A digital twin performance extrapolation model for long short-term memory networks based on physical information constraints and its construction method.

Abstract

The application belongs to the technical field of fault prediction, and particularly discloses a digital twin performance deduction model based on a long short-term memory network of physical information constraint and a construction method thereof, which comprises the following steps: training a neural network model through a training set, and taking the trained neural network model as the digital twin performance deduction model; the training set comprises road surface physical parameters X and road surface performance parameters Y; in the neural network model: a first LSTM network extracts time sequence features of the parameters X to obtain a preliminary performance parameter prediction value; an automatic differentiation module calculates a partial derivative with respect to time t and a partial derivative with respect to the parameters X by using an automatic differentiation technology; a second LSTM network obtains according to and the parameters X, adjusts according to to make it evolve in line with physical prior knowledge, and realizes physical information constraint. The application can effectively improve the digital twin performance deduction precision under a complex environment.

Description

Technical Field

[0001] This invention belongs to the field of fault prediction technology, and more specifically, relates to a digital twin performance extrapolation model of long short-term memory networks based on physical information constraints and its construction method. Background Technology

[0002] Digital twin technology, by constructing a dynamic mapping between physical entities and virtual models, has become a core technology in fields such as intelligent manufacturing, smart energy, and aerospace. Its core value lies in predicting and optimizing system states through real-time performance simulation, thereby reducing maintenance costs and improving operational efficiency. However, with the increasing complexity of industrial systems, traditional performance simulation methods face two major challenges: how to extract dynamic patterns from multi-source heterogeneous data, and how to ensure the rationality of the simulation results in accordance with physical mechanisms.

[0003] Currently, mainstream digital twin performance extrapolation methods can be divided into two categories: model-based methods and data-driven methods. Traditional simulation methods based on explicit mathematical models construct deterministic mechanistic models through physical laws, such as using differential equations or conservation equations to describe the dynamic behavior of the system. These methods have high accuracy in simple systems or steady-state scenarios, but in complex dynamic systems, they rely on explicit mathematical expressions for modeling, leading to significant limitations. For example, for multi-body coupled, nonlinear time-varying, or high-dimensional multiphysics systems such as those in road engineering, the modeling process needs to introduce linearization assumptions, order reduction, or ignore minor factors, causing the model to deviate from the actual physical process, i.e., model distortion. In addition, real-time solution of explicit models involves high computational costs, making it difficult to meet the low-latency requirements of digital twins, and model parameter calibration relies on expert experience, resulting in insufficient adaptability to unknown operating conditions. Pure data-driven methods directly learn the dynamic characteristics of the system from historical data through deep learning algorithms, avoiding the complexity of explicit modeling. Time-series models, represented by Long Short-Term Memory networks, are widely used in equipment degradation prediction and dynamic parameter inversion due to their ability to capture long-term dependencies. However, such methods rely entirely on data distribution, ignore prior physical knowledge, and are easily affected by data noise, sparsity, and distribution shift, which may lead to inference results that violate basic physical laws such as energy conservation and mass conservation, and their generalization ability is insufficient in scenarios outside the training data. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a digital twin performance extrapolation model and its construction method based on physical information constraints of long short-term memory network, the purpose of which is to effectively improve the accuracy of digital twin road surface performance extrapolation in complex environments.

[0005] To achieve the above objectives, according to a first aspect of the present invention, a method for constructing a digital twin performance extrapolation model of a long short-term memory network based on physical information constraints is proposed, comprising the following steps:

[0006] The neural network model is trained using a training set, and the trained neural network model is used as a performance inference model for digital twins.

[0007] The training set includes pavement physical parameters X and pavement performance parameters Y, wherein the physical parameters X include time-series dynamic parameters and static parameters;

[0008] The neural network model includes a first LSTM network, an automatic differentiation module, and a second LSTM network. The first LSTM network is used to extract the temporal features of parameter X to obtain preliminary performance parameter predictions. The automatic differentiation module is used to calculate using automatic differentiation techniques. Partial derivative with respect to time t as well as Partial derivative with respect to parameter X The second LSTM network is used to... And the parameter X, to obtain the predicted value According to the predicted value Preliminary performance parameter predictions Make adjustments to make The evolution conforms to prior physical knowledge, realizing physical information constraints.

