Performance Prediction Method of Bionic Self-Similar Hierarchical Structure Based on Machine Learning

Abstract

The present invention discloses a performance prediction method for a bionic self-similar hierarchical structure based on machine learning. An initial database of the structure model is obtained by finite element simulation or experimental method, and the data in the initial database is cleaned. GA is used for variable screening, and the screened variables are processed for advantages and disadvantages according to the Pareto dominance idea. Training and test data sets for establishing a BP neural network model are randomly selected. The ten-fold cross-validation method combined with the evaluation method of R^2 is used to determine the final data set selection method and the corresponding weights and thresholds. A final neural network model is established, and the prediction result of the above model is evaluated through the test data set. The present invention combines machine learning with known data and uses a data-driven mode to predict the energy absorption performance of the structure. When the geometric parameters or types of the bionic self-similar hierarchical structure change, only by changing a limited number of variables in the model can a new model be obtained to adapt to the new structure.

Description

Technical Field

[0001] The present invention belongs to the technical field of automotive passive safety, and particularly relates to a performance prediction method for a bionic self-similar hierarchical structure based on machine learning. Background Art

[0002] With the rapid increase in the number of automobiles in China, the status of automotive passive safety has also been increasing day by day. Introducing the bionic design concept into lightweight and high-strength sandwich structures to form excellent bionic self-similar hierarchical structures has become a research hotspot in recent years. The bionic self-similar hierarchical structure not only improves the designability of the structure but also has the advantages of improving the structural strength and energy absorption capacity.

[0003] Existing bionic self-similar hierarchical structures, such as those in the master's thesis of Huaqiao University, "Crashworthiness Research on Hierarchical Self-Similar Thin-Walled Bionic Structures" and "Crashworthiness Research on Self-Similar Hierarchical Honeycomb Structures under Multiple Collision Conditions" submitted by Zeng Yi on May 29, 2018, and Ma Fangwu et al., "Automotive Engineering", Vol. 44, No. 6, pp. 886-892, June 2022, are all hierarchical self-similar hierarchical structures formed by bionic design. Some influencing factors and design ideas for the energy absorption performance of the bionic self-similar hierarchical structure have been explored, and the optimization of the structure has been completed. However, in the actual application process, due to factors such as processing methods, deviations will occur, resulting in a slight decrease in the energy absorption performance of the actually produced structure, and a complete system of influencing factors is not given; when applied, the final energy absorption result of the bionic self-similar hierarchical structure is affected by multiple factors: in addition to the external shape, unit cell structure, and selected materials, etc., the relationship between the types, compositions, processes, microstructures, and properties of the materials used in itself is extremely complex, and there are various interactions, making it difficult to obtain accurate results through methods such as derivation formulas. Only accurate results of the energy absorption value can be obtained through experiments or simulations. When the geometric parameters or types of the bionic self-similar hierarchical structure change, it is necessary to conduct simulations or experiments again to obtain the energy absorption value, which limits its wide application and takes a long time. Summary of the Invention

[0004] The purpose of the present invention is to solve the above problems by providing a performance prediction method for a bionic self-similar hierarchical structure based on machine learning. This prediction method will reduce the deviation caused by the processing method, thereby minimizing the reduction value of the energy absorption performance of the bionic self-similar hierarchical structure. Moreover, when the geometric parameters or types of the bionic self-similar hierarchical structure change, only by changing the limited variables in the model can a new model be obtained to adapt to the new structure, and there is no need to conduct experiments again to obtain the energy absorption value, thereby expanding its scope of application and saving time and material costs.

[0005] To achieve the above object, the present invention provides a performance prediction method for a bionic self-similar hierarchical structure based on machine learning, comprising the following steps:

[0006] S1: Collect data. The data obtained through finite element simulation or experimental methods is used as the initial database for establishing a bionic self-similar hierarchical structure model. The initial database includes the mechanical properties of materials. If the material is metal, the mechanical properties of the metal material include normal elastic modulus, shear elastic modulus, proportional limit, elastic limit, strength limit, tensile strength, yield limit, yield strength, fatigue limit; if the selected material is a composite material, the mechanical property characteristics of the composite material include longitudinal / transverse tensile strength, longitudinal / transverse compressive strength, longitudinal / transverse elastic modulus, major Poisson's ratio, shear modulus.

