An interpretable physical information neural network aging prediction method

Abstract

This invention relates to the fields of computer applications and reliability assessment technology, and particularly to an interpretable physical information neural network aging prediction method. The method first designs a feature attention module to weight the multi-stress aging features of solid propellants, obtaining a weighted feature vector. Second, based on the weighted feature vector, a physical prior module is constructed, embedding a parameterized physical model to calculate the physical prior prediction value. Then, using the physical prior prediction value as a benchmark, combined with the weighted feature vector, a correction network module is designed to learn the residuals and obtain data-driven prediction values. Finally, an adaptive fusion mechanism is designed to dynamically fuse and jointly optimize the physical prior prediction value and the data-driven prediction value, outputting the final aging state prediction result. Experiments show that this method has extremely high fitting accuracy and stability under multi-field coupling conditions, with a maximum coefficient of determination of 0.9950 and a root mean square error (RMSE) remaining below 0.06.

Description

Technical Field

[0001] This invention relates to the fields of computer applications and reliability assessment technology, and in particular to an interpretable physical information neural network aging prediction method, applicable to the performance degradation prediction and analysis of solid propellants under multi-stress coupling conditions. Background Technology

[0002] Solid rocket engines, as the core power system for aerospace launch vehicles and national defense equipment, are directly related to mission success or failure and national strategic security. Solid propellant grains, serving as the engine's energy source and load-bearing structure, are subjected to a long-term multi-stress coupled environment involving temperature, constant strain, and aging time during service and storage. Their performance degradation process exhibits significant nonlinear, phased, and uncertain characteristics. Accurately predicting their aging state is of great engineering significance for assessing engine lifespan.

[0003] Traditional prediction methods have many limitations, making it difficult to balance physical consistency with prediction accuracy. For example, patent publication number CN109655397A discloses a method for predicting the reliable storage life of solid propellants. This method obtains performance degradation data through high-temperature accelerated aging tests and uses the Arrhenius equation to extrapolate and assess storage life. However, such methods are often based on the ideal single stress (temperature) assumption, making it difficult to accurately describe the complex nonlinear aging behavior of solid propellants under multi-field coupling; moreover, they heavily rely on a large amount of destructive test data, resulting in long test cycles and high costs. Patent application number CN202610162168.5 discloses a method for predicting the thermal state of AUV lithium-ion batteries. This method obtains an initial physical estimate by constructing a reduced-order thermal model and uses spatiotemporal dynamic graph network output data to drive correction quantities, finally obtaining the prediction result by direct summation. However, this method uses a fixed summation method when integrating physical priors and data-driven results, lacking an adaptive weight adjustment mechanism. When the physical laws and data characteristics of different aging stages differ significantly, this approach is difficult to achieve effective coordination, which limits the prediction accuracy and model interpretability under complex operating conditions.

[0004] In summary, existing multi-stress prediction models suffer from insufficient physical prior constraints and a lack of adaptive coordination, resulting in limited key feature extraction, model "black box" behavior, and poor physical consistency. This makes it difficult for existing methods to simultaneously achieve prediction accuracy, generalization ability, and internal interpretability. Summary of the Invention

[0005] In view of the above, this invention proposes an interpretable physical information neural network aging prediction method, which aims to solve the problems in the prior art where the fitting accuracy of a single physical model under multi-stress coupling is limited, the pure data-driven model is difficult to reliably extrapolate known degradation characteristics to unknown working conditions due to the lack of physical constraints, resulting in poor interpretability of health prediction, and the difficulty in achieving adaptive dynamic fusion between the two.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] An interpretable physical information neural network aging prediction method includes the following steps:

[0008] Step 1: Design a feature attention module to model the importance of multi-stress aging features involved in the thermo-mechanical coupling aging process of solid propellants: weight the original feature vectors to obtain weighted feature vectors;

[0009] Step 2: Construct a parameterized double exponential aging degradation physical model and embed it into a neural network structure to build a physical prior module. Input the weighted feature vector obtained in Step 1 into the physical prior module to calculate the physical prior prediction value.

[0010] Step 3: Using the physical prior predictions and weighted feature vectors as inputs, design a correction network module to learn the residual relationship between the actual observations and the physical prior predictions, and obtain the corresponding data-driven predictions through a feedforward neural network.

