Optimal Design with Non-normally Distributed Random Parameters, Conditional Probability, and Joint Constraint Reliabilities: a Case Study in Vehicle Emissions Regulations to Achieve Ambient Air Quality Standards

Making appropriate environmental policy decisions requires considering various sources of uncertainty. An air pollution example is formulated as a design optimization problem with probabilistic constraints, also referred to as reliability-based design optimization (RBDO). Environmental applications with a large number of constraints and significant model complexity present special challenges. In this paper an efficient active set strategy is integrated with a reliability contour surface approach to solve probabilistic problems with non-normal variable probability distributions. Discrete random parameters, which result in Bayesian probability, are also present and they are incorporated using delta function approximations. Joint constraint reliability that considers satisfying all regulatory constraints is also discussed. A demonstration example of setting the optimal vehicle speed limit while maintaining high reliability for CO and NOx standards of a residential area near two highway systems is included. ∗Corresponding author, Phone/Fax: (734) 647-8401/8403 1