Aero-engine residual life prediction method based on TOC-NCINN

Abstract

The application discloses an aero-engine residual useful life prediction method based on TOC-NCINN, which comprises the following steps: S1, dividing the collected time sequence sample set into a training set and a verification set; S2, establishing a residual useful life prediction model, which comprises a multi-scale feature extraction network and a regression network; the multi-scale feature extraction network comprises a time sequence convolution module, a self-attention mechanism module and a feature fusion module; S3, embedding the physical mechanism of material creep damage into the loss function of the multi-scale feature extraction network to form a Norton creep guided neural network NCINN; S4, introducing a TOC optimizer as an outer driving engine of the NCINN to realize adaptive optimization of key superparameters of the NCINN. The aero-engine RUL prediction method can realize higher RUL prediction precision, stronger robustness and excellent generalization performance, and provides a technical approach for reference for aero-engine RUL prediction.

Description

Technical Field

[0001] This invention relates to the field of engine life prediction technology, and in particular to a method for predicting the remaining life of aero-engines based on TOC-NCINN. Background Technology

[0002] As the core power subsystem of an aircraft, the health of the aero-engine is the most fundamental guarantee of flight safety. However, due to its highly complex structure and long-term operation under extreme conditions of high temperature, high pressure, and high speed, it is a component prone to failure. Once an aero-engine fails and is not promptly warned and dealt with, it can easily lead to catastrophic flight accidents. As the core of Prognostics and Health Management (PHM), Remaining Useful Life (RUL) prediction, by identifying engine degradation trends in advance and accurately predicting remaining usable life, can issue early warnings before potential failures occur, effectively reducing flight safety hazards caused by sudden aero-engine failures. It has become a key technology for achieving condition-based maintenance of aero-engines and avoiding major risks. Therefore, conducting research on high-precision and high-reliability aero-engine RUL prediction is of vital theoretical and engineering significance for ensuring aircraft flight safety and improving aviation operation and maintenance efficiency.

[0003] Currently, mainstream RUL prediction methods for aero-engines are mainly divided into two categories: physics model-driven methods and data-driven methods. Physics model-driven methods describe component degradation using differential equations or constitutive models, possessing clear physical meaning. However, aero-engines are highly complex systems, and their overall performance degradation is the result of the coupling of multiple failure modes. Establishing an accurate full-system model of an aero-engine is extremely difficult, leading to insufficient generalization ability of physics model-driven RUL prediction methods when applied to aero-engine RUL prediction under complex actual operating conditions. Unlike model-based RUL prediction methods, data-driven RUL prediction methods do not rely on precise modeling of physical mechanisms. Instead, they mine degradation patterns from historical data and establish a mapping relationship between monitoring data and RUL, demonstrating better adaptability. In recent years, with the rapid development of artificial intelligence, significant progress has been made in the field of deep learning, especially the advancement of deep learning technology for automatically extracting deep degradation features from high-dimensional data. This has greatly improved the predictive capabilities of deep learning in complex systems, making deep learning the most representative technical approach in the field of data-driven aero-engine RUL prediction. Li Jingfeng et al. combined Long Short-Term Memory Neural Network (LSTM), Deep Belief Network (DBN), and failure threshold to deeply mine degradation information in the time-series data of turbofan aero-engines and predict the RUL of the aero-engines. GUO et al. constructed an hourglass-shaped multi-scale feature extractor based on a one-dimensional convolutional neural network and combined it with a Transformer to predict the RUL of turbofan engines. ZHANG et al. used the SDAGCN model, which captures the spatiotemporal correlation between sensor signals through adaptive graph convolution, to predict the RUL of turbofan engines. LIU et al. extracted the temporal features of turbofan engine sensor signals using a bidirectional gated recurrent unit (Bi-GRU) and a self-attention network, and combined it with an asymmetric constraint loss function to predict the RUL of the aero-engines. However, pure data-driven methods are essentially "black box" models. Their predictions heavily depend on the scale and quality of the training data and lack physical constraints. This results in insufficient generalization ability and RUL prediction accuracy when data is scarce or when encountering new conditions not covered by the training set. Furthermore, the prediction results may lose physical rationality and interpretability.

[0004] Time series prediction methods based on Physics-informed Neural Networks (PINNs) typically embed physical laws such as governing equations and constitutive relations into the loss function as regularization terms. This guides the neural network to follow known physical laws while learning the time series, providing a new approach to solving the RUL prediction problem for aero-engines. ZHAO et al. used PINN integrated with a finite element dynamics model for RUL prediction of gears. Zhang Yu et al. used a PINN model based on Paris's law for RUL prediction of aero-engine blades. However, when applying PINN to aero-engine RUL prediction, how to select and construct physical constraints that accurately reflect the damage mechanism of key aero-engine components remains a crucial area for exploration. Among various failure modes of aero-engines, high-temperature creep is one of the most important mechanisms limiting the lifespan of their hot-end components. Aero-engines operate under high temperature and pressure for extended periods, causing their materials to undergo time-related, continuous plastic deformation, i.e., creep, until a critical value is reached and fracture occurs.

[0005] The two existing mainstream RUL prediction methods for aero-engines suffer from the following problems: data-driven aero-engine RUL prediction methods lack physical interpretability, and the prediction results often violate engineering mechanisms; physical equation-based aero-engine RUL prediction methods struggle to characterize the nonlinear degradation behavior of aero-engines under complex operating conditions. These problems result in insufficient prediction accuracy and limited reliability of existing mainstream aero-engine RUL prediction methods. Summary of the Invention

[0006] To address the above issues, this invention provides a Tornado-optimized Norton creep-informed neural network with TOC optimizer (TOC-NCINN) and a TOC-NCINN-based RUL prediction method for aero-engines. The aim is to obtain a novel PINN for aero-engine RUL prediction that possesses good long-term and short-term feature fusion capabilities, good physical consistency, robustness, and extrapolation generalization, as well as higher hyperparameter adaptive optimization efficiency. This will achieve more accurate, robust, and reliable aero-engine RUL prediction results than existing mainstream aero-engine RUL prediction methods.

[0007] The objective of this invention is achieved through the following technical solution: a method for predicting the remaining life of aero-engines based on TOC-NCINN, comprising the following steps:

[0008] S1. Randomly divide the collected time series sample set into a training set and a validation set;

[0009] S2. Establish a remaining lifetime prediction model, including a multi-scale feature extraction network and a regression network;

[0010] The multi-scale feature extraction network includes a temporal convolution module, a self-attention mechanism module, and a feature fusion module;

[0011] The temporal convolution module uses a multi-layer one-dimensional convolutional neural network to perform deep processing on temporal samples. The original input temporal samples are transformed into high-level local feature representations rich in aero-engine degradation information.

