A ship type optimization method based on partitioned hybrid proxy model

Abstract

The application discloses a ship type optimization method based on a partitioned hybrid proxy model, and aims at parameter optimization of an engineering problem; two-stage partition of an engineering parameter sample space is completed through I-DBSCAN clustering and Voronoi geometric division; sample balance is realized in combination with a Monte Carlo method and an improved SMOTE algorithm; adaptive sampling optimization is performed on a global Kriging model based on a G-EBM, local RBF models are constructed for each subspace, model weights are determined through error reciprocal weighting and boundary distance smoothing, the prediction results of the local RBF and global Kriging models are fused, and high-precision parameter analysis and optimization of the engineering problem are realized. The method solves the problems of unreasonable partition of the engineering parameter sample space, uneven sample distribution and large boundary prediction error, greatly improves the efficiency and precision of parameter optimization of the engineering problem, and is especially suitable for complex ship engineering parameter design scenes such as ship type optimization.

Description

Technical Field

[0001] This invention relates to the field of surrogate model technology, specifically to a ship shape optimization method based on a partitioned hybrid surrogate model, applicable to expensive optimization problems such as automobile collision safety optimization, aircraft airfoil optimization, and spacecraft optimization. Background Technology

[0002] Engineering optimization design and analysis often rely on physical experiments to obtain data, which has drawbacks such as long design cycles and high experimental costs. Although numerical simulation technology is gradually replacing physical experiments, its application is limited by its high time cost for expensive optimization problems. Surrogate model technology can replace the real model for optimization calculations by constructing a mapping relationship between design variables and objective functions. Commonly used surrogate models include Kriging models, radial basis function (RBF) models, and neural networks.

[0003] Existing surrogate models are divided into two categories: global surrogate models and local surrogate models. Global models excel at capturing overall trends, while local models focus on detailed fitting. However, a single model cannot adequately address both global and local needs. Hybrid surrogate models, by combining the advantages of different models, have become a research hotspot. However, existing hybrid models suffer from the following shortcomings: First, local modeling accuracy is unstable. Multi-region divisions lack correlation with subspace error distributions, and imbalanced sample distribution leads to poor local fitting results. Second, global sampling efficiency is low. Traditional sampling strategies cannot accurately identify error extreme value regions, resulting in high sampling costs. Third, global-local modeling synergy is poor. Weight allocation relies on fixed formulas, leading to a disconnect between sample optimization and model updates, and the risk of abrupt changes in predicted values ​​at the boundary. Summary of the Invention

[0004] This method is applicable to parameter analysis and optimization design of various complex engineering problems, especially for multi-parameter, high-dimensional, and nonlinear ship engineering problems such as hull form optimization. It enables reasonable partitioning, accurate sampling, and efficient prediction of hull form parameter samples, providing data support and model references for the optimization design of performance indicators such as hull resistance, speed, and stability. The core of this method is two-stage partitioning and adaptive error balancing. Through multi-model fusion, it achieves high-precision prediction of engineering parameters, ultimately serving the parameter optimization goal of the engineering problem. The following detailed implementation process of this method is illustrated using a hull form optimization engineering problem as a specific example. To achieve the above objectives, this invention adopts the following technical solution: A ship hull optimization method based on a partitioned hybrid agent model includes the following steps: 1. Two-stage partitioning and sample balancing based on I-DBSCAN and Voronoi (1) Initial sample generation and clustering Using the design variables for hull form optimization as the dimension, an initial sample set of hull form parameters is generated using Latin Hypercube Design (LHS). Each sample in the set corresponds to a combination of hull form parameters, and each parameter meets the specifications for ship design. The I-DBSCAN density clustering algorithm is used to partition the initial sample set of hull form parameters into clusters, automatically determining the cluster neighborhood radius and minimum sample number parameters: a real symmetric distance matrix of hull form samples is constructed, the distance values ​​in each row are sorted in ascending order, the k-th distance value is extracted and assumed to follow a Poisson distribution, and the cluster neighborhood radius is calculated based on maximum likelihood estimation; the number of samples in the neighborhood of each hull form sample point is counted, and the expected value is calculated as the minimum sample number. Through the above clustering partitioning, the hull form parameter sample space is divided into several clusters with similar hull form parameter characteristics.

[0005] (2) Voronoi geometric partitioning and misclassified sample adjustment Using cluster core points (core ship type parameter samples) as generators, a Voronoi geometric partition is performed on the ship type parameter sample space to obtain several ship type parameter subspaces. Each subspace corresponds to the design range of a class of ship type parameters. The matching degree between each Voronoi subspace and the original I-DBSCAN cluster is verified to determine whether there are "misclassified samples" of ship type parameters, that is, the cluster affiliation of the sample is inconsistent with the subspace affiliation. For these samples, a symmetric transformation is used to adjust them so that the adjusted ship type parameter samples are accurately assigned to the corresponding Voronoi subspaces, ensuring the rationality of the ship type parameter subspace partition.

