information in the time and frequency domains is extracted. Then, the complementary features are superimposed back onto the original modal features through residual connections. Finally, the scale difference of the fused features is eliminated by standardization through LayerNorm layers, resulting in time-domain-frequency domain fused features and frequency-domain-time domain fused features, respectively. The residual fusion design can effectively alleviate the gradient vanishing problem in model training. At the same time, when a modal feature is disturbed by noise, information compensation is performed using another modal feature, which improves the robustness of the fused features.

[0128] S4-4: End-time step aggregation

[0129] To ensure the causality of RUL prediction for aero-engines (i.e., the current RUL is determined solely by historical data), the fused feature sequences of the two paths are aggregated at time steps. Only the feature vector of the last time step in the fused feature sequence is extracted, and this vector is used as the input feature of the subsequent prediction network. This approach not only guarantees the causality of the prediction but also compresses the feature dimension and improves the model's inference efficiency.

[0130] Step S5: Gradient-guided consistency training and prediction, such as... Figure 3 As shown,

[0131] This step is the core of model training and prediction. It achieves RUL prediction through a multilayer perceptron and introduces gradient-guided consistency loss (GGCL) to constrain the consistency between the model's attention weights and the true contribution of features, addressing the issues of "attention fidelity" and poor interpretability in deep learning models. Simultaneously, it achieves global optimization of the model through a joint loss function. Specific implementation details are as follows:

[0132] S5-1: Predicted Output

[0133] The fused feature vector from S4-4 is input into a multilayer perceptron (MLP) prediction network. The MLP uses two fully connected layers with ReLU activation function and a single-neuron linear output layer, ultimately outputting the predicted remaining service life of the aero-engine. .

[0134] S5-2: Constructing a Teacher Distribution Model

[0135] To quantify the true physical contribution of features to RUL prediction, a gradient-sensitivity-guided teacher distribution model is constructed as a supervisory benchmark for attention weights. Specifically, during the model's backpropagation process, the predicted values ​​are calculated. Gradient relative to the attention map The absolute value is taken to obtain the feature sensitivity map (the larger the gradient, the higher the contribution of the corresponding feature to the RUL prediction); a temperature coefficient is applied to the sensitivity map. The Softmax function with a value of 1.0 is used for normalization to construct a teacher distribution model T that reflects the true contribution of features.

[0136] S5-3: Calculate the consistency loss

[0137] The original attention weight distribution model (i.e., student distribution model S) generated during the forward propagation process is compared with the teacher distribution model T constructed in S5-2. The KL divergence between the two is calculated, and this KL divergence is defined as the consistency loss. The formula is:

[0138] ;

[0139] in This is a gradient sensitivity map (teacher distribution model). The attention weights are used in the student distribution model. The smaller the KL divergence, the higher the consistency between the attention weights and the true contribution of the features, and the stronger the interpretability of the model. Figure 3 middle Represents the temporal attention feature weights during forward propagation. The weights of the time-frequency image domain attention features during forward propagation are represented. This represents the gradient of the temporal attention map during backpropagation. This represents the gradient of the attention map in the time-frequency domain during backpropagation.

[0140] S5-4: Joint Optimization

[0141] A multi-objective joint loss function is constructed to simultaneously constrain the model's prediction accuracy, attention consistency, and parameter count, thereby achieving global optimization of the model. The final loss function formula is as follows:

[0142] ;

[0143] Explanation of each loss item:

[0144] Mean squared error loss, which is the predicted value. The mean squared error between the model and the true RUL label y(t) ensures the accuracy of the model's RUL prediction and is the core term of the loss function;

[0145] Weighted consistency loss The consistency loss weight coefficient (set to 0.1 in this embodiment) is used to impose an interpretability constraint on the model, forcing the attention mechanism to focus on the key features that truly reflect engine degradation;

[0146] Weighted regularization loss The regularization loss weight coefficient is set to 0.001 in this embodiment. The network parameters of the model are constrained by L2 regularization to solve the overfitting problem caused by the excessive number of model parameters.

