The main task of RBDO(Reliability based design optimization) is to obtain reliability efficiently and accurately, especially for structural systems which involve finite element analyses or mechanical systems with a large number of random variables. Various methods have been developed up to now such as first-order reliability method (FORM), second-order reliability method(SORM), the Monte-Carlo simulation, and experimental design techniques. Experimental design technique is getting popular. In this thesis, a method of improving its numerical accuracy is suggested by establishing a multi-level DOE (design of experiments).
Experimental design technique needs no derivatives and less computation as compared to the Monte-Carlo simulation or first or second order reliability methods. The reliability analysis for non-normal distributions using the three level DOE method was developed by Seo and Kwak in 2002. Although this method estimates only up to the first four moments(mean, standard deviation, skewness, and kurtosis) of the system response function, the results and the type of probability distribution determined by using the Pearson system are shown very good. However the accuracy can be low in case of nonlinear performance function and sometimes, the level calculated is outside of the region in which the random variable is defined.
In this study we have suggested a modified three level DOE method to overcome these weaknesses and to obtain the optimum choice for 3 levels and weights to handle non-normal distributions. Furthermore we have extended it to finding the optimum choice for 5 levels and weights to increase the accuracy. Although the extension to multi-levels requires much larger amount of computations compared to the three level cases, the method is mathematically elegant and provides reference solutions for comparison. Finally using the response surface methodology, we decrease the number of experiments. A systematic procedure for reliability analysis is then proposed by using the Pearson system.
The proposed procedure of reliability analysis is applied to several examples containing various non-normal distributions. They show that the proposed method is indeed very accurate and practicable regardless of the types of distributions.
실험계획법을 이용한 신뢰도 계산 방법은 계산 과정이 간단하므로 구현하기가 쉽고, 시스템의 미분 값을 계산할 필요가 없다는 장점을 가지고 있다. 또한 피어슨 시스템과 연계하여 해석 결과를 단지 손상 확률이나 신뢰도 값으로 나타낼 뿐만 아니라 시스템의 확률 밀도 함수와 분포 함수 또한 수학적인 형태로 구할 수 있었다. 본 연구에서는 이러한 장점이 있는 실험계획법을 이용한 신뢰도 계산 방법에 있어서 기존의 방법을 분석하고 개선하고자 하였다.