[0012] The global features are obtained by weighted fusion of local features through a self-attention mechanism module.

[0013] The feature fusion module adopts a self-attention-based feature fusion strategy: First, local and global features are concatenated along the feature dimension to form an initial fused feature; then, a lightweight self-attention layer is used to process the initial fused feature to generate a fused feature.

[0014] The fused features are input into the regression network to obtain the predicted value of the remaining life of the aero-engine. ;

[0015] S3. Introduce a physical constraint mechanism based on the Norton creep equation, embed the physical mechanism of material creep damage into the loss function of the remaining life prediction model, and the resulting network is called the Norton creep guided neural network, denoted as NCINN.

[0016] Norton's creep equation is expressed as follows:

[0017] ;

[0018] In the formula: For steady-state creep rate, For material constants, The equivalent stress acting on the material, Operating temperature For creep activation energy, Let be the ideal gas constant. Stress index;

[0019] The engine turbine outlet temperature was selected as the creep characteristic temperature. As the operating temperature in Norton's creep equation proxy variables;

[0020] A damage equivalent stress model that comprehensively considers both mechanical and aerodynamic loads is constructed, and its expression is as follows:

[0021] ;

[0022] In the formula: Core machine speed; This refers to the outlet pressure of the high-pressure compressor. , and These are learnable weight parameters;

[0023] After obtaining the creep characteristic temperature Equivalent stress of damage Then, they are normalized to the [0,1] interval to obtain the normalized creep characteristic temperature. and normalized damage equivalent stress ;

[0024] Next, a damage rate prediction network is used. Will and Mapped to dimensionless instantaneous damage rate ;exist In the network, the vector is first... The input is fed into a three-layer fully connected network to learn the key parameters of the Norton equations. , and The equivalent material constants are obtained. Equivalent stress index Equivalent creep activation energy ;

[0025] Then, substituting the learned parameters into the Norton creep equation and taking the logarithm of both sides of the equation, we get:

[0026] ;

[0027] Subsequently, the following final instantaneous damage rate was obtained:

[0028] ;

[0029] By summing the instantaneous damage rates over time, we obtain the result corresponding to the current moment. Cumulative damage The critical cumulative damage at the time of aero-engine failure is defined as... ;

[0030] Utilizing the instantaneous damage rate at the current moment By approximating the remaining degradation trajectory with a tangent, the instantaneous equivalent remaining lifetime under the physical path is derived, as expressed below:

[0031] ;

[0032] In the formula: It is a very small constant added to ensure the stability of the remaining useful life value;

[0033] Define the data fitting loss function respectively and physical constraint loss function in residual form as follows:

[0034] ;

[0035] ;

[0036] For aircraft engines during operation The actual remaining service life at that time This represents the number of samples in the current training batch.

[0037] Finally, the total loss function of NCINN yes and The weighted sum, i.e.:

[0038] ;

[0039] In the formula: These are the weight hyperparameters of the physical constraint loss function;

[0040] The total loss function is calculated relative to the weight parameter set of NCINN using automatic differentiation techniques. gradient ;

[0041] Based on the obtained gradient The Adam optimization function is used to update all weight parameters, and the process is expressed as follows:

[0042] ;

[0043] In the formula, Optimize the function for Adam. For learning rate, , The first Subsequent The next updated set of weight parameters; This is the weight decay coefficient;

[0044] S4. Introduce the TOC optimizer as the outer driving engine of NCINN to achieve adaptive optimization of key hyperparameters of NCINN; retain the trained remaining lifetime prediction model for feature extraction and remaining lifetime prediction of input samples.

[0045] The specific optimization method is as follows: define the hyperparameter vector of the NCINN to be optimized as follows: ,Right now:

[0046] ;

[0047] In the formula: These are the weight hyperparameters of the physical constraint loss function; The initial learning rate; This represents the number of self-attention heads in the self-attention mechanism module. The length of the time window; This is the weight decay coefficient;

[0048] Each hyperparameter is constrained to a pre-search space with explicit physical or engineering significance. Within this framework, the optimization objective of TOC is to optimize within the predefined search space. Within this framework, we find the hyperparameter configuration that optimizes NCINN's performance on the independent validation set. The collaboration between TOC and NCINN constitutes a two-layer nested recurrent architecture of outer metaheuristic search and inner gradient descent training, where the outer layer is dominated by TOC and responsible for training in the pre-search space. The global search is performed in the middle layer; the inner layer consists of the training and validation process of NCINN, which is responsible for evaluating the quality of each set of hyperparameters.

[0049] The beneficial effects of this invention are:

[0050] 1) In TOC-NCINN, a novel multi-scale feature extraction network was designed. This network combines a temporal convolution module with a self-attention mechanism to deeply fuse the short-term local features and long-term temporal dependencies of aero-engine sensor signals (i.e., it has the ability to fuse short-term and long-term features) to solve the problems of limited receptive field and easy forgetting of historical information in long sequence prediction. This effectively captures the complex nonlinear degradation information of aero-engines and lays the data foundation for high-precision RUL prediction.

[0051] 2) A physical constraint mechanism based on the Norton creep equation was established in TOC-NCINN. This mechanism constructs a dual-supervision network of data-driven and physical mechanism by embedding the material creep constitutive relation into the loss function in the form of residuals. This mechanism guides TOC-NCINN to follow known physical evolution laws, thereby endowing TOC-NCINN with excellent physical interpretability, robustness, and extrapolation generalization ability when facing operating condition changes and noise interference.

[0052] 3) This invention combines the powerful nonlinear fitting capability of data-driven methods with the clear mechanistic significance of physical models through the synergy of data paths and physical paths, thus achieving a more fundamental characterization of the performance degradation process of aero-engines.

[0053] 4) A Tornado optimizer with Coriolis force (TOC) was introduced as an outer driving engine for TOC-NCINN. By utilizing the unique "tornado-thunderstorm-storm" evolution mechanism of TOC and the deflection effect of Coriolis force, adaptive global optimization of key hyperparameters such as physical constraint weights and learning rate can be achieved. This effectively avoids the training process of TOC-NCINN from getting stuck in local optima and improves the training efficiency of TOC-NCINN.

[0054] 5) Due to the reasons mentioned in 1) to 4) above, the TOC-NCINN of the present invention has more obvious advantages in terms of physical interpretability, robustness, extrapolation generalization ability, and training efficiency. Therefore, the TOC-NCINN-based RUL prediction method for aero-engines of the present invention can achieve higher RUL prediction accuracy, stronger robustness and excellent generalization performance, providing a technical approach for reference in aero-engine RUL prediction. Attached Figure Description

[0055] Figure 1 This is a theoretical framework diagram of the TOC-NCINN of the present invention;

[0056] Figure 2 This is a simplified schematic diagram of a turbofan engine;

[0057] Figure 3 The method invented is used to predict the RUL of engine number 24 in the FD001 subset.

