응답면 기법을 이용한 구조 신뢰성 해석

Structural Reliability Analysis via Response Surface Method

일반 구조물의 신뢰성 해석에서는 한계상태 방정식이 implicit한 이유로 추출법이나 확률 유한요소법이 주로 이용되나, 이들 방법은 여러번의 구조해석 결과가 필요하므로 시간과 노력이 크게 소요된다. 반면 응답면 기법은 적은 횟수의 구조해석 결과를 이용하여 implicit한 응답면을 관심있는 영역에서 근사하는 방법으로 일반 구조물의 신뢰성 해석에 효율적으로 이용할 수 있다. 본 논문에서는 응답면 기법으로서 중심합성 계획법, Bucher-Bourgund법, 그리고 인공신경망에 의한 근사법을 이용하여 일반 구조물의 신뢰성 해석에 적용하고, 각 방법의 장단점을 비교하였다.

In the reliability analysis of general structures, the limit state equations are implicit and cannot be described in closed form. Thus, sampling methods such as the Crude Monte-Carlo simulation, and probabilistic FEM are often used, but these methods are not so effective in view of computational cost, because a number of structural analysis are required and the derivatives must be calculated for probabilistic FEM. Alternatively the response surface approach, which approximates the limit state surface by using several results of structural analysis in the region adjacent to MPFP, could be applied effectively. In this paper, the central composite design, Bucher-Bourgund method and the approximation method using artificial neural network are studied for the calculation of probability of failure by the response surface method. Through the example comparisons, it is found that Bucher-Bourgund method is very effective and Neural network method for the reliability analysis is comparable with other methods. Specially, the central composite design method is found to be rational and useful in terms of mathematical consistency and accuracy.