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

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Abstract

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.

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Acknowledgments

This research was partially supported by the Automotive Research Center, a U.S. Army Center of Excellence in Modeling and Simulation of Ground Vehicles at the University of Michigan and by the National Science Council in Taiwan under NSC95-2218-E-006-045. These supports are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan

    Kuei-Yuan Chan

  2. Department of Mechanical Engineering, University of Michigan, Ann Arbor, USA

    Panos Y. Papalambros & Steve J. Skerlos

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  1. Kuei-Yuan Chan
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  2. Panos Y. Papalambros
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Correspondence to Kuei-Yuan Chan.

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Chan, KY., Papalambros, P.Y. & Skerlos, S.J. A method for reliability-based optimization with multiple non-normal stochastic parameters: a simplified airshed management study. Stoch Environ Res Risk Assess 24, 101–116 (2010). https://doi.org/10.1007/s00477-009-0304-4

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