[0009] As a further preferred option, the loss function used when training the neural network model is... as follows:

[0010] ;

[0011] ;

[0012] ;

[0013] in, This represents the data-driven loss term. , They represent the first i The actual values ​​of pavement performance parameters and the preliminary predicted values ​​of pavement performance parameters corresponding to the set of data. N This indicates the amount of data in the training set. Indicates hyperparameters; Represents the physical constraint loss term. The definition is as follows:

[0014] ;

[0015] in, , These represent the first LSTM network and the second LSTM network, respectively. , These represent the parameters of the first LSTM network and the second LSTM network, respectively.

[0016] As a further preferred embodiment, the training set includes a simulation training set and a measured training set. The parameters X and Y in the simulation training set are obtained by simulating a finite element model of the road surface, while the parameters X and Y in the measured training set are obtained by actual monitoring of the road surface.

[0017] As a further preferred approach, when training the neural network model using the training set, a phased training strategy is adopted:

[0018] Pre-training phase: The neural network model is pre-trained using a simulation training set. During this process, the parameters are fixed. ;

[0019] Joint training phase: The pre-trained neural network model is trained using a real-world training set, during which adjustments are made dynamically. This yields a trained neural network model.

[0020] As a further optimization, dynamic adjustment during the joint training phase The method is as follows: ,in and For hyperparameters, the range is in , This represents the error of the neural network model on the validation set.

[0021] As a further optimization, the simulation based on the finite element model covers both normal road surface degradation and extreme working conditions, thereby expanding the amount of simulation training data; all data in the training set have undergone max-min normalization processing.

[0022] As a further preferred option, static parameters are broadcast to the time step dimension and spliced ​​with time-series dynamic parameters to form road surface physical parameters.

[0023] As a further preferred embodiment, the time-series dynamic parameters include traffic load and climate environment, the static parameters include pavement structure properties, and the pavement performance parameters are pavement smoothness index (IRI), pavement ride quality index (RQI), or pavement quality index (PQI).

[0024] According to a second aspect of the present invention, a digital twin performance extrapolation model is provided, which is constructed using the above-described method for constructing a digital twin performance extrapolation model based on a long short-term memory network constrained by physical information.

[0025] According to a third aspect of the present invention, a method for extrapolating the performance of a digital twin road surface is provided, wherein the digital twin system of the road surface uses the above-mentioned digital twin performance extrapolation model to extrapolate the road surface performance.

[0026] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages:

[0027] 1. This invention addresses the complex dynamic characteristics of digital twin pavement performance extrapolation by combining time-series dynamic and static multi-source physical data. It calculates the sensitivity of performance indicators to input physical quantities through automatic differentiation technology and utilizes dual LSTM networks to learn the coupling effect of multi-source parameters, effectively improving the accuracy of digital twin pavement performance extrapolation under complex environments.

[0028] 2. This invention utilizes automatic differentiation technology to calculate the sensitivity of performance indicators to key physical quantities, dynamically analyzes the intrinsic relationship between physical laws and performance degradation, and embeds these implicit constraints into the neural network training process, avoiding the limitations of explicit equation modeling. Compared to traditional methods, this invention, through implicit physical constraints and a multi-source data collaboration mechanism, improves robustness to data noise and sparsity while ensuring the consistency of physical constraints, providing reliable technical support for performance extrapolation driven by digital twins.

[0029] 3. This invention adopts a phased training strategy, which learns prior knowledge of physical laws through pre-training with simulation data, and then dynamically optimizes it with measured data, breaking through the bottleneck of physical law representation in traditional models and effectively solving the problem of data sparsity in complex scenarios.

[0030] 4. To address the heterogeneous nature of multi-source data, an input feature vector integrating physical information is constructed based on a dynamic-static parameter fusion strategy. This vector covers multiple dimensions of information, including road structure attributes, climate environment, and traffic load. Combined with the ability of long short-term memory networks to model the temporal dependence of degradation processes, high-precision performance extrapolation of the digital twin system is achieved. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the construction method of a digital twin performance extrapolation model for a long short-term memory network based on physical information constraints, according to an embodiment of the present invention.

[0032] Figure 2 This is a schematic diagram illustrating the error changes during model training in an embodiment of the present invention.

[0033] Figure 3 This is a comparison chart of the actual values ​​and predicted values ​​in an embodiment of the present invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0035] This invention provides a method for constructing a digital twin performance extrapolation model of a long short-term memory network based on physical information constraints. Figure 1 As shown, it includes the following steps:

[0036] (1) Training set construction.

