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浙江大学学报(工学版)  2022, Vol. 56 Issue (9): 1815-1823    DOI: 10.3785/j.issn.1008-973X.2022.09.015
计算机与控制工程     
基于自适应采样的复杂模型全局近似
殷小亮(),钱承*()
嘉兴学院 信息科学与工程学院,浙江 嘉兴 314001
Global approximation of complex model based on adaptive sampling
Xiao-liang YIN(),Cheng QIAN*()
College of information science and engineering, Jiaxing University, Jiaxing 314001, China
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摘要:

针对复杂模型近似处理的问题,提出自适应采样结合曲面曲率的全局近似方法. 采用自适应设计域分割采样方法获取新增采样点,逐步提高源模型的响应面近似模型精度. 引入判定响应面近似模型精度,提出利用几何方法计算曲面曲率,并结合启发式直接搜索算法(DIRECT)搜索响应面模型上的最大曲率点及设计域最佳分割位置. 所提方法可以运用于其他响应面模型,并适合用于大设计域、大数据源模型的近似处理. 函数源模型及复杂电动车模型的近似处理测试结果表明,所提方法具有实用性和有效性.

关键词: 响应面方法自适应采样多项式响应面曲面曲率设计域分割    
Abstract:

A global approximation method combining adaptive sampling and surface curvature was proposed to deal with the problem of approximation processing of complex models. The adaptive design domain segmentation sampling method was used to obtain the new sampling points, and gradually improve the accuracy of the response surface approximation model of the source model. A method to determine the accuracy of the response surface approximation model was introduced, and a geometric method was proposed to calculate the surface curvature, and combined with the heuristic search algorithm (DIRECT) to search the maximum curvature point on the response surface model and the best segmentation position of the design domain. The proposed method can be applied to other response surface models and is suitable for the approximate processing of large design domain and large data source models. The approximate processing test results of function source model and complex pure electric vehicle model show that the proposed method is practical and effective.

Key words: response surface methodology    adaptive sampling    polynomial response surface    surface curvature    design domain segmentation
收稿日期: 2021-09-03 出版日期: 2022-09-28
CLC:  TP 391.9  
基金资助: 浙江省基础公益研究计划项目 (GF20E090020)
通讯作者: 钱承     E-mail: 407392952@qq.com;qc117@sina.com
作者简介: 殷小亮(1982—),男,讲师,博士,从事模型近似处理、多领域建模及半物理仿真研究. orcid.org/0000-0001-9011-2193. E-mail: 407392952@qq.com
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引用本文:

殷小亮,钱承. 基于自适应采样的复杂模型全局近似[J]. 浙江大学学报(工学版), 2022, 56(9): 1815-1823.

Xiao-liang YIN,Cheng QIAN. Global approximation of complex model based on adaptive sampling. Journal of ZheJiang University (Engineering Science), 2022, 56(9): 1815-1823.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.09.015        https://www.zjujournals.com/eng/CN/Y2022/V56/I9/1815

图 1  利用ASCGA进行的设计域前2次迭代分割过程
图 2  基于ASCGA的全局近似流程图
算例编号 δ1 δ2 δ3
1) 0.2 10?3 10?3
2) 0.2 10?3 10?3
3) 0.2 10?3 10?3
4) 0.1 10?3 10?3
表 1  模型参数及ASCGA参数设定
S R1 R2 R3 R4
LHCS ASRS ASCGA LHCS ASRS ASCGA LHCS ASRS ASCGA LHCS ASRS ASCGA
25 27.471 25.535 25.498 0.178 0.107 0.106
50 23.707 9.8004 7.8934 0.128 0.044 0.044
75 17.608 5.7585 5.6250 0.066 0.040 0.027
100 14.416 2.9364 2.9280 0.058 0.029 0.023 3.378 5.279 6.3039 1.136 1.294 1.1825
125 12.511 1.8283 1.7880 0.045 0.013 0.011
150 7.1561 1.4775 1.5980 0.024 0.010 0.009
200 2.847 3.430 3.553 0.986 1.132 0.905 0
300 2.283 2.877 2.934 0.859 1.584 0.843 0
400 2.138 2.422 2.102 0.760 1.338 0.768 0
500 1.618 1.994 1.515 0.703 1.330 0.700 0
表 2  在不同采样数量情况下3种方法构造的函数近似模型精度对比
R1 T1 R2 T2 R3 T3 R4 T4
LHCS ASRS ASCGA LHCS ASRS ASCGA LHCS ASRS ASCGA LHCS ASRS ASCGA
20 48 42 44 0.10 61 28 25 6 <10 89 109 1.5 43 68 55
15 51 49 47 0.05 117 41 43 5 <10 110 138 1.0 137 失败 144
10 144 55 51 0.03 138 88 68 4 <10 151 161 0.8 362 失效 314
5 182 86 90 0.02 166 103 106 3 166 256 244 0.5 826 失效 739
2 325 131 118 2 452 488 441
表 3  在不同精度情况下3种方法构造函数近似模型的效率对比
图 3  利用ASCGA方法对GF函数源模型的近似处理(采样数为100)
图 4  利用ASCGA方法对Schaffer’s函数源模型的近似处理(采样数为150)
图 5  电动车仿真模型
图 6  轻型车辆行驶工况FTP75
图 7  仿真模型的3个状态
图 8  仿真模型的独立仿真模块
图 9  独立仿真模块中的状态变量处理
图 10  车辆模型的独立仿真模块
图 11  在电动车上验证近似模型精度
图 12  在相同工况下不同模型的仿真结果对比
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