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

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.

[1]  H C Joksch,et al.  Velocity change and fatality risk in a crash--a rule of thumb. , 1993, Accident; analysis and prevention.

[2]  W. Cooper,et al.  Survey of mathematical programming models in air pollution management , 1997 .

[3]  M. Bergin,et al.  Application of Bayesian Monte Carlo analysis to a Lagrangian photochemical air quality model , 2000 .

[4]  A. Yegnan,et al.  Uncertainty analysis in air dispersion modeling , 2002, Environ. Model. Softw..

[5]  Ezra Hauer,et al.  ACCIDENTS, OVERTAKING AND SPEED CONTROL , 1971 .

[6]  J. A. Carta,et al.  Influence of the data sampling interval in the estimation of the parameters of the Weibull wind speed probability density distribution: a case study , 2005 .

[7]  H. Bayraktar,et al.  Assessment of regional air pollution distribution by point cumulative semivariogram method at Erzurum urban center, TURKEY , 2005 .

[8]  Robert Joumard,et al.  Influence of speed limits on road and motorway on pollutant emissions , 1987 .

[9]  Panos Y. Papalambros,et al.  Monotonicity and active set strategies in probabilistic design optimization , 2005 .

[10]  O. Ditlevsen.  Narrow Reliability Bounds for Structural Systems , 1979 .

[11]  D. M. Hossain,et al.  Vehicular headway distribution and free speed characteristics on two-lane two-way highways of Bangladesh , 1999 .

[12]  S Ponnuswamy,et al.  USE OF DELPHI TO STUDY THE TRANSPORT POLICY ISSUES AND SCENARIO IN CHENNAI , 1998 .

[13]  D. Martin.  The Change of Concentration Standard Deviations with Distance , 1976 .

[14]  P. E. Benson.  CALINE4 - A DISPERSION MODEL FOR PREDICTING AIR POLLUTANT CONCENTRATIONS NEAR ROADWAYS. FINAL REPORT , 1984 .

[15]  D. Sprevak,et al.  The estimation of the parameters of the distribution of wind speed and direction , 1980 .

[16]  M. André,et al.  Driving speeds in Europe for pollutant emissions estimation , 2000 .

[17]  H. Christopher Frey,et al.  Quantification of Variability and Uncertainty in Air Pollutant Emission Inventories: Method and Case Study for Utility NOx Emissions , 2002, Journal of the Air & Waste Management Association.

[18]  D. Hearn,et al.  A first best toll pricing framework for variable demand traffic assignment problems , 2005 .

[19]  S K Rao,et al.  HEADWAY AND SPEED STUDIES ON TWO-LANE HIGHWAYS. , 1998 .

[20]  D Solomon,et al.  Accidents on main rural highways related to speed, driver, and vehicle , 1964 .

[21]  Mitsuru Arai,et al.  A two-dimensional air quality model in an urban street canyon: evaluation and sensitivity analysis , 2000 .

[22]  G. Campbell,et al.  An Introduction to Environmental Biophysics , 1977 .

[23]  Jery R. Stedinger,et al.  Probabilistic risk and uncertainty analysis for bioremediation of four chlorinated ethenes in groundwater , 2007 .

[24]  Nancy J. Brown,et al.  Evaluating Uncertainties in Regional Photochemical Air Quality Modeling , 2003 .

[25]  Peter Newman,et al.  Fuel consumption, time saving and freeway speed limits , 1986 .

[26]  Robert W. McMullen,et al.  The Change of Concentration Standard Deviations with Distance , 1975 .

[27]  G. Bishop,et al.  Automobile emissions are statistically gamma distributed. , 1994, Environmental science & technology.

[28]  G. H. Huang,et al.  A fuzzy-stochastic robust programming model for regional air quality management under uncertainty , 2003 .

[29]  Sven Leyffer,et al.  Nonlinear programming without a penalty function , 2002, Math. Program..

[30]  Robert E. Melchers,et al.  Structural Reliability: Analysis and Prediction , 1987 .

[31]  D. S. Berry,et al.  Distribution of Vehicle Speeds and Travel Times , 1951 .

[32]  R D Stephens,et al.  Remote sensing data and a potential model of vehicle exhaust emissions. , 1994, Air & waste : journal of the Air & Waste Management Association.

[33]  Orley Ashenfelter,et al.  Using Mandated Speed Limits to Measure the Value of a Statistical Life , 2002, Journal of Political Economy.

[34]  Ali Mekky,et al.  TOLL REVENUE AND TRAFFIC STUDY OF HIGHWAY 407 IN TORONTO , 1995 .

[35]  Samuel Kotz,et al.  Sums, products, and ratios for downton’s bivariate exponential distribution , 2006 .

[36]  R. Rackwitz,et al.  Non-Normal Dependent Vectors in Structural Safety , 1981 .

[37]  Koulis Pericleous,et al.  Model sensitivity and uncertainty analysis using roadside air quality measurements , 2002 .

[38]  Walter F. Dabberdt,et al.  Uncertainty, ensembles and air quality dispersion modeling: applications and challenges , 2000 .

[39]  Michael R. Flynn,et al.  The beta distribution – a physically consistent model for human exposure to airborne contaminants , 2004 .

[40]  Tony Markel,et al.  ADVISOR: A SYSTEMS ANALYSIS TOOL FOR ADVANCED VEHICLE MODELING , 2002 .

[41]  H. Saunders,et al.  Probabilistic Engineering Design—Principles and Applications , 1987 .

[42]  R. Rackwitz.  Reliability analysis—a review and some perspectives , 2001 .

[43]  Guo H. Huang,et al.  ITSSIP: Interval-parameter two-stage stochastic semi-infinite programming for environmental management under uncertainty , 2008, Environ. Model. Softw..

[44]  Kumares C. Sinha,et al.  To Increase or Not to Increase Speed Limit: A Review of Safety and Other Issues , 2000 .

[45]  M. Aral,et al.  Probabilistic-fuzzy health risk modeling , 2004 .

[46]  Frank von Hippel,et al.  Automobile fuel economy , 1987 .

[47]  N P Humphrey.  MANAGING SPEED: REVIEW OF CURRENT PRACTICE FOR SETTING AND ENFORCING SPEED LIMITS: NEW TRB SPECIAL REPORT , 1998 .

[48]  Q. G. Lin,et al.  IFTEM: An interval-fuzzy two-stage stochastic optimization model for regional energy systems planning under uncertainty , 2009 .

[49]  John G. Watson,et al.  A Method for Propagating Measurement Uncertainties through Dispersion Models , 1986 .

[50]  Ram S. Gupta.  Introduction to environmental engineering and science , 2004 .

[51]  Kyung K. Choi,et al.  A NEW STUDY ON RELIABILITY-BASED DESIGN OPTIMIZATION , 1999 .

[52]  A. Saidane,et al.  Optimal Reliability Design: Fundamentals and Applications , 2001 .

[53]  R. Rackwitz,et al.  First-order concepts in system reliability , 1982 .

[54]  Panos Y. Papalambros,et al.  An Adaptive Sequential Linear Programming Algorithm for Optimal Design Problems With Probabilistic Constraints , 2007 .

[55]  Ove Ditlevsen,et al.  Principle of Normal Tail Approximation , 1981 .

[56]  R. Fletcher.  Practical Methods of Optimization , 1988 .