Multi-objective topology optimization design of truss structures based on evidence theory under limited information

有限信息下基于证据理论的桁架结构多目标拓扑优化设计

¹ School of Civil Engineering, Architecture and Environment, Hubei University of Technology, Wuhan 430068, China
² College of Civil Engineering, Tongji University, Shanghai 200092, China

Received: 5 September 2022

Abstract

Uncertainty information is often limited and has great discreteness, how to ensure the structure having good robustness under epistemic uncertainty becomes a technical problem for multi-objective topology optimization design. In this paper, the evidence theory is used to quantify the epistemic uncertainty; the plausibility measurement expressing upper limit of failure probability is applied to be a new evaluation of reliability. The total weight and the reliability of structures are taken as the optimization objectives, and a multi-objective robust topology optimization design model based on evidence theory is proposed. Parallelization technique based differential evolution for multi-objective optimization (DEMO) is preferable to search above robust Pareto front due to its merits of non-requirement of any gradient and superior mechanisms of non-dominate strategy. In order to verify the effectiveness of the proposed method, the multi-objective reliability optimization of a wood truss structure is implemented with considering elastic modulus and structural load as uncertain variables. According to the optimization results, six same truss specimens are made for the static random loading test. The failure probability of the truss structure is judged by the stress and node displacement obtained from the test, so as to verify the feasibility of the reliability optimization method based on evidence theory. The experimental results also indicate that the proposed method can avoid the deviation of the optimization results caused by the fluctuation of epistemic uncertainty, and provide a new method for designers to make the optimization results robust even when the data information is insufficient and the cognitive level is limited.

摘要

不确定信息往往是缺乏的、具有较大的离散性, 如何在认知不确定性扰动下保证结构具有良好的稳健性成为多目标拓扑优化设计的技术难题。引入证据理论量化认知不确定, 采用基于失效似然度的失效概率区间上限建立新的可靠性指标, 将结构总质量和结构可靠性同时作为优化目标, 提出了基于证据理论的多目标拓扑优化设计模型。采用无需梯度信息且具有出色非支配策略的多目标并行化微分演化算法求解Pareto最优前沿。为了验证所提方法的有效性, 以木桁架结构为优化对象, 选取木材的弹性模量和结构荷载为不确定变量, 采用所提方法进行多目标拓扑优化。根据优化结果制作6榀相同的桁架试件进行随机静力加载试验, 通过试验所得的应力及节点位移判断桁架结构的失效概率, 以此验证基于证据理论的稳健性拓扑优化方法的可行性。试验结果表明, 基于证据理论的优化方法可以避免认知不确定波动造成的优化结果的偏差, 为设计人员提供了一种在考虑数据信息不充足、认知水平有限等情况下仍能使优化结果具有稳健性的新方法。