Method for predicting remaining useful life of aero-engine based on MDGODE

Abstract

The application discloses an aero-engine RUL prediction method based on MDGODE, which comprises the following steps: (1) collecting aero-engine performance degradation data and constructing RUL labels; (2) establishing an MDGODE model, including a multi-scale autocorrelation decomposition module, a multi-scale dynamic graph structure learning module, a space-time coupling graph neural ordinary differential equation module and a multi-scale attention fusion module; (3) training the MDGODE model by using the collected aero-engine performance degradation data; (4) extracting the comprehensive space-time representation of the aero-engine performance degradation data to be predicted by using the trained MDGODE, and inputting the comprehensive space-time representation into a regressor to predict the final remaining useful life value of the aero-engine. The MDGODE has strong space-time representation capability and robustness for the complex non-stationary performance degradation process of the aero-engine, and can significantly improve the RUL prediction accuracy of the aero-engine.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine life prediction technology, and specifically relates to an aero-engine RUL prediction method based on MDGODE. Background Technology

[0002] As the most critical component of an aircraft, aero-engines operate under extreme conditions of high temperature, high pressure, and high speed for extended periods. Inevitably, their components undergo performance degradation (such as creep, fatigue, and corrosion), leading to sudden failures. Sudden failures of aero-engines can cause flight safety accidents and result in severe economic losses. Remaining Useful Life (RUL) prediction, as a key technology for predictive and health management, can provide timely assessment and early warning of the health status of aero-engines. This is of great significance for reducing aero-engine maintenance costs, preventing sudden flight failures, and improving the safety and reliability of aero-engines and aircraft.

[0003] Currently, the mainstream methods for predicting the remaining service life (RUL) of aero-engines fall into two categories: physical model-based methods and data-driven methods. Physical model-based methods characterize the performance degradation process of aero-engines by establishing precise physical mechanism models, describing the damage accumulation process of engine components under extreme environments such as high temperature, high pressure, and high speed, thereby predicting the overall RUL of the aero-engine. However, due to the complexity of aero-engine structure and mechanical principles, as well as the interference of uncertain factors, the development cost of precise physical models is high, thus limiting the accuracy and adaptability of RUL prediction using physical model-based methods. Data-driven methods collect historical operating data of aero-engines and use machine learning or deep learning techniques to learn the performance degradation patterns from this data, thereby establishing predictive models to achieve overall RUL prediction for aero-engines. For example, Deng et al. extracted features from key operating parameter data of aero-engines using a convolutional neural network (CNN), and then input the extracted features into a long short-term memory neural network (LSTM) model to predict the RUL of aero-engines; Lu et al. combined channel attention CNN and Transformer to enhance the capture of key nodes of temporal degradation for the prediction of aero-engine RUL; Pater et al. built an aero-engine RUL prediction model based on a long short-term memory autoencoder (LSTM-AE), that is, first reconstructed the temporal degradation data of the engine through an autoencoder (AE) to extract aero-engine health indicators, and then used LSTM to capture the temporal dependence of the health indicators to predict the RUL of aero-engines. However, these existing data-driven RUL prediction methods (mainly represented by deep learning-based RUL prediction methods) tend to utilize the time dimension of dependencies, while they are significantly insufficient in utilizing the inherent spatial topological relationships in aero-engine sensor signals (i.e., key operating parameter data). Focusing solely on the time dependence of sensor signals will limit the accuracy of aero-engine RUL prediction and make it difficult to adapt to the complex actual operating conditions of aero-engines.

[0004] To efficiently capture the spatial correlation of aero-engine sensor signals, researchers have begun using Graph Neural Networks (GNNs) to extract spatial features from multiple sensor signals and perform RUL prediction of aero-engines by combining temporal and spatial features. For example, Li et al. used a bidirectional long short-term memory network to capture the temporal correlation of sensor signals and a hierarchical graph representation layer to capture the spatial correlation of sensor signals, thereby capturing the spatiotemporal dependence of sensor signals and attempting to improve the prediction accuracy of aero-engine RUL in this way. Kong et al. first used an improved attention mechanism to extract the temporal features of aero-engine sensor signals, then used GNNs to mine the spatial features and structural information of sensor signals, and finally input the spatiotemporal fusion features into a fully connected layer for aero-engine RUL prediction.

[0005] While the aforementioned GNN-based methods have shown some positive effects in RUL prediction for aero-engines, they still have the following drawbacks: Existing GNN models often employ discrete neural architectures, which are prone to oversmoothing, meaning they lose the ability to capture local differences, making it difficult to uncover deep spatial correlations in sensor signals; discrete neural architectures also lead to discontinuous latent state trajectories, thus increasing prediction errors; simultaneously, existing fixed graph structure learning models rely too heavily on prior knowledge and cannot accurately reflect the dynamic spatial interactions of sensor signals during the complex degradation process of aero-engines; furthermore, considering only the spatial dependencies of sensor signals at a single time scale ignores the differences in potential degradation patterns at different time granularities, thus limiting the ability to capture non-stationary degradation features. These theoretical shortcomings all contribute to the low accuracy of GNNs in aero-engine RUL prediction tasks. Summary of the Invention

[0006] To inherit the theoretical advantages of GNNs and overcome their existing shortcomings, thereby improving the adaptability and practicality of GNNs in the RUL prediction application of aero-engines, this invention provides an aero-engine RUL prediction method based on MDGODE. By using a novel graph neural network with multi-scale dynamic graph neural ordinary differential equations, this invention focuses on and enhances the dynamic correlation and deep spatiotemporal representation of aero-engine sensor signals (i.e., performance degradation time series data), achieving a significant improvement in RUL prediction accuracy.

[0007] The objective of this invention is achieved through the following technical solution: a method for predicting the RUL (Range Limit Intake) of aero-engines based on MDGODE, comprising the following steps:

[0008] (1) Collect data on the performance degradation of aero-engines and construct RUL tags;

[0009] (2) Establish the MDGODE model: The MDGODE model is a multi-scale dynamic graph neural network ordinary differential equation model, which includes a multi-scale autocorrelation decomposition module, a multi-scale dynamic graph structure learning module, a spatiotemporally coupled graph neural network ordinary differential equation module, and a multi-scale attention fusion module.

