In the early stage of exploring a complex system, a preliminary experiment is used to capture the key characteristics of the model. Symmetrical global sensitivity analysis (SGSA) is one such experiment that explores the symmetrical structure of model by decomposing the model into independent symmetric functions. However, the existing experimental plans for SGSA rely on deterministic computational models that produce unique values of outputs when executed for specific values of inputs. In this paper, the problem of designing experiments for non-parametric SGSA is considered. Here the phrase “non-parametric” refers to model outputs containing random errors. The main result in the paper shows that a symmetrical design with certain constraints achieves A-optimum for the estimation of each output element function, and guarantees the superiority of the SGSA result. The statistical properties of non-parametric SGSA based on the optimal designs are further discussed, showing that the non-influential sensitivity indices can be estimated with low bias and volatility. Two explicit structures of the optimal designs are obtained. The optimality of the derived design is validated by simulation in the end.

在探索复杂系统的早期阶段，使用初步实验来捕捉模型的关键特征。对称全局灵敏度分析（SGSA）就是这样一种实验，它通过将模型分解为独立的对称函数来探索模型的对称结构。然而，现有的 SGSA 实验计划依赖于确定性计算模型，这些模型在针对特定输入值执行时会产生唯一的输出值。在本文中，考虑了设计非参数 SGSA 实验的问题。这里的短语“非参数”是指包含随机误差的模型输出。论文的主要结果表明，对称设计在一定的约束条件下，每个输出元素函数的估计达到A最优，保证了SGSA结果的优越性。进一步讨论了基于最优设计的非参数 SGSA 的统计特性，表明可以以低偏差和波动性估计无影响的敏感性指数。得到了最优设计的两个显式结构。最后通过仿真验证了派生设计的最优性。