Sai Hung Cheung

Reliability based design optimization with approximate failure probability function in partitioned design space

This paper presents an efficient method for reliability-based design optimization (RBDO), which is robust to complex systems involving computationally expensive numerical models and/or a large number of random variables. This novel method belongs to a type of decoupling approaches in which the failure probability function (FPF) is approximated in the partitioned design space. In the setting of augmented reliability formulation, for a specific design configuration, the failure probability of a system is proportional to the probability density value of design variables conditioned on the failure event, thus transforming FPF approximation into a problem of density estimation. In this paper, we partition the design space into several subspaces and then estimate the density of failure samples in each subspace by binning and constructing regression functions. Sufficient failure samples are efficiently generated in each subspace using Markov Chain Monte Carlo method, which guarantees the accuracy of FPF approximation over there and ultimately over the entire design space. Three illustrative examples involving structural systems subjected to static or dynamic loadings are discussed to demonstrate the efficiency and accuracy of the proposed method.

On the evaluation of multiple failure probability curves in reliability analysis with multiple performance functions

Abstract Many systems have multiple failure modes that result in multiple performance functions. In this paper, a new stochastic simulation based approach is proposed for evaluation of multiple failure probability curves in a reliability problem with multiple performance functions. The state-of-the-art stochastic simulation based techniques, such as subset simulation and auxiliary domain method, are efficient in evaluating a failure probability curve but only consider a single performance function. Standard Monte Carlo simulation is robust to the type and dimension of the problem and is applicable to evaluate multiple failure probability curves for a problem with multiple performance functions but is computationally expensive especially while estimating small probabilities. The proposed approach for simultaneous consideration of multiple performance functions generalizes the subset simulation and is an improvement of the generalized subset simulation. The output of an analysis using the proposed approach is multiple failure probability curves with each corresponding to one performance function. The proposed approach is robust with respect to the dimension of the failure probability integral, model complexity, the degree of nonlinearity, number of performance functions, and efficient in cases involving the computation of small failure probabilities. The effectiveness and efficiency of the proposed approach are demonstrated by three numerical examples.

A stochastic simulation algorithm for updating robust reliability of nonlinear structural dynamic systems based on incomplete modal data

In this paper, we are interested in using the incomplete modal data identified from the system to update the robust failure probability that any particular response of a nonlinear structural dynamic system exceeds a specified threshold during the time when it is subjected to future stochastic dynamic excitation. Uncertainties from structural modeling - the modeling of the stochastic excitation that the structure will experience during its lifetime - and any other uncertainties can all be taken into account. A new efficient approach based on stochastic simulation methods, which is very robust to the number of random variables and uncertain model parameters, is proposed to update the robust reliability of the structure. The efficiency and effectiveness of the proposed approach are illustrated by a numerical example involving a nonlinear structural dynamic model of a building.

A subset simulation based approach with modified conditional sampling and estimator for loss exceedance curve computation

A new stochastic simulation-based approach for the evaluation of loss exceedance curve without repeated reliability analyses, and the generation of samples of input random variables and any function of them conditioned on different levels of loss exceedance is proposed for a comprehensive risk and loss analysis, and investigation. The proposed approach involves the modification of the simulation algorithms in the Subset Simulation and the development of new estimators. It allows for a more comprehensive characterization of the probability distribution of the loss including the tail parts due to combinations of scenarios which can lead to extreme and catastrophic consequences. The approach is robust to the number of random variables involved. The effectiveness and efficiency of the proposed method are shown by an illustrative example involving a seismic loss analysis of a multi-story inelastic structure. A stochastic ground motion model coupled with a stochastic nonlinear dynamic model, and probabilistic fragility and loss functions are considered.

Stochastic Simulation Algorithm for Robust Reliability Updating of Structural Dynamic Systems Based on Incomplete Modal Data

AbstractThis paper presents an approach for updating the robust structural reliability that any particular response of a structural dynamic system will not reach some specific failure or unfavorabl...

Stochastic Simulation Based Reliability Analysis with Multiple Performance Objective Functions

In this paper, a stochastic simulation approach is proposed to estimate small failure probabilities of multiple limit states. The proposed approach allows for the simultaneous consideration of multiple performance functions and the corresponding thresholds. The approach modifies the stochastic subset simulation algorithm that can efficiently compute small failure probabilities. The proposed approach is robust with respect to the dimension of the failure probability integral, model complexity and nonlinearity. The effectiveness and efficiency of the proposed method are illustrated by a numerical example involving a structural dynamic system subjected to future earthquake excitations modeled as a stochastic process and the results are compared to those obtained using crude Monte Carlo simulation.