Comparison Of Stochastic Radial Basis Function And Pest For Automatic Calibration Of Computationally Expensive Groundwater Models With Application To Miyun Huai Shun Aquifer

Comparison of Stochastic Radial Basis Function and PEST for Automatic Calibration of Computationally Expensive Groundwater Models with Application to Miyun-Huai-Shun Aquifer

Groundwater numerical models have been widely used as effective tools to analyze and manage water resources. However, the accuracy and reliability of a groundwater numerical model largely depends on model parameters calibration, which is extremely computationally expensive. Therefore, it is highly desirable that efficient optimization algorithms be applied to automatic calibration problems. In this study, we compare the performance of three optimization algorithms and propose a new hybrid method. The algorithms are applied to calibration of a model for part of Beijing water supply. We first outline the three algorithms and briefly describe our hybrid method. The first algorithm referred as PEST in this paper is the Gauss-Marquardt-Levenberg (GML) method including truncated singular value decomposition, which is widely applied in the field of model parameter calibration. As the second one, CMAES_P is a "PEST compatible" implementation of CMA-ES (Covariance Matrix Adaptation Evolution Strategy) global optimization algorithm. PEST derivative-based algorithm and CMAES_P are both encapsulated in the automated parameter optimization software PEST, which has advanced predictive analysis and regularization features to minimize user-specified objective functions. The third one, called Stochastic Radial Basis Function (Stochastic RBF) method, is developed by Regis and Shoemaker (2007), which utilizes radial basis function as the response surface model to approximate the expensive objective function. Our new hybrid method combines Stochastic RBF and PEST derivative-based algorithm, which provides PEST derivative-based algorithm with the starting points found by Stochastic RBF. This paper compares the performances of the aforementioned four algorithms for automatic parameter calibration of a groundwater model on three 28-parameter cases and two synthetic test function calibration problems. We employ the following characteristics as our comparison criteria on all the cases: (1) efficiency in giving good objective function for a given number of function evaluations; (2) performance for different statistical criteria; (3) variability of solutions in multiple trials; (4) improvements if more function evaluations are performed. On the basis of 20 trials, the results indicate that Stochastic RBF is best among the three and CMAES_P is superior to PEST. In addition, our hybrid method still failed to beat Stochastic RBF in highly computationally expensive nonlinear cases. To sum up, our results show that Stochastic RBF method is a more efficient alternative to PEST for automatic parameter calibration of computationally expensive groundwater models. ii.

Optimal Calibration, Uncertainty Assessment, and Long-term Monitoring Using Computationally Expensive Groundwater Models

Applications of Multi-objective, Mixed-integer and Hybrid Global Optimization Algorithms for Computationally Expensive Groundwater Problems

This research focuses on the development and implementation of e cient optimization algorithms that can solve a range of computationally expensive groundwater simulationoptimization problems. Because groundwater model evaluations are expensive, it is important to find accurate solutions with relatively few function evaluations. As a result, all the algorithms tested in this research are evaluated on a limited computation budget. The first contribution to the thesis is a comparative evaluation of a novel multi-objective optimization algorithm, GOMORS, to three other popular multi-objective optimization methods on applications to groundwater management problems within a limited number of objective function evaluations. GOMORS involves surrogate modeling via Radial Basis Function approximation and evolutionary strategies. The primary aim of the analysis is to assess the effectiveness of multi-objective algorithms in groundwater remediation management through multi-objective optimization within a limited evaluation budget. Three sets of dual objectives are evaluated. The objectives include minimization of cost, pollution mass remaining/pollution concentration, and cleanup time. Our results indicate that the overall performance of GOMORS is better than three other algorithms, AMALGAM, BORG and NSGA-II, in identifying good trade-off solutions. Furthermore, GOMORS incorporates modest parallelization to make it even more e cient. The next contribution is application of SO-MI, a surrogate model-based algorithm designed for computationally expensive nonlinear and multimodal mixed-integer black-box optimization problems, to solve groundwater remediation design problems (NL-MIP). SO-MI utilizes surrogate models to guide the search thus save the expensive function evaluation budget, and is able to find accurate solutions with relatively few function evaluations. We present numerical results to show the effectiveness and e ciency of SO-MI in comparison to Genetic Algorithm and NOMAD, which are two popular mixed-integer optimization algorithms. The results indicate that SO-MI is statistically better than GA and NOMAD in both study cases. Chapter 4 describes DYCORS-PEST, a novel method developed for high dimensional, computationally expensive, multimodal calibration problems when the computation budget is limited. This method integrates a local optimizer PEST into a global optimization framework DYCORS. The novelty of DYCORS-PEST is that it uses a memetic approach to improve the accuracy of the solution in which DYCORS selects the point at which the search switches to use of the local method PEST and when it switches back to the global phase. Since PEST is a very e cient and widely used local search algorithm for groundwater model calibration, incorporating PEST into DYCORS-PEST is a good enhancement for PEST and easy for PEST users to learn. DYCORS-PEST achieves the goal of solving the computationally expensive black-box problem by forming a response surface of the expensive function, thus reducing the number of required expensive function evaluations for finding accurate solutions. The key feature of the global search method in DYCORS-PEST is that the number of decision variables being perturbed is dynamically adjusted in each iteration in order to be more effective for higher dimensional problems. Application of DYCORS-PEST to two 28parameter groundwater calibration problems indicate this new method outperforms PEST by a large margin for high dimensional, computationally expensive, groundwater calibration problems.