Sensitivity Constrained Nonlinear Programming: A General Approach for Planning and Design Under Parameter Uncertainty and an Application to Treatment Plant Design
Uber, James Gregory
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https://hdl.handle.net/2142/69978
Description
Title
Sensitivity Constrained Nonlinear Programming: A General Approach for Planning and Design Under Parameter Uncertainty and an Application to Treatment Plant Design
Author(s)
Uber, James Gregory
Issue Date
1988
Doctoral Committee Chair(s)
Brill, E. Downey, Jr.,
Department of Study
Civil Engineering
Discipline
Environmental Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Civil
Engineering, Industrial
Engineering, Sanitary and Municipal
Abstract
One important problem with using mathematical models is that parameter values, and thus the model results, are often uncertain. A general approach, Sensitivity Constrained Nonlinear Programming (SCNLP), was developed for extending nonlinear optimization models, to include functions that depend on the system sensitivity to changes in parameter values. Such sensitivity-based functions include first-order measures of variance, reliability, and robustness. Thus SCNLP can be used to generate solutions or designs that are good with respect to modeled objectives, and that also reflect concerns about uncertainty in parameter values. A solution procedure and an implementation based on an existing nonlinear programming code are presented. SCNLP was applied to a complex activated sludge wastewater treatment plant design problem. The alternative designs generated represent the tradeoff between cost and system robustness, where robustness is related inversely to the sensitivity of effluent quality to changes in 55 parameter values. The results show a significant tradeoff between cost and robustness and significant design trends associated with improvements in robustness. These design trends are generally more consistent with recommended design practice than is the minimum cost design. SCNLP should be applicable to many problems where parameter value uncertainty is important, e.g., the design of contaminated groundwater remediation schemes.
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