[0006] (3) Subspace sample balancing process The Monte Carlo method is used to approximate the hypervolume of each ship type parameter subspace. Combined with the design requirements of ship type optimization, the target number of samples for each subspace is calculated. For dense subspaces (subspaces with too many ship type parameter samples, such as the parameter range of conventional cargo ships), a sample distance matrix is ​​constructed, and the nearest neighbor distance for each sample is calculated using the formula... Calculate the spatial value index and delete redundant samples in ascending order of the index. For sparse subspaces, use the improved SMOTE algorithm with Voronoi constraints to generate candidate samples on the nearest neighbor lines of the samples. Verify whether the candidate samples are located in the target subspace. If not, halve the interpolation step size and regenerate until the constraint conditions are met, thus completing the sample supplementation.

[0007] Through the above operations, sample balance is achieved in the subspace of each ship type parameter, ensuring sample coverage for different ship type parameter ranges.

[0008] 2. Adaptive Sampling Optimization of Global Kriging Model Based on G-EBM This step uses ship performance indicators (such as total resistance coefficient, speed performance, etc.) as prediction targets, constructs a global Kriging model based on a sample set of ship parameters, and improves the model's global prediction accuracy of ship performance through adaptive sampling optimization.

[0009] (1) Error extreme point identification Based on the initial sample set of ship type parameters before balancing, a global Kriging model with ship type performance indicators as output is constructed. The leave-one-out method is used to calculate the ship type performance prediction error for each ship type parameter sample point. According to the numerical distribution of the prediction error, the extreme error points (i.e., the sample points with the largest ship type performance prediction error) are selected. These points correspond to the weak areas predicted by the model in the design of ship type parameters.

[0010] (2) Construction of hypercubic domain Let the dimension of the ship type parameter sample space be d (e.g., ship length, ship width, depth, and draft are 4-dimensional). Calculate the Euclidean distance between the error extreme point and the nearest 2d neighbor ship type samples to determine the side length of the hypercube neighborhood: Calculate the minimum distance between the error extreme point and the nearest neighbor sample in each ship type parameter dimension, and take this distance as half the side length of the hypercube. Construct an anisotropic hypercube centered on the error extreme point. This hypercube is within the reasonable design range of the ship type parameters.

[0011] (3) Adaptive sampling and model update Within the aforementioned hypercubic domain, LHS is used to generate candidate sample points for ship type parameters. The parameter combinations of the candidate sample points all meet the ship design specifications. The candidate point with the greatest Euclidean distance from the error extreme point is selected as a new ship type parameter sample. It is added to the global sample set and the ship type parameter sample library is updated. Based on the updated sample set, the global Kriging model is reconstructed to improve the global prediction accuracy of the model for ship type performance.

[0012] 3. Construction of a hybrid proxy model integrating local RBF and global Kriging This step constructs a multi-model fusion prediction system based on the balanced hull parameter subspace sample set, achieving high-precision prediction of hull performance indicators and providing direct basis for hull optimization design.

[0013] (1) Construction of local and global models and calculation of GMSE Based on the balanced sample sets of ship type parameter subspaces, a local RBF model with ship type performance indices as output is constructed for each Voronoi subspace. The generalized cross-validation error of each local RBF model in the corresponding subspace is calculated using the leave-one-out method. Simultaneously, based on the updated global sample set, the generalized cross-validation error of the global Kriging model is calculated. .

[0014] (2) Dynamic weight calculation For any point to be predicted, its Voronoi subspace is determined by nearest neighbor search; the initial weights are calculated using the inverse error weighting method, as shown in the formula: , ,in Pick To avoid the denominator being 0, the initial weights are normalized to ensure that the sum of the weights is 1.

[0015] (3) Boundary smoothing When the combination of ship morphology parameters to be predicted is located near the boundary of the ship morphology parameter subspace, i.e., the distance to the perpendicular bisector of the line connecting the core points of adjacent subspaces is less than 5%-10% of the average side length of the subspace, the local GMSE of adjacent subspaces is fused, and the smoothed initial weights are calculated using a distance-weighted method, as follows: ,in , These are the distances from the point to be predicted to the core points of the two subspaces, respectively. , The GMSEs are for the local models of the two subspaces respectively; the weights are recalculated based on the smoothed GMSEs to avoid abrupt changes in the ship performance prediction results.

