The nonlinear regression trees for retrieving missed data during sea-level measurement

Sea surface displacement (SSD) is a crucial parameter in environmental engineering. The measurements of SSD are susceptible to the failure of instruments and equipment, data losses, and other unpredictable events. In this study, we developed an innovative nonlinear regression trees (NRT) technique to retrieve the missing data of SSD. The model was used on the record of SDD for the ADCPs deployed in the Gdansk Gulf along the Vistula Lagoon. The NRT suggests using a nonlinear machine learning algorithm instead of linear regression at the end nodes of a tree. Two different NRT models were developed. One of them is based on the support vector regression (SVR) and the other on adaptive neuro-fuzzy inference system (ANFIS). The performance of both models was validated by comparing their results with the state-of-the-art algorithms. The models were trained using four input parameters, including the pressure and SDD of two other ADCPs, which recorded complete time series data. The analysis shows that NRT methods, with an average RMSE of 0.019 m, provide about 71.13% more accurate prediction than random forest (RF). Among all models, the NRT-SVR, with the lowest RMSE of 0.009 m and MAE of 0.002 m, and the highest R² of 0.997, NSE of 0.997, and IA of 0.999, is ranked as the most accurate model. The simplicity, as well as the high efficiency of the developed NRT models, enable us to apply them for pattern recognition of other environmental and engineering problems.