比例-积分-微分控制算法求解结构拓扑优化问题

王文玥; 赵清海; 张洪信; 张铁柱; 袁林; 李信卿; 王新亮

doi:10.13433/j.cnki.1003-8728.20200058

比例-积分-微分控制算法求解结构拓扑优化问题

doi: 10.13433/j.cnki.1003-8728.20200058

王文玥^1,,
赵清海^{1, 2, ,},
张洪信²,
张铁柱²,
袁林¹,
李信卿¹,
王新亮³

1.
青岛大学机电工程学院，山东青岛　266071
2.
青岛大学电动汽车智能化动力集成技术国家地方联合工程研究中心，山东青岛　266071
3.
山东凯马汽车制造有限公司，山东潍坊　262700

基金项目: 国家自然科学基金项目（51705268）与中国博士后科学基金面上项目（2017M612191）

详细信息

作者简介:
王文玥（1993−），硕士研究生，研究方向为车辆节能减排与新能源技术，wwyue617@163.com

通讯作者:
赵清海，讲师，博士，zqhbit@163.com

中图分类号: TH122
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- 文章访问数: 297
- HTML全文浏览量: 91
- PDF下载量: 35
- 被引次数: 0
出版历程
- 收稿日期: 2019-11-06
- 刊出日期: 2021-02-02

Proportional-integral-differential Control Method on Solving Structural Topology Optimization Problems

1.
Mechanical and Electrical College, Qingdao University, Qingdao 266071, Shandong, China
2.
National and Local Union Engineering Research Center of Electric Vehicle Intelligent Power Integration Technology, Qingdao University, Qingdao 266071, Shandong, China
3.
Kama Automobile Company, Weifang 262700, Shandong, China

摘要

摘要: 拓扑优化具有设计变量多、目标性能与约束条件为设计变量的非线性、非单调隐式函数的特征，计算效率值得商榷。因此探索高效稳定的求解方法是结构拓扑优化的核心问题。提出一种基于PID控制算法的拓扑优化求解方法，采用固体各向同性微结构材料惩罚模型（SIMP）方法建立单工况条件下质量约束条件下结构柔度最小化拓扑优化模型，推导出基于PID法的设计变量迭代格式，引入基于Helmholtz偏微分方程的过滤方式抑制出现的数值不稳定问题，并将所提方法扩展到两类多工况结构拓扑优化问题，通过与优化准则法（Optimality criteria, OC）和移动渐近线法（Method of moving asymptotes，MMA）进行数值结果比较可知，PID控制方法具有设置简便、高效求解、收敛稳定且无需梯度信息的优点。
- 拓扑优化 /
- PID控制 /
- SIMP模型 /
- 非梯度
Abstract: Under the inherent characteristics of nonlinear and non-monotonic implicit function with tremendous design variables, the corresponding computational efficiency of topology optimization must be considered. Therefore, the kernel question is to explore efficient and stable solution strategy. The solution methodology based on the proportional-integral-differential (PID) control algorithm is proposed, under the solid isotropic microstructures material penalty (SIMP) model. The structural compliance minimization topology optimization model under the condition of single working condition is established. The iterative format of the design variables of PID algorithm is illustrated, and the filter method of Helmholtz partial differential equation is introduced to suppress the numerical instability problem. Then the proposed method is extended to the multi-loading condition topology optimization problems. Through the comparison of the optimization criteria method (OC) and the moving asymptote method (MMA), the numerical results demonstrated that the PID method exhibits the property of easy implementation, efficient solution, stable convergence and non-gradient information.
- topology optimization /
- PID control /
- SIMP model /
- non-gradient

HTML全文

图 1 PID控制原理图

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图 2 悬臂梁结构设计区域

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图 3 采用PID法获得结构拓扑优化构型

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图 4 悬臂梁结构柔度与体积约束迭代曲线

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图 5 米歇尔结构设计区域

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图 6 采用PID法获得多工况结构拓扑优化构型

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图 7 多工况结构拓扑优化目标函数迭代过程

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表 1 单工况条件下结构柔度最小值与最大值

方法	F₁			F₂			F₃
方法	C_min	C_max	迭代次数	C_min	C_max	迭代次数	C_min	C_max	迭代次数
PID	23.7787	221.6250	73	3235.3469	25519.7488	21	23.7787	221.6250	73
OC	23.6413	221.6250	187	3227.9401	25519.7488	27	23.6413	221.6250	187
MMA	23.6303	221.6250	387	3221.3308	25519.7488	106	23.6290	221.6250	387

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