Airborne system multi-physical field complex model order reduction method and airborne system multi-physical field complex model order reduction system

Abstract

The invention provides an airborne system multi-physics field complex model order reduction method and system, and belongs to the technical field of airborne system design, and the method comprises the steps: determining a calculation region of an airborne system multi-physics field model, and employing a test design method to obtain sample points covering all working conditions based on the calculation region; performing simulation calculation on the sample points, dynamically adjusting the distribution density of the sample points based on a calculation result, and obtaining a training data set based on the adjusted sample points and a corresponding simulation calculation result; on the basis of the training data set, a dimension reduction training data set is obtained in an AI corrected feature value iteration mode; constructing a multi-model staged order reduction model, and training the order reduction model by using the dimension reduction training data set; and after training, verification, optimization and packaging are carried out in sequence. According to the scheme, the order reduction efficiency and precision of the airborne system model are improved, the consumption of computing resources is reduced, and the accuracy and reliability of the order reduction model under all working conditions are ensured.

Description

Technical Field

[0001] This application relates to the field of airborne system design technology, and in particular to a method and system for reducing the order of complex multiphysics models of airborne systems. Background Technology

[0002] In the simulation and design of airborne systems (such as flight control systems and thermal management systems), model order reduction faces a core challenge: drastic changes in system operating conditions (such as flight altitude, Mach number, and control surface deflection) cause nonlinear evolution of the essential characteristics of the physical field. Traditional POD methods, which extract fixed eigenvector bases, can capture the global dominant modes near the design point, but cannot adapt to this feature drift across operating conditions. Meanwhile, data-driven neural network methods require large amounts of data to learn low-dimensional representations, lack physical interpretability, and suffer from insufficient stability. Summary of the Invention

[0003] In view of this, embodiments of this application provide a method and system for reducing the order of complex multiphysics models of airborne systems, which at least partially solves the problems of traditional methods being unable to adapt to feature drift across operating conditions and low model learning efficiency in the prior art.

[0004] In a first aspect, embodiments of this application provide a method for order reduction of complex multiphysics models of airborne systems, including: The computational domain of the multiphysics model of the airborne system is determined, and experimental design methods are used to obtain sample points covering all operating conditions based on the computational domain. The sample points are simulated and calculated, and the distribution density of the sample points is dynamically adjusted based on the simulation results. The training dataset is obtained based on the adjusted sample points and the corresponding simulation results. Based on the training dataset, an AI-corrected feature value iteration method is used to obtain a dimensionality-reduced training dataset; Construct a multi-model staged reduction model and train it using a dimensionality reduction training dataset; The trained reduced-order model is then validated, optimized, and encapsulated sequentially.

[0005] According to a specific implementation of an embodiment of this application, the step of obtaining a dimensionality-reduced training dataset based on a training dataset and using an AI-corrected feature value iteration method includes: Based on the training dataset, principal component extraction is performed to obtain the global feature space; Extract the first n feature vectors from the global feature space to form the global feature base; A dynamic corrector for feature maps with AI correction is constructed to correct and iterate the feature scale in the global feature base to obtain a dimensionality-reduced training dataset.

[0006] According to a specific implementation of an embodiment of this application, the construction of the AI-corrected feature map dynamic corrector includes: Construct a feature map dynamic corrector based on a multilayer feedforward neural network.

[0007] According to a specific implementation of an embodiment of this application, the step of correcting and iterating the feature scale in the global feature base includes: The current real-time operating parameters and the initial coefficients derived from the global feature base are used as the input data for the multilayer feedforward neural network. For different specific operating parameters, a nonlinear mapping is learned based on a multilayer feedforward neural network: f(δ, a0)->Δa(δ). This nonlinear mapping serves as the kernel of the feature mapping dynamic corrector and is used to calculate Δa(δ) during the inference phase. Here, f is the mapping relationship function, δ is the operating parameter, a0 is the initial coefficient, and Δa(δ) is the correction amount of the basis function coefficient. Based on the initial coefficients, the basis function coefficient corrections, and the global feature basis, the feature state space of dynamic iteration is obtained; The output response of a multilayer feedforward neural network is obtained based on the dynamically iterated feature state space and feature weight vector.

[0008] According to a specific implementation of an embodiment of this application, the expression for the feature state space of the dynamic iteration is: , , Where B is the feature state space of dynamic iteration, b i (δ) is the eigenvector after the i-th iteration, Δa i (δ) represents the correction factor for the i-th basis function coefficient, p i Let x be the i-th eigenvector in the global feature basis. i Let be the boundary conditions of the system at time i.

[0009] According to a specific implementation of an embodiment of this application, the expression for the output response of the FNN neural network is: , Among them, y i (δ) represents the i-th output response of the multilayer feedforward neural network, and wi(δ) represents the i-th feature weight vector.

[0010] According to a specific implementation of an embodiment of this application, the construction of the order reduction model based on a multi-model stage includes: A two-stage order reduction model is constructed based on a multilayer feedforward neural network model, a response surface model, and a long short-term memory neural network model.