[0037] (1.1) Data Acquisition:

[0038] Simulation data and measured data were acquired through finite element model simulation and field measurement, respectively, forming a dataset. Both simulation data and measured data include pavement physical parameters X and corresponding pavement performance parameters Y. Physical parameters X include time-series dynamic parameters and static parameters.

[0039] Furthermore, a finite element model of the road surface is constructed based on its physical characteristics and failure mechanism, and multiphysics simulations are conducted to generate a dataset of physical and performance parameters. subscript This refers to the time step. By using a finite element model to simulate normal degradation and extreme conditions, sample data is generated to augment neural network data.

[0040] physical parameters Includes timing dynamic parameters With static parameters Performance parameters In order to reflect the health status of the digital twin system corresponding to the road surface, the static parameters in the physical parameters are broadcast to the time step dimension and concatenated with the time-series dynamic parameters.

[0041] Specifically, time-series dynamic parameters include traffic load and climate environment; static parameters include pavement structural properties, which include the pavement layer structure, the total number of pavement layers, the functional type of each layer, and the material type, i.e., the material category of each structural layer of the pavement. Pavement performance parameters include the pavement smoothness index (IRI), the road quality index (RQI), or the pavement quality index (PQI), etc.

[0042] (1.2) Data preprocessing:

[0043] The time series segmentation method is adopted to divide the acquired dataset into continuous intervals in chronological order. The first 70% of the time period is the training set, the middle 15% is the validation set, and the last 15% is the test set to avoid future information leakage.

[0044] Preprocessing is performed using maximum-minimum value normalization, and the calculation formula is as follows:

[0045] ;

[0046] In the formula, The global minimum value of the corresponding feature in the dataset is calculated by iterating through the time series data of all samples. The global maximum value of the corresponding feature in the dataset is calculated in the same way. ; These are the normalized eigenvalues, and their range is... .

[0047] (2) Model training.

[0048] The neural network model is trained using a training set, and the trained neural network model is used as a performance projection model for digital twins.

[0049] (2.1) Model structure:

[0050] The neural network model includes the first LSTM network. Automatic Differentiation Module and Second LSTM Network The first LSTM network is used to extract the temporal features of parameter X to obtain preliminary performance predictions. The automatic differentiation module is used to calculate using automatic differentiation techniques. Partial derivative with respect to time t as well as Sensitivity to parameter X The second LSTM network is used to... And the parameter X, to obtain the predicted value And then based on this predicted value Predicted values ​​of performance parameters Adjustments are made to obtain the final output, thereby embedding physical information, realizing physical information constraints, and enabling... The evolution conforms to prior knowledge of physics. Specifically:

[0051] 1) First LSTM network : Through this temporal feature extraction network Extract the long-term dependencies of the parameters and output preliminary performance characterization predictions:

[0052] ;

[0053] In the formula, These are predicted values ​​of performance characterization quantities; The input feature parameters are t; t is the time variable. These are network parameters.

[0054] 2) Automatic Differentiation Module: Utilizes automatic differentiation technology to calculate... Partial derivative with respect to time t and its sensitivity to the physical parameter X .

[0055] 3) Second LSTM network :Will The original feature X is input into the second LSTM network. The implicit fitting of the degradation rate and the dynamic relationship between physical parameters:

[0056] ;

[0057] In the formula, These are network parameters.

[0058] To balance computational accuracy and complexity, only the first-order partial derivative is used here. Online direct learning The nonlinear mapping replaces the traditional explicit equations, avoiding the simplification errors of manually defined equations.

[0059] (2.2) Construction of loss function:

[0060] Define the joint loss function Integrating data-driven error and physical degradation constraints:

[0061] ;

[0062] ;

[0063] ;

[0064] in, It is a data-driven loss term used to calculate predicted values. Compared with the true value The mean square error; It is the physical constraint loss term, which represents the matching between the constraint degradation rate and the physical model; For hyperparameters, optimization is performed using a grid search.

[0065] (2.3) Phased training strategy:

[0066] During the pre-training phase, training is conducted using only simulated data. and Network, Fixed Learn prior knowledge of physical laws. During the joint training phase, introduce measured data and follow... Dynamically modulated weights, and For hyperparameters, the range is in , This is the network's error on the validation set. As the validation error increases... This reduces physical constraints, thus balancing data-driven adaptive learning. An early stopping mechanism is used during training to prevent overfitting; the training process is automatically terminated when the model's loss function value on the validation set does not show a decreasing trend for five consecutive training epochs.