[0010] (2.1) The multi-scale autocorrelation decomposition module includes two stages: periodicity identification and multi-scale decomposition;

[0011] Periodicity identification: Extracting the importance of each potential period in the time series of the original sensor signal using the autocorrelation coefficient;

[0012] Multi-scale decomposition: A 1D convolutional neural network is used to perform multi-scale decomposition on the original time series to obtain... Feature representation at different scales , ;

[0013] (2.2) The data processing flow in the multi-scale dynamic graph structure learning module is as follows: First, for each time scale... Construct a scale-specific node embedding matrix ;

[0014] The embedding matrix of each node is mapped to two learnable feature matrices. , ;

[0015] Subsequently, through two sets of feature matrices , The asymmetric combination of the directed adjacency matrix is ​​constructed as follows:

[0016] ;

[0017] In the formula, For the first The directed adjacency matrix generated at each scale is also called the dynamic graph adjacency matrix; superscript Indicates transpose;

[0018] In generation At the same time, two regularization constraints are introduced, namely the sparsity constraint. With low-rank constraints ; and It will be included as an auxiliary loss term in the final MDGODE overall objective function for joint optimization;

[0019] (2.3) Construct spatiotemporal coupled graph god ordinary differential equations, make the interlayer propagation of discrete graph convolution continuous in the spatial dimension, make the dynamic dilation rate temporal convolution continuous in the temporal dimension, and fuse the two into a unified ordinary differential equation system through a nested coupling mechanism to obtain deep spatiotemporal representations at various scales.

[0020] (2.4) Multi-scale attention fusion module: First, the deep spatiotemporal representations at each scale are concatenated and global average pooled to generate a global information vector. ;

[0021] Secondly, the global information vector Mapped to query vector Aggregate deep spatiotemporal representations at various scales into key vectors. ;

[0022] Subsequently, through calculation and The dot product similarity is used to measure the first The importance scores of deep spatiotemporal representations at each scale to the global prediction task were obtained, and the weights of the importance of deep spatiotemporal representations at each scale were obtained by Softmax normalization. ;

[0023] Finally, the importance weights are used to perform a weighted summation of the multi-scale features to generate a highly discriminative spatiotemporal representation. ;

[0024] (3) The MDGODE model is trained using the aero-engine performance degradation data collected in step (1); the training objective function is minimized using the backpropagation algorithm to complete the training of the MDGODE model; the overall objective function Loss due to main task regression Graph structure sparsity constraints Low-rank constraints of graph structure It consists of three parts, and its form is as follows:

[0025] ;

[0026] In the formula, and The hyperparameter used to balance the weights between prediction accuracy and graph structure constraints; the main task regression loss. Mean square error is used;

[0027] (4) Use the trained MDGODE to extract the comprehensive spatiotemporal representation of the aero-engine performance degradation data to be predicted, and input the comprehensive spatiotemporal representation into a regressor composed of fully connected layers to predict the final remaining life value of the aero-engine.

[0028] The beneficial effects of this invention are:

[0029] 1) MDGODE, through a multi-scale framework, can adaptively identify and fuse the periodic characteristics of aero-engine sensor signals, thereby enabling it to fully capture engine performance degradation patterns at different time granularities.

[0030] 2) MDGODE’s multi-scale dynamic graph structure learning module can accurately characterize the complex spatial interaction relationships between sensor signals as the performance of aero-engines degrades by adaptively generating dynamic adjacency matrices and combining them with sparse and low-rank regularization constraints.

[0031] 3) MDGODE’s spatiotemporal coupled graph neural network ODE unifies spatial propagation and temporal evolution in a continuous ODE framework, effectively alleviating the oversmoothing problem of deep GNNs and reducing the accumulation of numerical errors caused by discrete architectures, thus enabling effective capture of deep spatiotemporal representations of aero-engine sensor signals.

[0032] 4) Due to the reasons mentioned in 1) to 3) above, the MDGODE of the present invention has strong spatiotemporal representation capabilities and robustness to complex non-stationary performance degradation processes of aero-engines. Therefore, the present invention can significantly improve the RUL prediction accuracy of aero-engines. Attached Figure Description

[0033] Figure 1 This is a theoretical framework diagram of MDGODE;

[0034] Figure 2 This is a simplified schematic diagram of a turbofan engine;

[0035] Figure 3 This is the predicted RUL curve of engine number 34 in the FD001 subset using the method of the present invention;

[0036] Figure 4 This is the predicted RUL curve of engine No. 236 in the FD002 subset using the method of the present invention;

[0037] Figure 5 This is the predicted RUL curve of engine No. 99 in the FD003 subset using the method of the present invention;

[0038] Figure 6 This is the predicted RUL curve of engine No. 71 in the FD004 subset using the method of the present invention;

[0039] Figure 7 These are the RMSE values ​​after performing 50 predictions using 5 different RUL prediction methods;

[0040] Figure 8 It is the score value of 50 predictions performed using 5 different RUL prediction methods. Detailed Implementation

[0041] This invention first develops the Multi Scale Dynamic Graph Neural Ordinary Differential Equations (MDGODE) model. The theoretical framework of the MDGODE model is as follows: Figure 1 As shown, in the MDGODE model, a multi-scale autocorrelation decomposition module is first constructed. This module hierarchically decomposes the initial time series of aero-engine sensor signals using autocorrelation coefficients to preserve the potential temporal dependence of sensor signals at different time scales. Based on this, a multi-scale dynamic graph structure learning module is designed. This module can adaptively learn the dynamic graph structure at different time scales without relying on prior structures, automatically adjusting the spatial interaction relationships of different sensor signals and capturing the dynamic correlation between sensor signals at different time scales. Next, a novel spatiotemporally coupled graph neural network (GCN) is constructed. This equation unifies the description of the graph convolutional network (GCN) and the temporal evolution process in a continuous form, achieving a fine characterization of the potential spatiotemporal dynamics of aero-engine performance degradation data. Furthermore, this equation effectively alleviates the oversmoothing problem of deep graph neural networks through continuous propagation and gating mechanisms, and captures the deep spatiotemporal representation in aero-engine performance degradation data. Finally, the multi-scale attention fusion module adaptively assigns weights to the deep spatiotemporal representations at each time scale based on their contribution to the RUL prediction task, thereby achieving effective integration of cross-scale information and forming a more discriminative comprehensive spatiotemporal representation for aero-engine RUL prediction.

