Parallel heuristic search strategy based on a Bayesian approach for simultaneous recognition of contaminant sources and aquifer parameters at DNAPL-contaminated sites

In this study, we develop a parallel heuristic search strategy based on a Bayesian approach for simultaneously recognizing groundwater contaminant sources and aquifer parameters (unknown variables) at sites contaminated with dense non-aqueous phase liquids (DNAPLs). The parallel search strategy is time-consuming because thousands of simulation models must run in order to calculate the likelihood. Various stand-alone surrogate systems for the simulation models have been established, but they also have unavoidable limitations. Thus, we develop an optimal combined surrogate system by combining Gaussian process, kernel extreme learning machine, and support vector regression methods using a differential evolution algorithm with a variable mutation rate based on the rand-to-best/1/bin strategy, thereby improving the approximation accuracy of the surrogate system to the simulation model and significantly decreasing the high computational cost. Utilizing the optimal combined surrogate system reduced the CPU time by more than 400 times. In the iterative parallel heuristic search process, each round of iteration involves determining the candidate points and state transitions. The Monte Carlo approach is used widely for selecting candidate point, but this approach does not readily converge to the posterior distribution for unknown variables when the probability density function types are complex with weak search ergodicity. In order to improve the search ergodicity, we develop a particle swarm optimization algorithm with a non-linear decreasing inertia weight and Metropolis criterion, which is more suitable for unknown variables with complex probability density functions. The recognition results are obtained simultaneously when the iterative process terminates. We assess our proposed approaches based on a hypothetical case study at a three-dimensional site contaminated with DNAPLs. The results demonstrate that the parallel heuristic search strategy is helpful for the simultaneous recognition of DNAPL contaminant sources in groundwater and aquifer parameters.