[0058] Figure 4 The method invented is used to predict the RUL of engine number 176 in the FD002 subset.

[0059] Figure 5 The method invented is used to predict the RUL of engine number 100 in the FD003 subset.

[0060] Figure 6 The method invented is used to predict the RUL of engine number 12 in the FD004 subset.

[0061] Figure 7 It is the RMSE value of 50 predictions performed using 5 RUL prediction methods;

[0062] Figure 8 It is the score value of 50 predictions performed by 5 different RUL prediction methods. Detailed Implementation

[0063] This invention first developed a tornado-optimized Norton creep-informed neural network with TOC optimizer (TOC-NCINN). In TOC-NCINN, a novel multi-scale feature extraction network is first designed to effectively capture short-term local features and long-term temporal dependencies in aero-engine sensor signals, thus addressing the problems of limited receptive field and easy forgetting of historical information in long-sequence prediction. Next, by introducing a physical constraint mechanism based on the Norton creep equation, the creep constitutive relation of the material is embedded into the loss function as a residual term, thus constructing a novel Norton creep-informed neural network (NCINN) framework to achieve dual supervision of data-driven learning and physical mechanisms, thereby fundamentally realizing the physical interpretability, robustness, and extrapolation generalization ability of NCINN. Finally, to further optimize training efficiency and improve the generalization performance of NCINN, a Tornado optimizer with Coriolis force (TOC) is used to adaptively adjust the physical constraint weights, learning rate, and other hyperparameters of NCINN. This not only improves the training efficiency of NCINN but also further enhances its generalization performance and RUL prediction accuracy. The theoretical framework of TOC-NCINN is as follows: Figure 1 As shown.

[0064] Building upon this foundation, this invention further designs a TOC-NCINN-based RUL prediction method for aero-engines. First, the aero-engine performance degradation sample set used as the training set is input into TOC-NCINN to train its hyperparameters and parameters. Then, the trained TOC-NCINN is used to predict the RUL value of the aero-engine. Because the TOC-NCINN model possesses excellent long-term and short-term feature fusion capabilities, clear physical interpretability, strong robustness and extrapolation generalization ability, and high hyperparameter adaptive optimization efficiency (i.e., training efficiency), the TOC-NCINN-based aero-engine RUL prediction method exhibits high RUL prediction accuracy, stronger robustness, and excellent generalization performance. An application example using the NASA C-MAPSS turbofan engine dataset for aero-engine RUL prediction verifies the effectiveness and superiority of the invented TOC-NCINN-based aero-engine RUL prediction method.

[0065] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0066] like Figure 1As shown, the present invention provides a method for predicting the remaining life of an aero-engine based on TOC-NCINN, comprising the following steps:

[0067] S1. Collect the time series sample set Randomly divided into training sets and verification set The raw sensor monitoring signals are characterized by high noise, inconsistent dimensions, and inconsistent sequence lengths. Directly inputting them into TOC-NCINN will make it difficult for TOC-NCINN to converge during training, thus hindering the achievement of ideal RUL prediction results. Therefore, conventional preprocessing operations such as min-max normalization, time series equal-length segmentation, and RUL label construction are performed on the sample signals in the time series sample set to adapt them to the input format of TOC-NCINN. This helps improve the training and prediction performance of TOC-NCINN.

[0068] S2. Establish a remaining lifetime prediction model, including a multi-scale feature extraction network and a regression network;

[0069] The multi-scale feature extraction network is a core component of TOC-NCINN. Its design goal is to fully mine the aero-engine performance degradation information contained in the time-series sensor data, that is, to capture both short-term local features and long-term global evolution trends in the aero-engine degradation process by adopting a hierarchical architecture. The network consists of three core parts: a temporal convolution module, a self-attention mechanism module, and a feature fusion module.

[0070] The temporal convolution module is responsible for extracting local time-scale degradation features from the input sequence (i.e., the acquired sensor signals), typically used to reflect short-term fluctuations, abrupt changes, and local trend changes in the sensor signals. (Time-counting) The input time series samples are ,in, Indicates at time Normalized sensor measurements dimensional vector, The time window length, For vector feature dimensions, For the real number field. The temporal convolution module uses a multi-layer one-dimensional convolutional neural network to process temporal samples. Deep processing is performed, which involves stacking multiple layers of "convolution-activation-pooling" to process the original input temporal samples. It is transformed into a high-level local feature representation rich in aero-engine degradation information, denoted as , The length of the sequence after pooling. This represents the final number of feature maps.

[0071] Building upon the local feature extraction by the temporal convolution module, a self-attention mechanism module is introduced to capture long-term dependencies spanning the entire time window during aero-engine degradation. This self-attention mechanism enables adaptive weighted fusion of local features to obtain global features. First, the output of the temporal convolution module is linearly transformed... Projected into the hidden space, obtain projection ,Right now:

[0072] (1);

[0073] In the formula: Let be the projection weight matrix. This is a unified hidden layer dimension within the self-attention mechanism module;

[0074] Then projection The query matrix is ​​generated through three independent linear transformations. Key matrix Sum matrix and to , and Perform a scaled dot product operation, that is, use each attention head to independently perform the following attention calculation:

[0075] (2);

[0076] In the formula: For attention layer functions; , , All are learnable projection matrices; Key matrix The dimension, and satisfying , For the number of attention heads, and ;

[0077] Subsequently, a multi-head attention mechanism module is used to fuse the attention from each head. To jointly extract global feature information on aero-engine performance degradation from different subspaces, the process is expressed as follows:

[0078] (3);

[0079] In the formula: A function for concatenating arrays. The output projection matrix of the multi-head attention mechanism;

[0080] Next, the output of the multi-head attention mechanism module. A nonlinear transformation is performed on each position vector, and the calculation is expressed as follows:

[0081] (4);

[0082] In the formula: It is a linear rectified function; , All are learnable matrices. for and Feature dimensions, take ;

[0083] Finally, a residual connection is introduced to handle the input of the self-attention mechanism module. The output matrix obtained from equation (4) The training process of the multi-scale feature extraction network is stabilized by summing and performing layer normalization, as follows:

[0084] (5);

[0085] In the formula: For layer normalization function, For regularization functions, This represents the global features that are ultimately output by the self-attention mechanism module.