[0042] Based on this, this invention implements RUL prediction for aero-engines using the MDGODE model: First, the raw aero-engine performance degradation data is input into MDGODE to train the MDGODE network parameters; then, the trained MDGODE is used to extract a comprehensive spatiotemporal representation of the aero-engine performance degradation data to be predicted, and this comprehensive spatiotemporal representation is input into a regressor composed of fully connected layers to predict the final remaining life value of the aero-engine. Because MDGODE has strong spatiotemporal representation capabilities and robustness to complex non-stationary performance degradation processes of aero-engines, the MDGODE-based aero-engine RUL prediction method can significantly improve the accuracy of RUL prediction.

[0043] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0044] like Figure 1As shown, the present invention provides a method for predicting the RUL (Range Limit Intake) of aero-engines based on MDGODE, comprising the following steps:

[0045] (1) Collect aero-engine performance degradation data and construct RUL labels; collect engine operation data through multiple sensors as performance degradation data; the original sensor monitoring signals have characteristics such as high noise, inconsistent dimensions and inconsistent sequence lengths. Directly inputting them into MDGODE will make it difficult for MDGODE to converge during training, thus making it difficult to obtain ideal RUL prediction results. Therefore, the collected original sensor monitoring signals are first preprocessed by performing Min-Max standardization, time series equal-length segmentation, and constructing RUL labels to adapt to the input format of MDGODE. This is beneficial to improving the training and prediction effect of MDGODE.

[0046] First, redundant variables with constant values ​​or no obvious degradation trend in the original data are removed to reduce the interference of redundant information on MDGODE training and reduce the computational complexity of MDGODE.

[0047] Then, to eliminate the different physical dimensions of the sensor signals and avoid certain sensor data with large numerical ranges and high noise dominating the training process of MDGODE, and to accelerate the convergence speed of MDGODE, the Min-Max normalization method is used to map all retained sensor signal data to the [0,1] interval, that is:

[0048] ;

[0049] In the formula, Indicates the first The first time step The raw values ​​output by each sensor and The first The sensor outputs the minimum and maximum values ​​from the raw values.

[0050] The time series of sensor signals is divided into samples of fixed length using the sliding window technique. This serves as data on the performance degradation of aero-engines, used for subsequent model training; among which... The length of the sliding window. This represents the number of sensors.

[0051] Finally, a smooth RUL tag for the turbofan engine is constructed using a piecewise linear function. This process can be expressed as follows:

[0052] ;

[0053] In the formula, For the first The true RUL of the turbofan engine at all times The preset RUL threshold is used. This RUL labeling smoothing strategy helps MDGODE focus on the failure evolution process after the inflection point of aero-engine performance degradation (i.e., the RUL threshold point), which in turn helps to verify the effectiveness of the aero-engine RUL prediction method based on MDGODE.

[0054] (2) Establishing the MDGODE model: The MDGODE model, or Multi-Scale Dynamic Graph Equation Model, consists of a multi-scale autocorrelation decomposition module, a multi-scale dynamic graph structure learning module, a spatiotemporally coupled graph equation model, and a multi-scale attention fusion module. First, the original aero-engine sensor signal time series is hierarchically processed based on the multi-scale autocorrelation decomposition module, dividing the sensor signal into multi-level feature representations from fine to coarse according to different time scales, providing a differentiated temporal feature foundation for the subsequent multi-scale dynamic graph structure learning. Subsequently, the multi-scale dynamic graph structure learning module adaptively constructs its unique dynamic graph structure for each time scale, breaking through the limitation that traditional static graph structures cannot reflect the dynamics of the aero-engine degradation process. Building upon this foundation, a spatiotemporally coupled graph neural network (MDGODE) is constructed to unify the description of the graph convolutional network (GCN) and the temporal evolution process in a continuous form, enabling a fine characterization of the potential spatiotemporal dynamics of aero-engine performance degradation data. This equation effectively alleviates the oversmoothing problem of deep graph neural networks through continuous propagation and gating mechanisms, improving the ability to capture long-range correlations of sensor signals and non-stationary degradation behavior of aero-engines. Finally, a multi-scale attention fusion module adaptively assigns weights to features at different time scales based on their contribution to the prediction task, achieving effective integration of cross-scale information and forming a more discriminative comprehensive spatiotemporal representation for aero-engine RUL prediction. The theoretical framework of MDGODE is shown in the figure below. Figure 1 As shown.

[0055] (2.1) A multi-scale autocorrelation decomposition module is constructed in MDGODE to extract time features at different scales. This overcomes the problem that traditional multi-scale decomposition methods, which rely on manually preset fixed scales (e.g., downsampling step size, window size), cannot adaptively match the inherent periodicity of the data, easily leading to the loss of key patterns or the introduction of redundant features, thus reducing the efficiency and accuracy of RUL prediction. The core idea of ​​this module is to adaptively identify the true periodicity of the original sensor signal time series through autocorrelation coefficients and deconstruct the original time series into a series of feature representations at different time scales, thereby providing MDGODE with a more comprehensive and richer foundation of time series information. Among them, smaller scales can capture fine-grained time series details, while larger scales can preserve the long-term trend of the time series. The multi-scale autocorrelation decomposition module includes two stages: period identification and multi-scale decomposition.

[0056] Periodicity identification: The importance of each potential period in the time series of the original sensor signal is extracted using the autocorrelation coefficient. This process is expressed as follows:

[0057] (1);

[0058] In the formula, The periodicity of the original time series; yes The larger the absolute value of the autocorrelation coefficient, the stronger the autocorrelation coefficient. The more pronounced the periodicity, The mean of the original time series is used; the value with the largest absolute value is extracted. Each autocorrelation coefficient corresponds to As the potential periodic set to be extracted This potential set of periods will serve as the basis for the subsequent parallel scaling decomposition.