[0067] This invention utilizes automatic differentiation technology to calculate the sensitivity of performance indicators to key physical quantities, dynamically analyzes the intrinsic relationship between physical laws and performance degradation, and embeds these implicit constraints into the neural network training process, avoiding the limitations of explicit equation modeling. Simultaneously, addressing the heterogeneous characteristics of multi-source road surface data in the spatiotemporal dimensions, it constructs an input feature vector that integrates physical information based on a spatiotemporal alignment strategy. This vector covers multiple dimensions of information, including material properties, environmental loads, and monitoring signals. Combined with the time-series dependency modeling capability of long short-term memory networks for the degradation process, it achieves high-precision performance extrapolation for digital twin systems. Compared to traditional methods, this invention, through implicit physical constraints and a multi-source data collaborative mechanism, improves robustness to data noise and sparsity while ensuring the consistency of physical constraints, providing reliable technical support for performance extrapolation driven by digital twins of road surfaces.

[0068] The following are specific examples:

[0069] The Long-Term Pavement Performance (LTPP) database was chosen as the data source for method validation due to its authority and comprehensiveness in the field of pavement engineering. As the world's largest long-term pavement monitoring project, the LTPP database systematically collects full life-cycle performance data covering different climate zones, pavement structure types, and traffic load levels. Its multi-dimensional and long-term characteristics provide an ideal data foundation for validating predictive models constrained by physical information. This database not only includes periodic monitoring records of performance indicators such as the International Roughness Index (IRI) and rutting depth, but also integrates material properties of each pavement structural layer, annual traffic axle load spectra, and environmental parameters continuously monitored by meteorological stations, enabling a complete characterization of the dynamic correlation between pavement performance degradation and multi-source physical factors.

[0070] Regarding the selection of performance characterization metrics, the IRI, as one of the core monitoring indicators of the LTPP, has a clear physical meaning and standardized quantification methods. The IRI inverts the changes in the longitudinal profile elevation of the pavement through vehicle dynamic response, and its numerical increase directly characterizes the cumulative effect of damage to the pavement structural layer materials and the decline in driving comfort. Compared to other performance indicators, the IRI has the characteristic of continuous monitoring throughout its entire life cycle, capable of capturing the entire degradation trajectory from the initial initiation of microcracks to later structural fragmentation. Furthermore, the evolution of the IRI is driven by the coupling of multiple physical fields such as repeated traffic loads, alternating temperature stress, and humidity penetration. The complexity of its inherent degradation law can effectively verify the modeling capability of the physical information constraint mechanism for nonlinear dynamic systems.

[0071] The input data relies on the multi-source heterogeneous data structure of the LTPP database, extracting key physical parameters from three dimensions: structural properties, traffic load, and climate environment. By integrating these multi-source features, the model can analyze the nonlinear evolution law of IRI under the interaction of traffic, climate, and materials, thus maintaining prediction accuracy under complex operating conditions. The structured storage and quality control system of LTPP data further ensures the physical rationality and temporal integrity of the feature parameters, providing reliable data support for verifying the generalization ability of the method of this invention.

[0072] During data preprocessing, categorical features, such as the material types of each pavement layer, are converted into binary vectors using one-hot encoding to eliminate the interference of disordered categorical variables on model training. Numerical features, such as axle load counts and temperature, are normalized using maximum and minimum values, linearly mapping the data to the 0-1 range. The normalization parameters are calculated based on global statistics from the training set to avoid information leakage from the test set. The dataset is divided into training, validation, and test sets in chronological order, with proportions of 70%, 15%, and 15%, respectively, ensuring the continuity of the time series is not disrupted.

[0073] The model employs a temporal feature extraction network. and physical constraint networks A dual LSTM architecture for collaborative training. The hyperparameter configurations of the two networks are shown in Table 1: the number of hidden units is set to 64 to balance model capacity and computational efficiency; the dropout rate is set to 0.1 to suppress overfitting; the training batch size is set to 2, and the time step size is set to 2 to capture the evolution of road performance.

[0074] .