[0007] S2: Clean the data in the initial database; adjust the attribute parameters in the initial database in S1 through experiments and simulations, and clean and eliminate the data according to the influence on the final performance.

[0008] S3: Use the genetic algorithm to screen variables for the data in S2, obtain the variables to be included in the subsequent model, perform superiority and inferiority processing on the screened variables according to the Pareto dominance idea, and use the data after the superiority and inferiority processing as the total database.

[0009] S4: Randomly select the training data set and test data set for establishing the BP neural network model; use the ten-fold cross-validation method to divide the total database in S3 into ten groups, randomly select 80% of the data (i.e., eight of them) as the training data set of the BP neural network, and use the remaining 20% of the data (i.e., the remaining two groups) as the test data set of the model; repeat this operation to obtain a total of 45 different training sets and their corresponding test sets; the training data set is used to determine the parameters of the BP neural network model and establish the model, and the test data set is used to evaluate the prediction effect of the subsequent established model.

[0010] S5: Establish a BP neural network model through all the training data sets and their corresponding test data sets obtained in S4, a total of 45 models, and each model is run 10 times. Determine the optimal weight and threshold of each model through the R^2 result of the model fitting in 10 runs; use the ten-fold cross-validation method and the evaluation method combined with R^2 to determine the data set selection method and the corresponding weight and threshold of the optimal model among the 45 models.

[0011] S6: Determine the network parameters. The network parameters include the number of network layers, the number of network nodes, the activation function, and select a single hidden layer; the formula for the number of hidden layer nodes is:

[0012]

[0013] Wherein: N h is the number of hidden layer nodes, N in is the number of input layer nodes. For a BP neural network, the number of input layer nodes is the number of input features, N out is the number of output layer nodes, and h is an adjustment constant that can be any one of 1 - 10.

[0014] S7: Evaluate the prediction results of the already established neural network model through the test dataset; Apply the neural network model established based on the parameters in S6 to the test dataset divided in S4 for model verification, and compare the data in the actual test dataset obtained through experiments or simulations with the results predicted by the model, and evaluate the prediction ability of the model through the network training regression in the network model results.

[0015] S8: Evaluate the model prediction results in S7 using the correct rate evaluation formula; The correct rate evaluation formula is:

[0016]

[0017] Where R is the correct rate of the model prediction results, n is the number of correct tests, and N is the total number of tests.

[0018] S9: Appropriately adjust the proportion of the selected random data to test the model results; Adjust the proportion of the training dataset and the test dataset in S4, and change it to randomly select 90% or 70% as the training dataset, and use the remaining 10% or 30% as the test dataset, and repeat the above S5 to S8 for repeated calculations to determine the difference between the predicted results of the model and the actual results, and evaluate the dependence degree of the model on the proportion.

[0019] Advantages and beneficial effects of the present invention

[0020] 1. The present invention establishes a model directly driven by data and provides an efficient method for quantitatively solving the energy absorption value. In the actual application process, it will reduce the deviation caused by the processing method, thereby minimizing the reduction value of the energy absorption performance of the bionic self-similar hierarchical structure. Moreover, when the geometric parameters or types in this application change, the energy absorption value can be obtained without the need for modeling or experimentation, saving a large amount of time and material costs, and the accuracy of the results can also be verified through experiments or simulations.

[0021] 2. The present invention comprehensively considers influencing factors. For the selected structure, the model parameters, material selection, processing technology, etc. are mainly analyzed. The data obtained through finite element simulation or experimental materials are used as a database. If the material selected is metal, it includes the mechanical properties of the metal, and the mechanical properties of the metal include normal elastic modulus, shear elastic modulus, proportional limit, tensile strength, yield limit, yield strength, fatigue limit, major Poisson's ratio, shear modulus, etc., all of which are taken into account, thus forming a complete system of influencing factors and giving a sufficiently accurate prediction of the energy absorption performance of the bionic self-similar hierarchical structure.

