CAJ | 학술논문

针对含有正态相关变量的多设计点/多失效模式系统的可靠性问题,提出了两种有效的基于方向抽样的可靠性灵敏度分析方法.可靠性灵敏度分析方法的基本思路是首先将正态相关变量进行等价独立标准正态变换,利用改进的方向抽样可靠性灵敏度分析方法得到独立标准正态空间的可靠性及灵敏度结果;通过复合求导法则,将独立标准正态空间的可靠性及灵敏度结果转化到正态相关空间,得到失效概率对相关正态变量分布参数(均值、标准差和相关系数)的偏导数,并对所推导的可靠性及灵敏度估计值进行了方差分析.与经典的Monte Carlo数字模拟法相比较,文中所列的数值算例和简单工程算例的分析结果验证了所提方法的可行性与有效性.
침대함유정태상관변량적다설계점/다실효모식계통적가고성문제,제출료량충유효적기우방향추양적가고성령민도분석방법.가고성령민도분석방법적기본사로시수선장정태상관변량진행등개독립표준정태변환,이용개진적방향추양가고성령민도분석방법득도독립표준정태공간적가고성급령민도결과;통과복합구도법칙,장독립표준정태공간적가고성급령민도결과전화도정태상관공간,득도실효개솔대상관정태변량분포삼수(균치、표준차화상관계수)적편도수,병대소추도적가고성급령민도고계치진행료방차분석.여경전적Monte Carlo수자모의법상비교,문중소렬적수치산례화간단공정산례적분석결과험증료소제방법적가행성여유효성.
For the reliability problem of systems of multiple design points or multiple failure modes with normal correlated variables, two reliability sensitivity analysis methods based on directional simulation are presented. First, the normal correlated variables are transformed into equivalent independent standard normal variables. Second, two reliability sensitivity methods based on directional simulation are employed for multiple design point or multiple failure mode systems with independent standard normal variables. Third, the reliability sensitivity of independent standard normal variables, the partial derivatives of the distribution parameters of independent standard normal variables, can be transformed into those of normal correlated variables by means of equivalent transformation. The variances of reliability estimators and sensitivity estimators are analyzed to realize convergence. Compared with the classical Monte Carlo numerical simulation, the results of numerical examples and engineering examples can validate the feasibility and validity of the proposed methods.