Identification of groundwater contamination sources using a statistical algorithm based on an improved Kalman filter and simulation optimization

Identification of groundwater contamination sources, as a solution to an inverse problem, is mainly based on simulation optimization methods. However, the establishment and solution of an optimization model are extremely complicated for the inverse problem, where many decision variables need to be identified. Combining simulation optimization methods with other mathematical methods can effectively avoid this shortcoming. In order to identify features of contamination sources, the Kalman filter is combined with a mixed-integer nonlinear programming optimization model (MINLP). Firstly, the Kalman filter is improved by U-D decomposition (a matrix decomposition method) to identify the number and approximate locations of real contamination sources among potential contamination sources. A 0–1MINLP solution is then employed to identify the accurate location and release history of the contamination source. Kriging is used to produce a surrogate model for the numerical simulation model. The surrogate model approximates the numerical simulation model, which can be embedded in the 0–1MINLP instead of the numerical simulation model and it can be called directly during the iteration of the optimization model, thereby avoiding manually coupling the numerical simulation model with the optimization model during the solution process. Results demonstrate that the improved Kalman filter exhibits better numerical stability, where it can effectively avoid the filter divergence problem as well as solve the number and approximate locations of contamination sources in the inverse identification problem. The accurate location and release history of the contamination source can be effectively identified by using the 0–1MINLP.