Research paperGroundwater level simulation and forecasting using interior search algorithm-least square support vector regression (ISA-LSSVR)
Graphical abstract
Introduction
With the increase of computational capability of computers, the application of data-driven methods in groundwater level simulation and forecasting has been increased. Artificial neural network (ANN), adaptive neural fuzzy inference system (ANFIS), genetic programming (GP) and support vector regression (SVR) can be mentioned as some of these methods. Several studies reported the use of ANN (Coppola et al., 2003; Maier and Dandy, 2000; Wunsch et al., 2018), ANFIS (Gong et al., 2016; Moosavi et al., 2013; Shiri and Kişi, 2011), and GP (Fallah-Mehdipour et al., 2013, 2014; Shiri et al., 2013) for groundwater level simulation and forecasting. Although these methods provide some degree of flexibility and accuracy in groundwater modelling, some demerits have been reported. High uncertainty associated with ANN was reported by Yoon et al. (2011) for groundwater level forecasting in a coastal aquifer. Over-fitting of ANFIS was reported by Fallah-Mehdipour et al. (2013) in Karaj plain, and high computational demand to find solutions was stated as a major disadvantage of GP by Meier et al. (2013).
The SVR method, first presented by Vapnik (1995), is a relatively new data-driven method in hydrology. The SVR has been applied to forecast groundwater level. Liu et al. (2009) used a least square support vector regression (LSSVR) based on chaos dynamic and a radial basis function (RBF) as the kernel to forecast groundwater level. Behzad et al. (2010) modeled groundwater level under different pumping and weather conditions, by ANN and SVR methods. They used the RBF kernel and identified SVR parameters by grid search (GS-SVR). The results indicated that the SVR, especially when the data is insufficient, is more accurate and generalized in comparison to ANN. Yoon et al. (2011) compared ANN and SVR methods in groundwater level simulation in a coastal aquifer. The results illustrated that the average error in SVR method was lower than those in ANN method. Also, uncertainty analysis showed lower uncertainty for SVR method. Shiri et al. (2013) made a comparison between the ANN, ANFIS, GP, SVR and autoregressive moving average (ARMA) methods for groundwater level forecasting. The results showed that the GP has the highest capability to forecast groundwater level up to 7 days beyond the recorded data. They chose RBF kernel and the SVR parameters were tuned by trial and error. None of these studies dealt with the urban aquifers. The recharge of unconfined aquifers in urban areas is complex due to the impact of impervious surface as a result of urban development (Renouf et al., 2019) and urbanization in general (Salvadore et al., 2015), for example leakage from urban water infrastructure. In this case, the link between groundwater recharge and meteorological variables (e.g. precipitation, temperature, etc.) might not be straightforward and linear. Data-driven methods has potential to be used in this context.
Previous studies showed that the SVR results' accuracy largely depends on tuning its parameters. The SVR theory doesn't provide any specific methodology for parameter selection (Su et al., 2014). Trial and error have been performed in previous studies (Behzad et al., 2010; Bhagwat and Maity, 2013; Yoon et al., 2011). Trial and error approach is a time-consuming process and greatly affects the SVR results' accuracy. Achieving a high accuracy with trial and error approach is computationally expensive because the model needs to be evaluated at various points within the grid for each parameter. Meta-heuristic optimization algorithms can be used to overcome this limitation (Raghavendra and Deka, 2015). The Meta-heuristic optimization algorithms were successfully applied in many water resources problems (Bozorg-Haddad et al., 2015; Fayaz et al., 2020; Hosseini-Moghari et al., 2015, 2017) and their strength and weaknesses have been reviewed (Maier et al., 2014; Moravej, 2017, 2018; Sörensen, 2015).
