Hybrid homotopy-PSO global searching approach with multi-kernel extreme learning machine for efficient source identification of DNAPL-polluted aquifer

Groundwater pollution source identification (GPSI), which is critical for taking effective measures to protect groundwater resources, assess risks, and design remediation strategies, typically involves the solution of a nonlinear and ill-posed inverse problem. Regarding the inversion of dense non-aqueous phase liquid (DNAPL) sources, the special characteristics of pollutants render related research more complex. In the present study, homotopy-based optimization inverse theory and multi-kernel extreme learning machine (MK-ELM) were combined for efficiently solving GPSI problem while estimating aquifer parameters at a DNAPL-polluted site. The extreme learning machine incorporating multi kernels and whose parameters are obtained by means of a genetic algorithm (GA) was embedded in an optimization model for GPSI to replace the multiphase flow simulation model and to mitigate the considerable computational burdens of inversion iteration. The hybrid homotopy-particle swarm optimization (PSO) algorithm was constructed as a more efficient method for segmentally searching the global optimum in wide areas with low dependence on initial values. Results showed that the application of GA-based MK-ELM and hybrid homotopy-PSO effectively accomplish the simultaneous identification of source characteristics and aquifer parameters. The MK-ELM approximate the outputs of multiphase flow simulation model sufficiently with the certainty coefficient (R2) increased to 0.9982, whereas the mean relative error was limited to 1.5168%. Compared to the widely used PSO algorithm, the hybrid homotopy-PSO algorithm significantly reduced the mean relative error of identification results from 6.77% to 2.89%. •A new approximation model and an improved global optimization method were proposed for efficiently solving GPSI problems.•A multi-kernel extreme learning machine is proposed to approximate the simulation model with higher robustness.•A hybrid homotopy-PSO algorithm is constructed as a more efficient tool for searching the global optimum in wide areas.