[0022] 3. The present invention has strong generalization ability. When the geometric parameters or types in the bionic self-similar hierarchical structure change, only by changing the finite variables in the model can a new model be obtained to adapt to the new structure, thereby expanding its scope of application and being more suitable for structures with relatively complex processing and manufacturing and high costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0024] Figure 1 is the flowchart of the prediction method of the present invention;

[0025] Figure 2 is the schematic diagram of the bionic self-similar hierarchical honeycomb structure of the present invention;

[0026] Figure 3 is the schematic diagram of the unit cell of the structure in the embodiment of the present invention;

[0027] Figure 4 is the schematic diagram of the network structure of the present invention;

[0028] Figure 5 is the schematic diagram of the Pareto front based on the genetic algorithm of the present invention

[0029] Figure 6 is the schematic diagram of the result after the model training regression of the present invention;

[0030] Figure 7 is the comparison diagram of the energy absorption prediction result of the test set of the present invention and the true value. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] Here, the bionic self-similar hierarchical honeycomb structure is taken as an example, but all other materials that can form the energy absorption prediction of this structure are within the scope of the present invention. In this embodiment, the performance index is evaluated starting from the energy absorption (EA).

[0032] As Figure 2 shown, the energy absorption of the embodiment structure in the present invention takes axial compression energy absorption as an example. However, the present invention includes the energy absorption performance during oblique impact, and Figure 3 is Figure 2 a schematic diagram of the single-cell structure, where t is the wall thickness of all hexagons in the single cell, θ is the cell wall angle of all hexagons, l0 is the side length of the cell wall of the outermost hexagon structure, l1 and l2 are the side lengths of the central hexagon and the vertex hexagon respectively, and their relational formulas are as follows:

[0033]

[0034] where n represents the evolution order of the self-similar honeycomb structure; when n is odd, l n represents the side length of the central hexagon of the ((n + 1) / 2)-th order evolution; when n is even, l n represents the side length of the central hexagon of the n / 2-th order evolution, and ε is a constant used to fit the side length formulas of the central hexagon and the vertex hexagon. The specific prediction method is as follows (see Figure 1 ):

[0035] S1: Collect data. The data obtained through finite element simulation or experimental methods is used as the initial database for establishing the bionic self-similar hierarchical structure model. The initial database includes the common mechanical properties of materials, the properties of materials, and the parameter content related to loading conditions. In this embodiment, two materials, polylactic acid (PLA) and aluminum alloy, are respectively prepared, and the common mechanical properties of polylactic acid (PLA) and aluminum alloy are shown in Table 1;

[0036] Table 1

[0037] Common mechanical property attributes

[0038]

[0039] S2: Clean the data in the initial database; adjust the attribute parameters in the initial database in S1 through experiments and simulations, and clean and eliminate the data according to the influence on the final performance. Since the relationship between the attributes in the bionic self-similar hierarchical structure is not a strictly linear relationship, in order to explore the correlation between variables, it is necessary to use a non-linear BP neural network as the machine learning method of the present invention. As Figure 4 shown, since the BP neural network with a single hidden layer can approximate any continuous non-linear curve, thus completing a more comprehensive feature extraction of the data. If this step is omitted and the data with less or no correlation is not cleaned and eliminated, the accuracy of the model cannot be guaranteed.