[0011] Step 4: Based on the physical prior predictions obtained in Step 2 and the data-driven predictions obtained in Step 3, an adaptive weighted fusion and joint constraint optimization module is designed. The physical prior predictions and data-driven corrections are dynamically weighted and fused using learnable fusion weights to obtain fused predictions. A joint loss function including data fitting, physical constraints, and regularization is constructed to update feature weights, physical parameters, network weights, and fusion weights, thereby achieving unified model training until convergence and outputting the final prediction results.

[0012] Furthermore, in step one above, the multi-stress aging characteristics are used as input to the model. The modeling process is as follows: constructing the original feature vector. ,in, , , These correspond to temperature, constant strain, and aging time, respectively.

[0013] A set of learnable raw weight parameters is introduced, and they are normalized using the Softmax function to calculate the raw feature weight vector for feature attention. ; the original feature weight vector After normalization and the original feature vector Perform element-wise multiplication to obtain the weighted eigenvector. .

[0014] Furthermore, in step two above, from the weighted feature vector The aging time features are extracted and denormalized to physical scale to restore the aging time to the true physical dimensions. ;

[0015] Construct a physical model of bi-exponential aging degradation, and substitute the aging time. Calculate the physical prior prediction value The calculation formula is:

[0016] (5)

[0017] In the formula, and These are the amplitude and rate parameters for the rapid aging stage, respectively. and These represent the initial amplitude and rate constant for the slow aging stage, respectively. The value constraint range of each parameter is set based on the actual physical state of the solid propellant, and the boundary constraints of the physical parameters are realized by mapping the underlying network parameters through a nonlinear activation function.

[0018] Furthermore, in step three above, a residual learning objective is established between the physical prior module and the actual observed aging behavior, and the deviation relationship is defined as follows:

[0019] (7)

[0020] In the formula, For residuals that the physical prior module could not explain, Represents the actual observed value. These are physical prior predictions;

[0021] The physical prior prediction value With the weighted feature vector Feature concatenation is performed to form a joint input vector; a feedforward neural network is constructed, comprising an input layer, multiple hidden layers, and an output layer, wherein the number of neurons in the multiple hidden layers decreases layer by layer; the joint input vector is fed into the network, and nonlinear residual mapping features are extracted through the hidden layers and the Tanh activation function, and the data-driven prediction value is generated through the output layer. .

[0022] Furthermore, in step four above, learnable original fusion weight parameters are introduced. The value obtained by mapping through the Sigmoid function is in Dynamic fusion weights within the interval During the model initialization phase, initial values ​​are set to assign higher initial decision weights to the physical prior model; the dynamic fusion weights are then utilized. For the physical prior prediction value Data-driven forecasts A linear combination is performed to obtain the fused prediction value. ;

[0023] Furthermore, construct a joint loss function. The joint loss function is a weighted combination of the mean squared error loss of data fitting, the L2 regularization loss of predicted values, the physical prior fitting loss, the attention sparsity loss, and the parameter smoothing regularization loss.

[0024] (15)

[0025] in: Mean square error; The item is the predicted value; The loss function is a double exponential function fitting loss. This is due to attention sparsity loss. Representative parameter: smoothing loss; , , , The weight coefficients are used to update the model parameters uniformly through the backpropagation algorithm based on the joint loss function.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] 1. This invention designs a nonlinear residual learning correction architecture based on physical benchmarks, cleverly resolving the challenge of a single physical model failing to accurately characterize the complex aging behavior of multiple coupled fields. The correction network no longer blindly fits global degenerate data, but instead precisely focuses on the residual between actual observations and physical prior predictions. This "physical backbone + data trimming" strategy significantly reduces the risk of overfitting the neural network to the entire process mapping, balancing rigorous physical constraints with extremely high data fitting accuracy.

[0028] 2. This invention employs a model training method combining adaptive weighted fusion and joint constraint optimization, effectively addressing the problems of incoordination between physical models and data-driven models, fixed fusion ratios, and insufficient stability during training in existing technologies. Specifically, by introducing learnable fusion weights, the physical prior predictions and data-driven corrections are dynamically weighted and fused, enabling the model to adaptively adjust the contribution ratio of both based on different aging stages and operating conditions. Simultaneously, by constructing a joint loss function, the feature attention module, physical prior module, and correction network module are trained and optimized uniformly, avoiding error accumulation that may result from independent optimization of each module. This design makes the overall model structure more coordinated and the prediction results smoother and more reliable.