[0075] Model training consists of two phases: pre-training and joint optimization. In the pre-training phase, only simulation data is used for training. and The network is initialized with fixed physical constraint weights, and learns prior knowledge of physical laws. During the joint training phase, measured data is introduced, and training proceeds according to... Dynamic modulation weights, where the initial value attenuation coefficient , This represents the network's error on the validation set, achieving an adaptive balance between data-driven approaches and physical constraints. The training process uses the Adam optimizer with an initial learning rate of 0.01. An early stopping mechanism monitors the validation set loss; if the loss improvement is less than the threshold of 0.01 for 10 consecutive training epochs, training is terminated to avoid overfitting.

[0076] Figure 2 The study demonstrates the trend of mean squared error during training. The model's loss value rapidly converges to a stable range within 30 training epochs, and the validation set error fluctuates less than the expected threshold for several consecutive training epochs, indicating that the model possesses excellent generalization performance and training stability.

[0077] Figure 3 The temporal evolution patterns of the actual and predicted IRI values ​​on the test set were compared. The results show that the predicted curves and measured values ​​exhibit a high degree of consistency in both the normal and accelerated degradation stages. Particularly in the nonlinear abrupt change region, the model can still accurately capture the abrupt changes in pavement performance. The overall mean square error of the test set is 0.0051, significantly lower than that of the traditional LSTM model, demonstrating the effectiveness of the physical information constraint mechanism in improving prediction accuracy.

[0078] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing a digital twin performance deduction model based on a long short-term memory network with physical information constraints, characterized in that, Comprising the following steps: Training the neural network model through the training set, and taking the trained neural network model as the digital twin performance deduction model; The training set comprises road surface physical parameters X and road surface performance parameters Y, and the physical parameters X comprise time-series dynamic parameters and static parameters; The neural network model includes a first LSTM network, an automatic differentiation module, and a second LSTM network. The first LSTM network is used to extract the temporal features of parameter X to obtain preliminary performance parameter predictions. The automatic differentiation module is used to calculate using automatic differentiation techniques. Regarding time partial derivatives as well as For parameters partial derivatives The second LSTM network is used to... And the parameter X, to obtain the predicted value According to the predicted value Preliminary performance parameter predictions Make adjustments to make The evolution conforms to prior physical knowledge, thus realizing physical information constraints; When training the neural network model, a loss function is adopted As follows: wherein, represents a data-driven loss term, , represent the real value of the road performance parameter and the preliminary performance parameter prediction value corresponding to the first i group of data, respectively, N represents the amount of data in the training set, represents a hyperparameter; represents a physical constraint loss term, is defined as follows: wherein, , respectively represent a first LSTM network, a second LSTM network, , respectively represent a first LSTM network, a second LSTM network parameter; denotes a time variable.

2. The method of claim 1, wherein the method is characterized by, The training set comprises a simulation training set and a measured training set, the parameters X and Y in the simulation training set are obtained through simulation after building a road surface finite element model, and the parameters X and Y in the measured training set are obtained through actual monitoring of the road surface.

3. The method of claim 2, wherein the method is characterized by: When the neural network model is trained through the training set, a phased training strategy is adopted: Pre-training stage: the neural network model is pre-trained by the simulation training set, and the process is fixed ; The joint training phase: the pre-trained neural network model is trained by the measured training set, and the dynamic adjustment is performed during the process to obtain the trained neural network model.

4. The method of claim 3, wherein the method is characterized by: Joint training phase dynamic adjustment The method is: wherein and is a hyperparameter, with a value range of , is the error of the neural network model on the validation set.

5. The method of claim 2, wherein the method is characterized by: The simulation training set covers normal degradation and extreme working conditions during finite element model simulation, and the amount of simulation training set data is expanded; the data in the training set are all processed through maximum and minimum normalization.

6. The method of claim 1, wherein the method is characterized by, The static parameters are broadcast to the time step dimension and spliced with the time-series dynamic parameters to form road surface physical parameters.

7. The method of claim 1-6, wherein the method is characterized in that, The time-series dynamic parameters comprise traffic load and climate environment, and the static parameters comprise road surface structure attributes; the road surface performance parameters are road surface smoothness index IRI, road surface driving quality index RQI or road surface quality index PQI.

8. A digital twin performance extrapolation model, characterized in that, The digital twin performance deduction model based on the long short-term memory network with physical information constraint is constructed by adopting the construction method according to any one of claims 1-7.

9. A digital twin performance extrapolation method, characterized in that, The digital twin system of the road surface performs road surface performance deduction by adopting the digital twin performance deduction model according to claim 8.

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