[0011] According to a specific implementation of an embodiment of this application, the construction of a two-stage order reduction model based on a multilayer feedforward neural network model, a response surface model, and a long short-term memory neural network model includes: Based on the application scenarios of complex multiphysics models that require order reduction, we analyze the complexity requirements, rapid verification requirements, order reduction accuracy requirements, and real-time requirements of the target model. Based on the analysis results, we select at least one model from the multilayer feedforward neural network model, response surface model, and long short-term memory neural network model as the order reduction surrogate model. Cross-validate the reduced-order surrogate model and adjust the parameters of the selected model or reduced-order surrogate model based on the validation results.

[0012] According to a specific implementation of an embodiment of this application, the step of selecting at least one model from a multilayer feedforward neural network model, a response surface model, and a long short-term memory neural network model as a reduced-order surrogate model based on analysis results includes: A multi-layer feedforward neural network model and a long short-term memory neural network model were selected and fused using a sequential modeling approach to serve as a reduced-order surrogate model. The sequential modeling approach for model fusion includes: A static multilayer feedforward neural network model is obtained by training the multilayer feedforward neural network model, and a direct mapping from any set of flight parameters to the corresponding steady-state aerodynamic forces is established. Time series data were collected and constructed. Based on the long short-term memory neural network model, the transition of aerodynamic forces at different times was established. The trained static multilayer feedforward neural network model was embedded into the long short-term memory neural network model to form a fusion model. The fusion model learns a correction relative to a static baseline using transient data, and then uses this correction to make the final aerodynamic prediction.

[0013] Secondly, embodiments of this application also provide a system for reducing the order of complex multiphysics models of airborne systems, used to implement the method for reducing the order of complex multiphysics models of airborne systems as described in any embodiment of the first aspect, the system comprising: The sample point design module is used to determine the computational domain of the multiphysics model of the airborne system, and to obtain sample points covering all operating conditions based on the experimental design method using the computational domain. The training dataset acquisition module is used to perform simulation calculations on sample points and dynamically adjust the distribution density of sample points based on the simulation calculation results. Based on the adjusted sample points and the corresponding simulation calculation results, the training dataset is obtained. The feature value iteration module is used to obtain a dimensionality-reduced training dataset based on the training dataset by using feature value iteration. The order reduction model building module is used to build an order reduction model based on a multi-model stage and train the order reduction model using a dimensionality reduction training dataset. The reduced-order model encapsulation module is used to verify, optimize, and encapsulate the trained reduced-order model in sequence.

[0014] Beneficial effects: This application presents a method and system for reducing the order of complex multiphysics models of airborne systems, proposing an AI-based variable-scale eigenvector iteration strategy. Based on using feature constraint decomposition to construct a robust initial global feature space, a lightweight neural network model dynamically and finely adjusts the basis function coefficients and scale in this space, thereby achieving micro-iteration and scale reconstruction of the eigenvectors. This method eliminates the need for costly recalculations under changing operating conditions, allowing online invocation of the lightweight neural network to correct the output results, meeting the simulation efficiency requirements of airborne systems while reducing reduction loss. Furthermore, since the feature basis originates from the physical modes of PCA, its output physical consistency and interpretability are far superior to those of pure black-box reduction model neural networks.

[0015] Therefore, the method described in this application can reduce the analytical difficulty of complex multiphysics models of airborne systems and decrease the amount of data computation required for simulation, while maintaining the basic behavior and explicit characteristics of the airborne system. It is applicable to various scenarios such as real-time simulation, control, and prediction of aircraft. This technology has high application value and provides strong support for the rapid design, optimization, and debugging of airborne systems. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart of a method for reducing the order of a complex multiphysics model of an airborne system according to an embodiment of the present invention; Figure 2 A specific diagram of a recurrent neural network according to an embodiment of the present invention; Figure 3 This is a schematic diagram of a recurrent neural network unfolded along a timeline according to an embodiment of the present invention. Detailed Implementation

[0018] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0019] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0021] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0022] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0023] In a first aspect, embodiments of this application provide a method for order reduction of complex multiphysics models of airborne systems, including: The computational domain of the multiphysics model of the airborne system is determined, and experimental design methods are used to obtain sample points covering all operating conditions based on the computational domain. The sample points are simulated and calculated, and the distribution density of the sample points is dynamically adjusted based on the simulation results. The training dataset is obtained based on the adjusted sample points and the corresponding simulation results. Based on the training dataset, an AI-corrected feature value iteration method is used to obtain a dimensionality-reduced training dataset; Construct a multi-model staged reduction model and train it using a dimensionality reduction training dataset; The trained reduced-order model is then validated, optimized, and encapsulated sequentially.

[0024] In this embodiment, an AI-based variable-scale feature vector iteration strategy is proposed. Based on feature bounded decomposition as a robust initial global feature space, a lightweight neural network model dynamically and finely adjusts the basis function coefficients and scale within this space, thereby achieving micro-iteration and scale reconstruction of the feature vectors. This method eliminates the need for costly recalculations under changing operating conditions, allowing online invocation of the lightweight neural network to correct the output results, meeting the efficiency requirements of airborne system simulation while reducing reduction loss. Furthermore, since the feature basis originates from the physical modes of PCA, its output physical consistency and interpretability are far superior to pure black-box reduction model neural networks.