[0029] 3. Targeting the thermo-mechanical coupling aging mechanism of solid propellants, temperature, constant strain, and aging time are selected as core features to construct a low-dimensional input representation. This ensures complete characterization of key degradation information while reducing interference from redundant features. Based on this, learnable weights are introduced to adjust the importance of each feature, achieving adaptive characterization of the influence of multiple stresses. This improves the effectiveness of the input information and the stability of the model, providing a reliable foundation for subsequent physical modeling and data correction.

[0030] 4. This invention extracts aging time features to construct a bi-exponential model that conforms to the degradation mechanism of solid propellants. This model characterizes the aging process in stages, simultaneously describing both rapid decay and slow degradation characteristics, thus improving the accuracy of physical modeling. Furthermore, physical constraints are imposed on the model parameters to ensure their values ​​remain within a reasonable range. This prevents the model from deviating from actual patterns during training, enhancing the stability and physical consistency of prediction results and providing support for reliable predictions under complex operating conditions.

[0031] 5. This invention constructs a complete interpretable physical information neural network aging prediction method through the collaborative design of the aforementioned feature attention modeling, physical prior embedding, residual correction learning, and adaptive fusion optimization. This effectively solves the comprehensive problems of insufficient prediction accuracy, poor physical consistency, and limited model generalization ability in existing technologies for multi-stress aging modeling. This method can stably characterize the aging evolution process of materials under complex service environments, balancing physical constraints with data-driven flexibility, and has strong engineering applicability and promotional value. Attached Figure Description

[0032] Figure 1 This is an overall flowchart of the present invention;

[0033] Figure 2 Modify the structure of the network module;

[0034] Figure 3The degradation trend prediction diagram of the model designed in this invention, wherein (a) is the degradation trend of health factors at 50℃ and different constant strains; (b) is the degradation trend of health factors at 60℃ and different constant strains; and (c) is the degradation trend of health factors at 70℃ and different constant strains. Detailed Implementation

[0035] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments and accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] See Figure 1 This invention proposes an interpretable physical information neural network aging prediction method. First, a feature attention module is designed to model the importance of the input multi-stress aging: the original feature vector is weighted to obtain a weighted feature vector. Second, a parameterized double-exponential aging degradation physical model is embedded into the neural network structure to construct a physical prior module. The weighted feature vector obtained in step one is input into the physical prior module to calculate the physical prior prediction value. Then, based on the physical prior prediction value, a correction network module is designed in conjunction with the weighted feature vector to learn the difference between the actual observed data and the physical prior prediction results, obtaining a data-driven prediction value. Finally, an adaptive weighted fusion and joint constraint optimization mechanism is designed to dynamically fuse the physical prior prediction value and the data-driven prediction value, and the model is uniformly trained and optimized to output the final aging state prediction result.

[0037] Example: This example applies to solid propellants. The presented interpretable physical information neural network aging prediction method specifically includes the following steps:

[0038] Step 1: Design a feature attention module to model the importance of the multi-stress aging features involved in the thermo-mechanical coupling aging process of the input solid propellant: weight the original feature vector to obtain a weighted feature vector.

[0039] 1.1 Construct the original feature vector and define the original feature weight parameters;

[0040] The multi-stress aging characteristics involved in the thermo-mechanical coupling aging process of solid propellants—temperature, constant strain, and aging time—are obtained as inputs to the model for importance modeling. The process involves constructing a three-dimensional input original feature vector.

[0041] (1)

[0042] in, , , These correspond to three input values: temperature, constant strain, and aging time. This is for the original feature vector. In the feature attention module, learnable original feature weight parameters are introduced. During the training process, the neural network learns the original feature weight vectors that correspond one-to-one with the input features. In the model initialization phase, to avoid introducing subjective prior biases, it is assumed that each original feature has the same initial impact on aging and degradation. Therefore, the original feature weights of each feature are all equivalently set to 1 / 3. During the subsequent neural network training process, this weight parameter will be continuously learned and updated through the backpropagation algorithm to quantify the relative contribution of different force features to the prediction of health factors.

