Water level prediction of pumping station pre-station based on machine learning methods

As an indispensable natural resource for human development, water is a major factor in economic growth and social progress. Long-distance water transportation projects alleviate the problem of the uneven spatial and temporal distribution of water resources caused by the large geographical area of China. During the water transfer, safety accidents due to a significant rise or fall in the water level can be avoided by maintaining a stable water level. Therefore, in terms of operations and dispatching, a field-measurement-based prediction model of water level at pumping stations is significant for pumping station regulation, water dispatching, and building safety. The prediction model can also provide scientific guidance for dispatchers during water transfer.

Water level prediction methods mainly include simulations based on physical mechanisms and machine learning. For simulations based on physical mechanisms, Pramanik et al. (2010) built the MIKE 11 hydrodynamic model for simulating cross-sectional water levels of rivers; MIKE 11 is based on the extracted cross-sections of the digital elevation model. Jian et al. (2017) proposed the use of bias correction to improve the simulation accuracy of the hydrological model. However, the physical simulation-based approach has greater data requirements, including complete and accurate topographic information and measured hydrological data for model building and validation (Desmarais & Kuerten 2014; Dimitriadis et al. 2016; Lei et al. 2019; Tu et al. 2021). Additionally, the model implementation is highly iterative and tedious, making the water level prediction extremely complicated and time-consuming (El-Diasty & Al-Harbi 2015). In contrast, the data-driven machine learning approach has the advantages of requiring only a few input parameters and obtaining a high prediction accuracy, avoiding the multifaceted requirements and several limitations of hydrodynamic modeling while directly exploring intrinsic patterns in data for efficient water level prediction (Jordan & Mitchell 2015; Hong et al. 2021). Khan & Coulibaly (2006) applied a support vector machine (SVM) to predict lake water levels, and Behzad et al. (2010) demonstrated that SVM outperforms artificial neural networks (ANNs) in predicting groundwater levels. Chang et al. (2018) applied SVM to predict water levels 1–3 h ahead using the previous flood inundation prediction results of the Yilan River basin in Taiwan. SVMs were applied to predict groundwater level anomalies, and satisfactory results were obtained (Malakar et al. 2021). Therefore, SVM is a promising machine learning method for water level prediction. Meanwhile, neural networks have also shown excellent nonlinear mapping capabilities in water level prediction. Siddiquee & Hossain (2015) explored the applicability of ANNs in predicting river water levels and found that ANNs overcome the drawbacks of a lack of hydrological data and long model run time, being less complicated and faster. Kusudo et al. (2021) applied the single-output long short-term memory and the codec long short-term memory for simulating the water level of the Takayama Reservoir (Nara Prefecture, Japan). They found that the codec long short-term memory model was more accurate. With the continuous advancements in artificial intelligence and machine learning, coupling multiple machine learning methods has become a frequent practice in water level prediction research. Li et al. (2019) used the artificial bee colony-backpropagation (BP) neural network algorithm for groundwater level prediction. The prediction accuracy and convergence speed of the coupled algorithm were better than those of the particle swarm optimization-BP (PSO-BP), genetic algorithm optimized BP (GA-BP), and BP models. The AdaBoost algorithm was used to optimize the traditional BP neural network to improve the accuracy of water level prediction, minimizing the BP neural network prediction error (Xiong et al. 2021).

Relative to water level prediction, research is relatively limited in using machine learning to predict water levels of pumping station pre-station. Gao et al. (2018) combined a numerical simulation and a water transfer scheme to build a BP neural network model for water level prediction, obtaining a small prediction error and verifying the better prediction accuracy of the BP neural network. Similarly, a multilayer perceptron and a recurrent neural network were used for a 2, 4, and 6 h water level overprediction with high accuracy (Ren et al. 2020). Zhang et al. (2021) built a relevance vector machine (RVM) model for pre-station water level prediction, and the RVM model achieved considerably reduced root mean square error (RMSE) and mean absolute error (MAE) compared with those of BP neural networks. Liu et al. (2022) compared and analyzed the nonlinear autoregressive model with the exogenous input (NARX) model and the gray relation analysis-BP (GRA-BP) model in the prediction of water level at Tuncui. They found that the accuracy of the GRA–NARX–Bayesian regularization (GRA–NARX–BR) model considered the influencing factors more comprehensively. Xue et al. (2022) used a BP neural network model for 2, 4, and 6 h pre-pump water level prediction at Dongsong of the Jiaodong Water Transfer Project. The results showed that the BP neural network is suitable for hydrological predictions.