[0086] Local features were obtained through temporal convolution and self-attention mechanisms, respectively. and global features Then, the two complementary feature representations are fused through a feature fusion module and input into the regression network to achieve residual lifetime regression prediction under the data path. Considering that local and global features may differ in degradation information and (time) scale, simply... and While splicing preserves all information, it may introduce noise. Therefore, this invention designs a strategy based on self-attention feature fusion. First, local features... and global features The initial fused features are constructed by concatenating them along the feature dimension. This process can be expressed as follows:

[0087] (6);

[0088] Subsequently, a lightweight self-attention layer is used to further process the initial fused features. This self-attention layer can automatically evaluate and weight the importance of features from different sources (i.e., sequential convolutional paths and self-attention mechanism paths) and different time steps, thereby generating a refined fused feature representation with higher information intensity. This secondary processing step is represented as follows:

[0089] (7);

[0090] In the formula: This is the attention layer function.

[0091] This process enables the multi-scale feature extraction network to autonomously filter and enhance the most discriminative aero-engine performance degradation information from the dual paths.

[0092] Finally, the fusion features obtained from equation (7) are... Input a regression network to obtain predicted values ​​of the remaining service life of aero engines under the data path. Considering the continuous nature of the aero-engine degradation process, a multilayer perceptron was constructed as a regression network. This regression network first fuses features... pass The function is flattened into a one-dimensional vector, and this process is expressed as follows:

[0093] (8);

[0094] Subsequently, a nonlinear transformation is performed using two fully connected layers to obtain the predicted remaining service life of the aero-engine under the data path. The first fully connected layer is followed by... Activation functions are used to perform nonlinear transformations to obtain the feature matrix. ,Right now:

[0095] (9);

[0096] In the formula: , These are the weight matrix and bias vector of the first fully connected layer, respectively.

[0097] Finally, the feature matrix is ​​obtained. The predicted remaining service life of the aero-engine can be output through the second fully connected layer, and this process can be expressed by the following formula:

[0098] (10);

[0099] In the formula: , Here are the weight matrix and bias vector for the second fully connected layer.

[0100] S3. After completing the design of the remaining lifetime prediction model, a physical constraint mechanism based on the Norton creep equation is introduced. The physical mechanism of material creep damage is embedded into the loss function of the remaining lifetime prediction model to achieve deep integration and dual supervision of data-driven learning and physical mechanism. The resulting network is called the Norton Creep Guided Neural Network, denoted as NCINN.

[0101] Hot-end components of aero-engines (such as turbine blades, turbine disks, turbine casings, and combustion chamber flame tubes) operate under high temperature and high pressure environments for extended periods. Creep is a key physical mechanism leading to the degradation of material properties in these components. The Norton creep equation is a classical constitutive model describing the steady-state creep behavior of materials, expressed as follows:

[0102] (11);

[0103] In the formula: For steady-state creep rate, For material constants, The equivalent stress acting on the material, Operating temperature For creep activation energy, Let be the ideal gas constant. The stress exponent is represented by this equation. This equation clearly reveals the physical nature of creep rate, which exhibits a power-law dependence on the stress applied to the material and an exponential dependence on the material's operating temperature.

[0104] To effectively correlate the creep equation with the sensor signals of the aero-engine, it is necessary to establish a mapping relationship from sensor data to creep parameters. Therefore, the turbine outlet temperature is selected as the creep characteristic temperature. , as the operating temperature in Norton's creep equation (11) The proxy variables are then used. Based on rotor dynamics and aerodynamic load analysis, a damage equivalent stress model that comprehensively considers both mechanical and aerodynamic loads is constructed. The model's construction expression is as follows:

[0105] (12);

[0106] In the formula: The rotational speed of the core engine (which mainly consists of a high-pressure compressor, a combustion chamber, and a high-pressure turbine); This refers to the outlet pressure of the high-pressure compressor. , and These are learnable weight parameters, which are then optimized and learned through the subsequent step S4.

[0107] After obtaining the creep characteristic temperature Equivalent stress of damage Then, they are normalized to the [0,1] interval to obtain the normalized creep characteristic temperature. and normalized damage equivalent stress To accommodate the numerical stability requirements of neural networks, the normalization process is expressed as follows:

[0108] (13);

[0109] (14);

[0110] In the formula: and These are the maximum and minimum values ​​of the creep characteristic temperature, respectively; and These represent the maximum and minimum values ​​of the damage equivalent stress, respectively.

[0111] Next, a damage rate prediction network is used. Will and Mapped to dimensionless instantaneous damage rate The damage rate prediction network employs a lightweight fully connected neural network, as shown below:

[0112] (15);

[0113] In the formula: for The network's parameter set; and They are respectively The first in the network The weight matrix and bias vector of the layer, ; This represents the critical cumulative damage value at the time of aircraft engine failure.

[0114] exist In the network, the vector is first... The input is fed into a three-layer fully connected network to learn the key parameters of the Norton equations. , and The output vector is obtained. The process is represented as follows:

[0115] (16);

[0116] In the formula: This is a function for a three-layer fully connected network.

[0117] To ensure that the learned parameters conform to the physical meaning of Norton's equations, the output vector... The equivalent material constants are obtained by performing the following transformation. Equivalent stress index Equivalent creep activation energy :

[0118] (17);

[0119] In the formula: For activation functions, used to ensure and All are positive numbers.

[0120] Then, substituting the parameters learned in equations (15) and (17) into the Norton creep equation (11), and taking the logarithm of both sides of the equation, we get:

[0121] (18);

[0122] In the formula: It is the natural logarithm.

[0123] Subsequently, the following final instantaneous damage rate can be obtained:

[0124] (19);

[0125] Output instantaneous damage rate This characterizes the relative rate of damage accumulation in aero engines under current operating conditions.

[0126] Next, by summing the instantaneous damage rates over time, the value corresponding to the current moment can be obtained. Cumulative damage The calculation process is as follows:

[0127] (20);

[0128] Finally, based on the damage mechanics mechanism, the critical cumulative damage at the time of aero-engine failure is defined as... To embed physical constraints into the neural network in real time, a first-order Taylor series expansion method is used to estimate the remaining lifetime. This involves utilizing the instantaneous damage rate at the current moment. By approximating the remaining degradation trajectory with a tangent, the instantaneous equivalent remaining lifetime under the physical path is derived, as expressed below:

[0129] (twenty one);

[0130] In the formula: It is a very small constant added to ensure the stability of the remaining useful life value.

[0131] Equation (21) essentially uses the current degradation rate to make a first-order linear prediction of the remaining lifetime. Although it ignores the higher-order acceleration terms of damage, under the real-time update mechanism of the sliding window, this value can effectively constrain the prediction trend of the neural network to not violate the physical monotonicity.

[0132] Thus, the remaining lifespan of the aero-engines, output by the remaining lifespan prediction model, has been obtained. and physical path predicted remaining useful life The core objective of the physical constraints based on the Norton creep equation is to guide the predicted remaining useful lives of these two paths toward consistency. To this end, data fitting loss functions are defined respectively. and physical constraint loss function in residual form as follows:

[0133] (twenty two);

[0134] (twenty three);

[0135] For aircraft engines during operation The actual remaining service life at that time This represents the number of samples in the current training batch.