[0059] Multi-scale decomposition: To simultaneously preserve feature integrity and temporal alignment at different scales, a 1D convolutional neural network is used to perform multi-scale decomposition on the original time series. The 1D convolutional neural network contains multiple parallel convolutional kernels. First, the original time series is retained as the initial scale, and then the extracted latent period set is... These are respectively used as the size of each convolutional kernel in the 1D convolutional neural network, and then an activation function is applied to obtain... The process can be expressed as follows: (Features at different scales)

[0060] (2);

[0061] In the formula, For the first Feature representation at each scale ; The original time series, Represents the convolution operation. and They represent the first Convolution kernels and bias vectors of a 1D convolutional neural network at various scales This is the activation function. We obtain... After representing features at different scales, each scale contains features of a specific temporal pattern, providing a differentiated temporal feature foundation for subsequent multi-scale dynamic graph structure learning.

[0062] (2.2) In order to characterize the spatial dependence between aero-engine sensor signals at different time scales, a multi-scale dynamic graph structure learning module was designed. Based on the time features of each scale obtained by the multi-scale autocorrelation decomposition module, this module learns the corresponding graph structure for each time scale, enabling MDGODE to characterize scale-specific spatial interaction patterns, thereby improving the prediction accuracy of the aero-engine RUL prediction task.

[0063] The data processing flow in the multi-scale dynamic graph structure learning module is as follows: First, considering that the interaction patterns between sensor signals may differ significantly at different time scales, for each time scale... Directly construct a learnable scale-specific node embedding matrix .in, For the number of sensors, This is the embedding dimension. The embedding matrix directly encodes the potential topological features and spatial attributes of each sensor node at the current time scale, forming the feature basis for realizing "one map per scale".

[0064] Obtain scale-specific node embedding matrix Subsequently, to capture the possible directed dependencies between nodes, two sets of learnable parameters are introduced. and The embedding matrix of each node is mapped to two learnable feature matrices, and the mapping method is as follows:

[0065] (3);

[0066] It is the hyperbolic tangent activation function;

[0067] Subsequently, through two sets of feature matrices , The asymmetric combination of the directed adjacency matrix is ​​constructed as follows:

[0068] (4);

[0069] In the formula, For the first The directed adjacency matrix generated at each scale is also called the dynamic graph adjacency matrix; Represents the real number field, superscript This indicates transpose. Equation (4) uses the ReLU function to ensure that the generated directed adjacency matrix is ​​non-negative.

[0070] Because aero-engine sensor monitoring data exhibits sparsity due to local interactions between key state variables within the system and low rank due to redundancy of high-dimensional information, in order to guide MDGODE to learn a graph structure that conforms to physical laws, during the generation process... At the same time, two regularization constraints are introduced, namely the sparsity constraint. With low-rank constraints First, adopt Norm pairs of directed adjacency matrices Applying sparsity constraints to adaptively eliminate noisy connections can be expressed as follows:

[0071] (5);

[0072] Secondly, the nuclear norm is used to pair the directed adjacency matrix. Applying low-rank constraints to enhance global collinearity patterns among sensor signals can be expressed as follows:

[0073] (6);

[0074] In the formula, These represent the singular values ​​of the matrix. The two regularization constraints mentioned above... and The auxiliary loss term is incorporated into the final MDGODE overall objective function for joint optimization, thereby improving the generated dynamic graph adjacency matrix. It possesses both explicit topological sparsity and the ability to effectively capture global degradation patterns, providing scale-distinguishable spatial topological priors for the next step of the spatiotemporally coupled graph-based frequent differential equation module.

[0075] (2.3) Spatiotemporal Coupled Graphical Regular Differential Equations

[0076] Obtaining feature representations at different time scales and the corresponding directed adjacency matrix Subsequently, a spatiotemporally coupled graph constant differential equation is constructed to uniformly describe the spatial graph propagation and temporal evolution process in the form of a continuous dynamical system. This overcomes the limitations of graph convolution in deep information transmission, such as oversmoothing, potential trajectory discontinuities, and numerical error accumulation, thus achieving a fine characterization of the potential spatiotemporal dynamics of aero-engine degradation. The core of this equation is to make the interlayer propagation of discrete graph convolution continuous in the spatial dimension and the temporal convolution of dynamic dilation rate continuous in the temporal dimension, and to fuse the two into a unified ordinary differential equation (ODE) system through a nested coupling mechanism.

[0077] In the spatial dimension, to characterize the dependencies between the multi-sensor signals of the aero-engine at each moment, discrete graph convolution (GCN) is typically used to extract spatial features, and its inter-layer propagation can be written as:

[0078] (7);

[0079] In the formula, Represents the discrete graph convolution of the first... Hidden state of layer nodes, superscript This represents Discrete Graph Convolution (GCN). For directed adjacency matrix Normalized adjacency matrix of the dynamic graph. Discrete graph convolutions, when stacked in deep layers, can cause feature convergence (oversmoothing) and amplify the cumulative error layer by layer, limiting the effective capture of long-range spatial correlations.

[0080] To make the above discrete layer propagation continuous, the layer index is regarded as a discrete time step, and the inter-layer propagation interval is set to... And rewrite equation (7) in difference form, the process can be derived as follows:

[0081] (8);

[0082] Represents the identity matrix;

[0083] when When the discrete difference converges to the continuous-time derivative, the Tuscan ordinary differential equation is obtained, namely:

[0084] (9);

[0085] To preserve key local differences in the graph god's ordinary differential equations during deep evolution and prevent the degradation features between aero-engine sensor signals from being forcibly smoothed out, the propagation intensity of the decision graph is adaptively determined by the gating unit. The gated graph god's ordinary differential equations can be expressed as follows:

[0086] (10);

[0087] In the formula, Represents element-wise multiplication. and These are the weights and biases of the gating unit, respectively. The activation function is used. Integrating equation (10) yields the output of the graph propagation, which can be derived as follows:

[0088] (11);

[0089] In equation (11), This refers to a numerical ordinary differential equation solver (such as the Euler or Runge-Kutta solver). The gating graph represents the frequent differential equation at the integration time point. The output state at the point. By using the gated graph constant differential equation shown in equation (10) to make the discrete GCN continuous, the stability and robustness of the spatial representation can be improved without increasing the number of discrete layers.

