A high-dimensional output aircraft structure global surrogate model construction method

Abstract

This application belongs to the field of aircraft structure simulation calculation, and specifically relates to a method for constructing a high-dimensional output aircraft structure global proxy model, including: step 1, according to the probability distribution f of the structural model input variable X X (x), extract N input samples {x (1) ,…,x (N)} T , build a sample pool for global modeling. Step 2: Select N0 input samples from the sample pool and substitute each input sample into the finite element model for calculation to obtain the corresponding output response sample. Step 3: Perform PCA dimensionality reduction decomposition on the output response sample and convert the output response sample into the mean-centered output principal component sample. Step 4: Construct the Kriging model g with the input sample output principal component sample. K (X); Step 5, use the variance learning function to learn the Kriging model g K (X) is updated to obtain the Kriging model g for calculation K (X); Step 6: Calculate the Kriging model g K (X), perform matrix reconstruction to obtain a high-dimensional output prediction model.

Description

Technical Field

[0001] The present application belongs to the field of aircraft structure simulation calculation, and specifically relates to a method for constructing a high-dimensional output global proxy model of an aircraft structure. Background Art

[0002] In engineering practice, the simulation and calculation of finite element models of aircraft structures often consume a lot of time. For complex aircraft structural models, such as wing structures, fuselage structures, and key aircraft structural component models such as engines, the computational cost and time consumption of modeling and simulation are even greater, resulting in low efficiency in the analysis and design of aircraft structures. This brings huge computational challenges to the analysis, design, and optimization of related structures, and seriously restricts the rapid iteration of aircraft structural design and improvement.

[0003] To address the above problems, an effective solution is to use the global surrogate model method to construct a global surrogate model with low computational cost and high fidelity in the design variable space of the original model to improve the efficiency of model calculation.

[0004] Currently, global surrogate model technology has played a significant role in improving the computational efficiency of finite element models and computational fluid dynamics models, providing powerful support for accelerating the analysis and calculation of related structures. However, when studying aircraft structural performance, high-dimensional outputs are often encountered. For example, studying the performance of an aircraft structure over a certain period of time requires obtaining the structural output responses at a large number of discrete moments, which leads to a significant increase in the model output dimension. This situation imposes a huge computational burden on the construction of the global surrogate model, preventing the global surrogate model technology from fully realizing its inherent advantages.

[0005] This application is proposed in view of the existence of the above technical problems. Summary of the Invention

[0006] The purpose of this application is to provide a method for constructing a high-dimensional output global proxy model of an aircraft structure to overcome or alleviate at least one of the known technical deficiencies.

[0007] The technical solution of this application is:

[0008] A method for constructing a high-dimensional output global proxy model of an aircraft structure, comprising:

[0009] Step 1: Input the probability distribution f of variable X according to the structural model X (x), extract N input samples {x (1) ,…,x (N)} T , building a sample pool for global modeling

[0010] Step 2: From the sample pool Select N0 input samples from Substitute each input sample into the finite element model for calculation to obtain the corresponding output response sample

[0011] Step 3: Output response sample Perform PCA dimensionality reduction decomposition and output the response sample Converted into mean-centered output principal component samples

[0012] Step 4: Input sample Output principal component samples Construct Kriging model g K (X);

[0013] Step 5: Use variance learning function to learn Kriging model g K (X) is updated to obtain the Kriging model g for calculation K (X);

[0014] Step 6: Calculate the Kriging model g K (X), perform matrix reconstruction to obtain a high-dimensional output prediction model.

[0015] According to at least one embodiment of the present application, in the above-mentioned high-dimensional output aircraft structure global proxy model construction method, in step one, for the wing structure, the structural model variables include the length L of the box segment, the cross-sectional area A of the rod unit, the thickness θ2 of the plate unit used for the ribs and wing walls, the thickness θ1 of the plate unit used for the skin, the elastic moduli E1 and E2 of the rod unit and the plate unit, and the external load concentrated force P.

[0016] According to at least one embodiment of the present application, in the above-mentioned method for constructing a high-dimensional output aircraft structure global proxy model, in step 2, for the wing structure, the output response can be designed to be the difference between the displacement of the wing structure in the Y direction and the displacement limit.

[0017] According to at least one embodiment of the present application, in the above-mentioned method for constructing a high-dimensional output aircraft structure global proxy model, step three is specifically as follows:

[0018]

[0019]

[0020] in,

[0021] Output response sample Perform PCA dimensionality reduction projection matrix;

[0022] Z is the output principal component, whose dimension is smaller than the output response sample Dimensionality;

[0023] is the mean of the output samples.

