Significant wave height prediction based on improved fuzzy C-means clustering and bivariate kernel density estimation

Significant wave height prediction, as a precursor technology for wave energy utilization, plays a crucial role in the effective harnessing of wave energy. However, existing prediction models overlook the heterogeneity of data patterns in wave height sequences, lack independent modeling of different types of data, and lack interval estimation algorithms capable of simultaneously describing non-normality and heteroscedasticity. To address this, this paper proposes a novel hybrid model. Firstly, a classification method combining feature selection and Improved Fuzzy C-Means clustering (IFCM) is proposed to address the heterogeneity of the data. Subsequently, the Optimal Variational Mode Decomposition (OVMD) and Bidirectional Long Short-Term Memory neural network (BiLSTM) based on Multi-Head Attention mechanism (MHA) are combined to enhance the adaptability of the prediction model to different data types. Finally, to address the shortcomings of existing interval algorithms, a Bivariate Kernel Density Estimation (BKDE) is used to describe the relationship between predicted values and error values, aiming to improve the performance of interval prediction. The model is evaluated using data from buoys 40025 and 51001. The results show that the MAE of this paper's model in the 40025 dataset is reduced by an average of 56.44 %, 33.75 %, and 15.37 % compared to LSTM、OVMD-BiLSTM and OVMD-MHA-BiLSTM respectively, which significantly improves the stability and accuracy of the model, BKDE has the smallest composite interval evaluation metric CWC compared to KDE, Bootstrap and GPR, with an average value of 0.1457, which is significantly better than the common interval construction algorithms.