[0147] S5-5: Model Training Strategy

[0148] To ensure the model's training efficiency and generalization ability, the Adam optimizer is used to optimize model parameters, and a stepped learning rate decay and early stopping mechanism are designed. Specific training parameters and strategies are as follows:

[0149] Optimizer and Initial Learning Rate: The Adam optimizer is selected, and the initial learning rate is set to 1e−3. Set it to 0.9. Set it to 0.999;

[0150] Learning rate decay: Implement a step decay strategy, keeping the learning rate constant for the first 10 training epochs, and then halving the learning rate every 20 epochs thereafter to gradually improve the convergence accuracy of the model.

[0151] Training epochs and early stopping mechanism: The model is trained for a maximum of 150 epochs. At the same time, an early stopping mechanism with Patience=30 is set, that is, when the Ltotal of the validation set does not decrease for 30 consecutive epochs, training is stopped immediately to prevent the model from overfitting.

[0152] Training batches: Mini-batch training is used, with a batch size of 32, to improve the training stability and convergence speed of the model.

[0153] The prediction method of this invention significantly improves the prediction accuracy under multiple operating conditions and solves the problem of insufficient generalization ability caused by data distribution offset; the bidirectional cross-modal attention fusion mechanism effectively mines the complementary features of the time domain and frequency domain, greatly improves the robustness of the model in strong noise environment, and can accurately capture the weak degradation signs of aero-engines; the gradient-guided consistency loss improves the consistency between the model attention weight and the true contribution of features, solves the problem of "attention infidelity", and makes the model decision logic have clear physical meaning, meeting the stringent requirements of model interpretability in high-safety fields such as aerospace.

[0154] Validation data from the comparative experiment:

[0155] In this study, we adopted the root mean square error (RMSE), a commonly used evaluation metric for assessing the performance of RUL prediction models. RMSE is a standard metric for regression problems in deep learning. RMSE is defined as follows:

[0156] .

[0157] Experimental data setup:

[0158] All experiments were implemented using the TensorFlow 2.10 deep learning framework and run on a workstation equipped with an NVIDIA GeForce RTX 3090 GPU and 32GB of RAM. To ensure the reproducibility of the experimental results, we fixed the random seeds for Python, NumPy, and TensorFlow during the initialization phase.

[0159] Network model parameter settings:

[0160] Input dimension: The sliding window size (L) is uniformly set to 30. Therefore, the time-domain input shape is (30, 14). In the frequency domain, the time-frequency image generated using the continuous wavelet transform (CWT) of the ComplexMorlet wavelet is adjusted to (16, 30, 14).

[0161] Hybrid Temporal Encoder: To balance local feature extraction and temporal dependency modeling, the temporal branch employs a parallel structure. The CNN path contains two 1D convolutional layers (16 filters, kernel size 3), followed by Batch Normalization. The RNN path uses a gated recurrent unit (GRU) with 16 hidden units. To enhance the model's robustness to sensor noise, we apply [missing information - likely a specific algorithm or feature] to the input layer. Gaussian noise injection layer.

[0162] Frequency Encoder: The CWT branch utilizes a 2D-CNN structure consisting of two modules. The first module contains 32 filters, and the second module contains 64 filters, both using (3,3) convolutional kernels and (2,1) pooling layers to compress the frequency dimension while preserving temporal information.

[0163] Attention Mechanism: The latent dimension (dmodel) of the bidirectional cross-modal attention mechanism is set to 48. We employ four attention heads to capture diverse correlation patterns between the time and frequency domains. To prevent overfitting, especially on the FD001 dataset with its limited sample size, we apply a high dropout rate of 0.5 after the attention layers. The parameter settings are shown in Table 1.

[0164] Table 1:

[0165]

[0166] The models currently in use include HDNN, IAI (2023), MR-LSTM (2024), and CNN-LSTM.

[0167] SSFM (2025), MSCCAN (2025), PKGART (2025). Table 2 shows the RMSE values ​​obtained by the above models and the present invention on the FD0001, FD0002, FD0003, and FD0004 datasets.

