A Probabilistic Prediction Method for Remaining Service Time of Aero-engines Based on the GRU-NAR Model

Abstract

This invention discloses a probabilistic prediction method for the remaining service time of aero-engines based on a GRU-NAR model. The method includes: establishing an engine fleet health index prediction model based on a GRU neural network using sensor monitoring data throughout the engine's life cycle; constructing a health index prediction model library reflecting the remaining service time; training a NAR model using sensor monitoring data of the engine under test to predict the future trends of engine degradation characteristic parameters; inputting the predicted degradation characteristic parameters into the GRU network health index model library to obtain predicted health index values; using a failure threshold to determine whether the engine has degraded to a failure state; solving for the probability distribution characteristic parameters; and obtaining the predicted engine remaining service time interval. This invention proposes a novel probabilistic prediction method for the remaining service time of aero-engines, which has high accuracy and feasibility, and can provide data support for aero-engine health management technology.

Description

Technical Field

[0001] This invention belongs to the field of remaining service time technology for aero-engines, and particularly relates to a probability prediction method for remaining service time of aero-engines based on the GRU-NAR model. Background Technology

[0002] As a core component of aircraft, aero engines face significant challenges due to their complex rotating mechanical structure and harsh operating environment. High temperature and high pressure conditions can easily trigger malfunctions in various components, affecting normal engine operation and even leading to engine failure. These phenomena further highlight the importance of aero engine maintenance and support. Engine failure can result in catastrophic accidents and severe loss of life and property. Considering current engine maintenance needs, on the one hand, maintenance must be carried out before aero engines fail to avoid such accidents. On the other hand, if maintenance strategies lead to maintenance well before the set service life threshold, it will result in unnecessary maintenance costs and may even affect the normal operation of the aircraft. For these reasons, aero engine maintenance strategies are evolving from traditional corrective maintenance after a failure and scheduled maintenance to more adaptable condition-based maintenance. Accurately predicting the remaining service life (RUL) of an aero engine is a crucial measure to ensure flight safety and reduce maintenance costs.

[0003] Existing RUL (Range Limitation) prediction models for aero-engines typically perform well in providing high-precision RUL point predictions. However, the degradation process of aero-engines involves complex developmental processes, and simply providing RUL point estimates is insufficient to offer sufficiently effective information for subsequent maintenance strategies. Therefore, it is necessary to conduct research on interval prediction of aero-engine RUL to provide stronger support for maintenance decisions. With the advent of the big data era and the continuous development of sensor technology, the measurement data acquired by sensors in various mechanical systems is exploding. Traditional machine learning algorithms face various problems when processing massive amounts of monitoring data, relying heavily on prior knowledge in specialized fields and signal processing techniques. Deep learning, as an emerging technology, has demonstrated its powerful feature analysis capabilities in various fields and can learn to analyze complex data structures. Various deep learning algorithms are also widely used in RUL prediction. Recurrent Neural Networks (RNNs) can model changes in data over time series and have achieved success in fields such as natural language processing and speech recognition. Gated Recurrent Unit Networks (GRUs), developed based on RNNs, have fewer network parameters, faster training speeds, and can still build accurate prediction models for time series data.

[0004] Furthermore, the rapid development of sensor and online monitoring technologies has made it possible to predict and analyze engine performance and status data during aircraft operation, providing favorable technical support and sufficient data preparation for predicting engine remaining service time. This invention, based on a GRU neural network and a nonlinear autoregressive (NAR) prediction model, designs a probabilistic prediction method for the remaining service time of aero-engines.

[0005] The method includes: establishing an engine health index prediction model based on GRU neural network according to sensor monitoring data throughout the engine's life cycle, and constructing a health index prediction model library reflecting the remaining service time; training a NAR model to predict engine degradation characteristic parameters for future times based on sensor measurement data of the engine under test; inputting the predicted degradation characteristic parameters into the GRU network health index model library, outputting the predicted health index value, using the failure threshold to determine whether the engine has degraded to a failure state, solving for the probability distribution characteristic parameters, and obtaining the prediction result of the engine's remaining service time interval. Summary of the Invention

[0006] To address the aforementioned technical issues, this invention provides a probability prediction method for the remaining service time of aero-engines based on the GRU-NAR model. This method has high accuracy and feasibility, and can provide data support for the health management technology of aero-engines.

