Efficient sampling-based inverse reliability analysis combining Monte Carlo simulation (MCS) and feedforward neural network (FNN)

Abstract

Inverse reliability analysis evaluates a percentile value of a performance function when the target reliability is given. In cases of high dimensional or highly nonlinear performance functions, sampling-based methods such as Monte Carlo simulation (MCS), Latin hypercube sampling, and importance sampling are considered to be better candidates for reliability analysis. The sampling-based methods are very accurate but require a large number of samples, which can be very time-consuming. Therefore, this paper proposes an efficient and/or accurate sampling-based reliability analysis method without using a surrogate model. The proposed method helps to improve the accuracy of reliability analysis with the same number of samples or to ensure the same accuracy of reliability analysis with fewer samples. This study starts with an idea of training relationship between limited samples constituting realization of the performance distribution—usually between 10 and 100—and its corresponding true percentile value where the performance distribution is defined as a one-dimensional distribution resulted from a performance function and its random variables. To this end, feedforward neural network (FNN), which is one of promising artificial neural network (ANN) models that approximate high dimensional models using layered structures, is introduced in this study, and limited samples constituting realizations of various performance distributions and their corresponding true percentile values are used as input and target data, respectively. Various beta distributions are used to create the training data sets. A FNN training method using kernel density estimation and equidistant points to represent the kernel distribution data is also proposed to remove dimensionality of the training inputs. Comparative study shows that the proposed method training FNN with samples constituting realization of the performance distribution (Method 2) is more accurate than a method that directly estimates the percentile value from the kernel distribution fitting the samples constituting realization generated through MCS (Method 1). In addition, compared to Method 2, another proposed method that trains FNN with the kernel density estimation and equidistant points (Method 3) is more accurate in reliability analysis and more computationally efficient in FNN training. Method 3 is also applicable to high reliability problems, and it is more accurate than Kriging-based method for high dimensional problems.