Hybrid water quality prediction based on attention combined with frequency enhancement and multi-seasonal decomposition

Water quality forecasting methods can reflect the water quality situation and development trend in the short or long-term future and provide important support for water environment management. Due to the influence of other factors fluctuating in the water environment and errors in collection equipment, water quality time series data are characterized by instability and high nonlinearity, and a nonlinear regression problem of non-smooth series data is difficult in the prediction field. This work proposes a hybrid model for water quality prediction called SMDF2 to improve the prediction accuracy. SMDF2 integrates the Savitsky-Golay (SG) filter, Multi-seasonal trend decomposition using loss (MSTL), Discrete Fourier Transform (DFT), Frequency Enhanced Block (FEB) and Frequency Domain Enhanced Attention (FEA) in an encoder-decoder architecture. The SG filter is employed to smooth out the noise to diminish the instability in time series. MSTL is used to extract periodic and trend components for the nonlinear sequences, and DFT is utilized to achieve the conversion between the time domain and the frequency domain. FEB and FEA are employed for the frequency-domain feature extraction and the frequency-domain feature correlation learning. Experimental results with real domestic and international water environment datasets for both long-term and short-term predictions demonstrate that SMDF2 surpasses various advanced models in accuracy for both single-element and multi-element predictions. Specifically, it improves prediction accuracy by an average of 21.73 % for single-element tasks and 18.14 % for multi-element tasks.