Based on the aforementioned idea of improving the accuracy of water level prediction, this paper introduces the concept of data staging, couples various machine learning methods, and applies them to the SNWDERP – Baliwan for pre-pump water level prediction research. The pumping station is an important hub and the highest pumping station in the Nansihu–Dongpinghu section of the SNWDERP, and the station's water level fluctuation affects the safe operation of the entire complex ‘river–lake–reservoir’ water transfer system. Therefore, this study aimed to (1) build a BP model, an improved PSO-BP model, a SVM model, and an improved PSO-SVM model, evaluating the accuracies in terms of the MAE, MSE, RMSE, MAPE, and R; (2) explore the prediction accuracy of the 4 h ahead and 8 h ahead water levels of the Baliwan pump, as well as to analyze the influence of forward period on prediction accuracy; (3) analyze the prediction accuracy of the ice formation period, aquatic grass period, normal scheduling period, and all the different datasets, and to explore the influence of different periods on the prediction accuracy of the pre-pump water level in the Baliwan pumping station and to improve the prediction accuracy.

The BP neural network, which is proposed by Rumelhart and McClelland, is a multilayer feedforward neural network based on an error BP algorithm (Xia & Lv 2005). The BP neural network uses a gradient descent algorithm to learn from the training data and minimize the square of the output errors. An error BP method is used to train the weights and bias values of the network nodes. The advantages of the BP neural network are its simple structure, strong nonlinear mapping capability, good self-learning capability, and high-accuracy approximation of arbitrary functions (Supplementary Fig. S1a).

The SVM regression (SVR) is a subset of SVMs (Cheng et al. 2022; Tipping 2001). The concept of the SVR is to build an ‘interval band’ with spacing on either side of the linear function. No loss is calculated for the samples in the interval band; thus, only the support vector influences the function model. The advantage of the SVR is that it does not involve probability measures and the law of large numbers. Hence, it avoids the traditional process of induction to deduction and achieves efficient ‘transductive reasoning’ from sample training to forecasting, which considerably simplifies the typical regression problem (Cheng et al. 2022) (Supplementary Fig. S1b).

The evolutionary algorithm known as the PSO was created by Kennedy et al in 1995, and it uses a parallel algorithm. The concept of the PSO is to search for multiple non-inferior solutions concurrently in a parallel way among the entire population of solution sets, beginning from a random solution. This approach is equivalent to multiple Pareto optimal solutions, and its advantages are its easy implementation, high search capability, high accuracy, and fast convergence, which demonstrate its superiority in solving practical problems (Supplementary Fig. S1c).

In solving complex nonlinearization problems, the BP neural network algorithm, which adjusts the network weights along the direction of local improvement, tends to fall into local extremes where the weights converge to local minima, leading to network training failure. In addition, BP neural networks are highly sensitive to the initial network weights; thus, initializing the network with different weights tends to result in convergence to different local minima. The PSO algorithm is a parallel computing method with high searchability and fast convergence. Combining the PSO algorithm with the BP neural network to optimize the threshold and weights of the BP neural network achieves a highly efficient particle swarm search and prevents the BP neural network from easily falling into local minima (Supplementary Fig. S2a).

The radial basis function is selected as the kernel in SVR and has two key parameters: the penalty function C; the higher the value of C, the easier it is to overfit the model, and the smaller the value of C, the easier it is to underfit the model, where the generalization ability of the model is poor for excessively large or small values of C. The second parameter is ⁠, which implicitly determines the data distribution after mapping to the new feature space. The larger the value of ⁠, the larger the number of support vectors; the smaller the value of ⁠, the larger the number of support vectors, where the number of support vectors affects the training and prediction speed (Supplementary Fig. S2a).

To evaluate the performance of different models, the following criteria are used:

In studying the future pre-station water level of the Baliwan pumping station, we considered the relationship between the water level and flow and the influence of human factors, the water level of the Wangzhuang control gate, the water level of the Denglou pumping station, the flow rate of the Denglou pumping station, and the flow rate, and water level of the Baliwan pumping station, the future flow rate of the Baliwan pumping station was selected as the influencing factor for prediction.

To predict the pre-station water level at the pumping station, we used the BP neural network, SVR, the improved PSO-BP neural network, and the improved PSO-SVR. The data were actual pumping station transfer data for 2013–2020, which were derived from Shandong South-to-North Water Diversion Eastern Route Corporation Limited. Seventy percent of the data after disordering were used as the training set and 30% as the testing set. The computer code was written in MATLAB (Education Edition) using the Neural Network Toolbox and LibSVM.

Remark. When new data become available in the future, the parameters of the methods can be updated to improve the accuracy of predictions.

The MSE evaluates the degree of variability in the data. The MSE of ALL is smaller than that of other periods, confirming the low variability in the ALL data. The MSE of the improved PSO-BP is smaller than that of the other models, which demonstrates that the improved PSO-BP model is the most effective for reducing the prediction MSE, as indicated in Figure 3(b).

Compared with the MSE, the RMSE amplifies and penalizes large errors, and it provides a better visualization of how the data change (Figure 3(c)).

