CAJ | 학술논문

输入随机变量的重要性测度分析是结构安全评估和工程优化设计的重要组成部分。针对工程结构系统中普遍存在的多维输出情况，提出一种使用无量纲模型的基于方差的重要性测度新指标，可以方便地综合衡量输入随机变量的变异性对多输出结构系统变异性影响的重要程度，而且能够有效地保留各输出提供的重要性测度信息。同时，针对 Monte Carlo 数字模拟方法巨大的计算代价问题，采用一种乘法降维的功能函数替代模型来求解指标。该方法可在保证求解精度的同时极大地降低了模型调用次数，节约了计算成本。最后，通过数值算例和工程算例说明所提指标的合理性以及求解模型的高效性。
수입수궤변량적중요성측도분석시결구안전평고화공정우화설계적중요조성부분。침대공정결구계통중보편존재적다유수출정황，제출일충사용무량강모형적기우방차적중요성측도신지표，가이방편지종합형량수입수궤변량적변이성대다수출결구계통변이성영향적중요정도，이차능구유효지보류각수출제공적중요성측도신식。동시，침대 Monte Carlo 수자모의방법거대적계산대개문제，채용일충승법강유적공능함수체대모형래구해지표。해방법가재보증구해정도적동시겁대지강저료모형조용차수，절약료계산성본。최후，통과수치산례화공정산례설명소제지표적합이성이급구해모형적고효성。
Global sensitivity analysis for input random variables is an important component of safety evaluation and optimal design in engineering structure. For many mathematical models encountered in engineering structure system involving multivariate outputs, this paper defines a set of new variance?based global sensitivity indices based on di?mensionless model. These indices can synthetically measure the uncertainty effect on the multivariate outputs in?duced by the corresponding input random variable expediently and can effectively keep global sensitivity analysis in?formation of each output. Simultaneously, to solve the costly computation problem in the Monte Carlo simulation, we calculate the new index by using a surrogate model which is based on a multiplicative version of the dimensional reduction method. The algorithm can greatly reduce model calls and save the calculation cost without decreasing its accuracy. Lastly, a numerical example and an engineering example are presented to show the reasonableness of the proposed index and the efficiency of the algorithm.