[0024] According to at least one embodiment of the present application, in the above-mentioned method for constructing a high-dimensional output aircraft structure global proxy model, step five includes:

[0025] S1. Using Kriging model g K (X) Sample pool Predict the input samples in and obtain the output mean and standard deviation of each input sample;

[0026] S2. If the output prediction standard deviation meets the stopping criteria, the Kriging model g is obtained. K (X), otherwise, select the Kriging model g K (X) Output the input sample x with the largest standard deviation new , calculate with the finite element model and get the corresponding output response sample y new , the sample {x new ,y new}Add the training sample set of the Kriging model and update the Kriging model g K (X), return to S1.

[0027] According to at least one embodiment of the present application, in the above-mentioned method for constructing a high-dimensional output aircraft structure global proxy model, the stopping criterion in S is:

[0028] |σ max,i -σ max,i-1 | / σ max,i-1 ≤δ;

[0029] in,

[0030] σ max,i To obtain the maximum prediction standard deviation of the Kriging model for the i-th sample, σ max,i-1 To obtain the maximum prediction standard deviation of the Kriging model for the i-1th sample, δ is the relative deviation threshold of the two maximum Kriging prediction standard deviations.

[0031] According to at least one embodiment of the present application, in the above-mentioned method for constructing a high-dimensional output aircraft structure global proxy model, the relative deviation threshold δ between the two maximum Kriging prediction standard deviations is set to 0.01.

[0032] According to at least one embodiment of the present application, in the above-mentioned method for constructing a high-dimensional output aircraft structure global proxy model, in step 6, the high-dimensional output prediction model is:

[0033] This application has at least the following beneficial technical effects:

[0034] A method for constructing a global proxy model of a high-dimensional output aircraft structure is provided. The principal component analysis (PCA) technique is used to process high-dimensional output variables, and an adaptive learning function is used to select samples that have an important contribution to the output accuracy of the proxy model. Thus, a high-precision global proxy model is obtained with fewer modeling samples. Thus, an adaptive global proxy model is established in a dimensionality-reduced space for high-dimensional output aircraft structures. The high-dimensional output of the aircraft structure is accurately predicted with high efficiency, which can well meet the needs of rapid iteration of aircraft structure design and improvement. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a schematic diagram of a simplified aircraft wing model provided in an embodiment of the present application;

[0036] Figure 2 is a schematic diagram of a cross-section of an aircraft wing structure provided by an embodiment of the present application;

[0037] Figure 3 Schematic diagram of a method for constructing a high-dimensional output global proxy model of an aircraft structure provided by an embodiment of the present application;

[0038] Figure 4 Schematic diagram of the global accuracy comparison of the Kriging and PCA-K models provided in the embodiments of the present application;

[0039] Figure 5 This is a schematic diagram of the global accuracy comparison of the three models of Kriging, PCA-K, and PCA-AK provided in the embodiments of this application.

[0040] In order to better illustrate this embodiment, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product. In addition, the drawings are only used for illustrative purposes and should not be understood as limiting this application. DETAILED DESCRIPTION

[0041] To make the technical solution and its advantages of this application more clear, the technical solution of this application will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described here are only some of the embodiments of this application and are only used to explain this application, not to limit this application. It should be noted that for ease of description, only the parts relevant to this application are shown in the accompanying drawings, and other relevant parts can refer to the general design.

[0042] In addition, unless otherwise defined, the technical terms or scientific terms used in the description of this application should have the usual meanings understood by those skilled in the art in the field to which this application belongs. The words indicating orientation used in the description of this application are only used to indicate relative directions or positional relationships. When the absolute position of the described object changes, its relative positional relationship may also change accordingly. The word "include" used in the description of this application means that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, but does not exclude other elements or objects.

[0043] In addition, it should be noted that, unless otherwise clearly stipulated and limited, the words "installation", "connection" and similar terms used in the description of this application should be understood in a broad sense. For example, the connection can be a fixed connection or a detachable connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium. Technical personnel in the field can understand its specific meaning in this application according to the specific circumstances.

[0044] The main task of this application is to establish an efficient and accurate global proxy model technology for high-dimensional output aircraft structures, thereby providing powerful assistance for the analysis, design and optimization of related structures.

[0045] The method established in this application is described using a research object, a simplified aircraft wing model, as an example. Figure 1 As shown, the cross section of the aircraft wing structure, such as Figure 2 As shown, the entire wing structure can be regarded as consisting of box segments extending from the cross section. The length of a box segment is denoted as variable L, and the cross-sectional area of ​​all rod units is represented by variable A. The thickness of the plate units used for the ribs and wing walls is θ2, and the thickness of the plate units used for the skin is θ1. The elastic moduli of all rod units and plate units in the wing structure are E1 and E2 respectively, and the Poisson's ratio is set to 0.3. During the flight of the aircraft, the function of the external load on the wing with time t is P = P0(0.8+cos(t / 4)), where P0 is the reference external load.

