A novel hybrid model based on two-stage data processing and machine learning for forecasting chlorophyll-a concentration in reservoirs

Abstract

The accurate and efficient prediction of chlorophyll-a (Chl-a) concentration is crucial for the early detection of algal blooms in reservoirs. Nevertheless, predicting Chl-a concentration in multivariate time series poses a significant challenge due to the complex interrelationships within the aquatic environment and the discrete and non-stationary nature of online monitoring of water quality data. To address the aforementioned issue, this paper proposes a novel prediction model named SGMD-KPCA-BiLSTM (SKB) for predicting Chl-a concentration. The model combines two-stage data processing and machine learning (ML). To capture nonlinear relationships in multivariate time series data, the optimal data subset is determined by combining symplectic geometry mode decomposition (SGMD) and kernel principal component analysis (KPCA). This subset is then input into a bidirectional long short-term memory (BiLSTM) model, and the model's hyperparameters are optimized using the sparrow search algorithm (SSA) to improve the accuracy of predictions. The performance of the model was evaluated at Qiaodian Reservoir in Shandong, China. To assess its superiority, the evaluation criteria included the root mean square error (RMSE), mean absolute percentage error (MAPE), mean absolute error (MAE), coefficient of determination (R²), frequency histograms of the prediction error, and the Taylor diagram. The prediction performance of five single models, namely the back-propagation (BP) neural network, support vector regression (SVR), long short-term memory (LSTM), convolutional neural network with long short-term memory (CNN-LSTM), and BiLSTM, as well as three hybrid models, namely SGMD-LSTM, SGMD-KPCA-LSTM, and SGMD-BiLSTM, were compared against the SKB model. The results demonstrated that the SKB model performs best in predicting Chl-a concentration (R² = 96.19%, RMSE = 1.05, MAE = 0.65, MAPE = 0.08). It significantly reduced the prediction error compared to other models for comparison. Furthermore, the multi-step predictive capabilities of the SKB model are also discussed. The analysis shows a decline in predictive performance with larger prediction time steps, and the SKB model exhibits slightly superior performance compared to the other model at corresponding prediction intervals. The model has significant advantages in terms of its ability to accurately predict the non-smooth and nonlinear Chl-a sequences observed by the online monitoring system. This study presents a potential solution for controlling and preventing reservoir eutrophication, as well as an innovative approach for predicting water quality.

Keywords: Bidirectional long short-term memory; Chlorophyll-a; Eutrophication; Kernel principal component analysis; Prediction; Symplectic geometry mode decomposition.