[0016] (4) Hybrid model prediction The predicted values ​​of the local RBF model and the global Kriging model are weighted and summed based on the final weights to obtain the final prediction result of the hybrid surrogate model. The formula is as follows: . Attached Figure Description

[0017] Figure 1 Flowchart for handling sample misclassification; Figure 2 This is a schematic diagram of a two-stage partitioning strategy; Figure 3 A supplementary schematic diagram for sample points in sparse regions; Figure 4 A schematic diagram of the G-EBM sampling method; Figure 5 A schematic diagram illustrating the process of building a hybrid agent model; Figure 6 The prediction accuracy of the method presented in this paper is compared with that of the comparative model. Detailed Implementation

[0018] To make the objectives, technical solutions, and effects of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0019] To verify the applicability and effectiveness of this method in engineering problems, a comparative experiment was conducted using bulk carrier optimization as the specific experimental object to verify the prediction accuracy and optimization effect of this method.

[0020] 1. Experimental setup (1) Design variables: The length L, breadth B, molded depth D, and design draft T of the bulk carrier are selected as optimization design variables, and the value range of each variable meets the "Rules for Classification of Steel Seagoing Ships"; (2) Prediction target: The total resistance coefficient of bulk carriers is the core prediction target. The smaller the total resistance coefficient, the better the speed performance of the ship type. (3) Comparison Model: This method is compared with the single Kriging model, the single RBF model, and the mixed model without sample balancing. All models are based on the same initial ship type parameter samples.

[0021] 2. Experimental Procedure (1) The initial bulk carrier parameter sample set (sample size 80) is generated using LHS. The two-stage partitioning and sample balancing are completed using this method, and finally the balanced sample set (sample size 100) is obtained. (2) The total resistance coefficient prediction model of the ship type was constructed by using this method and the comparative model respectively. The GMSE and mean absolute error (MAE) of each model were calculated by using the leave-one-out method to evaluate the prediction accuracy of the model. (3) Based on the prediction results of each model, the parameters of the bulk carrier are optimized by the genetic algorithm to obtain the optimal combination of ship type parameters corresponding to each model. The actual total resistance coefficient of the optimal ship type is verified by the ship model towing test, and the optimization effect of the model is evaluated.

[0022] (III) Experimental Results and Analysis Prediction accuracy analysis: The GMSE of the hybrid model constructed by this method is 0.0021 and the MAE is 0.0015, both of which are significantly lower than those of the single Kriging model (GMSE=0.0058, MAE=0.0042), the single RBF model (GMSE=0.0045, MAE=0.0031), and the hybrid model without sample balancing (GMSE=0.0033, MAE=0.0024). This indicates that the method significantly improves the prediction accuracy of ship performance indicators through sample balancing and multi-model fusion. Optimization effect analysis: Based on the parameter combination of the bulk carrier optimized by this method, the actual total resistance coefficient was 0.0189 after towing test of the ship model, which is 12.3% lower than the original ship type. In comparison, the total resistance coefficient of the ship type after optimization was reduced by 5.8% (single Kriging), 7.2% (single RBF), and 9.5% (mixed model without sample balancing), respectively. This shows that this method can more accurately capture the nonlinear relationship between ship type parameters and performance indicators, and provide a more reliable basis for ship type optimization. Engineering efficiency analysis: By deleting redundant samples and supplementing sparse samples, this method reduces the amount of invalid ship model tests and calculations. Compared with traditional methods, the overall cycle of ship optimization is shortened by more than 30%, which greatly improves the implementation efficiency of ship optimization engineering problems.

[0023] This embodiment uses ship hull optimization engineering problems as a specific application scenario. This method is also applicable to parameter analysis and optimization design of other complex engineering problems such as aerospace, mechanical manufacturing, and civil engineering. It can achieve high-precision parameter prediction and efficient optimization for various engineering problems and has broad engineering application value.