[0090] In the time dimension, multiple sequential Temporal Convolutional Networks (TCNs) are typically used to efficiently capture features over time. The propagation process between these TCNs is expressed as follows:

[0091] (12);

[0092] In the formula, It is a parameterized temporal convolutional network. For the first The hidden states of a temporal convolutional network, with superscript... This represents a Temporal Convolutional Network (TCN). Indicates the weights of the convolution kernel. This represents the dynamic expansion rate used to adjust the receptive field range. The zero-padding size required to ensure sequence timing alignment.

[0093] To adapt to the rate of change of the degradation sequence at different time scales, a dynamic expansion rate that adaptively increases with the number of layers is introduced, and its calculation method is as follows:

[0094] (13);

[0095] In the formula, Indicates the first A temporal convolutional network, For the first The inflation rate of a time-varying convolutional network. It is a parameter that controls the step size of the expansion rate change.

[0096] Meanwhile, to ensure that the sequence length is consistent before and after the convolution operation, the zero padding of the TCN receptive field satisfies the following formula:

[0097] (14);

[0098] In the formula, The value represents the size of the TCN convolution kernel. This design enables the TCN to flexibly learn the short-term fluctuations and long-term trends of time series signals from aero-engine sensors at different scales.

[0099] However, discrete TCNs require layer-by-layer parameterization, and increasing their depth leads to significant computational complexity and memory overhead. Therefore, we construct the following dynamic dilation rate temporal differential equation to make the temporal propagation of the temporal convolutional network continuous:

[0100] (15);

[0101] In the formula, Defined as a zero-padding operation, it is used to pad the edges of the convolution output to maintain the dimensionality consistency of the hidden state during the differentiation process. The temporal hidden trajectory in the continuous time domain can be obtained by integrating equation (15) using a numerical ordinary differential equation solver. .

[0102] To achieve a deep integration of spatial structure propagation and temporal evolution, spatial structure propagation is embedded within a temporal dynamic system, forming a nested and coupled spatiotemporal continuous model. This results in a unified ordinary differential equation system. The outer temporal dynamic system's ordinary differential equations characterize the continuous evolution of the degenerate sequence, while the inner graph dynamic system's ordinary differential equations, based on the current dynamic graph structure, perform continuous spatial diffusion of multi-sensor signals. This unified ordinary differential equation system is expressed as:

[0103] (16);

[0104] In the formula, inner operation To correspond to the continuous propagation process in spatial dimensions, it uses the current hidden state. As initial values, use the adjacency matrix of a dynamic graph. The graphical constant differential equation defined by equation (9) can be solved by integrating equation (10) to obtain its output, which is the intermediate feature containing spatial dependencies. ; The spatiotemporally coupled graph represents the internal spatial integral variables of the frequent differential equations; the outer operations represent the dynamic evolution process corresponding to the time dimension, which incorporates spatial characteristics. As input, temporal features are extracted using the temporal neural frequent differential equation defined by equation (15).

[0105] Representing features at different time scales Consider the initial state of the coupling equation, i.e., equation (16). Then, the coupled equations are numerically integrated using a numerical ordinary differential equation solver, enabling the MDG ordinary differential equations to jointly capture spatial dependence and temporal dynamics in the continuous time domain, thereby obtaining a discriminative deep spatiotemporal representation. Obviously, targeting Deep spatiotemporal feature representation sets can be extracted at different time scales. ,in Representing the A deep spatiotemporal representation at multiple scales.

[0106] (2.4) Multi-scale attention fusion module: Considering that the contribution of deep spatiotemporal feature representations at different time scales to RUL prediction is significantly different, an attention fusion module based on query-key mechanism is constructed. It aims to adaptively aggregate multi-scale information from a global perspective, realize the effective integration of cross-scale information, and form a more discriminative comprehensive spatiotemporal representation.

[0107] First, the deep spatiotemporal representations at various scales are concatenated and subjected to global average pooling to generate a global information vector representing the overall health status of the aero-engine. , Represents the global information vector The feature dimension size; this process can be represented as follows:

[0108] (17);

[0109] In the formula, This indicates a splicing operation. This indicates a global average pooling operation. It encodes an overview of the engine's current overall health status.

[0110] Secondly, in order to calculate the degree of matching between each scale and the global degradation state of the engine, the global information vector is... Mapped to query vector Furthermore, it represents deep spatiotemporal structures at various scales. Aggregate into key vectors These two processes can be expressed as follows:

[0111] (18);

[0112] (19);

[0113] In equation (18), and Let be the learnable weight matrix and bias vector of the linear transformation layer, respectively; in equation (19), This indicates the average pooling operation.

[0114] Subsequently, through calculation and The dot product similarity is used to measure the first The importance scores of deep spatiotemporal representations at each scale to the global prediction task were obtained, and the weights of the importance of deep spatiotemporal representations at each scale were obtained by Softmax normalization. ,Right now:

[0115] (20);

[0116] The larger the value, the richer the degradation information contained in the deep spatiotemporal representation at that scale.

[0117] Finally, the importance weights are used to perform a weighted summation of the multi-scale features to generate the final high-discrimination comprehensive spatiotemporal representation. The fusion process can be represented as follows:

[0118] (twenty one);

[0119] Through the aforementioned multi-scale attention fusion mechanism, MDGODE can learn the relative importance of different time scales end-to-end, adaptively strengthen the scale patterns that are highly correlated with the performance degradation of aero-engines, and suppress the interference of invalid scales, thereby improving the robustness and accuracy of aero-engine RUL prediction.

[0120] (3) The MDGODE model is trained using the aero-engine performance degradation data collected in step (1). To ensure that the MDGODE model can learn a graph structure that conforms to the aero-engine performance degradation law and achieve accurate RUL prediction, this invention designs a composite loss function that includes a prediction error loss function and a graph structure regularization loss function as the overall training objective function of MDGODE. Then, the backpropagation algorithm is used to minimize the overall training objective function to complete the training of the MDGODE model.

[0121] Overall objective function Loss due to main task regression Graph structure sparsity constraints Low-rank constraints of graph structure It consists of three parts, and its form is as follows:

[0122] (twenty two);

[0123] In the formula, and These are hyperparameters used to balance the weights between prediction accuracy and graph structure constraints. and The definition of is given by equations (5) and (6).

