## 1 Introduction  
In hydraulic engineering, the seepage parameters of dam materials change with the age of operation. This can lead to a reduction in the structural strength of the dam, triggering serious catastrophes such as dam failure. Seepage analysis based on monitoring data of dams can effectively understand the working condition of dams [1; 2; 3; 4; 5; 6]. One of the most important parameters in seepage calculations is the hydraulic conductivity [7]. Currently, there are three methods to determine hydraulic conductivity in hydraulic engineering including the test method, empirical formula method, and back analysis method [8]. The test method can in principle accurately obtain hydraulic conductivity based on in situ sampling. However, indoor and in situ tests are usually subject to large deviations from the actual results due to factors such as short test time, large workload, and discontinuous test time, and the economic costs are generally high. The empirical formula method, based on engineering experience and mathematical assumptions, allows for quick and easy derivation of hydraulic conductivity based on geologic data. However, when applied to complex structures, the results obtained by the empirical formula method are usually inaccurate. Inverse analysis is a method of inverting the hydraulic conductivity of a material based on seepage monitoring data [9; 10; 11; 12; 13; 14; 15]. In comparison to the preceding two methods, it is relatively simple to operate, economically inexpensive, and highly reliable. The method is therefore generally applicable to the determination of hydraulic conductivity in seepage calculations. Currently, the inverse analysis method is usually combined with optimization algorithms to accelerate the inversion process. Artificial intelligence algorithms are gradually introduced into the field of hydraulic engineering [16; 17; 18; 19; 20; 21]. [PERSON] [22] used Matlab to construct a BP neural network model applied to landslide prediction. [PERSON] [23] obtained the mapping of transmittance to hydraulic head by ANN. [PERSON] [24] introduced genetic algorithms in specific inverse problems in geotechnical engineering. [PERSON] et al. [25] combined finite elements and artificial neural networks to model a feed-forward three-layer model to invert seepage in an earth and rock dam using backpropagation learning. [PERSON] [26] obtained reasonable values by combining an artificial neural network and SEEP/W model in calculating the seepage properties of concrete dams. Support vector machine [27; 28] (SVM) is commonly used to solve nonlinear problems. Support vector regression (SVR) [29] is an application of support vector machines when dealing with regression analysis problems and is commonly used to solve small sample regression problems. At the early stage of the development of computer technology, scholars used traditional methods, such as the gradient descent method [30], to improve support vector machines. Such methods generally have some limitations such as low efficiency, high error, and heavy workload. Currently, support vector machines are commonly integrated with artificial intelligence algorithms to solve optimization problems. In 2016, the Whale Optimization Algorithm (WOA) was proposed by the Australian researcher [PERSON] [31]. The WOA has been applied in hydraulic engineering due to its simple mechanism, few parameters, and strong robustness. [PERSON] et al. [32] employed the WOA to optimize water resource allocation to mitigate the issue of water scarcity. [PERSON] et al. [33] applied an improved binary-coded WOA to formulate the power generation schedule for the Three Gorges Hydropower Station. [PERSON] et al. [34] combined WOA with an integrated machine learning model to achieve groundwater level prediction based on precipitation and temperature data. However, it was also found during the research process that when dealing with complex optimization problems, the convergence accuracy of the standard WOA tends to decrease, and the convergence speed becomes slower.