[0136] Finally, the total loss function of NCINN yes and The weighted sum, i.e.:

[0137] (twenty four);

[0138] In the formula: These are the weight hyperparameters of the physical constraint loss function.

[0139] The total loss function is calculated relative to the weight parameter set of NCINN using automatic differentiation techniques. gradient Weight parameter set It includes the following parameters: (1) Parameters of the multi-scale feature extraction network, including the kernel weight matrix and bias vector of each convolutional layer in the temporal convolution module; and the projection weight matrix in the self-attention mechanism module. Projection matrix , , Output projection matrix in the multi-head attention mechanism module ; Weight parameters of the self-attention layer in the feature fusion module. (2) Regression network parameters: weight matrices of the two fully connected layers. , and bias vector , (3) Parameters of the physical constraint module based on Norton's creep equation, including weight parameters in the damage equivalent stress model. , and Damage rate prediction network parameter set

[0140] Next, based on the obtained gradient The Adam optimization function is used to update all weight parameters, and the process is expressed as follows:

[0141] (25);

[0142] In the formula, Optimize the function for Adam. For learning rate, , The first Subsequent The next updated set of weight parameters; This is the weight decay coefficient. This ensures that the weights will slowly decay to zero over time even without gradient updates, preventing overfitting when training the weight parameters of NCINN.

[0143] By training the total loss function to convergence using the stochastic gradient descent method shown in equation (25), the weight parameters of NCINN can be optimized, thereby improving the accuracy of data path prediction. and physical path prediction As they converge, NCINN can output a predicted value for the optimal remaining lifetime, i.e.:

[0144] (26);

[0145] S4. After constructing an NCINN that incorporates physical constraints, how do you determine the weight hyperparameters to balance the data loss and physical loss? Learning rate Key hyperparameters, such as those mentioned above, become bottlenecks affecting NCINN performance. However, these hyperparameters cannot be automatically learned using the stochastic gradient descent method, and they exhibit complex coupling relationships. Traditional manual or grid search methods for hyperparameter optimization are inefficient and struggle to find globally optimal solutions for NCINN hyperparameters. To address this, a TOC optimizer is introduced as the outer driving engine of NCINN, enabling adaptive optimization of key hyperparameters. The pre-trained remaining lifetime prediction model is retained for feature extraction and remaining lifetime prediction of input samples.

[0146] TOC is a novel metaheuristic algorithm inspired by the formation and dissipation of tornadoes. It employs a hierarchical population mechanism, dividing individuals into three categories based on fitness: Tornado (current optimal solution), Thunderstorm (potentially excellent solution), and Storm (exploratory solution). Its core innovation lies in the introduction of an orthogonal momentum perturbation mechanism. This mechanism mathematically simulates the deflection characteristics of the Coriolis force effect. By applying random perturbations in the gradient normal vector direction, it effectively adjusts the trajectory of individuals, thereby achieving an excellent balance between global exploration and local exploitation, and avoiding the optimization process from getting trapped in local optima.

[0147] The specific optimization method is as follows: define the hyperparameter vector of the NCINN to be optimized as follows: ,Right now:

[0148] (27);

[0149] In the formula: These are the weight hyperparameters of the physical constraint loss function; The initial learning rate; This represents the number of self-attention heads in the self-attention mechanism module. The length of the time window; This is the weight decay coefficient.

[0150] Each hyperparameter is constrained to a pre-search space with explicit physical or engineering significance. Within this framework, the optimization objective of TOC is to optimize within the predefined search space. Within this framework, we find the hyperparameter configuration that optimizes NCINN's performance on the independent validation set. The collaboration between TOC and NCINN constitutes a two-layer nested recurrent architecture of outer metaheuristic search and inner gradient descent training, where the outer layer is dominated by TOC and responsible for pre-searching the space. The global search is performed in the middle layer; the inner layer consists of the training and validation process of NCINN, which is responsible for evaluating the quality of each set of hyperparameters.

[0151] When a nested loop begins, the TOC is at... Internal random generation Individuals constitute the initial population. :

[0152] and initialize the current outer iteration counter. .

[0153] Next, from the current population Each individual in To instantiate NCINN and on the training set Train the NCINN on the validation set until it converges. The root mean square error (RMSE) of the remaining useful life predictions of NCINN is calculated, and this RMSE value is used as the fitness. The TOC is returned to the outer layer. This completes one cycle of inner layer fitness evaluation.

[0154] Once the fitness of all individuals in the current population has been evaluated, the TOC in the outer loop begins to execute population evolution operations. First, based on fitness... For the current population Sort and classify: the individual with the best fitness value is denoted as Tornado. , representing the current global optimal solution; the top solution with better fitness. Each individual (the top 20% of the population) is recorded as a thunderstorm. The remaining individuals are referred to as storms. The storm will evolve and move to a better region.

[0155] Each storm individual An individual will be randomly assigned an attraction source and will move towards that source. This source can be either a tornado or a thunderstorm. By moving towards the attraction source, the next-generation location of that storm individual can be obtained as follows:

[0156] (28);

[0157] In the formula: , The attraction coefficient, It is a random number. For the location of the attraction source; The term is the Coriolis force deflection term. This term introduces the simulated Coriolis effect to provide a vertical deflection to the direction of movement, which can prevent the storm search from getting trapped in local optima. This is a simulated value for the Earth's rotational angular velocity. The simulated latitude is generated randomly. The vector representing the current velocity direction of the individual. is the Coriolis force deflection coefficient.

[0158] Since the fitness of the thunderstorm group is in the top 20% of the entire population, each individual thunderstorm... The location of the next generation of a thunderstorm can be obtained simply by making a small-scale random perturbation in its vicinity. This process is expressed as follows:

[0159] (29);

[0160] In the formula: This is the local search step size. It is a multidimensional Gaussian random vector with a mean of zero.

[0161] The tornado, being the optimal solution for the current population, will have its position directly preserved to the next generation.

[0162] (30);

[0163] Thus, a new generation of population was obtained through population evolution of the outer TOC. The input is given to the inner NCINN, thus completing one overall loop operation. If the position transformation, i.e., the generational update operation, shown in equations (28) and (29) can produce a storm or thunderstorm individual with a fitness better than the previous generation of tornadoes in the new generation population, then it is replaced with a new tornado individual. Obviously, the inner loop is the evaluation subroutine of the outer loop, and each outer iteration (i.e., the process of generating a new generation population) must be based on the completion of all inner evaluation tasks.

