Nonlinear programming model of a wastewater treatment system: Sensitivity analysis and a robustness constraint

A method for sensitivity analysis in nonlinear programming is described and then illustrated using a least-cost model of a secondary wastewater treatment system. A sensitivity equation approach is used to calculate normalized sensitivity coefficients, which approximate the percent changes in model variables and objective function due to a small parameter variation. Design changes predicted by the sensitivity coefficients are confirmed by a perturbation analysis of the optimal solution. Sensitivity concepts are used to develop a robustness measure which is incorporated into the constraint set of the nonlinear model. Robustness is narrowly defined as the ability of a model solution to maintain a level of performance that meets the system design criteria even if the actual values of model parameters are not exactly the same as the values assumed for design. A gradient optimization procedure is used to examine the tradeoff between total cost and the robustness measure. A preliminary analysis shows that the trends in robust wastewater treatment plant design are in direct conflict with the optimal decisions obtained when minimizing cost without a constraint on robustness but are in agreement with those designs observed to work in practice. The robustness constraint method presented should be applicable to other optimization models of water resources systems.U.S. Department of the InteriorU.S. Geological SurveyOpe

Sensitivity Constrained Nonlinear Programming: A General Approach for Planning and Design Under Parameter Uncertainty and an Application to Treatment Plant Design

188 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1988.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.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD