标题： 考虑输入分布不确定性的桁架分布鲁棒合规性优化的二阶锥规划 显示英文标题

标题： Second-order cone programming for distributionally robust compliance optimization of trusses considering input distribution uncertainty

摘要： 基于可靠性的设计优化（RBDO）是一种在假设输入分布完全已知的情况下，考虑不确定性进行结构设计的方法。 在实际工程中，输入数据的数量通常有限，这可能损害RBDO获得的最优结果的有效性。 为了考虑输入分布的不确定性，提出了基于置信度的设计优化（CBDO）方法。 然而，这种方法在处理高度非线性的性能约束时面临计算成本和精度的挑战。 本文研究了具有不确定外部载荷的桁架结构的柔度最小化问题。 借助先进的风险度量工具——条件风险价值（CVaR），我们构建了一个双目标优化问题，以解决柔度的最坏情况期望值和最坏情况CVaR，这使我们能够考虑CBDO未解决的性能函数尾部风险。 采用核密度估计来估计输入分布，可以消除对输入分布建模的需求。 我们证明，当采用均匀核或三角核时，该问题可简化为二阶锥规划问题。 最后，通过数值实验，我们获得了桁架结构柔度的最坏情况期望值和CVaR双目标优化问题的Pareto前沿，并验证了Pareto解的变化。 显示英文摘要

摘要： Reliability-based design optimization (RBDO) is a methodology for designing structures under the consideration for uncertainty with the assumption that the input distribution is completely known. In practical engineering, the number of input data is often limited, which can damage the validity of the optimal results obtained by RBDO. Confidence-based design optimization (CBDO) has been proposed to account for the uncertainty of the input distribution. However, this approach faces challenges, computational cost and accuracy when dealing with highly nonlinear performance constraints. In this paper, we consider the compliance minimization problem of truss structures with uncertain external forces. Armed with the advanced risk measure, conditional Value-at-Risk (CVaR), we formulate a bi-objective optimization problem for the worst-case expected value and the worst-case CVaR of compliance, which allows us to account for the tail risk of performance functions not addressed in CBDO. Employing kernel density estimation for estimation of the input distribution allows us to eliminate the need for modeling the input distribution. We show that this problem reduces to a second-order cone programming when assigning either uniform kernel or triangular kernel. Finally, through numerical experiments, we obtain the Pareto front for the bi-objective optimization problem of the worst-case expected value and CVaR of compliance of truss structures, and confirm the changes in the Pareto solutions.