Equipment residual life prediction method fusing dynamic decomposition and Koopman operator

Abstract

The invention discloses an equipment residual life prediction method fusing dynamic decomposition and a Koopman operator, and the method comprises the steps: decomposing the preprocessed multi-sensor time sequence data into a trend term and an unstable term through a time sequence decomposition module, and forming a comprehensive trend representation; establishing a Koopman-GRU module, extracting time sequence dependence characteristics in the comprehensive trend representation through the GRU module, and performing linear modeling on the time sequence dependence characteristics in a high-dimensional space by using a Koopman operator module to obtain a space-time state tensor; on the basis of a channel interactive learning module, global core representation between channels is used for capturing the dependency relationship between the sensors, and the feature expression ability is enhanced; generating a final RUL prediction result by using a linear layer of a residual structure in the prediction module; compared with the prior art, the method has the advantages that the feature representation of the multi-sensor time series data is more sufficient, dynamic aggregation and redistribution of the spatial-temporal features are achieved, and then accurate prediction of the nonlinear degradation process of multi-source data monitoring is achieved.

Description

Technical Field

[0001] This invention relates to the field of fault prediction and health management of industrial equipment, and in particular to a method for predicting the remaining life of equipment that integrates dynamic decomposition and the Koopman operator. Background Technology

[0002] Remaining Useful Life (RUL) prediction is a core component of Prognostics and Health Management (PHM) research, enabling the advance estimation of equipment's remaining service life. RUL reveals future degradation trends, helping equipment managers to develop and implement targeted maintenance plans in advance, thereby ensuring the continued stable operation of equipment and reducing maintenance costs. RUL prediction plays a crucial role in PHM; reliable RUL predictions can minimize the risk of catastrophic failures.

[0003] Currently, RUL prediction techniques are mainly divided into two categories: data-driven methods and physical model-based methods. Physical model-based methods use physical models of the equipment and its main components for RUL prediction, requiring researchers to have a deep understanding of the system's physical mechanisms. However, with the rapid development of technology, the internal structure of modern equipment is extremely complex and highly coupled, greatly increasing the difficulty of establishing accurate physical degradation models. Furthermore, physical model-based methods are computationally cumbersome and cannot efficiently handle constantly updated nonlinear parameters. Data-driven methods, on the other hand, do not need to consider the equipment's inherent physical behavior. They can directly capture the relationship between equipment condition monitoring data and the equipment's degradation state, mining hidden features related to equipment degradation from measurement data to achieve RUL prediction. Data-driven methods are easier to build with lower complexity RUL prediction models, can more efficiently collect data samples from different sensors, and facilitate adaptive parameter learning and updates. Overcoming the shortcomings of model-based methods, data-driven methods are increasingly popular in RUL prediction due to their outstanding generalization ability and robust nonlinear representation.

[0004] Two important branches of data-driven approaches in current technology are the currently popular deep learning (DL) and traditional machine learning (ML). Traditional machine learning methods mainly include Bayesian methods, particle filtering methods, and Extreme Learning Machines (ELM). However, traditional machine learning requires manual extraction of relevant features from the data; if feature extraction is inappropriate, it is difficult to achieve good prediction accuracy. The prediction performance of traditional machine learning relies excessively on the quality of data features, ignoring the time dependence of the data, making it unsuitable for processing multidimensional time series. In contrast, deep learning methods are better at extracting and processing data features. Deep learning methods do not require manual feature extraction and can directly learn complex feature representations from the data. From data input to RUL output, deep learning follows an end-to-end training process, effectively avoiding the influence of human factors. Compared to traditional machine learning, deep learning has superior robustness and prediction accuracy.

[0005] Deep learning models, such as Recurrent Neural Networks (RNNs) and Convolutional Neural Networks (CNNs), have been widely applied to the task of predicting Remaining Useful Life (RUL). Currently, equipment is rapidly developing towards automation and intelligence, becoming increasingly complex, and its operation and load are unstable. This leads to a strong nonlinear trend in the degradation trajectory of system performance, making it more difficult to grasp the failure patterns. The temporal and spatial characteristics of system monitoring data are the two most fundamental dimensions, especially when the system is complex or has multiple monitoring points, making the capture of spatial characteristics particularly important. However, existing methods for RUL prediction based on deep learning models mainly focus on modeling the temporal characteristics of time series data, neglecting the spatial relationships between data variables, and their modeling of the unstable changes in equipment performance degradation trends is insufficient. Therefore, the problem of insufficient prediction accuracy for nonlinear degradation processes monitored by multi-source data is particularly prominent. Summary of the Invention

[0006] The purpose of this invention is to provide a method for predicting the remaining life of equipment by integrating dynamic decomposition and the Koopman operator, so as to achieve accurate prediction of nonlinear degradation processes monitored by multi-source data.

[0007] The technical solution to achieve the purpose of this invention is: a method for predicting the remaining life of equipment by integrating dynamic decomposition and the Koopman operator, the specific steps of which are as follows:

[0008] Step 1: Acquire multi-sensor time-series data and perform preprocessing;

[0009] Step 2: Use the time series decomposition module to decompose the preprocessed multi-sensor time series data into trend terms and unstable terms, and form a comprehensive trend representation;

[0010] Step 3: Establish the Koopman-GRU module, extract the temporal dependency features in the comprehensive trend representation through the GRU module, and use the Koopman operator module to linearly model the temporal dependency features in the high-dimensional space to obtain the spatiotemporal state tensor.

[0011] Step 4: Using the spatiotemporal state tensor as input, and based on the channel interaction learning module, use the global core representation between channels to capture the dependencies between sensors and enhance feature representation capabilities.

[0012] Step 5: Generate the final RUL prediction result using the linear layer of the residual structure in the prediction module;

[0013] Step 6: Evaluate the prediction results using root mean square error and S-score.

[0014] The significant advantages of this invention compared to existing technologies are:

[0015] (1) The present invention decomposes the preprocessed multi-sensor time series data into separate trend terms and unstable terms through the time series decomposition module, so that the feature representation of the multi-sensor time series data is more complete, thereby improving the prediction accuracy of the nonlinear degradation process of multi-source data monitoring.

[0016] (2) In this invention, the channel interaction learning module (STAR) realizes the dynamic aggregation and redistribution of spatiotemporal features, which solves the problem of insufficient feature interaction in traditional methods, thereby improving the prediction accuracy of nonlinear degradation process of multi-source data monitoring.

[0017] (3) In this invention, by establishing the Koopman-GRU module, the nonlinear time series is mapped to a high-dimensional linear space, which can predict the future state or trend at a more distant time step, thereby significantly improving the long-term prediction capability. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the overall process of the equipment remaining life prediction method of the present invention;

[0019] Figure 2 This is a STAR diagram illustrating the equipment remaining life prediction method of the present invention.

[0020] Figure 3 This is the structure of the prediction module of the present invention;

[0021] Figure 4The results show the validation of the prediction method of the present invention on the C-MAPSS dataset, where (a) is a comparison between the predicted RUL and the actual RUL of the FD001 subset, (b) is a comparison between the predicted RUL and the actual RUL of the FD002 subset, (c) is a comparison between the predicted RUL and the actual RUL of the FD003 subset, and (d) is a comparison between the predicted RUL and the actual RUL of the FD004 subset. Detailed Implementation

[0022] The terminology used in this invention is for illustrative purposes only and is not intended to limit the invention. The following description, in conjunction with the appendix, further clarifies this concept. Figure 1-4 The following is a detailed description of some embodiments of the present invention.

[0023] This invention proposes a method for predicting the remaining life of equipment by integrating dynamic decomposition and the Koopman operator.

[0024] Step 1: Acquire multi-sensor time-series data and perform preprocessing.

[0025] Multi-source time series data is represented as X = {x1, x2, ..., x...} t ,...x T}, where x t ∈R N x t Let x be the multidimensional sensor observation vector at time step t, where T represents the historical window length and x is the vector vector at time step t. T Let R be the observation vector at the current time step, where N represents the number of sensors and R is the number of sensors. N It is an N-dimensional real number space.

[0026] After standardizing the multi-sensor time-series data by channel, in order to obtain a learnable data representation, a standard 1×1 convolution is used to initially fuse the inter-channel features, thereby mapping the input data to a high-dimensional latent space, as shown in formula (1).

[0027] O = Embedding(X) (1)

[0028] In the formula, O represents the preprocessed multi-sensor time-series data, and Embedding is the initial fusion operation of inter-channel features using standard 1×1 convolution.

[0029] Step 2: Use the time series decomposition module to decompose the preprocessed multi-sensor time series data into trend terms and unstable terms, and form a comprehensive trend characterization.

[0030] Affected by unstable loads and changing operating conditions, equipment degradation trajectories often exhibit nonlinearity. Therefore, accurately identifying stable degradation trends and unstable changes in time series data is crucial. Stable degradation trends (trend terms) reflect the long-term degradation behavior of equipment, while unstable changes (instability terms) capture short-term fluctuations and anomalies. This invention employs a moving average-based time series decomposition module to better separate trend and unstable components, thereby providing a more comprehensive feature representation for subsequent models.

[0031] Specifically, in the time series decomposition block of the moving average, the moving average kernel is used to extract the trend term of the time series, and the difference between the original series and the trend term is considered an unstable term. To more effectively separate the two, we adopt a quadratic decomposition method, as follows:

[0032] O t_1 =avgpool(padding(O)) (2)

[0033] O u1 =OO t_1 (3)

[0034] O t_2 =avgpool(padding(O u1 (4)

[0035] O u2 =O u1 -O t_2 (5)

[0036] Here, avgpool is the average pooling operation, and padding is the zero-padding operation at the boundaries in average pooling. t_1 For the trend term obtained from the first decomposition, O u1 For the unstable terms obtained from the first decomposition, O t_2 For the trend term obtained from the second decomposition, O u2 This is the unstable term obtained from the second decomposition.

[0037] By applying a linear transformation to the trend and instability terms, dimensional alignment and information enhancement of the feature space are achieved. The trend components from the two-level decomposition are then added element-wise to form a comprehensive trend representation, covering multi-scale trend features in the equipment degradation process.

[0038] P = Linear1(O u2 )+Linear2(O t_1 +O t_2 (6)

[0039] In the formula, Linear1 represents the linear transformation operation of the unstable term, Linear2 represents the linear transformation operation of the trend term, and P represents the comprehensive trend representation.

[0040] Step 3: Establish the Koopman-GRU module, extract the temporal dependency features in the comprehensive trend representation through the gated recurrent unit (GRU), and use the Koopman operator unit to linearly model the temporal dependency features in the high-dimensional space to obtain the spatiotemporal state tensor.

[0041] For Remaining Useful Life (RUL) prediction tasks, handling the complex dynamic processes in the sequence is a key challenge in model design. Koopman operator theory provides strong support for solving this problem by capturing the linear trends in the system by mapping the nonlinear dynamic system to a high-dimensional linear space. This invention innovatively designs a Koopman-GRU module. First, it extracts the temporal dependency features from the comprehensive trend representation through gated recurrent units (GRUs). Then, it uses Koopman operator units to perform linear dynamic evolution modeling of these features in a high-dimensional space to better describe the complex dynamic characteristics during system degradation.

[0042] Step 3.1: Extract the temporal dependency features from the comprehensive trend representation using a gated recurrent unit (GRU);

[0043] GRU is a recurrent neural network used for time series data. It dynamically controls the information flow by introducing update and reset gates to capture time-dependent features. GRU takes input p at time step t as input... t and the hidden state h from the previous moment t-1 Perform joint processing to generate the hidden state h at the current time. t The update method is as follows:

[0044] r t =σ(p t W xr +h t-1 W hr +b r (7)

[0045] u t =σ(p t W xu +h t-1 W hu +b u (8)

[0046] c t =Relu(p t W xc +r t ⊙W hc +b c(9)

[0047] h t =(1-u t )⊙h t-1 +u t ⊙c t (10)

