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The identification of groundwater contamination sources (IGCSs) is an important requirement for the remediation and treatment of groundwater contamination. The data assimilation methods such as ensemble Kalman filter (EnKF) and ensemble smoother (ES) have been applied to IGCSs in recent years and obtained good identification results. The unscented kalman filter (UKF) is also a data assimilation method with the potential to simultaneously identify hydraulic conductivity and GCSs. However, when UKF is applied to identify hydraulic conductivity and GCSs, it is necessary to use the observed data at different times separately, which increases the complexity of the update process and this may result in low identification accuracy. ES is a variant of EnKF that updates the system parameters with all observed data in all time periods, which makes ES faster and easier to implement than EnKF. Therefore, inspired by the ES, an unscented kalman smoother (UKS) based on UKF was proposed for simultaneously identifying the hydraulic conductivity and GCSs in this study. The UKS can use the data observed in all time periods simultaneously, while it is also simpler to operate and the calculation speed is faster. Present studies have shown that ES can solve IGCS problems. Thus, ES was also applied to identify the hydraulic conductivity and GCSs in this study, and its identification performance was compared with UKS. In contrast to previous applications of ES to IGCSs, both UKS and ES were set up with stop iteration conditions instead of only performing one update process, and thus both methods applied multiple update processes. The results showed that compared with ES, the identification results obtained by UKS were characterized by greater stability, higher accuracy, and the iterative process required less iteration process and computational time. [ABSTRACT FROM AUTHOR]

The simulation optimization (S/O) method is widely used in the identification of groundwater contamination sources (IGCSs). However, in most cases, the IGCSs has the characteristics of many variables to be identified and a high degree of nonlinearity. When the grey wolf optimization algorithm (GWO) is used to solve the optimization model for this kind of problem, due to the relatively weak local search ability it has the disadvantage of premature convergence. To improve the GWO, the GWO and gradient descent algorithm were integrated to construct a hybrid grey wolf gradient optimization algorithm (HGWGO) with little dependence on the initial value and a strong local search ability. The HGWGO was then applied to solve the optimization model and improve the accuracy of the IGCSs results. In addition, when solving the optimization model, calling the simulation model hundreds of times will generate a large calculation load and consume a massive amount of computing time, which would seriously hinder the IGCSs. Thus, a surrogate model of the simulation model was established by applying a deep belief neural network (DBNN) to participate in the iterative calculation. The results showed that compared with the simulated annealing algorithm and GWO, the HGWGO had a higher calculation accuracy and could improve the accuracy of IGCSs. Although the HGWGO requires a high computational cost, the improvement in solution accuracy was sufficient to compensate for this shortcoming. The DBNN surrogate model had a high accuracy and could save 99% of the computing time by participating in the iterative calculation instead of the simulation model. [ABSTRACT FROM AUTHOR]