Abstract
In this work, we propose a technique to automatically optimize the monitoring of any distributed indicator (concentration of a substance along a river, blood pressure of a patient over time, etc.) for which a reliable estimate is previously available. From a mathematical point of view, the problem is based on obtaining a reliable estimate of the chosen indicator (e.g., by numerical simulation), and then solving a multi-objective optimization problem (with mixed real and integer variables) whose solution must provide an efficient and satisfactory monitoring strategy. As an illustrative case, we show the steps to follow in order to implement that strategy when designing a system for monitoring water quality in a river. Finally, we present and analyze the results when applying the proposed technique to study a real case in the Neuse River (North Carolina, USA).
Similar content being viewed by others
References
Alvarez-Vázquez, L.J., García-Chan, N., Martínez, A., & Vázquez-Méndez, M.E. (2010a). Multi-objective Pareto-optimal control: an application to wastewater management. Computational Optimization and Applications, 46, 135–157.
Alvarez-Vázquez, L.J., García-Chan, N., Martínez, A., & Vázquez-Méndez, M.E. (2010b). Pareto-optimal solutions for a wastewater treatment problem. Journal of Computational and Applied Mathematics, 234, 2193–2201.
Alvarez-Vázquez, L.J., García-Chan, N., Martínez, A., & Vázquez-Méndez, M.E. (2010c). Optimal control in wastewater management: a multi-objective study. Communications in Appl. Industrial Math., 1, 62–77.
Alvarez-Vázquez, L.J., García-Chan, N., Martínez, A., & Vázquez-Méndez, M.E. (2015a). Stackelberg strategies for wastewater management. Journal of Computational and Applied Mathematics, 280, 217–230.
Alvarez-Vázquez, L.J., García-Chan, N., Martínez, A., & Vázquez-Méndez, M.E. (2015b). An application of interactive multi-criteria optimization to air pollution control. Optimization, 64, 1367–1380.
Alvarez-Vázquez, L.J., Martínez, A., Vázquez-Méndez, M.E., & Vilar, M. (2006). Optimal location of sampling points for river pollution control. Mathematics and Computers in Simulation, 71, 149–160.
Bermúdez, A., Muñoz-Sola, R., Rodríguez, C., & Vilar, M. (2006). Theoretical and numerical study of an implicit discretization of an one dimensional inviscid model for river flows. Mathematics Models Methods in Applied Science, 16, 375–395.
Chang, N.B., & Makkeasorn, A. (2010). Optimal site selection of watershed hydrological monitoring stations using remote sensing and grey integer programming. Environmental Modeling and Assessment, 15, 469–486.
de Gruijter, J., Brus, D., Bierkens, M., & Knotters, M. (2006). Sampling for natural resource monitoring: Springer.
García-Chan, N., Alvarez-Vázquez, L.J., Martínez, A., & Vázquez-Méndez, M.E. (2014). On optimal location and management of a new industrial plant: numerical simulation and control. Journal of the Franklin Institute, 351, 1356–1371.
García-Chan, N., Muñoz-Sola, R., & Vázquez-Méndez, M.E. (2009). Nash equilibrium for a multiobjective control problem related to wastewater management. ESAIM:Control Optimization and Calculus of Variations, 15, 117–138.
Gilbert, R.O. (1987). Statistical methods for environmental pollution monitoring, Van Nostrand Reinhold Society.
Kiefer, J. (1953). Sequential minimax search for a maximum. Proceedings of American Mathematical Society, 4, 502–506.
Miettinen, K.M. (1999). Nonlinear multiobjective optimization. Boston: Kluwer Academic Publishers.
Nelder, J.A., & Mead, R. (1965). A simplex method for function minimization. Computer Journal, 7, 308–313.
Ott, W.R. (1994). Environmental statistics and data analysis, Lewis Publishers.
Pollak, A.W., Peirce, J.J., Alvarez-Vázquez, L.J., & Vázquez-Méndez, M.E. (2013). Methodology for identifying optimal locations of water quality sensors in river systems. Environmental Modeling and Assessment, 18, 95–03.
Porter, J., Arzberger, P., Braun, H.W., Bryant, P., Gage, S., Hansen, T., Hanson, P., Lin, C.C., Lin, F.P., Kratz, T., Michener, W., Shapiro, S., & Williams, T. (2005). Wireless sensor networks for ecology. BioScience, 55, 561–572.
Strobl, R.O., Robillard, P.D., Shannon, R.D., Day, R.L., & McDonnell, A.J. (2006). A water quality monitoring network design methodology for the selection of critical sampling points: Part I. Environmental Monitoring Assessment, 112, 137–158.
Thompson, S.K. (2012). Sampling: Wiley.
Vázquez-Méndez, M.E., Alvarez-Vázquez, L.J., García-Chan, N., & Martínez, A. (2013). Improving the environmental impact of wastewater discharges with a specific simulation-optimization software. Journal of Computational and Applied Mathematics, 246, 320–329.
Acknowledgments
This work was supported by funding from the project MTM2015-65570-P of Ministerio de Economía y Competitividad (Spain) and FEDER.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Alvarez-Vázquez, L.J., Casal, G., Martínez, A. et al. A Novel Formulation for Designing a Monitoring Strategy: Application to the Design of a River Quality Monitoring System. Environ Model Assess 22, 279–289 (2017). https://doi.org/10.1007/s10666-016-9537-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10666-016-9537-z