[0048] Where, r t For the reset gate, ⊙ is the element-wise product, σ is the sigmoid activation function, and p t This represents the input of the layer at time t, h t-1 W represents the hidden state from the previous moment. xr Indicates input p t Reset gate r t The weight matrix, W hr Indicates the hidden state h in the previous moment. t-1 Reset gate r t The weight matrix, b r Indicates the offset term for resetting the door; u t To update the door, W xu This indicates the input p of this layer at time t. t Update gate u t The weight matrix, W hu Indicates the hidden state h in the previous moment. t-1 Update gate u t The weight matrix, b u This indicates updating the bias term of the gate; c t For the candidate hidden state, W xc This indicates the input p of this layer at time t. t For candidate hidden state c t The weight matrix, W hc Indicates the hidden state h in the previous moment. t-1 (After adjustment by the reset gate) regarding the candidate hidden state c t The weight matrix, b c is the bias term for the candidate hidden state; ReLU is the activation function.

[0049] The GRU structure can effectively capture the temporal dependency features in the comprehensive trend representation, obtain the hidden states H at all time steps, and represent H = {h1, h2, ..., h...} t ,...,h T}

[0050] Step 3.2: Use the Koopman operator unit to linearly model the temporal dependency features in the high-dimensional space to obtain the spatiotemporal state tensor;

[0051] The Koopman operator is a tool for mapping nonlinear dynamic systems to a high-dimensional linear space. By introducing the Koopman operator, the linear trend of nonlinear time-dependent features can be captured in a high-dimensional space. Specifically, the Koopman operator accepts the GRU hidden state H and projects it into a high-dimensional space, simulating dynamic evolution through a linear transformation.

[0052]

[0053] in, W represents the feature representation in high-dimensional space. proj This is a linear layer with ReLU activation. The Koopman operator is used for features. Perform a linear transformation to capture the dynamic evolution in the sequence and remap it to the same feature dimensions as the original data.

[0054]

[0055] Here, K is a trainable Koopman matrix, representing the linear dynamic relationship in the feature space. This represents the feature representation after a linear transformation. W inv Z is a linear layer with ReLU activation. Z is the spatiotemporal state tensor obtained in step 3.

[0056] Step 4: Using the spatiotemporal state tensor as input, and based on the channel interaction learning module, use the global core feature representation between channels to capture the dependencies between sensors and enhance the feature representation capability of each channel.

[0057] Capturing the dependencies between channels (variables) is a crucial method for improving the accuracy of remaining lifetime prediction. Traditional attention mechanisms, when used to capture these dependencies, only consider the temporal features of the time series, resulting in insufficient feature interaction and incurring computational complexity proportional to the square of the number of channels; for example... Figure 2 As shown, this invention introduces a Channel Interaction Learning Module (STAR) (STarAggregateRedistribute). This module generates a global core representation by aggregating information from each channel (Series) and redistributes this representation to each channel, realizing the dynamic aggregation and redistribution of spatiotemporal features, enhancing the feature representation capability of each channel, and with simple computational complexity.

[0058] Step 4.1: Extracting core information;

[0059] First, the sequence representation of each channel is projected and then combined using a multilayer perceptron (MLP) to generate a channel-level feature representation:

[0060] u i =MLP1(z i (14)

[0061] Where i represents the channel number (i.e., sensor number), i = 1, 2, ..., N, u i The feature representation at the i-th channel level, u i The output dimension is called the core dimension, MLP1 represents the operation on the i-th channel of the multilayer perceptron, z i For each channel input in the spacetime state tensor, z i ∈R N ,i=1,2,...,N.

[0062] Then, a stochastic pooling mechanism is used to integrate these channel-level feature representations to generate a global core feature representation. This core feature representation effectively extracts the important information from all channels and represents the global properties of the entire spatiotemporal state tensor.

[0063] U = Sto_Poolomh(u 1 ,u 2 ,...,u i (15)

[0064] Where Sto_Poolomh represents the random pooling operation, and U represents the global core feature representation.

[0065] Step 4.2: Information reallocation;

[0066] After generating the global core feature representation U, it needs to be redistributed to each channel to enhance the local feature representation of each channel. Therefore, the global core feature representation U is then compared with the feature representation u of each channel. i The features are concatenated to generate an enhanced channel feature representation f. i :

[0067] f i =Concat(u i ,U) (16)

[0068] Concat represents the concatenation operation.