[0046] The specific distribution of the above wing input variables is shown in the following table:

[0047]

[0048]

[0049] The output of the wing model is defined as the maximum equivalent stress of the wing model at each discrete moment. The maximum equivalent stress results are provided by ANSYS finite element analysis software. When the time domain of interest is t∈[1,50]s, by uniformly discretizing the time domain into 50 moments, the model output response at the corresponding discrete output moment can be obtained, thereby obtaining the time-varying output of the wing model output response in the time domain t∈[1,50]s.

[0050] For a wing model, its input-output relationship can be represented by the mathematical model Y(t) = g(X, t), where X = [A, E1, E2, θ1, θ2, P0, L] is the input variable, Y(t) is the time-varying output variable, and g(X, t) is the functional relationship established based on the finite element model. Because the calculation of complex finite element models is generally time-consuming, frequently changing input parameters to obtain output responses during the structural design and optimization process will significantly increase the time cost. To this end, the Kriging global surrogate model method can be used to construct a surrogate model of the wing finite element model. This surrogate model is fitted by an analytical mathematical function and thus has a higher calculation speed.

[0051] For a one-to-one input-output relationship, the model function of the Kriging model can be expressed as:

[0052] g K (X) = f T (X)β+Z(X)……………(1)

[0053] Among them, f T (X)β is a global trend model, and Z(X) is a local deviation model.

[0054] Through global and local fitting, the Kriging model g K (X) can replace the original simulation model g(X) to obtain the value of the output Y under a given input sample.

[0055] By optimizing a set of input-output samples to solve the Kriging model parameters, the Kriging model prediction output g can be obtained. K The expression of (X):

[0056] g K (X) = f T (X)β+r T (X)R -1 (y-Fβ)…………(2)

[0057] Prediction output variance The expression:

[0058]

[0059] Among them, F is the regression function matrix of the global model, β is the regression parameter, y is the output modeling sample, R is the correlation matrix between the input modeling samples, r(X) is the correlation matrix between the input modeling sample and any input variable X, and σ 2 is the variance of the local deviation model.

[0060] For the function relationship of input-multidimensional output, when performing Kriging modeling, the mean and variance corresponding to each dimension of the output will be optimized and solved. Therefore, when the output is high-dimensional, the burden of Kriging modeling will increase significantly. For this reason, a classical unsupervised dimensionality reduction method, namely the principal component analysis PCA method, can be adopted to reduce the dimension only for the output variables.

[0061] When performing PCA dimensionality reduction, a set of output samples is required Based on Performing PCA decomposition can obtain the corresponding dimensionality reduction projection matrix Therefore, the original m-dimensional output variable Y can be converted into an r-dimensional output principal component Z, and r < m, and there is:

[0062]

[0063] The output principal component Z after dimensionality reduction can also reconstruct the original high-dimensional output variable Y based on the matrix. Specifically:

[0064]

[0065] Among them, is the mean of the output samples, is the output principal component after centering.

[0066] [[ID=3,6]]According to the above PCA dimensionality reduction process, the 50-dimensional output variable of the wing model can be converted into a 1-dimensional output principal component, and this output principal component can explain nearly 100% of the variance information of the original output variable, so that the output samples reconstructed based on this principal component are very close to the high-dimensional output samples before dimensionality reduction.

[0067] Therefore, when constructing the Kriging model, it is completely possible to only construct the function relationship between the input variable X and the centered output principal component Z, and then obtain the high-dimensional output samples corresponding to the output principal component samples through Equation (5), which can greatly reduce the burden of Kriging modeling and calculation.

[0068] Furthermore, if one wishes to obtain a Kriging model with high output prediction accuracy, the quality of the modeling samples becomes crucial. Otherwise, it will be necessary to improve the output accuracy of the proxy model at the expense of consuming a large number of modeling samples. To this end, a variance learning function can be used to adaptively select Kriging modeling samples. Samples with large prediction variances indicate that the Kriging model is less confident in predicting the output at that point. Therefore, the variance learning function is defined as follows:

[0069]

[0070] The stopping criterion of the learning function can be defined as:

[0071] |σ max,i -σ max,i-1 | / σ max,i-1 ≤δ…………(7)

[0072] Among them, σ max,i To obtain the maximum prediction standard deviation of the Kriging model for the i-th adaptive sample, σ max,i-1 To obtain the maximum prediction standard deviation of the Kriging model for the i-1th adaptive sample, δ is the relative deviation threshold of the two maximum Kriging prediction standard deviations.

[0073] Based on the above, this application provides a method for constructing a high-dimensional output global proxy model of aircraft structure, and establishes an adaptive Kriging modeling method in the PCA output dimensionality reduction space, such as Figure 3 shown.

[0074] Step 1: Input the probability distribution f of variable X according to the structural model X (x), extract N input samples {x (1) ,…,x (N)} T , build a sample pool for global modeling

[0075] For the wing structure, the structural model variables include the length L of the box section, the cross-sectional area A of the rod element, the thickness θ2 of the plate element used for the ribs and wing walls, the thickness θ1 of the plate element used for the skin, the elastic moduli E1 and E2 of the rod element and plate element, and the external load concentrated force P.

[0076] Step 2: From the sample pool Select N0 input samples from Substitute each input sample into the finite element model for calculation to obtain the corresponding output response sample

[0077] For the wing structure, the output response can be designed as the difference between the displacement of the wing structure in the Y direction and the displacement limit.

[0078] Step 3: Output response sample Perform PCA dimensionality reduction decomposition and output the response sample Converted into mean-centered output principal component samples

[0079]

[0080]

[0081] in,

[0082] Output response sample Perform PCA dimensionality reduction projection matrix;

[0083] Z is the output principal component, whose dimension is smaller than the output response sample Dimensionality;

[0084] is the mean of the output samples.

[0085] Step 4: Input sample Output principal component samples Construct Kriging model g K (X).

[0086] Step 5: Use variance learning function to learn Kriging model g K (X) is updated to obtain the Kriging model g for calculation K (X).

[0087] S1. Using Kriging model g K (X) Sample pool Predict the input samples in and obtain the output mean and standard deviation of each input sample;

[0088] S2. If the output prediction standard deviation meets the stopping criteria, the Kriging model g is obtained. K (X), otherwise, select the Kriging model g K (X) Output the input sample x with the largest standard deviation new , calculate with the finite element model and get the corresponding output response sample y new , the sample {x new ,y new}Add the training sample set of the Kriging model and update the Kriging model g K (X), return to S1.

[0089] The stopping criteria are:

[0090] |σ max,i -σ max,i-1 | / σ max,i-1 ≤δ;

[0091] in,

[0092] σ max,i To obtain the maximum prediction standard deviation of the Kriging model for the i-th sample, σ max,i-1 To obtain the maximum prediction standard deviation of the Kriging model for the i-1th sample, δ is the relative deviation threshold of the two maximum Kriging prediction standard deviations.

[0093] Step 6: Calculate the Kriging model g K (X), perform matrix reconstruction to obtain a high-dimensional output prediction model.

[0094] The high-dimensional output prediction model is: This can be used to compute high-dimensional responses given input variables X.

[0095] For the simplified aircraft wing model above, if the modeling sample pool is set The capacity is 2500, the initial modeling sample size is 15, and the threshold δ is 0.01. The prediction accuracy of the final constructed global surrogate model can be quantified by the following mean square error, namely:

[0096]

[0097] in, is the predicted high-dimensional output of the Kriging model, Y is the real high-dimensional output obtained based on the finite element model, is the expectation operator.

[0098] In order to respectively verify the effects of output dimensionality reduction and adaptive variance learning function on the prediction accuracy of the Kriging model, three Kriging proxy models are established for comparison, namely, the Kriging model constructed based on the original input-high-dimensional output samples under random sampling, the PCA-K model constructed based on the input-low-dimensional output principal component samples under random sampling, and the PCA-AK model constructed based on the input-low-dimensional output principal component samples under adaptive sampling established by the above embodiment, which is based on the method for constructing a global proxy model of high-dimensional output aircraft structure.

[0099] After adaptive learning, the PCA-AK model adds 42 modeling samples, so the final modeling sample size of the PCA-AK model is 57. In order to ensure the fairness and rationality of the comparison, the modeling sample size of the Kriging model and the PCA-K model is also set to 57, but their modeling samples are obtained by random sampling. The time-varying finite element model output corresponding to the 2500 samples in the above three models is as follows: Figure 4 、 5 shown.