[0040] S3: Regarding the performance influencing factors of the bionic self-similar hierarchical structure, the genetic algorithm is used to screen variables from the data in S2 to obtain the variables to be included in the subsequent model, and the screened variables are processed for their advantages and disadvantages according to the Pareto dominance idea; and the data after the advantages and disadvantages processing is used as the total database; since the data that has been cleaned cannot be determined whether it is helpful for performance prediction, it is necessary to screen out useful data from numerous variables; there are many performance influencing factors of the bionic self-similar hierarchical structure, and through experiments and simulations, it is proved that some selected influencing factors have no influence on the final performance prediction, and after making a simple model based on this structure, it is found that by reducing some variables, the generalization ability of the model is improved. On this basis, the genetic algorithm is selected for variable screening because this genetic algorithm is a global optimization search algorithm, and the mutation mechanism of the algorithm itself endows it with the ability to jump out of local extreme values, which will have a certain improvement on the performance and values generated by uncertain influencing factors during the process of predicting the performance of this structure. If this step is omitted and the cleaned data is directly substituted into the model, it will lead to overfitting of the final result, making the prediction effect within a certain numerical range not good, so variable screening is required. Since the expected final energy absorption index is a multi-objective optimization problem, and the target dimensions obtained from the structure database are different, it is difficult to directly determine the optimal solution by comparison like a single-objective optimization problem, so it is also necessary to use the Pareto dominance idea for evaluating the advantages and disadvantages of solutions to multi-objective problems, such as Figure 5 as shown, the solid dots represent the Pareto optimal solutions, and all the Pareto optimal solutions form the Pareto optimal solution set, and these solutions are mapped by the objective function to form the Pareto front in this embodiment. Since this embodiment is a two-objective problem, the optimal front is a line.

[0041] S4: The training data set and the test data set for establishing the BP neural network model are selected by a random method; since the non-linear relationship between the parameters of the bionic self-similar hierarchical structure is strong, as much data as possible is needed for fitting, and the data directly obtained through experiments and simulations is less. In order to make full use of the existing data, the ten-fold cross-validation method is used to select the training data set and the test data set. When selecting, the ten-fold cross-validation method divides the total database in S3 into ten groups, and randomly selects 80% of the data (that is, eight of them) as the training data set of the BP neural network, and the remaining 20% of the data (that is, the remaining two groups) as the test data set of the model; repeat this operation, and a total of 45 different training sets and their corresponding test sets are obtained; the training data set is used to determine the parameters of the BP neural network model and establish the model, and the test data set is used to evaluate the prediction effect of the subsequent established model.

[0042] S5: Establish a BP neural network model using all the training datasets obtained in S4 and their corresponding test datasets, for a total of 45 models. Each model is run 10 times because for models with random initial points, after running more than 10 times, the error will fluctuate around a certain value and it is difficult to further decrease. Determine the optimal weights and thresholds for each model through the R^2 results of model fitting in 10 runs; Use the ten-fold cross-validation method and the evaluation method combined with R^2 to determine the dataset selection method and the corresponding weights and thresholds for the optimal model among the 45 models;

[0043] S6: Determine the network parameters. The network parameters include the number of network layers, the number of network nodes, the activation function, and select a single hidden layer; Since a single-hidden-layer BP neural network can approximate any continuous non-linear curve, a single hidden layer is selected. The single hidden layer is selected according to the non-linear relationship in the bionic self-similar hierarchical structure, and the number of hidden layer nodes is determined by the formula for the number of hidden layer nodes. The formula for the number of hidden layer nodes is:

[0044]

[0045] Where: N h is the number of hidden layer nodes, N in is the number of input layer nodes. For a BP neural network, the number of input layer nodes is the number of input features, N out is the number of output layer nodes, and h is an adjustment constant that can be any one of 1 - 10. Different values of it will affect the training error.

[0046] According to the principle of rounding, data such as the number of nodes needs to be integerized during training. Compare its estimation accuracy and generalization ability to determine the optimal number of hidden layer nodes; Through experiments, in this embodiment, the finally determined number of nodes is set to 13, the target accuracy is 0.001, the maximum number of iterations is 1000, and the learning rate is 0.01. The final result is as Figure 6 shown. Perform a regression of the fitted values against the true values. The higher the goodness of fit, the better the fitting effect. In this embodiment, the goodness of fit has reached a good level (above 85%).

[0047] S7: Evaluate the prediction results of the already established neural network model using the test dataset; Apply the neural network model established based on the parameters in S6 to the test dataset divided in S4 for model verification, and compare the data in the actual test dataset obtained through experiments or simulations with the results predicted by the model. Evaluate the prediction ability of the model through the network training regression in the network model results, and the error remains within 15%. As Figure 7As shown, a relatively intuitive evaluation criterion for the model prediction results is that the value of R^2 has reached 94.055%, indicating that the prediction effect is relatively accurate.