[0069] At this point, the features of each channel contain both local information from that channel and global information from other channels. Finally, another multilayer perceptron (MLP) is used to represent the concatenated strong channel feature representation f. i Projection is performed to generate the final channel feature representation.

[0070]

[0071] MLP2 represents another type of multilayer perceptron operation.

[0072] Step 5: Represent the final channel features The input device residual prediction module uses the linear layer of the residual structure in the prediction module to generate the final RUL prediction result.

[0073] The prediction module uses a linear layer of the residual structure to generate the final RUL point prediction results.

[0074] The prediction module of this invention is based on a linear layer with a residual structure, serving as the final output module. Specifically, as shown... Figure 3 As shown, the prediction module is a stacked linear layer structure with ReLU activation. Residual connections are used to mitigate gradient vanishing, and dropout (neuron dropping out) and layer normalization are applied to the output linear layer. Finally, the final prediction result Y is obtained using linear layers.

[0075] Step 6: Evaluate the prediction results using the root mean square error (RMSE) and S-score (standard score).

[0076] RMSE assesses the deviation between predicted and actual values, and is given by the following formula:

[0077]

[0078] Where m is the number of test samples, and q is the index of the test sample. Y represents the predicted RUL value for the q-th sample (q = 1, 2, ..., m). q This represents the true RUL value predicted for the q-th sample (q = 1, 2, ..., m). The lower the RMSE, the better the prediction performance.

[0079] The S-score is used to evaluate the performance of the RUL (Reliable Undergoing Range) prediction. The S-score focuses on whether the model can accurately predict the engine failure time. A predicted value less than the actual failure time is generally better than a predicted value greater than the actual failure time. This is mainly because when the predicted value is less than the actual failure time, maintenance personnel usually take measures earlier to prevent engine failure. Therefore, a predicted value greater than the actual failure time will be penalized more severely than a predicted value less than the actual failure time. The S-score is expressed as follows:

[0080]

[0081] In the formula, m is the number of test samples, a is a constant, and d q The difference between the actual RUL value and the predicted RUL value, i.e. When d q When < 0, a = -13; otherwise, a = 10.

[0082] Example:

[0083] Based on the C-MAPSS (Commercial Modular Aero-Propulsion System Simulation) dataset, the remaining service life of turbofan aero-engines is predicted. The C-MAPSS dataset simulates four datasets under different combinations of operating conditions and failure modes: FD001, FD002, FD003, and FD004. Data for each flight cycle in this dataset is measured by 21 sensors under three operating conditions; a single cycle data point is a 24-dimensional feature vector. The engine is healthy in the early stages of operation, then its performance begins to decline until failure occurs. In the test dataset, the degradation process ends sometime before system failure. Dataset information is shown in Table 1.

[0084] Table 1 Features of the four datasets

[0085]

[0086] Each dataset consists of three subsets: a training set, a test set, and the actual RUL for each engine in the test set. The training set data with complete degradation trajectories is used to train the proposed method, while the test set data with incomplete degradation trajectories is used to simulate an online application to obtain RUL predictions. The relevant parameters involved in the method include training epochs, batch size, time step, and optimizer. The training epochs are 100, and an early stopping mechanism is introduced: if the validation set loss does not improve within 10 consecutive epochs, training stops, and the current optimal model is saved. The optimizer is the Adam optimizer. Since the failure modes and operating conditions of the four subsets are different, the batch size, learning rate, and core dimension parameters are set differently for each subset, as shown in Table 2.

[0087] Table 2 Hyperparameter Settings

[0088]

[0089] As shown in Table 3, the MST-K (Mechanical Remaining Life Prediction Method Integrating Dynamic Decomposition and Koopman Operator) proposed in this paper achieves satisfactory results in engine RUL prediction. The method proposed in this patent essentially surpasses or is roughly on par with existing state-of-the-art solutions in RUL prediction.