[0043] 1.2 Normalize the original feature weights and complete the weighted output processing of the input original features to obtain the weighted feature vector.

[0044] To ensure comparability between different feature weights and to avoid the impact of inconsistent weight scales on model training stability, the original weight vector is normalized using the Softmax function, limiting its values ​​to the interval (0,1) and ensuring a sum of 1.

[0045] (2)

[0046] In the formula, This represents the attention weight after normalization of the i-th feature. The normalized feature attention weight vector is obtained as follows: The normalized feature attention weights are multiplied element-wise with the original input feature vector, and the weighted sum of each input feature is calculated to obtain the weighted feature vector. for:

[0047] (3)

[0048] This weighted processing allows features that have a greater impact on the decline of health factors to be included in the weighted average. In this case, the weighted features occupy a higher proportion, while the weights of features with less influence are correspondingly suppressed. The resulting weighted feature vector... This will serve as a unified input for subsequent physical prior modules and correction network modules, enabling a unified expression of multi-stress aging characteristics within the model.

[0049] Step 2: Embed the parameterized double exponential aging degradation physical model into the neural network structure to construct the physical prior module. Input the weighted feature vector obtained in Step 1 into the physical prior module to calculate the physical prior prediction value.

[0050] 2.1 Extract the aging time features from the weighted feature vector and perform physical scale inverse normalization.

[0051] The weighted feature vector obtained in step one Based on this, it includes attention-weighted aging time features. Since the input data of neural networks is usually normalized, and classical empirical physics formulas must be calculated at a real physical scale, the physics prior module first designs a physical scale restoration mechanism to address the issue of inconsistent data scales. The specific calculation is as follows:

[0052] (4)

[0053] in, This represents the aging time at the physical scale. This refers to the standardized aging time. and These represent the mean and standard deviation of the aging time in the training set, respectively. The restored aging time... It will be used as a direct time variable input for subsequent physical models.

[0054] 2.2, Construct a physical model for bi-exponential aging degradation and apply parameter boundary constraints to calculate the physical prior prediction values;

[0055] Based on the reduced aging time A physical prior module is constructed to physically model the aging process of solid propellants. This physical prior module employs a double-exponential aging degradation model to describe the evolution of solid propellant health factors, and its physical expression is as follows:

[0056] (5)

[0057] in, The aging time corresponds to the physical scale. Parameter 'a' represents the amplitude of the rapid aging stage, controlling the rate of decline in the initial aging phase, and its value is constrained between [0, 2]. Parameter 'b' represents the aging rate of the rapid aging stage, reflecting the rate of decay of health factors in the early stages of aging, and its value is set between [0.0001, 4]. Parameter 'c' represents the initial amplitude of the slow aging stage, and its value is constrained between [9, 11]. Parameter 'd' is the aging rate constant of the slow aging stage, and its value range is [0.00001, 0.001]. The value constraints of the above physical parameters are jointly determined by comprehensively considering the conservation law of initial health factors in solid propellants, the characteristic time scale differences of the two-stage aging mechanism, and the nonlinear prefit results of historical accelerated aging test data.

[0058] To ensure that the aforementioned double-exponential parameters always conform to objective laws during the backpropagation learning process of the neural network, this module designs a parameter boundary constraint mechanism. During training, the model does not directly optimize the physical parameters themselves, but rather optimizes a set of corresponding unconstrained original parameters. This invention optimizes the aforementioned four physical parameters (…). And mapped to a preset physical range via the Sigmoid function:

[0059] (6)

[0060] In the formula, The Sigmoid function maps the original parameters to (0, 1) and then linearly transforms them to the range of values. These are the original physical parameters. During model initialization, initial values ​​are assigned to these unconstrained original parameters so that the corresponding physical parameters are exactly at the midpoint of their value range. This ensures that the training starting point is within a reasonable range, enhancing the stability of model training. Finally, this module outputs the predicted values ​​calculated based on the physical model.

[0061] Step 3: Using the physical prior predictions and weighted feature vectors as inputs, design a correction network module to learn the residual relationship between the actual observation data and the physical prior predictions, and obtain the corresponding data-driven correction amount.