[0164] Repeat the fitness evaluation (inner loop) and population evolution (outer loop) operations described above until the maximum number of evaluations is reached or the position of the tornado individual remains stable across multiple iterations. At this point, the TOC optimizer terminates its training of the NCINN hyperparameters. The TOC optimizer then outputs the historical best individual. The TOC optimizer serves as the final hyperparameter optimization result for NCINN. It acts only as a "meta-learning" tool before training, searching for the optimal hyperparameter configuration. Once the optimal hyperparameters are determined, its task is complete, and it does not participate in subsequent predictions. The Norton creep physical constraint mechanism acts as a "teacher" or "constraint," correcting the weight updates of the multi-scale feature extraction network during training through a physical loss function. Therefore, when performing actual remaining lifetime prediction after NCINN training, the physical laws have been internalized into the weight parameters of the multi-scale feature extraction network. Only the trained remaining lifetime prediction model (including the multi-scale feature extraction network and the regression network) needs to be retained; this model can then be used to extract features from the input samples and predict the remaining lifetime of the aero-engine.

[0165] In this embodiment, the C-MAPSS turbofan engine experimental dataset provided by NASA is used to verify the effectiveness and superiority of the invented TOC-NCINN-based aero-engine RUL prediction method. Figure 2This 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.

[0166] 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.

[0167] Table 1. Basic information about the C-MAPSS dataset.

[0168]

[0169] Table 2 Basic Information of Sensor Monitoring Signals

[0170]

[0171] Continued from Table 2: Basic Information of Sensor Monitoring Signals

[0172]

[0173] The method of this invention for predicting the RUL of aero engines

[0174] (1) Sensor signal preprocessing: The original sensor monitoring signals are subjected to preprocessing operations such as min-max normalization, time series equal length segmentation, and RUL label construction to adapt to the input format of TOC-NCINN. This is beneficial to improve the training and prediction effect of TOC-NCINN.

[0175] 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 key sensors are used as inputs to TOC-NCINN to reduce the interference of redundant information on TOC-NCINN training and reduce the computational complexity of TOC-NCINN.

[0176] Then, to eliminate the differences in physical dimensions of sensor signals and to avoid sensor data with large numerical ranges and high noise dominating the TOC-NCINN training process, and to accelerate the convergence speed of TOC-NCINN, a minimum-maximum normalization method is used to map all retained sensor signal data to the [0,1] interval, i.e.:

[0177] (31);

[0178] In equation (31): 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.

[0179] Next, in order to transform the sensor signal data of the turbofan engine into supervised learning samples adapted to the TOC-NCINN input format, a sliding window technique was used to divide the sensor signal time series into samples of fixed length. ,in This represents the length of the time window.

[0180] Finally, a piecewise linear function is used to construct a smooth RUL label for the turbofan engine, the process of which is expressed as follows:

[0181] (32);

[0182] In the formula: This is the current running time; The maximum RUL value is set to 125 here; This represents the inflection point from the start of engine operation to the point where its performance begins to significantly degrade. This RUL labeling smoothing strategy helps TOC-NCINN focus on the failure evolution process after the inflection point of aero-engine performance degradation, thus facilitating the verification of the effectiveness of the TOC-NCINN-based aero-engine RUL prediction method.

[0183] (2) Output of RUL predictions: The hyperparameters and weight parameters of TOC-NCINN were trained using the training and validation sets from subsets FD001 to FD004, respectively. Before hyperparameter training, the population size of the TOC optimizer was set to 30, the maximum number of iterations (i.e., the maximum number of evaluations) was set to 50, and the attraction coefficient was set to... The Coriolis force deflection coefficient is set to The optimal values ​​of the hyperparameters obtained after training are as follows: physical constraint weights Initial learning rate Time window length Attention count Weight decay coefficient When training the weight parameters of TOC-NCINN using stochastic gradient descent based on the Adam optimization function, the training batch size is set to... Set the maximum number of iterations to It should be noted that during the training phase of TOC-NCINN, only the last time window of the time series data of each aero-engine sensor signal in the test set is extracted as the validation set to evaluate the RUL prediction accuracy of TOC-NCINN.

[0184] After optimizing the hyperparameters and weight parameters of TOC-NCINN, the trained TOC-NCINN is used to perform RUL prediction on the test sets 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 24 in the FD001 subset. Figure 4 Figure 5 shows the RUL prediction curve for engine No. 176 in the FD002 subset using the method of the present invention, and Figure 6 shows the RUL prediction curve for engine No. 100 in the FD003 subset using the method of the present invention. Figure 6 The method of this invention is used to predict the RUL of engine number 12 in the FD004 subset.

[0185] Depend on Figures 3 to 6 The predicted RUL values ​​of the turbofan engine, as presented, show that the invented TOC-NCINN-based RUL prediction method exhibits excellent RUL prediction accuracy on both single-condition subsets FD001 and FD003 and multi-condition subsets FD002 and FD004. For single-condition scenarios, 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 6As 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 stage of engine accelerated degradation, the invented method can still output stable and accurate RUL prediction values, objectively reflecting the actual health status evolution of the turbofan engine. The above RUL prediction results for turbofan engines verify the effectiveness of the invented method in capturing the short-term local performance degradation characteristics and long-term complex non-stationary degradation trends of aero-engines, as well as in the robust prediction of aero-engine RUL.

[0186] 6.3 Comparative Analysis

[0187] (1) Prediction Accuracy Comparison: To quantitatively evaluate the RUL prediction accuracy of TOC-NCINN, its RUL prediction accuracy is compared with that of four other mainstream RUL prediction methods: Feature-attention-based bidirectional gated recurrent unit convolutional neural network (AGCNN), Transformer, Dual self-attention mechanism and long short-term memory network (RFDA-LSTM), and Channel attention & temporal attention-based temporal convolutional network (CATA-TCN). Root mean square error (RMSE) and a scoring function are used as evaluation metrics for RUL prediction accuracy. These two metrics are defined as follows:

[0188] (33);

[0189] (34);

[0190] In equations (33) and (34), The total number of test samples, This is the predicted RUL value. For genuine RUL labels, This represents the RUL prediction error. A smaller RMSE value indicates higher RUL prediction accuracy. The scoring function is designed to simulate real-world aero-engine maintenance scenarios, assigning a higher penalty weight to lagged RUL prediction errors that could lead to engine failure. A smaller score indicates higher RUL prediction accuracy coupled with lower lagged prediction risk.

[0191] The comparison results of the RMSE and Score values ​​of the turbofan engine RUL prediction by TOC-NCINN with those of the other four RUL prediction methods are shown in Tables 3 and 4, respectively.