[0168] Table 2:

[0169]

[0170] Comparative analysis of experimental results:

[0171] 1. Advantages in complex multi-condition applications (FD002 / FD004):

[0172] Our proposed method achieves state-of-the-art RMSEs of 14.15 and 13.3 on the most challenging multi-condition datasets FD002 and FD004, respectively. Particularly noteworthy is the significant performance degradation on FD004, which includes six operating conditions and multiple concurrent faults. State-of-the-art 2025 methods (such as MSCCAN and PKGART) exhibit errors of 21.79 and 18.74, respectively. In contrast, our method achieves a substantial reduction in error (nearly 29% lower than PKGART). This strongly demonstrates the effectiveness of our proposed "cluster-based anti-condition normalization" combined with a "time-frequency dual-stream architecture." Traditional models tend to misinterpret changes in operating conditions as performance degradation when faced with drastic condition transitions; however, our method removes distribution bias at the input and utilizes CWT frequency domain information at the feature end to capture hidden fault impacts, thus maintaining extremely high predictive robustness even under extremely complex operating conditions.

[0173] 2. Reasonable trade-offs in simple single-operation conditions (FD001 / FD003):

[0174] On the FD001 and FD003 datasets, which have simple operating conditions without drastic fluctuations, the PKGART method from 2025 achieved the best performance (11.33 and 9.84), followed closely by our proposed method (14.0 and 11.13). This phenomenon is logical in deep learning: because the FD001 and FD003 datasets themselves lack complex frequency abrupt changes and operating condition jumps, models that rely purely on time-domain sequence pattern mining (such as PKGART) are prone to reaching the upper bound of fitting. Our proposed method, due to the introduction of complex CWT frequency domain transformation and cross-modal feature alignment mechanism (GGCL), may lead to a slight "model capacity overflow" on overly simple datasets. However, considering the significant safety improvement our proposed method brings in extreme, real-world industrial scenarios like FD002 / FD004, this trade-off in simple scenarios is worthwhile and has engineering value.

[0175] Ablation experiment:

[0176] Ablation experiments were conducted using the Time encoder only model (retaining only the time domain branch), the CWT encoder only model (using only the frequency domain branch), the No-crossattention model (simple concatenation of time and frequency domain features), the No-GGCL model (removing GGCL from the loss function and relying solely on traditional loss for training), and the proposed model (this invention). The specific data are shown in Table 3 below.

[0177] Table 3:

[0178]

[0179] Analysis of ablation test results:

[0180] To further verify the independent contributions of the proposed innovative modules to the final RUL prediction performance, we designed four variant models for ablation experiments. The results are shown in the table.

[0181] 1. Verification of complementarity between the time and frequency domains (comparison between Time encoder only / CWT encoder only):

[0182] Frequency domain missing: When only the time-domain branch is retained (Time encoder only), the RMSE of the model on the complex dataset FD004 surges from 13.3 to 16.89. This confirms that even after EWMA smoothing, the simple time-domain signal cannot completely decouple strong noise and complex degradation characteristics under multiple operating conditions, and frequency domain information must be introduced to supplement the implicit energy distribution.

[0183] Temporal domain deficiency: When only the frequency domain branch (CWT encoder only) is used, the model performs the worst on all datasets (e.g., FD002 shows a spike to 17.04). This indicates that while CWT can capture transient fault impacts, due to the locality of wavelet transform, it easily misses the macroscopic monotonic degradation trend of the device throughout its entire lifecycle. Therefore, the time domain manages the "global degradation trend," while the frequency domain captures "local anomalous changes," and the combination of both is indispensable.

[0184] 2. The Necessity of Cross-Modal Attention (Comparison with No-Crossattention): When cross-modal attention is removed and only simple concatenation of time-domain and frequency-domain features is performed, the model's performance on FD002 / 003 / 004 deteriorates by approximately 1 to 1.5. This indicates that brute-force feature fusion cannot effectively handle the heterogeneity between time-frequency features. The multi-head cross-modal attention mechanism introduced in this paper can dynamically calculate the feature importance of 14 sensors in the time and frequency domains at different degradation stages, effectively suppressing interference from redundant channels.

