Circular Regression for the Prediction of Ocean Wave Direction Using wrapped Double Lomax Neural Network

Abstract

Ocean wave direction is a significant circular parameter in oceanographic and marine engineering applications and for coastal engineering, offshore structure design, navigation and marine environmental assessment, accurate prediction of wave direction is a crucial part of the process. The direction of a wave is a circular quantity as the directions () are the same direction. Conventional regression methods can thus generate "wrong" predictions and errors near the circular boundary. To solve this problem, this work introduces a new ocean wave peak direction prediction model named Wrapped Double Lomax Neural Network (WDLNN), which is based on a CNN architecture. The model proposed here uses the Wrapped Double Lomax activation function derived using wrapping method that was applied to Double Lomax  Distribution and it was converted into circular probability modeel named as Wrapped Double Lomax  Distribution(WDLD), which is a probability-based activation function that can be used to model the directionality, and is applied to the CNN framework. The peak direction is converted to its sinusoidal components, sine and cosine, so that the direction can be represented with a circular structure, but without it being discontinuous at  and . The ocean wave observations in the coastal dataset from Mooloolaba is used to evaluate the model. Various combinations of the location and scale parameters of the Wrapped Double Lomax are explored to study the effect on prediction performance. Circular prediction error measures are used to evaluate model performance: Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and a circular coefficient of determination (). This proposed framework WDLNN shows a systematic application of circular probability distributions for deep learning and its ability to accurately predict the direction of the ocean waves.