Application of a Hybrid Model Based on CEEMDAN and IMSA in Water Quality Prediction

[Objectives] To enhance water quality prediction accuracy, this study aims to address the following challenges: (1) traditional prediction methods often rely on simple, elementary decomposition techniques, limiting their ability to extract meaningful data features. (2) Single models and basic optimization algorithms result in low prediction accuracy. (3) Most approaches fail to leverage the advantages of different networks to analyze components of varying complexity, leading to inefficient model utilization. (4) Few studies incorporate error correction after prediction. This study proposes a novel hybrid model for water quality prediction. [Methods] First, the original water quality sequence was decomposed using Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). Next, Fuzzy Dispersion Entropy (FuzzDE) categorized the components into high-, medium-, and low-complexity subsequences. Then, an Improved Mantis Search Algorithm (IMSA) optimized three distinct models: Bidirectional Long Short-Term Memory (BiLSTM) for high-complexity components, Least Squares Support Vector Regression (LSSVR) for medium-complexity components, and Extreme Learning Machine (ELM) for low-complexity components. The predictions were combined and reconstructed, and a BiLSTM-based error correction model further corrected the errors, yielding the final prediction results. [Results] The study introduced four key innovations to the original Mantis Search Algorithm (MSA): (1) combining Logistic-Tent chaotic mapping for population initialization, ensuring uniform and random distribution of initial solutions to enhance global search capability and convergence speed; (2) nonlinear acceleration factor, refining MSA’s core update formula to transition from global exploration to local exploitation, mitigating local optima entrapment; (3) elite-guided adaptive update strategy, addressing the excessive randomness in the position update strategy when Mantis attacks fail, improving late-stage search efficiency while preserving some randomness; (4) opposition-based learning, generating individuals opposite to the current individual to enhance global optimization. IMSA’s performance was validated using benchmark functions (Rosenbrock for unimodal, Michalewicz for multimodal), confirming improved global search and convergence precision. After determining the network hyperparameters, ablation experiments were conducted to analyze the contribution of each strategy to the network model, providing a clear understanding of how each strategy impacts prediction performance. Finally, the sequence of model usage was validated by using FuzzDE to calculate the complexity of each component, creating high-, medium-, and low-complexity subsequences. The learning capabilities of different networks for these subsequences were verified, with BiLSTM used to predict high-complexity components, LSSVR for medium-complexity components, and ELM for low-complexity components. [Conclusions] This study performed a simulation verification using dissolved oxygen (DO) concentrations from two sections of Youshui River (a tributary of the Yuanjiang River) and pH values from one station in the Xiangjiang River Basin. Missing values were addressed via linear interpolation. For outlier treatment, the study considered that outliers in the data might be caused by sudden pollution events and discontinuous non-point source pollution. Directly removing them could lead to information loss, so outliers were retained. After integrating decomposition, use of entropy, algorithm optimization, and error correction models, eleven comparative experiments were established to evaluate the effectiveness of each optimization method. The hybrid model’s effectiveness was validated using RMSE, R2, and MAPE metrics. Ultimately, the R2 reached over 90%, demonstrating that the prediction accuracy of the hybrid model outperformed other comparative models.