Joint inverse estimation of groundwater pollution source characteristics and model parameters based on an intelligent particle filter

Accurate groundwater pollution source estimation (GPSE) is the prerequisite for efficiently designing ground-water pollution remediation strategies and pollution risk assessment. However, deterministic point estimation of pollution source characteristics may not completely solve the problem for practical situations. Therefore, an interval estimation, capable of providing more comprehensive and abundant information for decision-makers, should also be considered. In GPSE, the particle filter (PF) method is a good means for the interval estima-tion. However, some inherent problems in the general PF method may compromise the estimation accuracy. Thus, this study made two improvements to the general PF method as a solution. First, to solve the problem of its weak local search ability when tackling complex problems, this study embedded the optimization method with strong local search ability into the importance sampling process, to strengthen the local search ability, better optimize the particle position, and guide the overall distribution of particles to move towards the true distri-bution. Secondly, in the resampling process, all particles need to be resampled in each iteration, which may lead to plunging into the local optima. Thus, this study introduced an intelligent resampling process that intelligently adjusted the number of resampling particles in each iteration to avoid plunging into the local optima. Through two improvements on the PF method, an intelligent PF method was innovatively constructed for GPSE, improving the estimation accuracy. Additionally, to alleviate the computational cost caused by the frequent simulation model invocation, we adopted a deep learning method (deep belief neural network method) to build the surrogate model of the simulation model, ensuring high approximation accuracy to the simulation model. Also, we applied the theories and methods mentioned above to two respective scenarios (inorganic and organic groundwater pollution). We simultaneously estimated the pollution source characteristics and simulation model parameters to verify the effectiveness. Finally, we obtained the point estimation, posterior probability distri-bution, and interval estimation results, capable of providing a more reliable and comprehensive reference for decision-makers.