[0048] S8: Evaluate the model prediction results in S7 using the correct rate evaluation formula; whether a single prediction is correct or not cannot correctly reflect the prediction performance of the model. The situation of multiple predictions must be examined; the correct rate evaluation formula is:

[0049]

[0050] Among them, R is the correct rate of the model prediction results, n is the number of correct tests, and the evaluation criterion for the number of correct times is that the difference between the value predicted by the model and the true value is within 10% is considered that the result predicted by the model is correct. N is the total number of tests. The model prediction results are evaluated using the correct rate evaluation formula, and the accuracy rate reaches more than 90%.

[0051] S9: Appropriately adjust the proportion of the selected random data to test the model results; when allocating the data proportion, adjust the proportion of the training data set and the test data set in S4, and change it to randomly select 90% or 70% as the training data set, and use the remaining 10% or 30% as the test data set, and repeat the above S5 to S8 for repeated calculations. By comparing the difference between the model prediction results and the actual results after the proportion change, the dependence degree of the model on the proportion is evaluated. In this embodiment, the fitting effect of the model obtained by the selected 80% proportion is the best.

[0052] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the embodiments of the present invention, and are not intended to limit them; although the embodiments of the present invention have been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A performance prediction method for a bionic self-similar hierarchical structure based on machine learning, characterized in that, It includes the following steps: S1: Collect data. The data obtained through finite element simulation or experimental methods is used as the initial database for establishing the bionic self-similar hierarchical structure model. The initial database includes the mechanical properties of materials. S2: Clean the data in the initial database. Adjust the attribute parameters in the initial database in S1 through experiments and simulations, and clean and eliminate the data according to the influence on the final performance. S3: Use the genetic algorithm to screen the variables in the data in S2, obtain the variables to be included in the subsequent model, process the advantages and disadvantages of the screened variables according to the Pareto dominance idea, and use the processed data as the total database. S4: Randomly select the training data set and test data set for establishing the BP neural network model. Use the ten-fold cross-validation method to divide the total database in S3 into ten groups, randomly select 80% of the data as the training data set of the BP neural network, and use the remaining 20% of the data as the test data set of the model. The training data set is used to determine the parameters of the BP neural network model and establish the model, and the test data set is used to evaluate the prediction effect of the subsequently established model. S5: Establish multiple BP neural network models through all the training data sets obtained in S4 and their corresponding test data sets, and each neural network model runs 10 times. Determine the optimal weight and threshold of each model through the R^2 result of the model fitting in 10 runs. Use the ten-fold cross-validation method and the evaluation method combined with R^2 to determine the data set selection method of the optimal model among multiple models and the corresponding weight and threshold. S6: Determine the network parameters. The network parameters include the number of network layers, the number of network nodes, the activation function, and select a single hidden layer. The formula for the number of hidden layer nodes is: Where: N h is the number of hidden layer nodes, N in is the number of input layer nodes. For a BP neural network, the number of input layer nodes is the number of input features, N out is the number of output layer nodes, and h is an adjustment constant that can be any one of 1 - 10; S7: Evaluate the prediction results of the established neural network model through the test data set. Apply the neural network model established based on the parameters in S6 to the test data set divided in S4 for model verification, and compare the data in the actual test data set obtained through experiments or simulations with the results predicted by the model. Evaluate the prediction ability of the model through the network training regression in the network model results. S8: Evaluate the model prediction results in S7 using the correct rate evaluation formula. The correct rate evaluation formula is: Where R is the correct rate of the model prediction results, n is the number of correct tests, and N is the total number of tests. S9: Appropriately adjust the proportion of the selected random data to test the model results. Adjust the proportion of the training data set and test data set in S4, and change it to randomly select 90% or 70% as the training data set, and use the remaining 10% or 30% as the test data set, and repeat the above S5 to S8 for repeated calculations to determine the difference between the model prediction results and the actual results, and evaluate the dependence of the model on the proportion.

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