A new aspect of the ApEn application to improve the PSO-ANFIS model to forecast Caspian Sea levels

Abstract

Short-term forecasting of sea levels at the Caspian Sea plays an important issue for coastal planning. Therefore, a new aspect of the Approximate Entropy (ApEn) method application is studied to improve the Combined Particle Swarm Optimization and the Adaptive Network-based Fuzzy Inference System (PSO-ANFIS), Auto-Regressive Integrated Moving Average (ARIMA) models and Back Propagation Neural Networks (BP-NN). To evaluate the idea, seawater levels from 1961 to 2021 are categorized as training, validation (from 1961 to 2007 at Anzali station), and testing data (from 2008 to 2021 at Amirabad station). Results show the PSO-ANFIS model performance for forecasting the seawater level changes for four randomly selected time intervals and three critical periods. In addition, it is concluded that there are no considerable changes in the PSO-ANFIS model accuracy for embedding dimensions greater than 13 in forecasting of sea water level in the Caspian Sea. At the same time, the employed ApEn shows that there are no significant changes in approximate entropy values for block numbers more than 13 for the Caspian Sea levels. This shows the ApEn method performance to determine embedding dimensions for the forecaster models of time series. In addition, it resulted that the Caspian Sea water levels are on a decreasing trend on average by 5.495 cm every year until 2024 and the PSO-ANFIS model is reliable for 36 months as a short-term forecaster model. Comparing the developed PSO-ANFIS model with Long Short-Term Memory (LSTM) networks shows the PSO-ANFIS model significant superiority to the LSTM.