Experimental design for estimating unknown groundwater pumping using genetic algorithm and reduced order model

Abstract

[1] An optimal experimental design algorithm is developed to select locations for a network of observation wells that provide maximum information about unknown groundwater pumping in a confined, anisotropic aquifer. The design uses a maximal information criterion that chooses, among competing designs, the design that maximizes the sum of squared sensitivities while conforming to specified design constraints. The formulated optimization problem is non-convex and contains integer variables necessitating a combinatorial search. Given a realistic large-scale model, the size of the combinatorial search required can make the problem difficult, if not impossible, to solve using traditional mathematical programming techniques. Genetic algorithms (GAs) can be used to perform the global search ; however, because a GA requires a large number of calls to a groundwater model, the formulated optimization problem still may be infeasible to solve. As a result, proper orthogonal decomposition (POD) is applied to the groundwater model to reduce its dimensionality. Then, the information matrix in the full model space can be searched without solving the full model. Results from a small-scale test case show identical optimal solutions among the GA, integer programming, and exhaustive search methods. This demonstrates the GA's ability to determine the optimal solution. In addition, the results show that a GA with POD model reduction is several orders of magnitude faster in finding the optimal solution than a GA using the full model. The proposed experimental design algorithm is applied to a realistic, two-dimensional, large-scale groundwater problem. The GA converged to a solution for this large-scale problem.Citation: Ushijima, T. T., and W. W.-G. Yeh (2013), Experimental design for estimating unknown groundwater pumping using genetic algorithm and reduced order model, Water Resour. Res., 49,[6688][6689][6690][6691][6692][6693][6694][6695][6696][6697][6698][6699]

A reduced order model‐based preconditioner for the efficient solution of transient diffusion equations

“…If the reduced-order model is a good approximation of the full-system model, we expect the nonzero eigenvalues of R to be close to 1, so that i 0. Assuming that this is true, then kE P k D 1 and inequality (19) readsˇ…”

“…The addition of basis vectors reduces the approximation errors, but increases the computational cost of the offline forward and backward steps. Model order reduction techniques are frequently applied to obtain a fast solution to computationally complex and parameter-dependent problems such as model calibration [14,15], Monte Carlo simulations [16][17][18] and experimental design [19].…”

Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions

“…projection) of a subset of the original model variables (Castelletti et al, 2012a). This approach has been used, for example, for reducing the dimension of a groundwater model (see McPhee and Yeh, 2008;Siade et al, 2012), for optimizing groundwater pumping rates (Ushijima and Yeh, 2013) and for water quality remediation planning in lakes and reservoirs (Castelletti et al, 2012b;Castelletti et al, 2014). It should be noted that this approach is particularly useful for specific mathematical tasks requiring knowledge of system behaviour over the whole simulation horizon (e.g.…”

High‐Performance Integrated Control of water quality and quantity in urban water reservoirs

“…The reduction is then achieved by retaining only those few basis functions that account for most of the variability in the data [ Willcox and Peraire , ; Antoulas , ]. During the last decade, model reduction has been successfully applied to a variety of groundwater problems, including inverse modeling [ Vermeulen et al ., ; Liu et al ., ; Boyce and Yeh , ; Lin and McLaughlin , ], simulation [ Vermeulen et al ., ; Siade et al ., ; Cardoso and Durlofsky , ], design of monitoring networks [ Ushijima and Yeh , ], stochastic flow problems [ Pasetto et al ., ], and optimal management [ McPhee and Yeh , ; Lin and McLaughlin , ] (see the review by Asher et al . []).…”