Enhancing gradient-based parameter estimation with an evolutionary approach |
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| Institution: | 1. Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, 410054 Saratov, Politehnicheskaya 77, and Cybernetic Institute, National Research Tomsk Polytechnic University, 634050 Tomsk, Lenin Avenue, 30, Russian Federation;2. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924 Lodz, and Department of Vehicles, Warsaw University of Technology, 84 Narbutta Str., 02-524 Warszawa, Poland;3. Department of Mathematics and Modeling, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov, Russian Federation;1. Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, SK, Canada;2. Canadian Light Source Inc., University of Saskatchewan, Saskatoon, SK, Canada |
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| Abstract: | Traditionally, the calibration of groundwater models has depended on gradient-based local optimization methods. These methods provide a reasonable degree of success only when the objective function is smooth, second-order differentiable, and satisfies the Lipschitz's condition. For complicated and highly nonlinear objective functions it is almost impractical to satisfy these conditions simultaneously. Research in the calibration of conceptual rainfall-runoff models, has shown that global optimization methods are more successful in locating the global optimum in the region of multiple local optima. In this study, a global optimization technique, known as shuffle complex evolution (SCE), is coupled to the gradient-based Lavenberg–Marquardt algorithm (GBLM). The resultant hybrid global optimization algorithm (SCEGB) is then deployed in parallel testing with SCE and GBLM to solve several inverse problems where parameters of a nonlinear numerical groundwater flow model are estimated. Using perfect (i.e. noise-free) observation data, it is shown SCEGB and SCE are successful at identifying the global optimum and predicting all model parameters; whereas, the commonly applied GBLM fails to identify the optimum. In subsequent inverse simulations using observation data corrupted with noise, SCEGB and SCE again outperform GBLM by consistently producing more accurate parameter estimates. Finally, in all simulations the hybrid SCEGB is seen to be equally effective as SCE but computationally more efficient. |
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