Robust Optimal Design for Wastewater Treatment. Part I: General Approach
Publication: Journal of Environmental Engineering
Volume 117, Issue 4
Abstract
One important problem with using mathematical optimization models for design of wastewater treatment systems is that parameter values, and thus, model results, are often uncertain. A general approach, called robust optimal design, is developed for extending nonlinear optimization models to include first‐order sensitivity‐based measures of system robustness. Robustness is defined narrowly as the ability of the system to maintain a level of performance even if the actual parameter values are different from the assumed values; thus less sensitive designs should be more robust. A solution procedure based on nonlinear optimization and system sensitivity analysis techniques is discussed. The approach can be used to generate alternative designs that recognize traditional modeled objectives such as cost and effluent water quality measures, and that also reflect concerns about uncertainty. The approach is applied in a companion paper to a complex activated sludge treatment system with 55 uncertain parameter values.
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References
1.
Ang, A. H.‐S., and Tang, W. H. (1975). Probability concepts in engineering planning and design, Volume I—Basic principles. John Wiley and Sons, New York, N.Y., 199.
2.
Brill, E. D., Jr. (1979). “The use of optimization models in public‐sector planning.” Mgmt. Sci., 25(5), 413–422.
3.
Chen, M. S. K., Erickson, L. E., and Fan, L.‐T. (1970). “Consideration of sensitivity and parameter uncertainty in optimal process design.” Ind. Engrg. Chem. Process Design Develop., 9(4), 514–521.
4.
Cohen, J. L. (1978). Multiobjective programming and planning. Academic Press, New York, N.Y.
5.
Fiering, M. B. (1976). “The role of systems analysis in water program development.” Natural Resour. J., 16(4), 759–771.
6.
Friedman, R., Ansell, C., Diamond, S., and Haimes, Y. Y. (1984). “The use of models for water resources management, planning, and policy.” Water Resour. Res., 20(7), 793–802.
7.
Gill, P. E., Murray, W., and Wright, M. H. (1983). Practical optimization. Academic Press, New York, N.Y.
8.
Golub, G. H., and Van Loan, C. F. (1983). Matrix computations. The Johns Hopkins Univ. Press, Baltimore, Md.
9.
Hashimoto, T., Loucks, D. P., and Stedinger, J. R. (1982). “Robustness of water resources systems.” Water Resour. Res., 18(1), 21–26.
10.
Kaplan, W. (1984). Advanced calculus. Addison‐Wesley, Reading, Mass., 110–121.
11.
Lasdon, L. S., Waren, A. D., Jain, A., Ratner, M. (1978). “Design and testing of a generalized reduced gradient code for nonlinear programming.” ACM Trans. on Math. Software, 4 (1), 34–50.
12.
Matalas, N. C., and Fiering, M. B. (1977). “Water‐resource system planning.” Climate, climatic change and water supply, National Academy of Sciences, Washington, D.C.
13.
Uber, J. G., and Brill, E. D., (1990). “Design optimization with sensitivity constraints.” Engrg. Optimization, 16(1).
14.
Uber, J. G., Kao, J.‐J., Brill, E. D., Jr., and Pfeffer, J. T. (1988). “Sensitivity constrained nonlinear programming: A general approach for planning and design under parameter uncertainty and an application to treatment plant design.” Final Tech. Report to the Department of the Interior, U.S. Geological Survey, Reston, Va.
15.
Uber, J. G., Pfeffer, J. T., and Brill, E. D., Jr. (1991). “Robust optimal design for wastewater treatment. II: Application.” J. Envir. Engrg. Div., ASCE, 117(4), 438–456.
16.
Verde, C., and Frank, P. M. (1982). “A design procedure for robust linear suboptimal regulators with preassigned trajectory sensitivity.” Proc. 21st Conf. on Decision and Control, IEEE Control Systems Society, Vol. 2, pp. 886–890.
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Copyright © 1991 ASCE.
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Published online: Jul 1, 1991
Published in print: Jul 1991
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