[0062] 3.1. Define the residual learning objective of the correction network and establish the bias relationship between physical prior predictions and actual observed aging behavior;

[0063] Based on the physical prior predictions obtained in step two, a data-driven correction network is constructed to characterize the deviation between the physical prior model and the actual observed aging behavior. This step uses the weighted feature vector output from step one and the physical prior predictions obtained in step two as joint inputs, and learns the nonlinear residual information that is not fully described by the physical model during the aging process through a neural network.

[0064] The learning objective of the modified network can be mathematically described as follows:

[0065] (7)

[0066] In the formula, For residuals that the physical model cannot explain, Indicates the actual value. These are the predicted values ​​from the prior physical model.

[0067] 3.2 Construct a correction network module based on a feedforward neural network architecture to extract features and generate data-driven correction values;

[0068] The correction network module adopts a feedforward neural network architecture, mainly consisting of an input layer, several hidden layers, and an output layer, such as... Figure 2 As shown. By Figure 2 It can be seen that the input layer consists of three weighted feature vectors that have been weighted by feature attention. The data then flows through three hidden layers, which employ a progressively decreasing structure with the number of neurons in each layer set to 64, 32, and 16 respectively. The hyperparameter settings for this network are based on the results of cross-validation experiments using a grid search approach. This progressive dimensionality reduction structure effectively filters redundant noise in multi-stress coupled input features, ensuring the model has sufficient nonlinear fitting capacity to learn complex residual relationships while maximizing the limitation of network parameter size. This effectively avoids overfitting issues that easily occur in purely data-driven models with small, aged data samples. Each layer is followed by a Tanh activation function to extract and abstract features, with an output range of (-1, 1). Finally, the output layer generates corrected data-driven predictions. This provides data support for the next step of the weighted fusion module.

[0069] Step four: Based on the physical prior predictions obtained in step two and the data-driven corrections obtained in step three, an adaptive weighted fusion and joint constraint optimization module is designed. The physical prior predictions and data-driven predictions are dynamically weighted and fused using learnable fusion weights. A joint loss function is constructed to uniformly train and optimize the feature attention module, the physical prior module, and the correction network module, so as to obtain the final aging state prediction result.

[0070] 4.1 Construct an adaptive weighted fusion mechanism to achieve dynamic coordination between physical laws and data-driven correction quantities;

[0071] Obtaining the physical prior prediction value in step two and the data-driven predicted values ​​in step three. Subsequently, an adaptive weighted fusion module is constructed to dynamically fuse the physical prior prediction results and the corrected results. To ensure the rationality of the fusion weight values, the original parameters of the fusion weights are adjusted. The Sigmoid mapping function is used to constrain its value to the interval [0,1]. The specific expression is as follows:

[0072] (8)

[0073] in, This represents the original weight parameter, set to 0.69. At this point, the initial fused weights, mapped by the Sigmoid function, account for approximately two-thirds of the total weights. This specific initialization strategy aims to give the physical prior model greater decision-making power in the early stages of training, achieving a "cold start dominated by physical laws." This effectively avoids drastic gradient fluctuations or predictions that violate physical principles from a purely data-driven correction network before it has fully fitted the model, greatly ensuring the numerical stability of the model during the initial convergence phase. The final aging state prediction value... Obtained through the following fusion relationship:

[0074] (9)

[0075] In the formula, the fusion weight It can adaptively adjust during training. When When the value approaches 1, it indicates that the model mainly relies on physical laws; when... When the value approaches 0, the model becomes more reliant on the results of data correction. This design allows the model to adaptively adjust the contribution ratio of physical constraints and data-driven factors based on different stress combinations.

[0076] 4.2 Construct a multi-objective joint loss function to perform unified backpropagation and collaborative optimization of the parameters of each module of the model;

[0077] To ensure the model simultaneously meets the requirements of high prediction accuracy, strong physical plausibility, interpretability, and stable parameter evolution, the loss function is designed as follows:

[0078] 1) Mean squared error (MSE) is defined as follows:

[0079] (10)

[0080] Where N is the number of training samples, It is the predicted value of the i-th sample. It is the true value of the i-th sample.

[0081] 2) The term applies L2 regularization to the predicted values ​​to encourage the model to produce smaller predicted values, which helps prevent overfitting. It is defined as:

[0082] (11)

[0083] 3) The loss function is a double exponential function fitting loss, defined as follows:

[0084] (12)

[0085] in, These are model parameters. It is the aging time of the i-th sample.