[0007] Technical solution: To achieve the above objectives, the technical solution adopted by this invention is as follows:

[0008] A method for predicting the remaining service time probability of an aero-engine based on the GRU-NAR model includes the following steps:

[0009] Step 1) Using known multi-dimensional sensor monitoring data of the engine, construct a regression prediction model of the comprehensive health index of the engine fleet based on GRU neural network, with engine degradation characteristic parameters as input and engine comprehensive health index as output. Train the GRU neural network prediction model of the engine individual using engine fleet degradation data throughout the entire life cycle, and establish a GRU neural network prediction model library of the engine fleet based on the GRU neural network prediction model of the engine individual.

[0010] Step 2) For the test engine that needs to be predicted for remaining service time, use sensor monitoring data to train the NAR prediction model and calculate the parameter trend of the degradation feature parameters in advance within a specified prediction window step size l.

[0011] Step 3) Calculate the predicted values ​​of the degradation parameters of the test engine using the NAR prediction model, and use them as input to the completed GRU neural network prediction model library to solve the prediction curve of the comprehensive health index; determine whether the engine has deteriorated to a failure state by setting a failure threshold. If the failure threshold is exceeded, solve the probability distribution characteristic parameters to obtain the prediction result of the remaining service time interval of the engine; otherwise, go to step 2) and increase the prediction window step size l of the backward prediction degradation characteristic parameters, and repeat the calculation steps.

[0012] Furthermore, in step 1), based on the multi-dimensional sensor monitoring data of the engine, a regression prediction model of the engine comprehensive health index based on the GRU neural network is established, and a health index prediction model library reflecting the remaining service time is constructed. The specific steps are as follows:

[0013] Step 1.1): Based on the sensor monitoring dataset of the entire life cycle of the aero-engine, select degradation characteristic parameters that can reflect the degradation of the engine, and use the data preprocessed as the training dataset for the GRU neural network.

[0014] Step 1.2): Construct a regression prediction model for the comprehensive health index of the engine fleet based on the GRU neural network and the training dataset. The model input is the engine degradation feature parameters, and the model output is the comprehensive health index HI of the engine. The constructed comprehensive health index expression is as follows:

[0015]

[0016] in, For the corresponding degenerate feature parameter x i The variance;

[0017] The expression for the GRU neural network prediction model is as follows:

[0018] HI p =GRU(x1,x2,...,x k )

[0019] Where, x i Let HI be the degradation data for the i-th degradation feature parameter, k be the number of degradation features, and HI be the degradation data. p This is a predicted value for the health index;

[0020] Step 1.3) Use the full life cycle sensor monitoring data of the engine fleet in the training dataset to train the GRU neural network prediction model of each engine, and establish the GRU neural network prediction model library of the engine fleet.

[0021] Furthermore, in step 1.3), the GRU neural network prediction model is trained to obtain a GRU prediction model library for predicting the health index of aero-engines. The specific steps are as follows:

[0022] Step 1.3.1): For specific sensor monitoring data, assume the input data at the current moment is X. t The state value output h of the GRU neural network at the previous time step t-1 The state value output of the GRU neural network at the current moment is calculated as follows:

[0023] r t =σ(W r X t +U r h t-1 +b r )

[0024]

[0025] z t =σ(W z X t +U z h t-1 +b z )

[0026]

[0027] Where σ(·) represents the activation function, r t ∈[0,1] D The reset gate, representing the GRU neural network, controls how much of the candidate state information at the current time step comes from the state information h at the previous time step. t-1 , z represents the candidate state information at the current moment. t ∈[0,1] D To update the gate's output value and balance the state information that needs to be retained and discarded, W * U * ,b * For the network parameters *∈{h,r,z} that need to be trained and updated in the GRU neural network.

[0028] Step 1.3.2): The input training dataset is calculated by forward propagating the output of the GRU neural network corresponding to all training samples in step 1.3.1), and the training error of each training sample is recorded.

[0029] Step 1.3.3): Based on the training error obtained from the forward calculation, train the GRU neural network using the backpropagation method until the requirements are met;

[0030] Step 1.3.4) Use the sensor monitoring data of the engine fleet throughout its entire life cycle in the training set to train the GRU neural network prediction model for different individual engines, and establish a GRU prediction model library for the health index of aero engines.