[0090] Table 3 Comparison and Analysis of Methods

[0091]

[0092] The predicted RUL is further compared with the actual RUL, and the results are visualized, such as... Figure 4 As shown. From Figure 4 As can be seen, with the increase of engine cycle number, the RUL predicted by the method proposed in this invention becomes closer and closer to the actual RUL. This indicates that the RUL prediction accuracy of the method proposed in this patent usually increases over time. The main reason is that as time goes by, more and more engine status data are detected, which enables the method proposed in this patent to predict the RUL of the engine more accurately.

[0093] Experimental results show that the method proposed in this invention outperforms other existing methods.

[0094] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for predicting remaining equipment lifetime by integrating dynamic decomposition and the Koopman operator, characterized in that, The specific steps are as follows: Step 1: Acquire multi-sensor time-series data and perform preprocessing; Step 2: Use the time series decomposition module to decompose the preprocessed multi-sensor time series data into trend terms and unstable terms, and form a comprehensive trend representation; Step 3: Establish the Koopman-GRU module, extract the temporal dependency features in the comprehensive trend representation through the GRU module, and use the Koopman operator module to linearly model the temporal dependency features in the high-dimensional space to obtain the spatiotemporal state tensor. Step 4: Using the spatiotemporal state tensor as input, and based on the channel interaction learning module, use the global core representation between channels to capture the dependencies between sensors and enhance feature representation capabilities. Step 5: Generate the final RUL prediction result using the linear layer of the residual structure in the prediction module; Step 6: Evaluate the prediction results using root mean square error and S-score.

2. The method for predicting the remaining life of equipment according to claim 1, characterized in that, In step 1, the multi-source time series data is represented as X = {x1, x2, ..., x...} t ,...x T }, where x t ∈R N x t Let x be the multidimensional sensor observation vector at time step t, where T represents the historical window length and x is the vector of the sensor observation vector at time step t. T Let R be the observation vector at the current time step, where N represents the number of sensors and R is the number of sensors. N It is an N-dimensional real number space; After standardizing the multi-sensor time-series data by channel, a standard 1×1 convolution is used to initially fuse inter-channel features, thereby mapping the input data to a high-dimensional latent space. The formula is as follows: O = Embedding(X); In the formula, O represents the preprocessed multi-sensor time-series data, and Embedding is the initial fusion operation of inter-channel features using standard 1×1 convolution.

3. The method for predicting the remaining life of equipment according to claim 1, characterized in that, In step S2, the time series decomposition module based on moving averages uses the moving average kernel to extract the trend term of the time series. The difference between the original series and the trend term is considered an unstable term. A quadratic decomposition method is used to decompose the trend term and the unstable term, as shown in the following formula: O t_1 =avgpool(padding(O)) The u1 =OO t_1 O t_2 =avgpool(padding(O u1 )) The u2 =O u1 -O t_2 Here, avgpool is the average pooling operation, and padding is the zero-padding operation at the boundaries in average pooling. t_1 For the trend term obtained from the first decomposition, O u1 For the unstable terms obtained from the first decomposition, O t_2 For the trend term obtained from the second decomposition, O u2 This is the unstable term obtained from the second decomposition.

4. The method for predicting the remaining life of equipment according to claim 3, characterized in that, By performing linear transformations on the trend and instability terms, dimensional alignment and information enhancement of the feature space are achieved. The trend components of the two-level decomposition are added element-wise to form a comprehensive trend representation, covering multi-scale trend features in the equipment degradation process. P=Linear1(O u2 )+Linear2(O t_1 +O t_2 ); In the formula, Linear1 represents the linear transformation operation of the unstable term, Linear2 represents the linear transformation operation of the trend term, and P represents the comprehensive trend representation.