[0086] 4) For attentional sparse loss, its main function is to enhance the discriminative power and interpretability of feature attention weights, and it is defined as follows:

[0087] (13)

[0088] This represents the attention weight after normalization of the i-th feature. . This means that by constructing the weights in this way, a penalty is imposed on the sum of squares, so that a few features are given larger weights, while the majority of features are given smaller weights, in order to prevent weight averaging and further enhance the discriminative power of the features.

[0089] 5) The representative parameter smoothing loss can effectively suppress the drastic fluctuations of model parameters during training, so as to ensure the stability and repeatability of the model. The specific description is as follows:

[0090] (14)

[0091] in, Original parameters representing physical parameters By applying L2 regularization penalties to the original parameters, the parameters are indirectly constrained, thereby enhancing the smoothness of the model.

[0092] Therefore, combining all the losses, the resulting total loss function consists of the following five weighted terms:

[0093] (15)

[0094] in: , , , These are the weighting coefficients, with values ​​of: , , , The values ​​of the hyperparameters mentioned above were determined through cross-validation experiments, taking into account the differences in the numerical magnitudes of the various loss terms and the priority of the optimization objectives. The model utilizes the backpropagation algorithm based on the total loss function. The parameters of the entire network are updated collaboratively until convergence, and the final multi-state prediction result is output.

[0095] 4.3 Parameter Settings and Training Strategies

[0096] To demonstrate the effectiveness of the network model in this invention, multiple rounds of experiments were conducted to adjust the model's hyperparameters, ultimately selecting the optimal parameter configuration for experimental verification. The algorithm was implemented on a Windows 10 operating system, equipped with an AMD Ryzen 75800X processor (8 cores) and 32GB of RAM. In terms of software environment, all experiments were conducted using Python 3.6 and the PyTorch 1.2.0 deep learning framework, with an NVIDIA RTX 2080Ti graphics card. During model training, the batch size was set to 32, and the total number of training epochs was set to 20,000. To ensure the reproducibility of experimental results, the data partitioning method between the training and test sets was fixed during model training. Model parameter optimization employed the Adam optimizer, with an initial learning rate of 0.0001 and a weight decay coefficient of 0.0001, thereby improving model convergence speed while ensuring training stability.

[0097] This invention employs a fixed-round training strategy and ensures model convergence by monitoring the evolution of the training loss curve. After training, performance evaluation metrics (RMSE, MAE, MAPE, R²) and interpretability analysis are comprehensively compared to verify the model's accuracy and rationality.

[0098] To verify the effectiveness of the model, this embodiment selected three temperature gradients (50℃, 60℃, and 70℃) and three constant strain levels (6%, 9%, and 12%) for combined testing. The selected temperature gradients fall within the high-temperature accelerated aging range of solid propellants, significantly shortening the test cycle while ensuring that the aging mechanism remains consistent with long-term storage at room temperature. The set constant strain levels effectively cover the typical static structural deformation envelope that engine propellant grains may undergo under long-term storage conditions. The degradation trend prediction results of the interpretable physical information neural network model under different temperature and constant strain combinations are as follows: Figure 3 As shown. By Figure 3 It can be seen that, under all test conditions, the prediction results of the interpretable physical information neural network model are quite close to the experimental values, and its degradation law with constant strain and temperature is consistent.

[0099] To provide a quantitative evaluation, Table 1 presents the evaluation metrics for the interpretable physical information neural network model under different thermo-coupling conditions. A comparative analysis of the data in Table 1 shows that the R² value is higher than 0.92 under all operating conditions, and exceeds 0.97 under most conditions, reaching a maximum of 0.9950, indicating that the present invention has extremely high fitting accuracy. Furthermore, RMSE, MAE, and MAPE all remain at low levels. Specifically, the highest RMSE does not exceed 0.06, the highest MAE is only 0.0507, and the highest MAPE value is 0.4914%, further demonstrating that the prediction accuracy of the model in this invention has been significantly improved.

