Iterative Global Sensitivity Analysis Algorithm with Neural Network Surrogate Modeling
Iterative Global Sensitivity Analysis Algorithm with Neural Network Surrogate Modeling
复制标题
神经网络代理建模的迭代全局敏感性分析算法
DOI：
10.1007/978-3-030-77970-2_23
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Pietrenko-Dabrowska, A.
中科院分区：
文献类型：
--
作者：
Liu, Y.C.;Nagawkar, J.;Leifsson, L.;Koziel, S.;Pietrenko-Dabrowska, A.
全局灵敏度分析（GSA）是一种量化输入参数对物理系统输出影响的方法。由于每个单独的基于物理的模型的高计算成本、大量输入参数以及需要执行重复的模型评估的综合影响，执行GSA可能具有挑战性。为了降低这种成本，神经网络（NN）被用来取代昂贵的物理模型在这项工作中。这引入了额外的挑战，即找到准确训练NN所需的最小数量的训练数据样本。在这项工作中，引入了一种新的方法，通过迭代训练NN所需的样本数量（使用外环灵敏度收敛标准终止）和计算GSA所需的模型响应数量（使用内环灵敏度收敛标准终止）来精确量化GSA值。基于迭代代理的GSA保证了Sobol指数的收敛值，同时，简化了代理模型的任意精度度量的规范。所提出的方法被证明在两种情况下，即，一个八变量钻孔功能和三变量无损检测（NDT）的情况下。对于钻孔函数，一阶和全阶Sobol'指数分别需要200和个数据点终止于外环和内环灵敏度收敛准则。对于NDT的情况下，这些值均为100的第一和总阶指数外环灵敏度收敛，和和内环灵敏度收敛，分别为第一和总阶指数，内环灵敏度收敛。所提出的方法与GSA对真函数的差异在分析情况下小于3%，在基于物理的情况下小于10%（其中大的误差来自小的Sobol指数）。
Global sensitivity analysis (GSA) is a method to quantify the effect of the input parameters on outputs of physics-based systems. Performing GSA can be challenging due to the combined effect of the high computational cost of each individual physics-based model, a large number of input parameters, and the need to perform repetitive model evaluations. To reduce this cost, neural networks (NNs) are used to replace the expensive physics-based model in this work. This introduces the additional challenge of finding the minimum number of training data samples required to train the NNs accurately. In this work, a new method is introduced to accurately quantify the GSA values by iterating over both the number of samples required to train the NNs, terminated using an outer-loop sensitivity convergence criteria, and the number of model responses required to calculate the GSA, terminated with an inner-loop sensitivity convergence criteria. The iterative surrogate-based GSA guarantees converged values for the Sobol’ indices and, at the same time, alleviates the specification of arbitrary accuracy metrics for the surrogate model. The proposed method is demonstrated in two cases, namely, an eight-variable borehole function and a three-variable nondestructive testing (NDT) case. For the borehole function, both the first- and total-order Sobol’ indices required 200 anddata points to terminate on the outer- and inner-loop sensitivity convergence criteria, respectively. For the NDT case, these values were 100 for both first- and total-order indices for the outer-loop sensitivity convergence, andandfor the inner-loop sensitivity convergence, respectively, for the first- and total-order indices, on the inner-loop sensitivity convergence. The differences of the proposed method with GSA on the true functions are less than 3% in the analytical case and less than 10% in the physics-based case (where the large error comes from small Sobol’ indices).
影响因子：
2.7
作者：
Kennedy, MC;O'Hagan, A
通讯作者：
O'Hagan, A