Reliability and Bayesian approaches to the probabilistic performance based design of structures

Performance based design (PBD) is emerging as the guiding principle for the next generation of structural design specifications. PBD provides the engineer with greater flexibility to select appropriate performance criteria and prediction techniques, but also demands more sophisticated analyses. The presence of uncertainty in structural analysis, behavior and design—especially in the prediction of new performance measures—requires a probabilistic approach to PBD.; The first component of this research considers reliability-based specifications for PBD, using the example of advanced analysis of steel frames. Design by advanced analysis uses non-linear structural analyses to predict system performance measures. Current advanced analysis proposals use the resistance factors of the load and resistance factor design (LRFD) specifications with no probabilistic justification. The probabilities of failure of sixteen, two-story, two-bay steel frames, designed by both LRFD and advanced analysis are estimated using Monte Carlo simulation and importance sampling schemes. The simulated strength and load distributions are used to develop resistance factors for the limit states of first plastic hinge and plastic collapse. The results indicate that design by advanced analysis can maintain the desired reliability for system failure, but may result in unsatisfactory serviceability performance. Two particular difficulties of reliability-based specifications for design by advanced analysis are discussed—practical calibration for system-based limit states, and the determination of resistance factors applicable to a wide class of structures.; The second component of this research applies Bayesian surrogate models to engineering design, which is viewed as an iterative process of information gathering and decision making. A Bayesian surrogate model relates individual design variables to system performance, including both aleatory and epistemic uncertainties. Bayesian surrogate models can incorporate prior knowledge, update knowledge based on evidence, and propose design revisions. A Bayesian network is used to update the parameters of the surrogate model based on information collected from trial designs. Techniques of Bayesian experimental design are applied to propose design revisions which maximize the expected information gain or relative entropy. The Bayesian surrogate framework is applied to several structural design examples. The results suggest the need to develop new information criteria specific to engineering design and PBD.