[0192] Table 3. Comparison of RMSE of 5 RUL prediction methods

[0193]

[0194] Table 4. Score Comparison of 5 RUL Prediction Methods

[0195]

[0196] As shown in Tables 3 and 4, on the FD001 and FD003 subsets corresponding to a single operating condition, TOC-NCINN's overall performance in RUL prediction accuracy is slightly better than the other four prediction methods, demonstrating TOC-NCINN's accurate fitting capability under the basic degradation mode. However, on the FD002 and FD004 subsets corresponding to multiple operating conditions, TOC-NCINN's overall performance in RUL prediction accuracy is significantly better than the other four prediction methods. This further demonstrates TOC-NCINN's excellent adaptability in predicting RUL for complex multi-condition performance degradation data of turbofan engines, and further verifies TOC-NCINN's effective capture of short-term local degradation characteristics and long-term global nonlinear degradation trends of aero-engines, as well as its accurate prediction capability for aero-engine RUL.

[0197] Robustness comparison

[0198] To quantitatively evaluate the robustness of the TOC-NCINN-based RUL prediction method, RUL prediction methods based on AGCNN, Transformer, RFDA-LSTM, CATA-TCN, and TOC-NCINN were repeatedly performed 50 times on the FD001 subset for turbofan engine RUL prediction. The RMSE and Score values ​​of the five prediction methods for each of the 50 RUL predictions were recorded, as shown below. Figure 7-8 As shown. Figure 7 The RMSE values ​​for 50 predictions performed for 5 RUL prediction methods. Figure 8 Score values ​​for 50 predictions performed for 5 RUL prediction methods.

[0199] It is evident that the TOC-NCINN-based RUL prediction method has the lowest RMSE and Score values ​​for 50 repeated RUL predictions on the FD001 subset compared to the other four prediction methods. Furthermore, the TOC-NCINN-based prediction method exhibits lower RMSE and Score dispersion on this subset, meaning that the fluctuation of its RUL prediction results with changes in random factors is significantly suppressed. This demonstrates that in the 50 repeated RUL prediction experiment, the TOC-NCINN-based aero-engine RUL prediction method demonstrates stronger robustness than the other four RUL prediction methods.

[0200] Generalization comparison

[0201] To quantitatively evaluate the generalization performance of RUL prediction methods based on TOC-NCINN, AGCNN, Transformer, RFDA-LSTM, and CATA-TCN, the mean squared error was used as the criterion. Mean absolute error Mean absolute error and fit As a metric for evaluating generalization performance, namely:

[0202] (35);

[0203] (36);

[0204] (37);

[0205] (38);

[0206] In the formula: The total number of test samples, This is the predicted RUL value. For genuine RUL labels; and They are respectively The mean and variance of each true RUL were calculated. To reduce random error, statistical analysis was performed on the generalization performance evaluation metrics of the five prediction methods. The average generalization performance evaluation metrics were obtained from 50 repeated RUL predictions on the FD001 dataset. , , and The comparison results are shown in Table 5.

[0207] Table 5. Comparison of generalization performance of five RUL prediction methods

[0208]

[0209] As shown in Table 5, compared with the other four RUL prediction methods, the prediction method based on TOC-NCINN has... , and The values ​​are all minimized, and the prediction method is based on TOC-NCINN. The value closest to 1 indicates that the TOC-NCINN-based RUL prediction method has the best generalization performance in repeated experiments.

[0210] Ablation Experiment Analysis

[0211] To further explore the contributions of the multi-scale feature extraction network, Norton creep physical constraint mechanism, and TOC optimizer in TOC-NCINN to turbofan engine RUL prediction, and to further verify the effectiveness and superiority of the invented TOC-NCINN-based RUL prediction method, the present invention designed the following three sets of ablation experiments:

[0212] TOC-NCLSTM: The multi-scale feature extraction network in TOC-NCINN is replaced with a single LSTM layer, while retaining physical constraints and the TOC optimizer to test whether the multi-scale feature extraction network can extract turbofan engine performance degradation features better than a simple time series model.

[0213] TOC-NN: Remove the Norton creep equation constraint terms, i.e., set the weight hyperparameters of the physical constraint loss function to... We retained the multi-scale feature extraction network and the TOC optimizer to verify the generalization performance of Norton creep physics constraints.

[0214] NCINN: Uses the full model, but with weight hyperparameters of the physical constraint loss function. Learning rate The optimal values ​​of hyperparameters are determined by grid search or manual tuning to compare the performance difference between TOC adaptive hyperparameter optimization and time-consuming manual tuning.

[0215] The comparison results of the predicted RMSE and Score values ​​of turbofan engine RUL obtained by the TOC-NCINN of the present invention with those obtained by the above three ablation experiments on the four subset datasets FD001~FD004 are shown in Tables 6 and 7, respectively.

[0216] Table 6 Comparison of RMSE in ablation experiments

[0217]

[0218] Table 7 Comparison of Ablation Test Scores

[0219]

[0220] Comparing the results of TOC-NCINN and TOC-NCLSTM reveals that, across all subsets from FD001 to FD004, TOC-NCINN, employing a multi-scale feature extraction network, outperforms models using a single LSTM layer in both RMSE and Score metrics. This indicates that a single recurrent neural network struggles to simultaneously handle both short-term local features and long-term global degradation trends in sensor signals. In contrast, the hierarchical architecture of TOC-NCINN, combining temporal convolution and attention mechanisms, can more deeply uncover complex nonlinear degradation information, laying a data foundation for high-precision RUL prediction. Secondly, the prediction accuracy of the TOC-NN model, after removing the Norton creep equation constraints, showed a significant decrease across all four datasets, particularly performing poorly on the FD002 and FD004 datasets, which involve multiple operating conditions, high noise, and mixed faults. This indicates that the data-driven "black box" model TOC-NN lacks robustness and generalization ability when facing complex operating conditions and mixed fault modes. In contrast, the physical constraint mechanism based on the Norton creep equation effectively guides the invented TOC-NCINN to follow known physical evolution laws, thereby improving the RUL prediction accuracy of TOC-NCINN for turbofan engines. Next, compared to NCINN using traditional grid search or manual parameter tuning, TOC-NCINN, with its adaptive hyperparameter optimization by the TOC optimizer, achieved optimal values ​​in both RMSE and Score evaluation metrics. Because of the complex coupling relationships between physical constraint weights, learning rate, and hyperparameters in the network structure, manual parameter tuning is not only time-consuming and labor-intensive but also prone to getting trapped in local optima. By introducing the TOC optimizer that incorporates Coriolis force, the unique "tornado-thunderstorm-storm" evolution mechanism greatly enhances TOC-NCINN's ability to locate the optimal hyperparameter configuration in the global search space.

