Development of fragility curves using high‐dimensional model representation

Fragility curves represent the conditional probability that a structure's response may exceed the performance limit for a given ground motion intensity. Conventional methods for computing building fragilities are either based on statistical extrapolation of detailed analyses on one or two specific buildings or make use of Monte Carlo simulation with these models. However, the Monte Carlo technique usually requires a relatively large number of simulations to obtain a sufficiently reliable estimate of the fragilities, and it is computationally expensive and time consuming to simulate the required thousands of time history analyses. In this paper, high‐dimensional model representation based response surface method together with the Monte Carlo simulation is used to develop the fragility curve, which is then compared with that obtained by using Latin hypercube sampling. It is used to replace the algorithmic performance‐function with an explicit functional relationship, fitting a functional approximation, thereby reducing the number of expensive numerical analyses. After the functional approximation has been made, Monte Carlo simulation is used to obtain the fragility curve of the system. Copyright © 2012 John Wiley & Sons, Ltd.     

An adaptive high-dimensional model representation method for reliability analysis of geotechnical engineering problems

In this study, a new reliability analysis method was developed based on the adaptive high-dimensional model representation (HDMR) and applied to geotechnical engineering problems. For practical problems requiring finite element (FE) analysis or other numerical methods to evaluate system responses such as stresses and deformations, an efficient and accurate metamodeling technique is needed because it is not efficient or straightforward to directly adopt the conventional sampling-based or gradient-based reliability analysis approaches. In this work, an adaptive metamodeling approach was created and studied based on the HDMR framework and augmented radial basis functions (ARBFs). In this adaptive ARBF-HDMR technique, a simple and inexpensive first-order ARBF-HDMR metamodel was first constructed to explicitly express a performance function, and an alternate first-order reliability method (FORM) was applied to locate the design point and compute the reliability index. A local window was then defined such that additional sample points were generated and a higher-order HDMR component function was created using ARBF and added to the existing ARBF-HDMR metamodel. The accuracy of the ARBF-HDMR metamodel was improved through this adaptive process, especially in the region surrounding the design point. One mathematical and four geotechnical engineering problems were studied and solved using the proposed adaptive ARBF-HDMR approach. The proposed method was found to be capable of obtaining accurate reliability indices within a few iterations in all test problems.