[0124] Main task return loss Mean squared error is used to measure the RUL prediction value of MDGODE. With real RUL The differences between them. For those containing training samples (i.e.) Individual performance degradation data training batches, The calculation formula is:

[0125] (twenty three);

[0126] For the first RUL prediction values ​​for each training sample, for The true RUL value of each training sample.

[0127] Here, minimizing the overall objective function shown in Equation (22) is used as the training objective of the Adam optimizer to update the parameters of MDGODE. A learning rate decay strategy is introduced during the training of MDGODE: when the overall objective function no longer decreases within a certain number of batches, the learning rate is automatically reduced. This learning rate decay strategy allows MDGODE to quickly search its parameter space in the early stages of training, and to perform a refined search of its parameter space in the later stages of training, thereby causing the parameters of MDGODE to converge to a better solution.

[0128] (4) Use the trained MDGODE to extract the performance degradation data of the aero-engine to be predicted (i.e., aero-engine sensor signal data). The comprehensive spatiotemporal representation is then obtained and input into a regressor consisting of fully connected layers to predict the final remaining life (RUL) value of the aero-engine.

[0129] After the MDGODE model is trained, the following aircraft engine RUL prediction process is performed:

[0130] (4.1) The aircraft engine sensor signal data to be predicted The pre-trained MDGODE model is input, and subsequence features at different time scales are decoupled through a multi-scale autocorrelation decomposition module. The multi-scale dynamic graph structure learning module generates a dynamic graph adjacency matrix that reflects the dynamic correlation between sensor signals. The process involves capturing deep spatiotemporal dependencies of sensor signals using a spatiotemporally coupled graph neural ODE, and effectively integrating cross-scale information using a multi-scale attention fusion module, ultimately outputting a comprehensive spatiotemporal representation. .

[0131] (4.2) will The input to the regressor, which consists of fully connected layers, will synthesize spatiotemporal representations. The mapping to scalar RUL prediction values ​​can be expressed as follows:

[0132] (twenty four);

[0133] In the formula, and These are the weight matrix and bias term of the regressor, respectively. The RUL prediction value of the aero-engine output by the regressor represents the estimated RUL value of the aero-engine at the current moment before complete failure.

[0134] In this embodiment, the C-MAPSS turbofan engine experimental dataset provided by NASA is used to verify the effectiveness and superiority of the invented MDGODE-based aero-engine RUL prediction method. Figure 2 This is a simplified schematic diagram of the turbofan engine corresponding to the C-MAPSS dataset. This experimental dataset contains four subsets (FD001~FD004) with different operating conditions and failure modes. Each subset is divided into a training set and a test set. The training set records the entire life cycle data of the turbofan engine from health to failure, while the test set only contains data covering a time span from operation to a specific point before failure. Basic information about this experimental dataset is shown in Table 1.

[0135] The experimental dataset contains 21 sensor monitoring signals, covering all turbofan engine operating scenarios, from single-condition single fault (corresponding to the FD001 subset) to multi-condition mixed fault (corresponding to the FD004 subset). The basic information of the 21 turbofan engine sensor monitoring signals is shown in Table 2.

[0136] Table 1 Description of the C-MAPSS dataset

[0137]

[0138] Table 2 Basic Information of Sensor Monitoring Signals

[0139]

[0140] 1. The method of this invention for predicting the RUL of aero engines

[0141] 1.1 Sensor Signal Preprocessing: First, redundant variables with constant values ​​or no obvious degradation trend were removed from the 21 sensors, ultimately retaining those from... The physical quantity signals of several key sensors are used as inputs to MDGODE. Then, the Min-Max normalization method is used to map all retained sensor signal data to the [0,1] interval. Next, a sliding window technique is used to divide the sensor signal time series into samples of fixed length. ,in The sliding window length is given. Finally, a smooth RUL label for the turbofan engine is constructed using a piecewise linear function.

[0142] 1.2 Setting of MDGODE hyperparameters: As shown in Table 3, in the MDGODE network structure, the hidden layer feature embedding dimension is... Scale quantity The kernel size of TCN The growth step of the dynamic expansion rate When using the Euler numerical solver to integrate the outer temporal neural ODE in the spatiotemporally coupled graph neural ODE module, the integration step size is... When using the Euler numerical solver to integrate the inner layer neural ODE, the integration step size is... .

[0143] During the training of MDGODE, the initial learning rate Training batch size Maximum number of iterations ; Sparse constraint weights in the overall objective function Low-rank constraint weights .

[0144] Table 3 MDGODE Hyperparameter Settings

[0145]

[0146] During the training phase of MDGODE, only the last time window data of the time series of sensor signals from each aero-engine in the test set is extracted as the validation set to facilitate the evaluation of the RUL prediction accuracy of MDGODE.

[0147] 1.3 Output of RUL Predictions: After completing the hyperparameter settings of MDGODE, according to the MDGODE training process, MDGODE is trained using the training and validation sets from subsets FD001 to FD004 respectively; then, the trained MDGODE is used to perform RUL predictions on the test sets from FD001 to FD004 respectively. The RUL prediction results for some aero-engines in the four test sets are as follows: Figures 3 to 6 As shown. Figure 3 The method of this invention is used to predict the RUL of engine number 34 in the FD001 subset. Figure 4 The method of this invention is used to predict the RUL of engine number 236 in the FD002 subset. Figure 5 The method of this invention is used to predict the RUL of engine number 99 in the FD003 subset. Figure 6 The method of this invention is used to predict the RUL of engine number 71 in the FD004 subset.