[0100] from Figure 4 It can be seen that the mean square errors of the Kriging model and the PCA-K model are very close, and the error values ​​are relatively low, which proves that the Kriging model and PCA-K model constructed using 57 modeling samples are accurate enough, and also proves that the PCA dimensionality reduction method has little effect on the surrogate model to provide accurate high-dimensional output predictions. Figure 5 It can be further seen that the mean square error of the PCA-AK model constructed based on adaptive learning is reduced by 41.7% compared to the Kriging model and PCA-K model. This proves that with the same modeling sample size, the modeling samples selected using the variance learning function contribute more significantly to improving the global accuracy of the surrogate model. Therefore, for aircraft structures with high-dimensional outputs, the PCA-AK model constructed based on the variance learning function in the PCA dimensionality reduction space has good global prediction accuracy. Furthermore, by reducing the output dimensionality, it can significantly reduce the computational burden of surrogate model modeling and simulation, improve the efficiency of model analysis, and thus provide powerful support for the design and optimization of related high-dimensional output structures.

[0101] The method for constructing a global proxy model of a high-dimensional output aircraft structure disclosed in the above embodiment adopts an adaptive modeling method to selectively and successively select modeling samples that help improve the output accuracy of the model, and constructs a high-fidelity proxy model based on a small number of modeling samples. In addition, considering that high-dimensional output of aircraft structures is very common, the high-dimensional output variables are processed based on the principal component analysis (PCA) technology to reduce the computational difficulty and burden of the proxy model method under high-dimensional output conditions, weaken the "curse of dimensionality" effect of high-dimensional output of aircraft structures on the modeling process, and establish adaptive global modeling under the output dimensionality reduction framework. Ultimately, based on the established global proxy model, the analysis and design of relevant aircraft structures can be more efficiently achieved.

[0102] So far, the technical solution of the present application has been described in conjunction with the preferred embodiments shown in the accompanying drawings. Those skilled in the art should understand that the scope of protection of the present application is obviously not limited to these specific embodiments. Without departing from the principles of the present application, those skilled in the art can make equivalent changes or replacements to the relevant technical features, and the technical solutions after these changes or replacements will fall within the scope of protection of the present application.

Claims

1. A method for constructing a high-dimensional output global proxy model of aircraft structure, characterized in that: include: Step 1: Input the probability distribution f of variable X according to the structural model X (x), extract N input samples {x (1) ,…,x (N) } T , build a sample pool for global modeling Step 2: From the sample pool Select N0 input samples from Substitute each input sample into the finite element model for calculation to obtain the corresponding output response sample Step 3: Output response sample Perform PCA dimensionality reduction decomposition to convert the output response sample N into the output principal component sample after mean centering Step 4: Input sample Output principal component samples Construct Kriging model g K (X); Step 5: Use variance learning function to learn Kriging model g K (X) is updated to obtain the Kriging model g for calculation K (X); Step 6: Calculate the Kriging model g K (X), perform matrix reconstruction to obtain a high-dimensional output prediction model; In step 1, for the wing structure, the structural model variables include the length L of the box segment, the cross-sectional area A of the rod element, the thickness θ2 of the plate element used for the rib and wing wall, the thickness θ1 of the plate element used for the skin, the elastic moduli E1 and E2 of the rod element and plate element, and the external load concentrated force P; In step 2, for the wing structure, the output response can be designed as the difference between the displacement of the wing structure in the Y direction and the displacement limit; Step three is as follows: in, The dimensionality reduction projection matrix for PCA dimensionality reduction decomposition of the output response sample N; Z is the output principal component, whose dimension is smaller than the dimension of the output response sample N; μ N is the mean of the output samples; Step five includes: S1. Using Kriging model g K (X) Sample pool Predict the input samples in and obtain the output mean and standard deviation of each input sample; S2. If the output prediction standard deviation meets the stopping criteria, the Kriging model g is obtained. K (X), otherwise, select the Kriging model g K (X) Output the input sample x with the largest standard deviation new , calculate with the finite element model and get the corresponding output response sample y new , the sample {x new ,y new }Add the training sample set of the Kriging model and update the Kriging model g K (X), return to S1; In step 6, the high-dimensional output prediction model is:

2. The method for constructing a high-dimensional output global proxy model of an aircraft structure according to claim 1, characterized in that: In S, the stopping criterion is: |s max,i -s max,i-1 | / s max,i-1 ≤δ; in, σ max,i To obtain the maximum prediction standard deviation of the Kriging model for the i-th sample, σ max,i-1 To obtain the maximum prediction standard deviation of the Kriging model for the i-1th sample, δ is the relative deviation threshold of the two maximum Kriging prediction standard deviations.

3. The method for constructing a high-dimensional output global proxy model of an aircraft structure according to claim 2, characterized in that: The relative deviation threshold δ between the two maximum Kriging prediction standard deviations is set to 0.01.

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