[0185] 3. Contribution of Graph Representation Consistency Loss (Comparison with No-GGCL): When GGCL is removed from the loss function (No-GGCL), and training is performed using only the traditional loss function, the prediction error of the model rebounds on all four datasets (e.g., FD004 increases from 13.3 to 13.7). This verifies that in complex variable operating condition noise environments, the time-domain representation and frequency-domain representation are prone to latent space deviation. The GGCL constraint acts as a link, forcibly bridging the distance between multimodal features under the same fault state, enhancing the model's noise resistance and consistency during feature extraction. Overall, the proposed complete model achieves optimal comprehensive performance.

[0186] The above description is merely a specific embodiment of the present invention. Various examples and illustrations do not constitute a limitation on the substantive content of the present invention. Those skilled in the art can modify or transform the specific embodiments described above after reading the specification without departing from the essence and scope of the invention.

Claims

1. A method for predicting the remaining service life of an aero-engine under operating conditions, comprising performing data preprocessing on monitoring data of the aero-engine in step S1, characterized in that: Following the data preprocessing in step S1, the following steps are also included: Step S2: Convert the preprocessed one-dimensional time series into a time-domain series and a time-frequency scale map; Step S3: Extract the evolution features in the time domain and the energy features in the frequency domain; Step S4: Construct time-domain guided frequency-domain paths and frequency-domain guided time-domain paths, generate cross-modal attention maps, obtain fused features through residual fusion, extract the feature vector of the last time step in the fused sequence, and input it into the subsequent prediction network; Step S5: Prediction; Input the fused feature vector output from step S4 into the multilayer perceptron prediction network to output the predicted remaining service life of the aero-engine. .

2. The method for predicting the remaining service life of an aero-engine under operating conditions according to claim 1, characterized in that: Step S5 includes: S5-1: Predicted Output: The fused feature vector output from step S4 is input into a multilayer perceptron prediction network. The multilayer perceptron uses two fully connected layers with ReLU activation function, and the output layer is a single-neuron linear layer. The final output is the predicted value of the remaining service life of the aero-engine. ; S5-2: Constructing a Teacher Distribution Model During the backpropagation process of the model, the predicted values ​​are calculated. Gradient relative to the attention map The absolute value is taken to obtain the feature sensitivity map; a temperature coefficient is applied to the sensitivity map. The Softmax function is used for normalization to construct a teacher distribution model T that reflects the true contribution of features; S5-3: Calculate the consistency loss: The original attention weight distribution model generated during the forward propagation process is compared with the teacher distribution model T constructed in S5-2, and the KL divergence between the two is calculated. This KL divergence is defined as the consistency loss. The formula is: ； in This is a gradient sensitivity map. Attention weights; S5-4: Joint Optimization Construct a multi-objective joint loss function, the formula of which is: ； Explanation of each loss item: Mean squared error loss, which is the predicted value. Mean square error compared to the true RUL label y(t); Weighted consistency loss This is the consistency loss weighting coefficient; Weighted regularization loss This represents the regularization loss weight coefficient.

3. The method for predicting the remaining service life of an aero-engine under operating conditions according to claim 1, characterized in that: The data preprocessing step S1 further includes the following steps: S1-1: Feature Optimization: Monitoring data is collected from multiple sensor monitoring channels to form an original dataset. Variance analysis is performed on the full life cycle data in the original dataset. If the data monitored by some sensors are constant in value or the variance approaches 0 throughout the entire operating cycle, the feature information corresponding to the data monitored by those sensors is removed. The set of feature information corresponding to the remaining data monitored by the sensors is used as the retained sensor sequence. S1-2: Exponentially weighted moving average noise reduction: The retained sensor sequences were smoothed using an exponentially weighted moving average and used as the training set. The smoothing process is as follows: for the observation value of the i-th sensor at time t... its smoothed value The calculation formula is as follows: ; in, For smoothing coefficients; S1-3: Anti-condition normalization based on K-Means clustering: Using the three operation settings channels of height, Mach number, and throttle resolution angle as the feature space, the K-Means algorithm is used to divide the samples into K clusters on the training set, with each cluster representing an operation mode; Calculate the mean vector of sensor data within each cluster. and standard deviation vector ; For samples belonging to the k-th cluster Standardization is performed, and the formula is: 。 4. The method for predicting the remaining service life of an aero-engine under operating conditions according to claim 3, characterized in that: During the testing phase, the test samples are first assigned to the training cluster center with the closest Euclidean distance based on their operational settings, and then the corresponding training set statistics are used. Perform the normalization process in steps S1-3.