[0148] Depend on Figures 3 to 6 The predicted RUL values ​​of the turbofan engine, as presented, show that the invented MDGODE-based RUL prediction method exhibits excellent RUL prediction accuracy and robustness on both single-condition (FD001, FD003) and multi-condition (FD002, FD004) subsets. For the single-condition scenario, as... Figure 3 and Figure 5 As shown, the invented method exhibits high RUL trend tracking capability. In the early healthy phase of turbofan engine operation, the predicted curve remains highly stable without significant fluctuations; while in its performance degradation phase, the predicted RUL value closely matches the labeled value; furthermore, the invented method can keenly identify the performance degradation inflection point transitioning from stable operation to rapid decline, and closely follow the subsequent linear decline trajectory, demonstrating its accurate capture capability of the degradation initiation moment. For complex multi-condition scenarios, although the original sensor signal experiences severe numerical fluctuations and noise interference due to condition switching and mixed fault modes, as shown... Figure 4 and Figure 6 As shown, the RUL prediction results of the invented method did not exhibit significant fluctuations. On the contrary, the output RUL prediction curve showed good smoothness, effectively suppressing the negative impacts of operating condition switching, fault mixing, and environmental noise on prediction performance. Especially in the later stages of engine accelerated degradation, the invented method can still output stable and accurate RUL prediction values, objectively reflecting the actual health evolution of the engine. The above RUL prediction results for turbofan engines verify the effectiveness of the invented method in capturing complex non-stationary degradation characteristics of aero-engines and in robustly predicting the RUL of aero-engines.

[0149] 2. Comparative Analysis

[0150] 2.1 Comparison of Prediction Accuracy

[0151] To quantitatively evaluate the RUL prediction accuracy of the invented MDGODE, its RUL prediction accuracy is compared with that of four other mainstream RUL prediction methods: Hierarchical Attention Graph Convolutional Network (HAGCN), Dual-View Graph Transformer (DVGTformer), Local–Global Correlation Fusion-Based Graph Neural Network (LOGO), and Spatio-Temporal Fusion Attention Graph Neural Network (STFA). Here, Root Mean Square Error (RMSE) and a scoring function are used as evaluation metrics for RUL prediction accuracy, defined as follows:

[0152] (27);

[0153] (28);

[0154] In the formula, The total number of test samples, This is the predicted RUL value. For genuine RUL labels, This represents the RUL prediction error. A smaller value indicates higher RUL prediction accuracy. The scoring function is designed to simulate actual aero-engine operation and maintenance scenarios, assigning a higher penalty weight to lagged RUL prediction errors that may lead to engine failure. Clearly, the scoring function value is... The smaller the value, the higher the accuracy of RUL prediction and the lower the risk of lag prediction.

[0155] The MDGODE method of this invention and four other RUL prediction methods for turbofan engines Value and The comparison results are shown in Tables 4 and 5, respectively.

[0156] Table 4. Different RUL prediction methods contrast

[0157]

[0158] Table 5. Different RUL prediction methods contrast

[0159]

[0160] As shown in Tables 4 and 5, on the FD001 and FD003 subsets corresponding to a single operating condition, MDGODE's overall performance in RUL prediction accuracy is slightly better than the other four prediction methods, demonstrating MDGODE's accurate fitting capability under the basic degradation mode. On the FD002 and FD004 subsets corresponding to multiple operating conditions, MDGODE's overall performance in RUL prediction accuracy is significantly better than the other four prediction methods. This further demonstrates MDGODE's excellent adaptability in predicting RUL for complex multi-condition performance degradation data of turbofan engines, and further verifies MDGODE's effective capture of deep spatiotemporal features and its accurate prediction capability for aero-engine RUL.

[0161] 2.2 Robustness Comparison: To quantitatively evaluate the robustness of the invented MDGODE-based RUL prediction method, RUL predictions for turbofan engines based on HAGCN, DVGTformer, LOGO, STFA, and MDGODE were repeatedly performed 50 times on the FD003 subset, and the results of each of the five prediction methods for 50 RUL predictions were recorded. Value and Values, respectively, as follows Figure 7-8 As shown. Figure 7 The RMSE values ​​for 50 predictions performed for 5 RUL prediction methods. Figure 8 The scores are obtained from 50 predictions performed for each of the five RUL prediction methods. Clearly, the MDGODE-based RUL prediction method outperforms the other four methods in terms of RUL prediction results on the FD003 subset. Value and The values ​​are all the smallest, and the prediction method based on MDGODE is the best in this subset of datasets. Value and The values ​​exhibit less dispersion, meaning that the fluctuation range of its RUL prediction results with changes in random factors is significantly limited. This demonstrates that in 50 repeated RUL prediction experiments, the MDGODE-based RUL prediction method shows stronger robustness than the other four RUL prediction methods.

[0162] 2.3 Ablation Experiment Analysis: To further explore the contributions of the multi-scale framework, dynamic graph structure learning, and spatiotemporally coupled graph neural network (ODE) in MDGODE to turbofan engine RUL prediction, and to further verify the effectiveness and superiority of the invented MDGODE-based RUL prediction method, the following three sets of ablation experiments were designed:

[0163] (1) MDGODE-NMS: Removes the multi-scale framework from MDGODE and extracts features only at a single original time scale.

[0164] (2) MDGODE-NDG: The multi-scale dynamic graph structure learning module is removed from MDGODE, and a fixed graph structure based on prior knowledge is used instead of the adaptively generated dynamic graph.

[0165] (3) MDGODE-NODE: Replace the spatiotemporally coupled graph neural network (ODE) in MDGODE with a conventional stacked architecture of discrete graph convolution and discrete-time convolution.

[0166] The MDGODE of this invention, along with the three ablation experiments mentioned above, obtained the turbofan engine RUL predictions on the four subsets FD001~FD004. Value and The comparison results are shown in Tables 6 and 7, respectively.

[0167] Table 6 Comparison of RMSE in ablation experiments

[0168]

[0169] Table 7 Comparison of Ablation Test Scores

[0170]

[0171] Tables 6 and 7 show that MDGODE-NODE performs the worst on each subset. This indicates that the discrete architecture suffers from oversmoothing and numerical error accumulation when processing deep information transmission, severely limiting MDGODE-NODE's ability to fit and predict the complex performance degradation process and RUL of turbofan engines. In contrast, after introducing the multi-scale framework, MDGODE's RUL prediction under the complex operating conditions and mixed fault conditions corresponding to subset FD004 is significantly improved. The value decreased significantly from 15.24 obtained by MDGODE-NMS to 14.06, which verifies that the multi-scale framework constructed for MDGODE can effectively capture the performance degradation characteristics of aero-engine sensor signals at different temporal granularities. Furthermore, the RUL prediction accuracy of MDGODE-NDG is consistently lower than that of MDGODE, demonstrating that the dynamic graph structure, compared to a fixed prior graph, can more accurately characterize the dynamic spatial interactions between sensor nodes as aero-engines degrade. These ablation experiment results fully demonstrate that each module of MDGODE plays an irreplaceable role in enhancing spatiotemporal representation capabilities and improving the accuracy and robustness of aero-engine RUL prediction.

