Bayesian optimization for robust design of steel frames with joint and individual probabilistic constraints
Bayesian optimization for robust design of steel frames with joint and individual probabilistic constraints
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DOI：
10.1016/j.engstruct.2021.112859
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发表时间：
2021-10
影响因子：
5.5
通讯作者：
B. Do;M. Ohsaki;M. Yamakawa
中科院分区：
文献类型：
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作者：
B. Do;M. Ohsaki;M. Yamakawa
提出了一种贝叶斯优化(BO)方法，用于解决外载荷和材料性能不确定性下钢框架的多目标稳健设计优化(RDO)问题。建立了考虑框架到达崩溃状态的两种不同方式的联合和个体概率约束RDO问题。每个问题涉及三个相互冲突的目标函数，即框架的总质量、最大层间位移的均值和方差。由于这两个问题的不确定目标和概率约束函数在有限元分析程序中都是隐含的，而概率约束的计算是一个NP-Hard问题，因此使用BO来指导优化过程在迭代完成后获得更好的解，并在迭代结束时提供一组接近Pareto最优解。具体地说，被称为高斯过程(GP)的贝叶斯回归模型用作结构响应的替代模型。然后针对这两个RDO问题建立了两个获取函数，并将这些函数的最大化问题表示为一个混合整数非线性规划(MINLP)问题。设计了一种新的随机搜索和模拟退火法相结合的方法来解决MINLP问题，从而在输入变量空间中找到最有希望的点，使当前解的改进机会最大化，并在BO开始新的迭代之前对GP模型进行改进。一个测试问题和两个设计实例表明，该方法可以在20次迭代中找到RDO问题的精确解或良好的Pareto最优解。
This work proposes a Bayesian optimization (BO) method for solving multi-objective robust design optimization (RDO) problems of steel frames under aleatory uncertainty in external loads and material properties. Joint and individual probabilistic constrained RDO problems are formulated to consider two different ways the frame reaches its collapse state. Each problem involves three conflicting objective functions, namely, the total mass of the frame, the mean and variance of the maximum inter-story drift. Since the uncertain objective and probabilistic constraint functions of both problems are implicit within a finite element analysis program and the computation of the probabilistic constraints is an NP-hard problem, BO is used to guide the optimization process toward better solutions after it completes an iteration and offers a set of near Pareto-optimal solutions when it terminates. Specifically, Bayesian regression models called Gaussian processes (GPs) serve as surrogates for the structural responses. Two acquisition functions are then developed for the two RDO problems and a maximization problem of these functions is formulated as a mixed-integer nonlinear programming (MINLP) problem. A new random search coupled with simulated annealing is devised to solve the MINLP problem, thereby locating the most promising point in the input variable space at which the current solutions maximize their chance to be improved and the GP models are refined before the BO starts a new iteration. A test problem and two design examples show that exact or good Pareto-optimal solutions to the RDO problems can be found by the proposed method with 20 iterations.