[0031] Furthermore, the specific steps in step 2) of training the NAR degradation feature parameter prediction model based on the test engine sensor monitoring data, designing the prediction window step size l, and predicting the degradation feature parameters at future times are as follows:

[0032] Step 2.1): If the sensor monitoring data of the test engine is known, establish a NAR prediction model for all degradation characteristic parameters. The mathematical expression is as follows:

[0033]

[0034] Among them, K y The model time delay step size is represented by y, the specific degradation feature parameter is represented by y, and f(.) represents the nonlinear function relationship between the input and output parameters of the nonlinear autoregressive model, or the fitting relationship of the neural network.

[0035] Step 2.2) Use a time-delayed neural network as the nonlinear function relationship between the input and output parameters of the NAR prediction model, and train and calculate the learning parameters of the NAR prediction model based on the sensor monitoring data of the test engine.

[0036] Step 2.3): Based on the obtained NAR prediction model, perform autoregressive prediction with a window step size of l for each degradation feature parameter to obtain the predicted value of each degradation feature parameter.

[0037] Furthermore, in step 3), the predicted data obtained from the NAR model and the test data are used together as the test input data for the GRU prediction model, and the corresponding health index prediction curve is calculated by the GRU model library. A predetermined failure threshold is used to determine whether the engine has deteriorated to a failure state. If the failure threshold is exceeded, the probability distribution characteristic parameters are solved to obtain the predicted value of the engine's remaining service time interval; otherwise, proceed to step 2), increase the prediction window step size by l, and repeat the calculation steps.

[0038] Step 3.1) Calculate the predicted values ​​of engine degradation characteristic parameters using the trained NAR prediction model, and use the predicted values ​​of degradation parameters as input to the constructed GRU neural network prediction model library to calculate the predicted value curve of the comprehensive health index.

[0039] Step 3.2) Using the GRU neural network prediction model library and the predicted values ​​of engine degradation characteristic parameters obtained in Step 2), the health index prediction time series is obtained. According to Step 3.1), it is determined whether the health index exceeds the failure threshold. If it exceeds the failure threshold, the engine RUL prediction value is calculated, and the Gaussian distribution function is used to solve the engine RUL prediction value to obtain the interval prediction result of engine RUL.

[0040] Step 3.3): If the health index does not exceed the failure threshold, proceed to step 2), increase the prediction window step size by l, and repeat the calculation. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of a probability prediction method for the remaining service life of an aircraft engine.

[0042] Figure 2 This is a schematic diagram of the system structure of a turbofan engine in the C-MAPSS dataset.

[0043] Figure 3 This is a graph showing the predicted trend of degradation characteristic parameters of engine No. 1 in the test set.

[0044] Figure 4 It is the probability prediction result of the remaining service time of engine No. 1 in the test set.

[0045] Figure 5 This is the probability prediction result of the remaining service time of engine No. 2 in the test set.

[0046] Figure 6 This is the probability prediction result of the remaining service time of engine No. 3 in the test set. Detailed Implementation

[0047] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0048] This invention describes a method for predicting the probability of remaining service time of an aero-engine based on the GRU-NAR model, which specifically includes the following steps:

[0049] Step 1) Using known multi-dimensional sensor monitoring data of the engine, construct a regression prediction model of the comprehensive health index of the engine fleet based on GRU neural network, with engine degradation characteristic parameters as input and engine comprehensive health index as output. Train the GRU neural network prediction model of the engine individual using engine fleet degradation data throughout the entire life cycle, and establish a GRU neural network prediction model library of the engine fleet based on the GRU neural network prediction model of the engine individual.

[0050] Step 1.1): Based on the sensor monitoring dataset of the entire life cycle of the aero-engine, select degradation characteristic parameters that can reflect the degradation of the engine, and use the data preprocessed as the training dataset for the GRU neural network.

[0051] Step 1.2): Construct a regression prediction model for the comprehensive health index of the engine fleet based on the GRU neural network and the training dataset. The model input is the engine degradation feature parameters, and the model output is the comprehensive health index HI of the engine. The constructed comprehensive health index expression is as follows:

[0052]

[0053] in, For the corresponding degenerate feature parameter x i The variance;

[0054] The expression for the GRU neural network prediction model is as follows:

[0055] HI p =GRU(x1,x2,...,x k )

[0056] Where, x i Let HI be the degradation data for the i-th degradation feature parameter, k be the number of degradation features, and HI be the degradation data. p This is a predicted value for the health index;

[0057] Step 1.3) Use the full life cycle sensor monitoring data of the engine fleet in the training dataset to train the GRU neural network prediction model of each engine, and establish the GRU neural network prediction model library of the engine fleet.