[0172] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for predicting the RUL (Range Limit Intake) of aero-engines based on MDGODE, characterized in that, Includes the following steps: (1) Collect data on the performance degradation of aero-engines and construct RUL tags; (2) Establish the MDGODE model: The MDGODE model is a multi-scale dynamic graph neural network ordinary differential equation model, which includes a multi-scale autocorrelation decomposition module, a multi-scale dynamic graph structure learning module, a spatiotemporally coupled graph neural network ordinary differential equation module, and a multi-scale attention fusion module. (2.1) The multi-scale autocorrelation decomposition module includes two stages: periodicity identification and multi-scale decomposition; Periodicity identification: Extracting the importance of each potential period in the time series of the original sensor signal using the autocorrelation coefficient; Multi-scale decomposition: A 1D convolutional neural network is used to perform multi-scale decomposition on the original time series to obtain... Feature representation at different scales , ; (2.2) The data processing flow in the multi-scale dynamic graph structure learning module is as follows: First, for each time scale... Construct a scale-specific node embedding matrix ; The embedding matrix of each node is mapped to two learnable feature matrices. , ; Subsequently, through two sets of feature matrices , The asymmetric combination of the directed adjacency matrix is ​​constructed as follows: ； In the formula, For the first The directed adjacency matrix generated at each scale is also called the dynamic graph adjacency matrix; superscript Indicates transpose; In generation At the same time, two regularization constraints are introduced, namely the sparsity constraint. With low-rank constraints ; and It will be included as an auxiliary loss term in the final MDGODE overall objective function for joint optimization; (2.3) Construct spatiotemporal coupled graph god ordinary differential equations, make the interlayer propagation of discrete graph convolution continuous in the spatial dimension, make the dynamic dilation rate temporal convolution continuous in the temporal dimension, and fuse the two into a unified ordinary differential equation system through a nested coupling mechanism to obtain deep spatiotemporal representations at various scales. (2.4) Multi-scale attention fusion module: First, the deep spatiotemporal representations at each scale are concatenated and global average pooled to generate a global information vector. ; Secondly, the global information vector Mapped to query vector Aggregate deep spatiotemporal representations at various scales into key vectors. ; Subsequently, through calculation and The dot product similarity is used to measure the first The importance scores of deep spatiotemporal representations at each scale to the global prediction task were obtained, and the weights of the importance of deep spatiotemporal representations at each scale were obtained by Softmax normalization. ; Finally, the importance weights are used to perform a weighted summation of the multi-scale features to generate a highly discriminative spatiotemporal representation. ; (3) The MDGODE model is trained using the aero-engine performance degradation data collected in step (1); the training objective function is minimized using the backpropagation algorithm to complete the training of the MDGODE model; the overall objective function Loss due to main task regression Graph structure sparsity constraints Low-rank constraints of graph structure It consists of three parts, and its form is as follows: ； In the formula, and The hyperparameter used to balance the weights between prediction accuracy and graph structure constraints; the main task regression loss. Mean square error is used; (4) Use the trained MDGODE to extract the comprehensive spatiotemporal representation of the aero-engine performance degradation data to be predicted, and input the comprehensive spatiotemporal representation into a regressor composed of fully connected layers to predict the final remaining life value of the aero-engine.

2. The MDGODE-based aero-engine RUL prediction method according to claim 1, characterized in that, The specific implementation method of step (2.3) is as follows: In the spatial dimension, discrete graph convolution is used to extract spatial features, and its inter-layer propagation is as follows: （7）； In the formula, Represents the discrete graph convolution of the first... Hidden state of layer nodes, superscript Represents discrete graph convolution; For directed adjacency matrix Normalized adjacency matrix of the dynamic graph; Let the interlayer propagation interval be And rewrite equation (7) in difference form as follows: （8）； Represents the identity matrix; when When the discrete difference converges to the continuous-time derivative, the Tuscan ordinary differential equation is obtained, namely: （9）； The propagation strength from the adaptive decision graph propagation through the gating unit is expressed by the following frequent differential equation of the gating graph: （10）； In the formula, Represents element-wise multiplication. and These are the weights and biases of the gating unit, respectively. For activation functions; Integrating equation (10) yields the output of the graph propagation. The process is as follows: （11）； In equation (11), This represents a numerical ordinary differential equation solver. The gating graph represents the frequent differential equation at the integration time point. Output status at; In the time dimension, multiple sequential temporal convolutional networks are typically used to capture features at the time scale. The propagation process between temporal convolutional networks is expressed as follows: （12）； In the formula, It is a temporal convolutional network. For the first The hidden states of a temporal convolutional network, with superscript... Represents a temporal convolutional network; Indicates the weights of the convolution kernel. Represents the dynamic expansion rate. Zero padding size; A dynamic expansion rate that adaptively increases with the number of layers is introduced, and its calculation method is as follows: （13）； In the formula, For the first The inflation rate of a time-varying convolutional network. It is a parameter that controls the step size of the expansion rate change; Meanwhile, to ensure that the sequence length is consistent before and after the convolution operation, the zero padding of the TCN receptive field satisfies the following formula: （14）； In the formula, This refers to the size of the TCN convolution kernel; We construct the following dynamic dilation rate temporal neural network ordinary differential equation to make the temporal propagation of the temporal convolutional network continuous: （15）； In the formula, Zero-filling operation; by integrating equation (15) using a numerical ordinary differential equation solver, the temporal hidden trajectory in the continuous time domain is obtained. ; Embedding the propagation of spatial structure within the temporal dynamical system forms a nested, coupled, spatiotemporal continuous model, which can be represented as: （16）； Representing features at different time scales Consider the initial state of the coupling equation, i.e., equation (16). Then, the coupled equations are numerically integrated using a numerical ordinary differential equation solver to obtain the deep spatiotemporal representation. .

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