Claims

1. A ship type optimization method based on a partitioned hybrid agent model, characterized in that: 1.1 Two-stage partitioning and sample balancing based on I-DBSCAN and Voronoi: 1.1.1 Taking the design variables of ship morphology optimization as the dimension, the Latin Hypercube Design (LHS) is used to generate an initial sample set of ship morphology parameters. Each sample in the sample set corresponds to a set of ship morphology parameter combinations, and each parameter meets the specifications of ship design. The initial sample set is divided into clusters by the I-DBSCAN density clustering algorithm, and the clustering neighborhood radius and minimum number of samples are automatically determined. 1.1.2 Using the cluster core points as generators, the sample space of ship type parameters is partitioned using Voronoi geometry to obtain several subspaces; the matching degree between the subspaces and the original clusters is verified, and "misclassified samples" are adjusted through symmetric transformation; 1.1.3 The Monte Carlo method is used to approximate the hypervolume of each ship type parameter subspace. Combined with the design requirements of ship type optimization, the target sample number of each subspace is calculated. (1) For dense subspaces, i.e., subspaces with too many ship type parameter samples, redundant samples are removed by constructing a sample distance matrix and calculating a spatial value index. The spatial value index calculation formula combines the nearest neighbor distance of ship type samples, where... For the first The nearest neighbor distance for each ship type sample and These are the minimum and maximum nearest neighbor distances for all ship type samples within the dense subspace, respectively. Redundant ship type samples with low spatial value index are removed to reduce invalid computation. (2) For sparse subspaces, i.e. subspaces with too few ship type parameter samples, the SMOTE improved algorithm with Voronoi constraints is used to supplement the samples. The supplemented samples all satisfy the ship type parameter constraints of the corresponding subspace. 1.2 Adaptive Sampling Optimization of Global Kriging Model Based on G-EBM 1.2.1 Based on the initial sample set of ship type parameters before balancing, a global Kriging model with ship type performance index as output is constructed. The leave-one-out method is used to calculate the prediction error of each sample point and screen out the error extreme points. 1.2.2 Let the dimension of the ship type parameter sample space be d (e.g., ship length, ship width, molded depth, and draft are 4-dimensional). Calculate the Euclidean distance between the error extreme point and the nearest 2d neighbor ship type samples to determine the side length of the hypercube neighborhood: Calculate the minimum distance between the error extreme point and the nearest neighbor sample in each ship type parameter dimension, and take this distance as half the side length of the hypercube. Construct an anisotropic hypercube centered on the error extreme point. This hypercube is within the reasonable design range of the ship type parameters. 1.2.3 In the above hypercubic domain, LHS is used to generate candidate sample points for ship type parameters. The parameter combinations of the candidate sample points all meet the ship design specifications. The candidate point with the greatest Euclidean distance from the error extreme point is selected as the new ship type parameter sample. It is added to the global sample set and the ship type parameter sample library is updated. The global Kriging model is reconstructed based on the updated sample set to improve the global prediction accuracy of the model for ship type performance. 1.3 Construction of a Hybrid Proxy Model Integrating Local RBF and Global Kriging 1.3.1 Based on the balanced sample set of each ship type parameter subspace, a local RBF model is constructed for each subspace. Each local RBF model corresponds to the performance prediction of a specific range of ship type parameters. The generalized cross-validation error (GMSE) of each local RBF model and the GMSE of the global Kriging model are calculated by leave-one-out method. The smaller the GMSE value, the higher the accuracy of the model in predicting ship type performance. 1.3.2 For any combination of ship morphology parameters to be predicted (i.e., a new ship morphology design scheme), the Voronoi ship morphology parameter subspace to which it belongs is determined through nearest neighbor search. The initial weights of the local RBF model and the global Kriging model in this subspace are calculated using the inverse error weighting method. The calculation formula is as follows: Where ε is a local minimum (taken as 3) to avoid a denominator of 0, GMSE_RBF is the GMSE of the corresponding subspace local RBF model, and GMSE_Kriging is the GMSE of the global Kriging model. The initial weights are normalized to ensure that the sum of the weights is 1. 1.3.3 When the ship type parameter combination to be predicted is located near the boundary of the ship type parameter subspace, that is, the distance between the ship type parameter combination and the adjacent subspace is less than the set threshold, the GMSE of the local RBF model of the adjacent subspace is fused, and the initial weight after smoothing is calculated by distance weighting. The closer the adjacent subspace is, the higher its GMSE weight ratio. This method eliminates the weight abrupt phenomenon at the subspace boundary and avoids the ship type performance prediction result from jumping. 1.3.4 Based on the smoothed final weights, the predicted ship performance values ​​of the local RBF model and the global Kriging model are weighted and summed to obtain the final prediction result of the hybrid model. This result is the predicted performance index (resistance, speed, etc.) corresponding to the parameter combination of the ship type to be predicted. Based on this prediction result, the parameter combination with the optimal ship performance can be selected to complete the ship type optimization design.

2. The method according to claim 1, characterized in that, The parameters of the I-DBSCAN density clustering algorithm described in 1.1.1 are determined as follows: a sample real symmetric distance matrix is ​​constructed, the distance values ​​in each row are sorted in ascending order, the k-th distance value is extracted and assumed to follow a Poisson distribution, and the clustering neighborhood radius is solved based on maximum likelihood estimation; the number of samples in the neighborhood of each sample point is counted, and the expected value is calculated as the minimum number of samples.

3. The method according to claim 1, characterized in that, The formula for calculating the spatial value index mentioned in section 1.1.3 is as follows: ,in Let i be the nearest neighbor distance. and These are the minimum and maximum nearest neighbor distances for all samples within the dense subspace, respectively.

4. The method according to claim 1, characterized in that, The method for determining the side length of the hypercube described in 1.2.2 is as follows: calculate the minimum distance between the error extreme point and the nearest neighbor sample in each dimension, and take this distance as half of the side length of the hypercube.

5. The method according to claim 1, characterized in that, The formula for calculating the initial weights described in section 1.3.2 is as follows: , ,in This is a local minimum value, used to avoid a denominator of 0.

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