[0058] Step 1.3.1): For specific sensor monitoring data, assume the input data at the current moment is X. t The state value output h of the GRU neural network at the previous time step t-1 The state value output of the GRU neural network at the current moment is calculated as follows:

[0059] r t =σ(W r X t +U r h t-1 +b r )

[0060]

[0061] z t =σ(W z X t +U z h t-1 +b z )

[0062]

[0063] Where σ(·) represents the activation function, r t ∈[0,1] D The reset gate, representing the GRU neural network, controls how much of the candidate state information at the current time step comes from the state information h at the previous time step. t-1 , z represents the candidate state information at the current moment. t ∈[0,1] D To update the gate's output value and balance the state information that needs to be retained and discarded, W * U * ,b * For the network parameters *∈{h,r,z} that need to be trained and updated in the GRU neural network.

[0064] Step 1.3.2): The input training dataset is calculated by forward propagating the output of the GRU neural network corresponding to all training samples in step 1.3.1), and the training error of each training sample is recorded.

[0065] Step 1.3.3): Based on the training error obtained from the forward calculation, train the GRU neural network using the backpropagation method until the requirements are met;

[0066] Step 1.3.4) Use the sensor monitoring data of the engine fleet throughout its entire life cycle in the training set to train the GRU neural network prediction model for different individual engines, and establish a GRU prediction model library for the health index of aero engines.

[0067] Step 2) For the test engine that needs to be predicted for remaining service time, use sensor monitoring data to train the NAR prediction model and calculate the parameter trend of the degradation feature parameters in advance within a specified prediction window step size l.

[0068] Step 2.1): If the sensor monitoring data of the test engine is known, establish a NAR prediction model for all degradation characteristic parameters. The mathematical expression is as follows:

[0069]

[0070] Among them, K y The model time delay step size is represented by y, the specific degradation feature parameter is represented by y, and f(.) represents the nonlinear function relationship between the input and output parameters of the nonlinear autoregressive model, or the fitting relationship of the neural network.

[0071] Step 2.2) Use a time-delayed neural network as the nonlinear function relationship between the input and output parameters of the NAR prediction model, and train and calculate the learning parameters of the NAR prediction model based on the sensor monitoring data of the test engine.

[0072] Step 2.3): Based on the obtained NAR prediction model, perform autoregressive prediction with a window step size of l for each degradation feature parameter to obtain the predicted value of each degradation feature parameter.

[0073] Step 3) Calculate the predicted values ​​of the degradation parameters of the test engine using the NAR prediction model, and use them as input to the completed GRU neural network prediction model library to solve the prediction curve of the comprehensive health index; determine whether the engine has deteriorated to a failure state by setting a failure threshold. If the failure threshold is exceeded, solve the probability distribution characteristic parameters to obtain the prediction result of the remaining service time interval of the engine; otherwise, go to step 2) and increase the prediction window step size l of the backward prediction degradation characteristic parameters, and repeat the calculation steps.

[0074] Step 3.1) Calculate the predicted values ​​of engine degradation characteristic parameters using the trained NAR prediction model, and use the predicted values ​​of degradation parameters as input to the constructed GRU neural network prediction model library to calculate the predicted value curve of the comprehensive health index.

[0075] Step 3.2) Using the GRU neural network prediction model library and the predicted values ​​of engine degradation characteristic parameters obtained in Step 2), the health index prediction time series is obtained. According to Step 3.1), it is determined whether the health index exceeds the failure threshold. If it exceeds the failure threshold, the engine RUL prediction value is calculated, and the Gaussian distribution function is used to solve the engine RUL prediction value to obtain the interval prediction result of engine RUL.

[0076] Step 3.3): If the health index does not exceed the failure threshold, proceed to step 2), increase the prediction window step size by l, and repeat the calculation.

[0077] To verify the effectiveness of the proposed GRU-NAR model-based probability prediction method for the remaining service time of aero-engines, a related digital simulation was conducted in the MATLAB environment. In this simulation, data from the files "train_FD001.txt" and "test_FD001.txt" in the C-MAPSS dataset were used as training and testing data, respectively. The module structure of the turbofan engine in the dataset is as follows: Figure 2 As shown in the figure. The training dataset contains 100 sets of sensor monitoring data for different engines throughout their entire lifecycle, from healthy state to failure. Therefore, this invention trains 100 health index prediction models using GRU neural networks and establishes a GRU neural network prediction model library. The test set contains 100 sets of observation data for different engines deteriorating to varying degrees. To verify the performance of the proposed method, 20 sets were randomly selected for remaining service time prediction simulation verification. Through analysis of 21 sensor parameters, 10 degradation feature parameters reflecting engine degradation were selected: P30, phi, W31, W32, BPR, T24, T30, T50, Ps30, and htBleed. The descriptions of each parameter are shown in Table 1.