Some meta-heuristic optimization algorithms were employed to find SVR parameters. Genetic algorithm (GA) was employed to choose the SVR parameters (GA-SVR) to forecast monthly reservoir storage (Su et al., 2014), monthly streamflow (Kalteh, 2015), water quality parameters in rivers (Bozorg-Haddad et al., 2017; Soleimani et al., 2016), daily reference evapotranspiration (Yin et al., 2017), and water temperature (Quan et al., 2020). Bat algorithm, Particle Swarm Optimization (PSO), and Artificial Bee Colony were coupled with SVR for streamflow forecasting (Xing et al., 2016) river-stage forecasting (Seo et al., 2016). The results indicate that PSO-SVR and ABC-SVR provided better results compared to GS-SVR and GA-SVR. Similar studies in groundwater level simulation and forecasting is missing. In addition, all meta-heuristics algorithms used for tuning the SVR parameters' suffer from having two or more parameters to tune themselves. The sensitivity of the meta-heuristic algorithms was reported in previous studies (Moravej, 2017, 2018). Interior search algorithm (ISA) is a new evolutionary algorithm which overcomes this limitation.
ISA is proposed by (Gandomi, 2014) showing its superiority over other optimization algorithms in a wide range of problems. Moravej and Hosseini-Moghari (2016) tuned the ISA parameter automatically using a linear equation as a function of optimization iteration. Therefore, the ISA algorithm potentially provides more reliability compared to other meta-heuristic algorithms. They employed the ISA to solve three reservoir operation problems (i.e. Karun 4, four-reservoir and ten-reservoir operation problems). They compared the results of the ISA with other meta-heuristic algorithms such as honey bee mating optimization (HBMO), water cycle algorithm (WCA), biogeography-based optimization (BBO), imperial competition algorithm (ICA), cuckoo optimization algorithm (COA), ant colony optimization (ACO) and bat algorithm from previous studies. The results indicate that the ISA outperform those algorithms in accuracy, reliability, and fast convergence (i.e., efficiency).
Groundwater is a vital source for municipal, industrial and agricultural usages in Karaj city, Iran; supporting socio-economic activities of more than 2 million people. Therefore, developing a reliable tool for simulating and forecasting water level is of interest in this region. In the current study, the ISA was employed to automatically tune the LSSVR (ISA-LSSVR) parameters for groundwater level simulation and forecasting in Karaj Plain. The aim is to evaluate the capability of the proposed method in groundwater level simulation and forecast. To tackle this, 12 different model structures were considered and the result of ISA-LSSVR in two separate categories of simulation and forecast were compared with GA coupled with LSSVR (GA-LSSVR), GP, and ANFIS.
Section snippets
The LSSVR
The LSSVR method was developed by Suykens et al. (2002). It is a modified version of the original method which was introduced by Vapnik (1995). The LSSVR provides a computational advantage over the regular SVR via converting a quadratic programming problem into a set of linear equations (Kalteh, 2015). The main advantage of this conversion is mentioned as decrease in the computational complexity and cost (Adnan et al., 2017; Raghavendra; Deka, 2015). Therefore, LSSVR is used in this study over
ISA-LSSVR and GA-LSSVR results
The values of the LSSSVR parameters were obtained using the ISA and the GA. The values range from 9 (well 1 model 1) to 925 (well 3 model 2) and the values of range from 20 (well 1 model 1) to 823 (well 3 model 4) optimized by the ISA. The measures of accuracy of training datasets are presented in Table 2. Also, results obtained by ANFIS and GP, which are presented by Fallah-Mehdipour et al. (2013), are mentioned in the table for comparison purposes. As Fallah-Mehdipour et al. (2013)
Conclusion
In the current study, the ISA was introduced to optimize the LSSVR parameters forming a new method for groundwater level simulation and forecast. The result is compared with other data-driven methods (i.e. GA-LSSVR, GP, and ANFIS). The comparison showed that the ISA-LSSVR improves the simulation results of GA-LSSVR by 71.8, 27.2 and 12.4 percent in terms of NS, RMSE and R2. Similar improvements for forecast were reported to be 62.7, 24.8 and 12.3 percent for NS, RMSE and R2. The results also
Declaration of competing interest
The authors declare no conflict of interest.
Acknowlegement
No financial support is needed to be acknowledged.
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