The MAPE is a relative error measure and shows an average situation. The MAPE values of the ice formation period, the aquatic grass period, the normal scheduling period, and ALL are relatively small and close. Hence, we assume that the relative errors of the predictions after staging are approximately the same. The MAPE values of the BP model, the improved PSO-BP model, and the SVR model are approximately the same for the same periods, as illustrated in Figure 3(d).

R reflects the degree of correlation between the predicted and actual values. Figure 3(e) shows that the improved PSO-BP model has the highest correlation coefficient, indicating that the algorithm achieved the best predictions.

Luo et al. (2021) adopted a staged-divided water level prediction method to improve model prediction accuracy, which is further confirmed by our study. The prediction models were evaluated from the perspective of sub-periods. Figures 2–4 show that the prediction simulation accuracy of the ice formation period and the aquatic grass period is higher than that of the ALL data for predicting 4 h ahead. Figures 5–7 intuitively show that the prediction simulation accuracy of the ice formation period and the aquatic grass period is higher than that of the ALL data for predicting 8 h ahead. The simulation accuracy of the sub-period prediction of 4 h ahead is higher than that of the sub-period prediction of 8 h ahead, as shown in Figure 8.

The prediction models were evaluated from an algorithmic perspective. Figures 2–4 show that the improved PSO-BP model achieved the best simulation results for predicting 4 h ahead, followed by the SVR model. The improved PSO-BP model achieved the best simulation results in predicting 8 h ahead, obtaining the highest R (as shown in Figures 5–7). Figure 8 shows that the accuracy of predicting 4 h ahead using the improved PSO-BP model is higher than that of predicting 8 h ahead.

We further analyzed the reasons for obtaining different prediction accuracies by comparing the prediction results of different models. From a modeling perspective, the performance of BP, improved PSO-BP, SVR, and improved PSO-SVR was weighed for comparison. The BP neural network has a strong nonlinear mapping ability, high self-learning, and self-adaptive ability, with a certain degree of fault tolerance (Xia & Lv 2005; Gao et al. 2018; Xue et al. 2022). However, the algorithm is a gradient descent algorithm, its fixed learning rate slows down convergence, and it has the possibility of falling into local minima. The SVR uses kernels, sparse solutions, and Vapnik–Chervonets for controlling the number of margins and support vectors. It does not depend on the dimensionality of the input space and has a long run time due to the need to calculate the predicted regression effect for each parameter (Khan & Coulibaly 2006; Behzad et al. 2010; Malakar et al. 2021). The particle swarm algorithm is highly effective for optimizing the parameters; the results (Figures 2–7) show that the prediction simulation accuracy of improved PSO-BP is higher than that of the BP neural network model. In contrast, improved PSO-SVM prediction is slightly worse than the other models, but it has the advantage of being the fastest model, and in the process of searching for the optimal parameters, the local optimum can be found promptly. Figures 4 and 7 show that the SVR significantly reduced the dispersion of the prediction, and the prediction accuracy was higher than that of the BP neural network. The improved PSO-BP neural network algorithm combines the advantages of particle swarm and BP neural network, has a fast convergence speed and high stability (Cheng et al. 2022), prevents the gradient descent from falling into local minima, shortens the training time, and improves the prediction effect of the whole model. Compared with the other models, the improved PSO-BP neural network has high prediction accuracy and short training time, which is also confirmed in the study of Li et al. (2019) and Xiong et al. (2021), and coupling multiple machine learning methods can improve the model prediction accuracy. The experimental results show that the improved PSO-BP neural network model is the most suitable for predicting water levels at pumping stations, and it has adequate practicality.

In this study, the BP neural network, the improved PSO-BP neural network, SVR, and improved PSO-SVR were used to predict water levels 4 and 8 h ahead under the ice formation period, the aquatic grass period, the normal scheduling period, and ALL conditions of Baliwan. According to the results of the five evaluations of MAE, MSE, RMSE, MAPE, and R, all four machine learning models achieved satisfactory prediction results, where the improved PSO-BP model was more effective in reducing the MSE and the RMSE of prediction. The prediction effect of the ice formation period and the aquatic grass period was better than that of the normal scheduling period and ALL conditions, and the prediction accuracy of predicting 4 h ahead was higher than that of predicting 8 h ahead. In the future, we will improve the prediction accuracy of the model by mining data features and studying more detailed working conditions of special periods. Additionally, we expect to combine numerical simulation and hybrid machine learning algorithms to obtain models with shorter prediction periods, faster operation speed, and higher prediction accuracy. This will allow us to achieve the effect of multiple inputs and multiple outputs and contribute to the optimization of long-distance water transfer scheduling projects.

The authors wish to gratefully acknowledge the financial assistance from the Natural Science Foundation of Shandong Province (ZR2020ME249), the Natural Science Foundation of Shandong Province (NSFS) (No. ZR2020QE282), the Science and Technology Plan Project of the University of Jinan (No. XBS2010), and the other anonymous reviewer whose comments greatly improved the quality of this paper.

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The authors declare there is no conflict.