[0078] Table 1 Explanation of Engine Degradation Characteristic Parameters

[0079]

[0080] Because the original data contained a lot of noise, it was first smoothed to reduce the adverse effects of noise on subsequent calculations. Figure 3 The result is the backward trend prediction of the degradation characteristic parameters of engine No. 1 in the selected test set data. Figure 4-6 Table 1 shows the predicted health index trends of engines 1-3 in the selected test set, along with the predicted remaining service time intervals. Table 2 shows the detailed predicted remaining service time obtained from the test data of all 20 engine groups in the test set.

[0081] Table 2: Predicted Remaining Service Time Results for All 20 Engine Test Data Sets

[0082]

[0083] Table 2 (continued)

[0084]

[0085] As shown in Table 2, the probabilistic prediction method for engine RUL based on the GRU-NAR model can provide high-precision prediction results for engine RUL. The relative prediction error is within 13%, and the absolute error is within 10 cycles, indicating that the prediction method has good accuracy and reliability.

[0086] The root mean square error (RMSE) is used to compare and evaluate the proposed model's ability to predict engine RUL. The calculation formula is as follows:

[0087]

[0088] in, and These represent the actual RUL and the predicted RUL, respectively. The smaller the root mean square error, the closer the predicted RUL is to the actual RUL, and the higher the prediction accuracy.

[0089] The prediction accuracy (RMSE) was compared with that of prediction models MLP, SVR, RVR, CNN, and LSTM in the field of remaining usage time prediction. The results are shown in Table 3.

[0090] Table 3 Comparison of the RUL prediction method of this invention with other methods

[0091]

[0092] Among the methods presented in Table 3, MLP, SVR, and RVR are three classic machine learning methods widely used for RUL prediction, while CNN and LSTM are deep learning methods. Table 3 shows that deep learning methods CNN and LSTM have a certain accuracy advantage over traditional machine learning methods MLP, SVR, and RVR in predicting RUL. Furthermore, the prediction method proposed in this invention can predict the remaining service time interval of an engine, exhibiting better prediction accuracy compared to a single prediction model.

[0093] It should be noted that the above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations and substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting the probability of remaining service time of an aero-engine based on the GRU-NAR model, characterized in that, Includes the following steps: Step 1) Using known multi-dimensional sensor monitoring data of the engine, construct a regression prediction model of the comprehensive health index of the engine fleet based on GRU neural network, with engine degradation characteristic parameters as input and engine comprehensive health index as output. Train the GRU neural network prediction model of the engine individual using engine fleet degradation data throughout the entire life cycle, and establish a GRU neural network prediction model library of the engine fleet based on the GRU neural network prediction model of the engine individual. Step 2): For the test engine that requires remaining service life prediction, use the sensor monitoring data of the test engine to train the NAR prediction model, and pre-calculate the parameter trends of the degradation feature parameters for future time steps within a specified prediction window step size l; the specific steps are as follows: Step 2.1): If the sensor monitoring data of the test engine is known, establish a NAR prediction model for all degradation characteristic parameters. The mathematical expression is as follows: Among them, K y The model time delay step size is represented by y, the specific degradation feature parameter is represented by y, and f(.) represents the nonlinear function relationship between the input and output parameters of the nonlinear autoregressive model, or the fitting relationship of the neural network. Step 2.2) Use a time-delayed neural network as the nonlinear function relationship between the input and output parameters of the NAR prediction model, and train and calculate the learning parameters of the NAR prediction model based on the sensor monitoring data of the test engine. Step 2.3): Based on the obtained NAR prediction model, perform autoregressive prediction with a window step size of l for each degradation feature parameter to obtain the predicted value of each degradation feature parameter. Step 3) Calculate the predicted values ​​of the degradation parameters of the test engine using the NAR prediction model, and use them as input to the completed GRU neural network prediction model library to solve the prediction curve of the comprehensive health index; determine whether the engine has deteriorated to a failure state by setting a failure threshold. If the failure threshold is exceeded, solve the probability distribution characteristic parameters to obtain the prediction result of the remaining service time interval of the engine; otherwise, go to step 2) and increase the prediction window step size l of the backward prediction degradation characteristic parameters, and repeat the calculation steps.

