The topic of this seminar is a new method for characterizing structural reliability and system uncertainty. Traditional probability-based reliability and uncertainty analysis methods fall into two broad categories: analytical techniques and sampling methods. Analytical methods typically rely on the iterative selection of a sample from the unknown performance function, the application of regression techniques to estimate the unknown performance function and then the use of gradient methods to search for the most probable point(s). The most probable points are then used to characterize the probability of a system performing in a certain manner. No information regarding the classification of the sample points (e.g., failure/success) is used in the analysis. Alternatively, sampling methods rely on exercising the unknown performance function at a variety of points and observing the success/failure of each point. No information regarding the performance function is used in characterizing the uncertainty in the system response. These two methods therefore lie on the extremes of information utilization in the uncertainty field. One method relies almost entirely on the performance function and ignores the sample observations, while the other ignores the performance function and relies completely on the sample observations. The method to be discussed in this seminar utilizes information available from both the performance function and the sample observations and combines this information in an optimal fashion.
The approach is based on quasi-Monte Carlo sampling augmented with statistical information available from spatial statistical methods. The approach is unique in two respects: it is based on quasi-Monte Carlo sampling of the likelihood function and not pseudo-Monte Carlo sampling and, second, it uses a probabilistic membership function as opposed to the 'crisp' indicator function commonly used in importance sampling. In particular, the new method assumes that the true location of the limit state function is known only in probabilistic terms. The new procedure also does not require identification of the limit state function or the Most Probable Point (MPP). Through the use of regionalized random variables, the response of the system is modeled as a random field, which permits probabilistic membership statements for any feasible input vector relative to the failure domain. Preliminary results indicate that the proposed method is superior to traditional as well as stratified sampling methods. For the same level of estimation accuracy, it has been demonstrated that the new technique requires fewer function evaluations than the currently popular analytical methods and, on the average, fewer function evaluations than random sampling methods such as stratified sampling or Latin hypercube sampling.