# Inverse Modeling of Seepage Parameters Based on an Improved Gray Wolf Optimizer
## 1 Introduction  
In hydraulic engineering, seepage parameters of dams and dam foundations change with operating time and loading conditions. The changes in seepage parameters weaken the strength of the structure and lead to failure. Seepage analysis is commonly used to monitor the working conditions of dams and dam foundations for the safety of hydraulic projects [1; 2; 3; 4; 5]. The hydraulic conductivity, a key parameter in seepage analysis, is closely related to the accuracy of the analysis results. Minimized error between the simulated and actual values of hydraulic conductivity could improve the reliability of the analysis. In-situ tests have been proven to be helpful in determining the hydraulic conductivity of dams and dam foundations. The hydraulic conductivity determined by in-situ testing agrees with the actual value when the test samples are small. However, this method is time-consuming and costly when there are large quantities of models. Another method to solve this problem is inverse analysis. The inverse research based on monitoring data and numerical simulation results demonstrates economy and efficiency. The essence of the inverse analysis is to determine the hydraulic conductivity by measurements and simulated results. In the inversion analysis, optimization algorithms are widely applied for iterative search over a range of hydraulic conductivity values. The optimal hydraulic conductivity is determined by iteration while minimizing the objective function. Considering the repetition of the iterative process, optimization algorithms are widely used to improve efficiency and accuracy in the searching process of the inverse problem. For example, on the basis of the Radial Basis Function (RBF) neural network optimized by Particle Swarm Optimization (PSO), [PERSON] et al. [6] constructed an inverse model for the permeability coefficient of a high core rockfill dam; Combining error Back-Propagation Neural Network (BPNN) and Genetic Algorithm (GA), [PERSON] and [PERSON] [7] proposed aninverse analysis method for determining the displacements. This method was successfully applied in the displacement identification of the lock profile of the Three Gorges Project, which led to reasonable results. [PERSON] et al. [8] developed the differential evolution (DE) algorithm to determine soil parameters in the field of deep excavation, which improved the stability of the backtracking parameters. Simulated annealing [9; 10; 11; 12] and ant colony optimization [13; 14; 15; 16; 17] have also been extensively used in the inverse problem. Significantly, much progress has been made in the research field of seepage because of optimization algorithms [18; 19; 20; 21; 22; 23; 24; 25]. [PERSON] et al. [26] proposed a biological immune mechanism-based quantum particle swarm optimization (IQPSO) algorithm to solve the inversion problem of seepage parameters. Based on back propagation neural network (BPNN) and genetic algorithm (GA), [PERSON] et al. [27] developed a new approach for inverse modeling of the transient groundwater flow in dam foundations, which improved the uniqueness and reliability of the inversed results and made tractable the large-scale inverse problems in engineering practices. [PERSON] et al. [28] proposed an inverse analysis model by using the genetic algorithm (GA) and finite element analysis technology, to solve the calcium leaching problems. Although optimization algorithms are frequently employed for inverse problems, they suffer from low accuracy, slow convergence, and poor robustness. The Gray Wolf Optimizer (GWO) proposed by [PERSON] [29] has been shown to be efficient and intelligent in engineering optimization. [PERSON] [29] compared the performance of GWO with Particle Swarm Optimization (PSO), Gravity Search Algorithm (GSA), Differential Evolution (DE), Evolutionary Programming (EP), and Evolutionary strategy (ES). The results demonstrate that the GWO can provide very competitive results compared to these well-known meta-heuristics.