2. The method for predicting the probability of remaining service time of an aero-engine based on the GRU-NAR model according to claim 1, characterized in that: In step 1), based on the multi-dimensional sensor monitoring data of the engine, a regression prediction model of the comprehensive health index of the engine fleet based on the GRU neural network is established, and a health index prediction model library reflecting the remaining service time is constructed. The specific steps are as follows: Step 1.1): Based on the sensor monitoring dataset of the entire life cycle of the aero-engine, select degradation characteristic parameters that can reflect the degradation of the engine, and use the data preprocessed as the training dataset for the GRU neural network. Step 1.2): Construct a regression prediction model for the comprehensive health index of the engine fleet based on the GRU neural network and the training dataset. The model input is the engine degradation feature parameters, and the model output is the comprehensive health index HI of the engine. The constructed comprehensive health index expression is as follows: in, For the corresponding degenerate feature parameter x i The variance; The expression for the GRU neural network prediction model is as follows: HI p =GRU(x1,x2,...,x k ) Where, x i Let HI be the degradation data for the i-th degradation feature parameter, k be the number of degradation features, and HI be the degradation data. p This is a predicted value for the health index; Step 1.3) Use the full life cycle sensor monitoring data of the engine fleet in the training dataset to train the GRU neural network prediction model of each engine, and establish the GRU neural network prediction model library of the engine fleet.

3. The method for predicting the probability of remaining service time of an aero-engine based on the GRU-NAR model according to claim 2, characterized in that: In step 1.3), the GRU neural network prediction model is trained to obtain a GRU neural network prediction model library for predicting the health index of aero-engines. The specific steps are as follows: Step 1.3.1): For specific sensor monitoring data, assume the input data at the current moment is X. t The state value output h of the GRU neural network at the previous time step t-1 The state value output of the GRU neural network at the current moment is calculated as follows: r t =σ(W r X t +U r h t-1 +b r ) z t =σ(W z X t +U z h t-1 +b z ) Where σ(·) represents the activation function, r t ∈[0,1] D The reset gate, representing the GRU neural network, controls how much of the candidate state information at the current time step comes from the state information h at the previous time step. t-1 , z represents the candidate state information at the current moment. t ∈[0,1] D To update the gate's output value and balance the state information that needs to be retained and discarded, W * U * ,b * For the network parameters *∈{h,r,z} that need to be trained and updated in the GRU neural network; Step 1.3.2): The input training dataset is calculated by forward propagating the output of the GRU neural network corresponding to all training samples in step 1.3.1), and the training error of each training sample is recorded. Step 1.3.3): Based on the training error obtained from the forward calculation, train the GRU neural network using the backpropagation method until the requirements are met; Step 1.3.4) Use the sensor monitoring data of the engine fleet throughout its entire life cycle in the training set to train the GRU neural network prediction model for different individual engines, and establish a GRU prediction model library for the health index of aero engines.

4. The method for predicting the probability of remaining service time of an aero-engine based on the GRU-NAR model according to claim 1, characterized in that: The predicted data obtained by the NAR prediction model in step 3) and the test data are used together as the test input data of the GRU neural network prediction model. The corresponding health index prediction curve is calculated by the GRU neural network prediction model library. The engine is judged to have deteriorated to the failure state by setting a failure threshold. If the failure threshold is exceeded, the probability distribution characteristic parameters are solved to obtain the predicted value of the remaining service time interval of the engine. Otherwise, proceed to step 2), increase the prediction window step size by l, and repeat the calculation steps. Step 3.1) Calculate the predicted values ​​of engine degradation characteristic parameters using the trained NAR prediction model, and use the predicted values ​​of degradation parameters as input to the constructed GRU neural network prediction model library to calculate the predicted value curve of the comprehensive health index. Step 3.2) Using the GRU neural network prediction model library and the predicted values ​​of engine degradation characteristic parameters obtained in Step 2), the health index prediction time series is obtained. According to Step 3.1), it is determined whether the health index exceeds the failure threshold. If it exceeds the failure threshold, the engine RUL prediction value is calculated, and the Gaussian distribution function is used to solve the engine RUL prediction value to obtain the interval prediction result of engine RUL. Step 3.3): If the health index does not exceed the failure threshold, proceed to step 2), increase the prediction window step size by l, and repeat the calculation.

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