[0025] In one embodiment, during experimental design, the key variables and their value ranges of the model are determined based on the model's input parameters and physical field characteristics, and the computational domain is divided. Design of Experiments (DOE) methods, such as Latin hypercube sampling (LHS) or uniform design, are employed to ensure a uniform distribution of sample points in the input space, covering all possible operating conditions. For physical constraints under specific operating conditions, the distribution of sample points is adjusted to approximate the real-world scenario as closely as possible while satisfying the constraints.

[0026] Furthermore, simulations are performed on the sample points. High-precision simulation tools are used to calculate the sample points in the design experiment, generating training and testing data. Outliers and inconsistent data in the calculated samples are checked and cleaned and preprocessed, including normalization and noise reduction, laying the foundation for subsequent training of the reduced-order model. Based on the preliminary solution results, the distribution density of the sample points is dynamically adjusted, and more sample points are added to complex regions to improve the local accuracy of the reduced-order model.

[0027] In one embodiment, obtaining the dimensionality-reduced training dataset using an AI-corrected feature value iteration method based on the training dataset includes: Based on the training dataset, principal component extraction is performed to obtain the global feature space; Extract the first n feature vectors from the global feature space to form the global feature base; A dynamic corrector for feature maps with AI correction is constructed to correct and iterate the feature scale in the global feature base to obtain a dimensionality-reduced training dataset.

[0028] Specifically, based on eigenvalue analysis or principal component analysis (PCA), principal components of the data are extracted, secondary information is removed, and the dimensionality of the input variables is reduced. Simultaneously, domain knowledge is incorporated to interpret the dimensionality-reduced features, preserving as many salient features as possible from the original data and ensuring that key physical behavior information is not lost during the dimensionality reduction process. During the dimensionality reduction process, an AI-driven dynamic correction layer is introduced on top of the global, linear feature vector basis provided by PCA. This layer iteratively adjusts the feature vector extraction calculation method during dimensionality reduction, thereby adjusting the shape of the hyperplane in the target space, optimizing the compact representation capability and adaptability of the data, and laying the foundation for building the dimensionality-reduced model.

[0029] In one embodiment, the principle of model order reduction is explained in detail. For solving general computational dynamics problems, the input is the initial boundary conditions. The result of a certain physical quantity of the physical field was obtained by solving the differential equation. This physical quantity is ultimately expressed as a function of space and time. The mapping is as follows:

[0030] Let X represent the initial boundary condition X( ), X i Let y represent the initial boundary conditions set for the i-th solution. i Let represent the result of the i-th solution. After n solutions, we have:

[0031] The above n series are obtained through one-to-one solutions. Now, we use a reduction model to transform the 1→1 mapping into an n→1 mapping, that is:

[0032] X in the above formula i Let X be the parameter and X be the variable; this is a simplified explanation of the principle of the order reduction model. When a new X is input... ), can be obtained through F mapping, utilizing samples The value of Y is reconstructed from the value of Y, without using the above formula to solve for the value of Y.

[0033] For computational dynamics problems, y i The amount of data involved is very large, and it is usually necessary to first reduce the data dimensionality through PCA or other reduction models, extract principal components, and construct a mapping from samples to responses.

[0034] Specifically, eigenvalue decomposition will be explained in detail. For a square matrix A(n×n), the eigenvalues ​​and eigenvectors satisfy the following relationship:

[0035] When the n eigenvectors are linearly independent, the corresponding eigenvalues ​​are decomposed as follows:

[0036] Where v is the eigenvector and λ is the eigenvalue. V is an n×n square matrix spanned by the eigenvectors of the square matrix A, and ∑ is a diagonal matrix composed of n eigenvalues. A(n×n) must have n eigenvalues ​​(including repeated root eigenvalues).

[0037] Eigenvalue decomposition has limitations. First, it requires that the square matrix A be an n×n square matrix. Second, it requires that the square matrix A have n linearly independent eigenvectors (the matrix is ​​non-singular).

[0038] Specifically, the SVD decomposition will be explained in detail. For any matrix A (m×n), two square matrices Am need to be constructed. T A(n×n) and AA T Both of these square matrices are (m×m), and are real symmetric matrices. A real symmetric matrix is ​​always diagonalizable and necessarily has n linearly independent eigenvectors, and these eigenvectors are orthogonal. Therefore, matrix A can be decomposed into:

[0039] Among them, U is composed of AA T V is composed of (m×m) eigenvectors, and V is composed of A T The eigenvectors of A(n×n) are composed of the eigenvectors. The diagonal of ∑(m×n) consists of the singular values ​​σ in descending order. i Composition, other values ​​are 0. σ i The method for finding it is as follows:

[0040] After matrix A is decomposed using SVD, the following relationship exists:

[0041]

[0042] Since U and V are orthogonal matrices, U T =U -1 By referring to the above formula, we can obtain the non-zero singular value σ. i For matrix AA T Or matrix A T The square root of the eigenvalue A. That is:

[0043] It is easy to prove that matrix AA T Eigenvalues ​​and matrix A T The eigenvalues ​​of A are equal:

[0044] Specifically, let's explain PCA (Principal Component Analysis) in detail. The core idea of ​​PCA is to maximize the reconstruction of the original information using the fewest possible orthogonal basis points. To minimize the number of orthogonal basis points, the information content of each basis point needs to be maximized. This leads to two optimization objectives. The first objective is to maximize the projected area (length, area, volume) of all points on this basis, meaning the projections of these points onto this basis are more dispersed. Dispersion is usually described using variance; the desired basis point should maximize the variance of the values ​​under this orthogonal basis (i.e., fully expand across orthogonal basis points). The second objective is to minimize, ideally eliminate, the information redundancy between orthogonal basis points. Correlation is usually characterized using covariance; the goal is to maximize the covariance of information between two basis points while maximizing the variance of information within a single orthogonal basis.

[0045] Therefore, it is natural to think of using the covariance matrix. The diagonal of the covariance matrix is ​​the variance, and the remaining values ​​are the covariances between the various bases.

[0046] When the covariance matrix of the data matrix is ​​reduced to zero after dimensionality reduction projection, and the values ​​of the diagonal are arranged in descending order, the optimization goal can be achieved.

[0047] Let C be the covariance matrix corresponding to the original data matrix X, and P be a matrix composed of a set of bases arranged row-wise. Let B = PX, then Y is the data after X is transformed by basis P. Let D be the covariance matrix of Y, then we have: , Where m is the sample size of the original data.

[0048] As shown in the above equation, diagonalizing the covariance matrix of the original data yields the projected, dimension-reduced covariance matrix D, which is the desired diagonal matrix form. The covariance matrix C is a real symmetric matrix.

[0049] A real symmetric matrix can always be decomposed into eigenvalues:

[0050] Where V is an n×n square matrix spanned by the eigenvectors of matrix A, and ∑ is a diagonal matrix composed of n eigenvalues. Transforming this, we get:

[0051] By comparing the above formula, we can obtain:

[0052] That is, each row of P is an eigenvector arranged in descending order of the eigenvalues ​​of the covariance matrix. B=PX is the boundary condition data of the airborne system model in the desired feature space.

[0053] In one embodiment, the construction of the AI-corrected feature map dynamic corrector includes: Construct a feature map dynamic corrector based on a multilayer feedforward neural network.

[0054] Furthermore, the correction and iteration of the feature scale in the global feature base includes: The current real-time operating parameters and the initial coefficients derived from the global feature base are used as the input data for the multilayer feedforward neural network. For different specific operating parameters, a nonlinear mapping is learned based on a multilayer feedforward neural network: f(δ, a0)->Δa(δ). This nonlinear mapping serves as the kernel of the feature mapping dynamic corrector and is used to calculate Δa(δ) during the inference phase. Here, f is the mapping relationship function, δ is the operating parameter, a0 is the initial coefficient, and Δa(δ) is the correction amount of the basis function coefficient. Based on the initial coefficients, the basis function coefficient corrections, and the global feature basis, the feature state space of dynamic iteration is obtained; The output response of a multilayer feedforward neural network is obtained based on the dynamically iterated feature state space and feature weight vector.

[0055] In this embodiment, a feature map dynamic corrector based on a multilayer feedforward neural network is configured. Leveraging the powerful nonlinear mapping capabilities of multilayer feedforward neural networks (MLNs), precise correction and iteration of feature scales in the global feature basis are performed. The MNN can automatically learn the complex relationships between parameters under different operating conditions and the correction amounts of basis function coefficients, eliminating the need for manually setting complex correction rules. During the inference phase, based on the current real-time operating parameters and the initial coefficients derived from the global feature basis, the correction amounts of the basis function coefficients are quickly calculated, resulting in a dynamically iterative feature state space. This dynamically iterative feature state space better adapts to the changes in the airborne system under different operating conditions, improving the accuracy and adaptability of the reduced-order model. Based on the dynamically iterative feature state space and feature weight vectors, the output response of the MNN is obtained. This output response more accurately reflects the actual state of the multiphysics field of the airborne system, providing reliable data support for subsequent model validation, optimization, and encapsulation.

[0056] Furthermore, the expression for the feature state space of the dynamic iteration is: , , Where B is the feature state space of dynamic iteration, bi (δ) is the eigenvector after the i-th iteration, Δa i (δ) represents the correction factor for the i-th basis function coefficient, p i Let x be the i-th eigenvector in the global feature basis. i Let be the boundary conditions of the system at time i.

[0057] Furthermore, the expression for the output response of the FNN neural network is: , Among them, y i (δ) represents the i-th output response of the multilayer feedforward neural network, and wi(δ) represents the i-th feature weight vector.

[0058] In practice, based on the construction of the feature vector basis of the global feature space using methods such as SVD and PCA, the first n feature vectors are extracted to form the global feature basis P.

[0059] The feature vector p n It represents the most energetic and characteristic physical properties, such as modes, within the entire design space.

[0060] Then, an AI-driven dynamic corrector is introduced, which corrects and iterates the feature scale by adding a lightweight FFN neural network. Specifically, it takes the current real-time operating parameters δ (such as Mach number and angle of attack) and the initial coefficients a0 derived from the global basis as inputs. For different specific operating conditions, the FNN neural network learns a nonlinear mapping f(δ, a0) -> Δa(δ) as the corrector kernel. During the inference phase, the basis function coefficient correction amount Δa(δ) is calculated to obtain the feature state space. The dynamic iteration takes the following form: , Combining the feature weight vector w(δ), the output response of the FFN reduced-order model can be expressed in one form: .

[0061] For example, in a specific scenario, flight simulation involves nonlinear changes in the physical field due to variations in operating conditions. When an aircraft transitions from cruise to landing preparation, the attached flow state changes. The global feature basis contains flow field modes representing both cruise and landing phases. A feature mapping corrector built on an FFN network automatically increases the weight w representing the latter flow field mode and corrects its coefficient a during landing, altering the feature mapping relationship and thus achieving "adaptive switching" of the basis functions.

[0062] The method in this embodiment realizes the reconstruction and solution of variable-scale feature vectors. Where x i Let Δa be the boundary condition of the system at time i. i The (δ) coefficient correction indicates that the FFN network fine-tunes the length of each global feature vector in a fixed feature direction according to the current working condition to fit the dynamic process of changes in physical field intensity, realizing real-time transformation of the basis function scale. The wi(δ) weighted reconstruction realizes the dynamic adjustment of the importance of different components, essentially dynamically constructing a subspace for the current physical working condition. An attention mechanism through the FFN determines which global feature dimensions are important under working condition δ and sets their wi(δ) to 1, while for feature dimensions with lower importance, their wi(δ) is closer to 0. Compared to directly building a reduced-order model that fits the entire working condition, this method decouples the working condition parameters from other boundary conditions during training, exhibiting better generalization ability for unsimulated working conditions while reducing computational costs and making the reduced-order model more likely to converge.

[0063] In one embodiment, the construction of the multi-model staged order reduction model includes: A two-stage order reduction model is constructed based on a multilayer feedforward neural network model, a response surface model, and a long short-term memory neural network model.

[0064] Specifically, when the computational load of a real-world problem (high-precision model) is very large and it is not easy to solve, a simplified model with a smaller computational load and faster solution can be used to replace the original model, which is called a reduced-order model.

[0065] Common order reduction models include response surface methodology, stochastic response surface methodology, neural network methodology, Kriging method, and support vector machine method. The main idea is to fit the response function within a region using sample data; that is, the function value at any point within the region is represented by sample data. A brief description of each algorithm follows.

[0066] Taking the Kriging method as an example: , Where z0 is the estimated value at (x0, y0). λ is the weighting coefficient, and the problem is transformed into an optimization problem of the weighting coefficient.

[0067] Response surface methodology is a method that uses simple expressions (usually polynomials of order four or lower) to fit the functional relationship between independent and dependent variables, thereby constructing an approximate model. This method uses simple polynomials to replace complex models, greatly reducing analysis time.

[0068] Since the 1990s, response surface methodology (RSM) has been widely applied in structural optimization design. RSM has advantages such as simplicity, ease of construction, explicit expressions, and fast convergence during optimization. A first-order RSM model is shown below:

[0069] Where y is the experimental output, β is the coefficient, x is the input variable, and ε is the random error term. Analysis reveals that the maximum to first-order term is too coarse and often differs significantly from the actual value. Practice has shown that the maximum to quadratic term generally provides a more satisfactory answer, i.e.

[0070] After multiple observations, the result can be written in matrix form as follows:

[0071] in,

[0072]

[0073]

[0074]

[0075] Define the fitting error loss function as:

[0076] When the loss function is minimized, the fitted surface is obviously closest to the actual value. That is, the theoretical response surface can be obtained when the partial derivative of L (variance) with respect to β is zero. At this point,

[0077] The estimated coefficient matrix can be obtained as follows:

[0078] The fitted response surface can be obtained as follows:

[0079] This method of simulating the true limit state surface through a series of deterministic "experiments" with multiple variables is called the response surface methodology. Similarly, higher-order limits are obtained using a similar method.

[0080] Long Short-Term Memory (LSTM) Neural Networks: These are a special type of recurrent neural network. The training parameters of LSTM neurons incorporate long short-term memory data, enabling them to better capture information from time-series data changes. LSTM neural networks use a "gating" mechanism to add or remove information from the cell state. An LSTM neural network unit consists of a cell state, a forget gate, an input gate, and an output gate.

[0081] Multilayer feedforward neural networks (FFN networks) are artificial neural networks that iteratively operate using an error backpropagation algorithm. They transform quantified data into a nonlinear optimization problem—finding the minimum error. A typical FFN consists of an input layer, one or more hidden layers, and an output layer. Each layer contains a number of neurons, with no linear connections between them. Neurons in each layer typically cross-propagate information through a sigmoid transfer function with values ​​in the range (-1, 1). The FFN processes information in two ways: first, the forward propagation of input data, where data enters through the input layer, undergoes cross-propagation through the transfer functions of neurons in the hidden layers, and is compared with the expected value in the output layer; second, the backpropagation of error, where errors are propagated back along the original path using the steepest descent method, modifying the permissions and thresholds of each neuron layer by layer. Through iterative learning and training, the FFN continuously reduces the error to a specified range, ultimately making the actual output value infinitely close to the expected value.

[0082] Recurrent Neural Networks (RNNs) possess feedback connections between neurons. This type of connection allows the network to store recently received input data in a form of activation (short-term memory), and this potential has wide-ranging implications for practical applications. An RNN consists of an input layer, a hidden layer, and an output layer. For example... Figure 2 Let X represent the input layer value, S represent the hidden layer value, and O represent the output layer value. U is the weight matrix from the input layer to the hidden layer, and V is the weight matrix from the hidden layer to the output layer. The hidden layer value S of a recurrent neural network depends not only on the current input X but also on the previous hidden layer value S. The weight matrix W represents the weights of the previous hidden layer values ​​used as the current input. The recurrent neural network can be unfolded chronologically, as follows: Figure 3 As shown, this network receives input X at time t. t After that, the value of the hidden layer is S. t The output value is O. t S t The value depends not only on X t It also depends on S t-1 The parameters of each node in a recurrent neural network can be calculated using the following formula:

[0083] .

[0084] In one embodiment, constructing a two-stage order reduction model based on a multilayer feedforward neural network model, a response surface model, and a long short-term memory neural network model includes: Based on the application scenarios of complex multiphysics models that require order reduction, we analyze the complexity requirements, rapid verification requirements, order reduction accuracy requirements, and real-time requirements of the target model. Based on the analysis results, we select at least one model from the multilayer feedforward neural network model, response surface model, and long short-term memory neural network model as the order reduction surrogate model. Cross-validate the reduced-order surrogate model and adjust the parameters of the selected model or reduced-order surrogate model based on the validation results.

[0085] In practice, the construction of the order reduction model includes: (1) Phase 1: Selecting a suitable reduction model. First, clarify the specific application scenario of the multiphysics model that needs to be reduced in order (such as auxiliary architecture design, system performance verification, aircraft control, real-time simulation, etc.), and use this as input conditions to intelligently analyze the complexity requirements, rapid verification requirements, reduction accuracy requirements, and real-time requirements of the target model in order to select a suitable reduction proxy model. This includes algorithms such as multilayer feedforward neural networks (FFN), response surface model (RSM), or long short-term memory neural networks (LSTM). The applicable characteristics of the three models are as follows: Multilayer feedforward neural networks (FFNs) establish input-output mapping relationships and are suitable for modeling nonlinear problems with multiple inputs and multiple outputs. Computational complexity and model accuracy can be balanced by adjusting the number of network layers, nodes, and activation functions.

[0086] Response surface methodology (RSM): By constructing a polynomial approximation model, it can quickly capture the global behavioral characteristics of sample points. It is suitable for rapid verification of linear or weakly nonlinear systems and uses regression analysis to optimize model parameters.

[0087] Long Short-Term Memory (LSTM) Neural Networks: Designed for data with temporal characteristics, they capture long-term dependencies and are suitable for reduced-order modeling of dynamic systems. Performance can be optimized by adjusting the number of memory units and the time step.

[0088] A specific example is as follows: In the conceptual design phase of airborne systems, to identify the key parameters that have the greatest impact on system performance, or to establish an approximate relationship between flight profiles and fuel consumption, Response Surface Modeling (RSM) is used as a reduced-order algorithm to achieve rapid parameter scanning within a large design space. However, for steady-state temperature field prediction and flight aerodynamic prediction under high-fidelity, steady-state, or quasi-static multiphysics coupling requirements, RSM cannot capture complex nonlinear relationships. Therefore, FFN is used to learn complex parameter coupling relationships, providing much higher accuracy than RSM while maintaining real-time performance. Furthermore, for unsteady dynamics that depend on historical changes, the model selector uses LSTM to model the dynamic coupling process. For example, predicting the aeroelastic vibration of the landing gear is a typical dynamic process, where current aerodynamic loads and structural deformations depend on previous motion history. Another example is predicting the actuator's response to flight control system input commands in the time domain.

[0089] (2) Phase Two: Conduct small-scale tests on the selected algorithms, evaluate the performance of each model through cross-validation to verify their applicability to the target model, and adjust the specific parameters of the algorithm or the ensemble strategy based on the test results. Optional implementations include directly selecting the optimal model or using an ensemble method to fuse multiple models to improve robustness and accuracy.

[0090] In one embodiment, two models are integrated. Specifically, based on the analysis results, at least one model is selected as the reduced-order surrogate model from a multilayer feedforward neural network model, a response surface model, and a long short-term memory neural network model. This includes: A multi-layer feedforward neural network model and a long short-term memory neural network model were selected and fused using a sequential modeling approach to serve as a reduced-order surrogate model. The sequential modeling approach for model fusion includes: A static multilayer feedforward neural network model is obtained by training the multilayer feedforward neural network model, and a direct mapping from any set of flight parameters to the corresponding steady-state aerodynamic forces is established. Time series data were collected and constructed. Based on the long short-term memory neural network model, the transition of aerodynamic forces at different times was established. The trained static multilayer feedforward neural network model was embedded into the long short-term memory neural network model to form a fusion model. The fusion model learns a correction relative to a static baseline using transient data, and then uses this correction to make the final aerodynamic prediction.

[0091] In this embodiment, during the high-fidelity order reduction modeling stage, a model fusion approach is adopted: a dual-data model-driven hybrid order reduction strategy is provided, using either a FFN or a static process learning method. The FFN is then integrated into a dynamic simulator containing an LSTM model to balance static nonlinearity and dynamic characteristics. The two data-driven models (FFN and LSTM) employ a sequential modeling approach, leveraging their respective advantages to form an end-to-end order reduction model that balances performance and efficiency. Specifically, high-fidelity structural and aerodynamic coupling simulations are run within a vast parameter space (such as Mach number, angle of attack, altitude, etc.), but only the output data after the system reaches a steady state or periodic steady state is collected. A static model is quickly trained using a multilayer feedforward neural network (FFN) to establish a direct mapping from any set of flight parameters to the corresponding steady-state aerodynamic forces. Based on this, time-series data is collected and constructed, and an accurate transition of aerodynamic forces between different time points is established based on the LSTM model. The trained static FFN module is embedded into the LSTM model, allowing the LSTM model to learn a correction relative to a static baseline through transient data. This method, while performing intelligent order reduction modeling, decouples the two interrelated dimensions of static nonlinearity and dynamic temporal characteristics and performs sequential fitting to achieve the analysis of the steady-state physical meaning of the surrogate model. On the other hand, it avoids possible non-physical oscillations or divergences by using steady-state prediction as a benchmark.

[0092] In one embodiment, the trained reduced-order model is sequentially validated, optimized, and encapsulated, including: Model validation: The reduced-order model is validated using an independent test dataset, including comparative analysis of static characteristics and dynamic behavior. Error metrics (such as mean squared error, relative error, etc.) are calculated to determine whether the model's accuracy meets the design requirements. Error correction: For areas with large errors, the model is retrained by increasing sample points or the model parameters are adjusted to gradually optimize model performance. Physical constraints are introduced to improve the model's predictive ability for abnormal operating conditions. Satisfaction assessment: If the verification results meet the standards, proceed to the next step; otherwise, repeat the sample point expansion and order reduction modeling steps until the order reduction model achieves the expected results. Reduced-order model encapsulation: The validated reduced-order model is encapsulated according to the Functional Tokenized Unit (FMU) standard to ensure its compatibility across multiple simulation platforms. For the target application platform, the calling efficiency and adaptability of the FMU file are tested, and necessary optimizations are performed. Detailed user documentation is compiled, including model parameter settings, usage limitations, and validation results, to ensure the model's operability in subsequent development and deployment.

[0093] Secondly, embodiments of this application also provide a system for reducing the order of complex multiphysics models of airborne systems, used to implement the method for reducing the order of complex multiphysics models of airborne systems as described in any embodiment of the first aspect, the system comprising: The sample point design module is used to determine the computational domain of the multiphysics model of the airborne system, and to obtain sample points covering all operating conditions based on the experimental design method using the computational domain. The training dataset acquisition module is used to perform simulation calculations on sample points and dynamically adjust the distribution density of sample points based on the simulation calculation results. Based on the adjusted sample points and the corresponding simulation calculation results, the training dataset is obtained. The feature value iteration module is used to obtain a dimensionality-reduced training dataset based on the training dataset by using feature value iteration. The order reduction model building module is used to build an order reduction model based on a multi-model stage and train the order reduction model using a dimensionality reduction training dataset. The reduced-order model encapsulation module is used to verify, optimize, and encapsulate the trained reduced-order model in sequence.

[0094] The embodiments provided in this invention propose a variable-scale feature vector iteration strategy based on AI correction. By using eigenvector decomposition as a robust initial global feature space, a lightweight FFN network model is used to dynamically and finely adjust the basis function coefficients and scale in this space, thereby achieving micro-iteration and scale reconstruction of the feature vectors. This method eliminates the need for costly recalculations under changing operating conditions, allowing online invocation of the lightweight FFN network to correct the output results, meeting the efficiency requirements of airborne system simulation while reducing reduction loss. Furthermore, since the feature basis originates from physical features such as the modalities of PCA, its output physical consistency and interpretability are far superior to pure black-box reduction model neural networks.

[0095] Meanwhile, a hybrid order reduction strategy driven by the data model of airborne systems is provided. While intelligently reducing the order model, the two interrelated dimensions of static nonlinearity and dynamic temporal characteristics are decoupled and sequentially fitted to realize the analysis of the steady-state physical meaning of the surrogate model. On the other hand, steady-state prediction is used as a benchmark to avoid possible non-physical oscillations or divergences.

[0096] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for order reduction of complex multiphysics models of airborne systems, characterized in that, include: The computational domain of the multiphysics model of the airborne system is determined, and experimental design methods are used to obtain sample points covering all operating conditions based on the computational domain. The sample points are simulated and calculated, and the distribution density of the sample points is dynamically adjusted based on the simulation results. The training dataset is obtained based on the adjusted sample points and the corresponding simulation results. Based on the training dataset, an AI-corrected feature value iteration method is used to obtain a dimensionality-reduced training dataset; Construct a multi-model staged reduction model and train it using a dimensionality reduction training dataset; The trained reduced-order model is then validated, optimized, and encapsulated sequentially.