[0100] Table 1 Evaluation metrics for interpretable physical information neural network models under different thermo-coupling conditions

[0101]

[0102] The above description is a specific illustration of the present invention, and not a limitation thereof. Those skilled in the art can make various equivalent technical solutions without departing from the scope of the present invention; therefore, all equivalent technical solutions should be included within the protection scope of the present invention.

Claims

1. An interpretable physical information neural network aging prediction method, comprising the following steps: Step 1: Design a feature attention module to model the importance of multi-stress aging features involved in the thermo-mechanical coupling aging process of solid propellants: weight the original feature vectors to obtain weighted feature vectors; Step 2: Construct a parameterized double exponential aging degradation physical model and embed it into a neural network structure to build a physical prior module. Input the weighted feature vector obtained in Step 1 into the physical prior module to calculate the physical prior prediction value. Step 3: Using the physical prior predictions and weighted feature vectors as inputs, design a correction network module to learn the residual relationship between the actual observations and the physical prior predictions, and obtain the corresponding data-driven predictions through a feedforward neural network. Step 4: Based on the physical prior predictions obtained in Step 2 and the data-driven predictions obtained in Step 3, an adaptive weighted fusion and joint constraint optimization module is designed. The physical prior predictions and data-driven corrections are dynamically weighted and fused using learnable fusion weights to obtain fused predictions. A joint loss function including data fitting, physical constraints, and regularization is constructed to update feature weights, physical parameters, network weights, and fusion weights, thereby achieving unified model training until convergence and outputting the final prediction results. 2.The physical information neural network aging prediction method with explainability according to claim 1, wherein: In step one, the multi-stress aging characteristics are used as input to the model. The modeling process is as follows: construct the original feature vector. ,in, , , These correspond to temperature, constant strain, and aging time, respectively. A set of learnable raw weight parameters is introduced, and they are normalized using the Softmax function to calculate the raw feature weight vector for feature attention. ; the original feature weight vector After normalization and the original feature vector Perform element-wise multiplication to obtain the weighted eigenvector. . 3.The explainable physical information neural network aging prediction method of claim 2, wherein: In step two, from the weighted feature vector The aging time features are extracted and denormalized to physical scale to restore the aging time to the true physical dimensions. ; Construct a physical model of bi-exponential aging degradation, and substitute the aging time. Calculate the physical prior prediction value The calculation formula is: (5) In the formula, and These are the amplitude and rate parameters for the rapid aging stage, respectively. and These represent the initial amplitude and rate constant for the slow aging stage, respectively. The value constraint range of each parameter is set based on the actual physical state of the solid propellant, and the boundary constraints of the physical parameters are realized by mapping the underlying network parameters through a nonlinear activation function. 4.The method of claim 1, wherein: In step three, a residual learning objective is established between the physical prior module and the actual observed aging behavior. The bias relationship is defined as follows: (7) wherein is the residual that the physical prior module fails to explain, denotes the actual observation, is the physical prior prediction; The physical prior prediction value With the weighted feature vector Feature concatenation is performed to form a joint input vector; a feedforward neural network is constructed, comprising an input layer, multiple hidden layers, and an output layer, wherein the number of neurons in the multiple hidden layers decreases layer by layer; the joint input vector is fed into the network, and nonlinear residual mapping features are extracted through the hidden layers and the Tanh activation function, and the data-driven prediction value is generated through the output layer. . 5.The explainable physical information neural network aging prediction method of claim 1, wherein: In step four, the original fusion weight parameters are introduced to be learnable , which are mapped by a sigmoid function to get dynamic fusion weights with values in the interval ; their initial values are set in the model initialization stage to give the physical prior model a higher initial decision weight; Utilizing the dynamic fusion weight To the physical prior prediction value With data-driven prediction value Linear combination is carried out, and the fusion prediction value is as follows: .

6. The interpretable physical information neural network aging prediction method of claim 5, wherein: Constructing a joint loss function The joint loss function is a weighted combination of the mean squared error loss of data fitting, the L2 regularization loss of predicted values, the physical prior fitting loss, the attention sparsity loss, and the parameter smoothing regularization loss. (15) in: Mean square error; The item is the predicted value; The loss function is a double exponential function fitting loss. This is due to attention sparsity loss. Representative parameter: smoothing loss; , , , The weight coefficients are used to update the model parameters uniformly through the backpropagation algorithm based on the joint loss function.

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