Abstract The solution of optimization problems with polymorphic uncertain data requires combining stochastic and non-stochastic approaches. The concept of uncertain a priori parameters and uncertain design parameters quantified by random variables and intervals is presented in this paper. Multiple runs of the nonlinear finite element model solving the structural mechanics with varying a priori and design parameters are needed to obtain a solution by means of iterative optimization algorithms (e.g. particle swarm optimization). The combination of interval analysis and Monte Carlo simulation is required for each design to be optimized. This can only be realized by substituting the nonlinear finite element model by numerically efficient surrogate models. In this paper, a multilevel strategy for neural network based surrogate modeling is presented. The deterministic finite element simulation, the stochastic analysis as well as the interval analysis are approximated by sequentially trained artificial neural networks. The approach is verified and applied to optimize the concrete cover of a reinforced concrete structure, taking the variability of material parameters and the structural load as well as construction imprecision into account.

中文翻译：

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多态不确定参数优化问题的多级代理建模方法

摘要 多态不确定数据优化问题的求解需要结合随机和非随机方法。本文提出了不确定的先验参数和不确定的设计参数的概念，这些参数由随机变量和区间量化。需要多次运行非线性有限元模型来求解具有变化的先验和设计参数的结构力学，以通过迭代优化算法（例如粒子群优化）获得解决方案。每个要优化的设计都需要区间分析和蒙特卡罗模拟的结合。这只能通过用数值有效的替代模型代替非线性有限元模型来实现。在本文中，提出了一种基于神经网络的代理建模的多级策略。确定性有限元模拟、随机分析以及区间分析由顺序训练的人工神经网络近似。该方法被验证并应用于优化钢筋混凝土结构的混凝土保护层，考虑材料参数和结构载荷的可变性以及施工不精确性。