2. The method for order reduction of complex multiphysics models of airborne systems according to claim 1, characterized in that, The method of obtaining a dimensionality-reduced training dataset based on the training dataset and using AI-corrected feature value iteration includes: Based on the training dataset, principal component extraction is performed to obtain the global feature space; Extract the first n feature vectors from the global feature space to form the global feature base; A dynamic corrector for feature maps with AI correction is constructed to correct and iterate the feature scale in the global feature base to obtain a dimensionality-reduced training dataset.

3. The method for order reduction of complex multiphysics models of airborne systems according to claim 2, characterized in that, The feature map dynamic corrector for constructing AI correction includes: Construct a feature map dynamic corrector based on a multilayer feedforward neural network.

4. The method for order reduction of complex multiphysics models of airborne systems according to claim 3, characterized in that, The correction and iteration of the feature scale in the global feature base includes: The current real-time operating parameters and the initial coefficients derived from the global feature base are used as the input data for the multilayer feedforward neural network. For different specific operating parameters, a nonlinear mapping is learned based on a multilayer feedforward neural network: f(δ, a0) -> Δa(δ). This nonlinear mapping serves as the kernel of the feature mapping dynamic corrector and is used to calculate Δa(δ) during the inference phase. Here, f is the mapping relationship function, δ is the operating parameter, a0 is the initial coefficient, and Δa(δ) is the correction amount of the basis function coefficient. Based on the initial coefficients, the basis function coefficient corrections, and the global feature basis, the feature state space of dynamic iteration is obtained; The output response of a multilayer feedforward neural network is obtained based on the dynamically iterated feature state space and feature weight vector.

5. The method for order reduction of complex multiphysics models of airborne systems according to claim 4, characterized in that, The expression for the feature state space of the dynamic iteration is: ， ， Where B is the feature state space of dynamic iteration, b i (δ) is the eigenvector after the i-th iteration, Δa i (δ) represents the correction factor for the i-th basis function coefficient, p i Let x be the i-th eigenvector in the global feature basis. i Let be the boundary conditions of the system at time i.

6. The method for order reduction of complex multiphysics models of airborne systems according to claim 5, characterized in that, The expression for the output response of the multilayer feedforward neural network is: ， Among them, y i (δ) represents the i-th output response of the multilayer feedforward neural network, and wi(δ) represents the i-th feature weight vector.

7. The method for order reduction of complex multiphysics models of airborne systems according to claim 1, characterized in that, The construction of the multi-model staged order reduction model includes: A two-stage order reduction model is constructed based on a multilayer feedforward neural network model, a response surface model, and a long short-term memory neural network model.

8. The method for order reduction of complex multiphysics models of airborne systems according to claim 7, characterized in that, The construction of the two-stage order reduction model based on a multilayer feedforward neural network model, a response surface model, and a long short-term memory neural network model includes: Based on the application scenarios of complex multiphysics models that require order reduction, we analyze the complexity requirements, rapid verification requirements, order reduction accuracy requirements, and real-time requirements of the target model. Based on the analysis results, we select at least one model from the multilayer feedforward neural network model, response surface model, and long short-term memory neural network model as the order reduction surrogate model. Cross-validate the reduced-order surrogate model and adjust the parameters of the selected model or reduced-order surrogate model based on the validation results.

9. The method for order reduction of complex multiphysics models of airborne systems according to claim 8, characterized in that, The selection of at least one model from the multilayer feedforward neural network model, response surface model, and long short-term memory neural network model as a reduced-order surrogate model based on the analysis results includes: A multi-layer feedforward neural network model and a long short-term memory neural network model were selected and fused using a sequential modeling approach to serve as a reduced-order surrogate model. The sequential modeling approach for model fusion includes: A static multilayer feedforward neural network model is obtained by training the multilayer feedforward neural network model, and a direct mapping from any set of flight parameters to the corresponding steady-state aerodynamic forces is established. Time series data were collected and constructed. Based on the long short-term memory neural network model, the transition of aerodynamic forces at different times was established. The trained static multilayer feedforward neural network model was embedded into the long short-term memory neural network model to form a fusion model. The fusion model learns a correction relative to a static baseline using transient data, and then uses this correction to make the final aerodynamic prediction.

10. A system for reducing the order of a complex multiphysics model of an airborne system, used to implement the method for reducing the order of a complex multiphysics model of an airborne system as described in any one of claims 1-9, characterized in that, The system includes: The sample point design module is used to determine the computational domain of the multiphysics model of the airborne system, and to obtain sample points covering all operating conditions based on the experimental design method using the computational domain. The training dataset acquisition module is used to perform simulation calculations on sample points and dynamically adjust the distribution density of sample points based on the simulation calculation results. Based on the adjusted sample points and the corresponding simulation calculation results, the training dataset is obtained. The feature value iteration module is used to obtain a dimensionality-reduced training dataset based on the training dataset using an AI-corrected feature value iteration method. The order reduction model building module is used to build an order reduction model based on a multi-model stage and train the order reduction model using a dimensionality reduction training dataset. The reduced-order model encapsulation module is used to verify, optimize, and encapsulate the trained reduced-order model in sequence.

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