[0221] The above ablation experiments fully demonstrate that the multi-scale feature extraction network, Norton creep equation constraint terms, and TOC optimizer in TOC-NCINN play an irreplaceable role in improving the RUL prediction accuracy of aero-engines. It is precisely this organic combination of the three that enables TOC-NCINN to exhibit stronger physical plausibility, robustness, and generalization ability than mainstream deep learning-based RUL prediction methods when performing RUL predictions for highly nonlinear and mechanistically complex systems like aero-engines.

[0222] 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 remaining life of aero-engines based on TOC-NCINN, characterized in that, Includes the following steps: S1. Randomly divide the collected time series sample set into a training set and a validation set; S2. Establish a remaining lifetime prediction model, including a multi-scale feature extraction network and a regression network; The multi-scale feature extraction network includes a temporal convolution module, a self-attention mechanism module, and a feature fusion module; The temporal convolution module uses a multi-layer one-dimensional convolutional neural network to perform deep processing on temporal samples. The original input temporal samples are transformed into high-level local feature representations rich in aero-engine degradation information. The global features are obtained by weighted fusion of local features through a self-attention mechanism module. The feature fusion module adopts a self-attention-based feature fusion strategy: first, local features and global features are concatenated along the feature dimension to form the initial fused features; Subsequently, a lightweight self-attention layer is used to process the initial fused feature again to generate a fused feature; The fused features are input into the regression network to obtain the predicted value of the remaining life of the aero-engine. ; S3. Introduce a physical constraint mechanism based on the Norton creep equation, embed the physical mechanism of material creep damage into the loss function of the remaining life prediction model, and the resulting network is called the Norton creep guided neural network, denoted as NCINN. Norton's creep equation is expressed as follows: ； In the formula: For steady-state creep rate, For material constants, The equivalent stress acting on the material, Operating temperature For creep activation energy, Let be the ideal gas constant. Stress index; The engine turbine outlet temperature was selected as the creep characteristic temperature. As the operating temperature in Norton's creep equation proxy variables; A damage equivalent stress model that comprehensively considers both mechanical and aerodynamic loads is constructed, and its expression is as follows: ； In the formula: Core machine speed; This refers to the outlet pressure of the high-pressure compressor. , and These are learnable weight parameters; After obtaining the creep characteristic temperature Equivalent stress of damage Then, they are normalized to the [0,1] interval to obtain the normalized creep characteristic temperature. and normalized damage equivalent stress ; Next, a damage rate prediction network is used. Will and Mapped to dimensionless instantaneous damage rate ;exist In the network, the vector is first... The input is fed into a three-layer fully connected network to learn the key parameters of the Norton equations. , and The equivalent material constants are obtained. Equivalent stress index Equivalent creep activation energy ; Then, substituting the learned parameters into the Norton creep equation and taking the logarithm of both sides of the equation, we get: ； Subsequently, the following final instantaneous damage rate was obtained: ； By summing the instantaneous damage rates over time, we obtain the result corresponding to the current moment. Cumulative damage The critical cumulative damage at the time of aero-engine failure is defined as... ; Utilizing the instantaneous damage rate at the current moment By approximating the remaining degradation trajectory with a tangent, the instantaneous equivalent remaining lifetime under the physical path is derived, as follows: ； In the formula: It is a very small constant added to ensure the stability of the remaining useful life value; Define the data fitting loss function respectively and physical constraint loss function in residual form as follows: ； ； For aircraft engines during operation The actual remaining service life at that time This represents the number of samples in the current training batch. Finally, the total loss function of NCINN yes and The weighted sum, i.e.: ； In the formula: These are the weight hyperparameters of the physical constraint loss function; The total loss function is calculated relative to the weight parameter set of NCINN using automatic differentiation techniques. gradient ; Based on the obtained gradient The Adam optimization function is used to update all weight parameters, and the process is expressed as follows: ； In the formula, Optimize the function for Adam. For learning rate, , The first Subsequent The next updated set of weight parameters; This is the weight decay coefficient; S4. Introduce the TOC optimizer as the outer driving engine of NCINN to achieve adaptive optimization of key hyperparameters of NCINN; retain the trained remaining lifetime prediction model for feature extraction and remaining lifetime prediction of input samples. The specific optimization method is as follows: define the hyperparameter vector of the NCINN to be optimized as follows: ,Right now: ； In the formula: These are the weight hyperparameters of the physical constraint loss function; The initial learning rate; This represents the number of self-attention heads in the self-attention mechanism module. The length of the time window; This is the weight decay coefficient; Each hyperparameter is constrained to a pre-search space with explicit physical or engineering significance. Within this framework, the optimization objective of TOC is to optimize within the predefined search space. Within this framework, we find the hyperparameter configuration that optimizes NCINN's performance on the independent validation set. The collaboration between TOC and NCINN constitutes a two-layer nested recurrent architecture of outer metaheuristic search and inner gradient descent training, where the outer layer is dominated by TOC and responsible for training in the pre-search space. The global search is performed in the middle layer; the inner layer consists of the training and validation process of NCINN, which is responsible for evaluating the quality of each set of hyperparameters.

2. The method for predicting the remaining life of aero-engines based on TOC-NCINN according to claim 1, characterized in that, In step S4, when the nested loop begins, TOC is at... Internal random generation Individuals constitute the initial population. : and initialize the current outer iteration counter. ; Next, from the current population Each individual in Instantiate NCINN and train it on the training set until it converges; Then, the root mean square error (RMSE) of the remaining lifetime predictions for NCINN is calculated on the validation set, and this RMSE value is used as the fitness score. Return the TOC to the outer layer; this completes one cycle of inner layer fitness evaluation.

3. Once the fitness of all individuals in the current population has been assessed, the TOC in the outer loop begins to execute population evolution operations. First, based on fitness... For the current population Sort and classify: the individual with the best fitness value is denoted as Tornado. , representing the current global optimal solution; the top solution with better fitness. Individually recorded as thunderstorms The remaining individuals are referred to as storms. The storm will evolve and move to a better region; Each storm individual Each individual storm will be randomly assigned an attraction source and will move towards that source. By moving towards the attraction source, the next generation position of this storm individual will be obtained as follows: ； In the formula: , The attraction coefficient, It is a random number. For the location of the attraction source; The term representing the Coriolis force deflection; Each thunderstorm individual The location of the next generation of a thunderstorm individual can be obtained by simply making a small-scale random perturbation in its vicinity. This process is expressed as follows: ； In the formula: This is the local search step size. It is a multidimensional Gaussian random vector with zero mean; The tornado, being the optimal solution for the current population, will have its position directly preserved to the next generation. ； Thus, a new generation of population was obtained through population evolution of the outer TOC. Inputting it into the inner NCINN completes one complete loop operation; Repeat the fitness evaluation and population evolution operations described above until the maximum number of evaluations is reached or the position of the tornado individual remains stable in multiple consecutive iterations, at which point the TOC optimizer terminates the training of the NCINN hyperparameters.

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