5. The method for predicting the remaining life of equipment according to claim 1, characterized in that, GRU, or Gated Recurrent Unit, dynamically controls the information flow by introducing update and reset gates to capture time-dependent features. GRU uses the input p at time step t... t and the hidden state h from the previous moment t-1 Perform joint processing to generate the hidden state h at the current time. t The update method is as follows: r t =σ(p t W xr +h t-1 W hr +b r ) u t =σ(p t W xu +h t-1 W hu +b u ) c t =Relu(p t IN xc +r t ⊙W hc +b c ) h t =(1-u t )⊙h t-1 +u t ⊙c t Where, r t For the reset gate, ⊙ is the element-wise product, σ is the sigmoid activation function, and p t This represents the input of the layer at time t, h t-1 W represents the hidden state from the previous moment. xr Indicates input p t Reset gate r t The weight matrix, W hr Indicates the hidden state h in the previous moment. t-1 Reset gate r t The weight matrix, b r Indicates the offset term for resetting the door; u t To update the door, W xu This indicates the input p of this layer at time t. t Update gate u t The weight matrix, W hu Indicates the hidden state h in the previous moment. t-1 Update gate u t The weight matrix, b u This indicates updating the bias term of the gate; c t For the candidate hidden state, W xc This indicates the input p of this layer at time t. t For candidate hidden state c t The weight matrix, W hc Indicates the hidden state h in the previous moment. t-1 For candidate hidden state c t The weight matrix, b c The bias term for the candidate hidden state; ReLU is the activation function; The GRU structure is used to capture temporal dependency features in the comprehensive trend representation, obtaining the hidden states at all time steps, defined as H = {h1, h2, ..., h...} t ,...,h T } 6. The method for predicting the remaining life of equipment according to claim 5, characterized in that, The Koopman operator captures the linear trend of nonlinear time-dependent features in a high-dimensional space; specifically, the Koopman operator accepts the GRU hidden state H and projects the hidden state H into a high-dimensional space, simulating dynamic evolution through linear transformation. Features in high-dimensional space are represented as follows: in, W represents the feature representation in high-dimensional space. proj A linear layer with ReLU activation function; the Koopman operator pairs features. Perform a linear transformation to capture the dynamic evolution in the sequence and remap it to the same feature dimensions as the original data; Where K is a trainable Koopman matrix, representing the linear dynamic relationship in the feature space. W represents the feature representation after linear transformation. inv Z is a linear layer with ReLU activation function, and Z is the spatiotemporal state tensor obtained in step 3.

7. The method for predicting the remaining life of equipment according to claim 1, characterized in that, The specific method for extracting core information in the channel interaction learning module in step 4 is as follows: The sequence representation of each channel is projected and combined using a multilayer perceptron to generate a channel-level feature representation; at i =MLP1(z i ) Where i is the channel number, i = 1, 2, ..., N, u i The feature representation at the i-th channel level and the output dimension are called the core dimension. MLP1 represents the multilayer perceptron operation on the i-th channel. i For each channel input in the spacetime state tensor, z i ∈R N i = 1, 2, ..., N; A random convergence mechanism is used to integrate channel-level feature representations to generate a global core feature representation. This global core feature representation effectively extracts important information from all channels and represents the global characteristics of the entire spatiotemporal state tensor. U=Sto_Poolomh(u 1 ,in 2 ,...,in i ) Where Sto_Poolomh represents the random pooling operation, and U represents the global core feature representation.

8. The method for predicting the remaining life of equipment according to claim 7, characterized in that, In the channel interaction learning module of step 4, the specific method for information redistribution is as follows: After generating the global core feature representation U, the generated global core feature representation needs to be redistributed to each channel to enhance the local feature representation of each channel; The global core representation U and the feature representation u of each channel are compared. i The channels are concatenated to generate an enhanced channel representation f. i : f i =Concat(u i ,U) Here, Concat represents the concatenation operation; At this point, the features of each channel contain both local information of that channel and global information from other channels; another MLP is used to project the concatenated features to generate the final channel feature representation. : MLP2 represents another type of multilayer perceptron operation.

9. The method for predicting the remaining life of equipment according to claim 1, characterized in that, The prediction module is a stacked linear layer structure with ReLU activation. Residual connections are used to mitigate gradient vanishing, and dropout and layer normalization are applied to the output linear layer. Finally, the final prediction result Y is obtained using the linear layer.

10. The method for predicting the remaining life of equipment according to claim 1, characterized in that, RMSE assesses the deviation between predicted and actual values, and is given by the following formula: Where m is the number of test samples, and q is the index of the test sample. Y represents the predicted RUL value for the q-th sample (q = 1, 2, ..., m). q This represents the true RUL value predicted for the q-th sample (q = 1, 2, ..., m). The lower the RMSE, the better the prediction performance.

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