5. The method for predicting the remaining service life of an aero-engine under operating conditions according to claim 3, characterized in that: The data preprocessing step S1 further includes the following steps: S1-4: Piecewise linear RUL tag construction; A piecewise linear function is used to truncate the true RUL, as follows: when the true RUL is greater than a set threshold, the label is set to the set threshold; otherwise, the true value is retained; the formula is as follows: 。 6. The method for predicting the remaining service life of an aero-engine under operating conditions according to claim 1, characterized in that: Step S2 includes the following: S2-1: Random noise injection based on manifold smoothing: Preprocessed input data during training Implement dynamic Gaussian noise injection; by superimposing zero mean and standard deviation Gaussian noise, smoothing the decision manifold in the feature space; The calculation formula is: ； S2-2: CWT Time-Frequency Feature Extraction: The frequency domain energy distribution is explored using continuous wavelet transform, and complex Morlet wavelet is selected as the basis function. The wavelet transform formula is: ； in, As a scale factor, The translation factor is... Let be the complex conjugate of the complex Morlet wavelet. The mathematical form of the complex conjugate of the complex Morlet wavelet is: ; Convert the N sensor signals within each time window into a time-frequency tensor of size (N, H, L). ， Time-frequency tensor As input to the frequency domain encoder.

7. The method for predicting the remaining service life of an aero-engine under operating conditions according to claim 1, characterized in that: Step S3 includes the following: S3-1: Noise-resistant hybrid timing coding; Local feature extraction: Two stacked one-dimensional convolutional layers are used. The first layer captures high-frequency noise and transient impacts, and the second layer aggregates local degradation patterns. Global dependency modeling: Accessing a gated loop unit containing hidden units to capture long-distance temporal dependencies; S3-2: Asymmetric time-frequency coding, processing time-frequency tensors : Asymmetric max pooling: Asymmetric max pooling is applied after each convolutional block to reduce dimensionality and keep the time step constant; Channel recalibration: At the end of frequency domain feature extraction, the SE-Block channel attention module is applied to learn the weights of the frequency domain feature channels, enhance the feature response of key engine fault frequency bands, suppress invalid frequency band interference, and finally output frequency domain feature codes. .

8. The method for predicting the remaining service life of an aero-engine under operating conditions according to claim 1, characterized in that: Step S4 includes: Two independent cross-modal attention interaction paths are constructed to achieve bidirectional guidance of temporal and frequency domain features: Time-domain guided frequency-domain path: encoding with time-domain features For the query vector, encoded using frequency domain features These are key vectors and value vectors; Frequency-domain to time-domain path: Encoding with frequency domain features The query vector is encoded using time-domain features. These are the key vector and the value vector.

9. The method for predicting the remaining service life of an aero-engine under operating conditions according to claim 8, characterized in that: In step S4, the fusion feature sequences of the two paths are aggregated at time steps, and only the feature vector of the last time step in the fusion feature sequence is extracted. This vector is then used as the input feature of the subsequent prediction network.

10. The method for predicting the remaining service life of an aero-engine under operating conditions according to claim 7, characterized in that: Step S3-1, following global dependency modeling, also includes adaptive feature recalibration. This adaptive feature recalibration includes: 1) Squeezing operation: For the temporal features output by the GRU, global average pooling is used to aggregate feature information along the time dimension, eliminating changes in the time dimension and generating a channel-level global descriptor reflecting the global response of the sensor channels; 2) Activation operation: A two-layer multilayer perceptron with a bottleneck structure is used to process the global descriptor, learning the nonlinear dependencies between different sensor channels, and generating feature importance weight coefficients s between 0 and 1 using an activation function; 3) Recalibration and mapping: Based on the generated weight coefficients s, the original feature channels are reorganized element-wise to enhance the feature weights of channels containing significantly degraded information, suppress channel interference containing high-frequency noise or irrelevant information, and map the weighted features to a unified latent space dimension through a fully connected layer with L2 regularization. The final output is the temporal feature code. .

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