A method for reliability-based optimization with multiple non-normal stochastic parameters: a simplified airshed management study

• Published in: Stochastic environmental research and risk assessment Vol. 24; no. 1; pp. 101 - 116
• Main Authors: Chan, Kuei-Yuan, Papalambros, Panos Y., Skerlos, Steve J.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.01.2010; Springer Nature B.V
• Subjects: Aquatic Pollution; Chemistry and Earth Sciences; Computational Intelligence; Computer Science; Decision making; Earth and Environmental Science; Earth Sciences; Environment; Environmental policy; Environmental regulations; Highways; Math. Appl. in Environmental Science; Optimization; Original Paper; Physics; Probability Theory and Stochastic Processes; Research methodology; Statistics for Engineering; Stochastic models; Waste Water Technology; Water Management; Water Pollution Control; Non-normal uncertainty; Joint constraint reliability; Environmental policy decisions under uncertainty; Reliability-based design optimization (RBDO)
• ISSN: 1436-3240; 1436-3259
• DOI: 10.1007/s00477-009-0304-4

We develop methodologies to enable applications of reliability-based design optimization (RBDO) to environmental policy setting problems. RBDO considers uncertainty as random variables and parameters in an optimization framework with probabilistic constraints. Three challenges in environmental decision-making problems not addressed by current RBDO methods are efficient methods in handling: (1) non-normally distributed random parameters, (2) discrete random parameters, and (3) joint reliability constraints (e.g., meeting constraints simultaneously with a single reliability). We propose a modified sequential quadratic programming algorithm to address these challenges. An active set strategy is combined with a reliability contour formulation to solve problems with multiple non-normal random parameters. The reliability contour formulation can also handle discrete random parameters by converting them to equivalent continuous ones. Joint reliability constraints are estimated by their theoretical upper bounds using reliability indexes and angles of normal vectors between active constraints. To demonstrate the methods, we consider a simplified airshed example where CO and NOx standards are violated and are brought into compliance by reducing the speed limits of two nearby highways. This analytical example is based on the CALINE4 model. Results show the potential of this approach to handle complex large-scale environmental regulation problems.