۱- Introduction

۲- Time Series Models

۳- Dataset and Methodology

۴- Results and Dicussion

۵- Conclusions and Future Works

References

Abstract

Autoregressive Integrated Moving Average (ARIMA) is one of the linear model that is good, flexible, and easy to use in univariate time series analysis and forecasting. Some research activities in time series forecasting also suggest Artificial Neural Network (ANN) model as an alternative nonlinear model for forecasting. ARIMA model has a good ability to capture the linear pattern while the ANN model is good to capture the nonlinear pattern. ARIMA and ANN models have been widely used in the prediction of roll motion. ARIMA and ANN can also be combine as a hybrid model to take advantage of the ability of ARIMA and ANN models in linear and nonlinear modeling compared to ARIMA and ANN model. In this paper, we adapt the hybrid methodology to combine ARIMA and Deep Neural Network (DNN) model, an ANN model with multiple hidden layers. The real dataset used is the roll motion of a Floating Production Unit (FPU). The empirical results show that the DNN-ARIMA hybrid model is the best model for predicting the roll motion compared to the non hybrid models and very effective to improve forecast accuracy.

Introduction

Roll motion is one of the ship motion that is the most frequently studied. The ship safety can be analyzed based on the roll motion. The purpose is to prevent the danger of the ship, e.g. ship capsizing [6]. The rolling motion can also cause damages to ship containers. Therefore, the prediction of roll motion is the important thing in order to understand the stability of the ship. The prediction of ship motion can be done by several approaches. One of them is time series forecasting. In time series modeling, Autoregressive integrated moving average (ARIMA) is one of the popular time series models [25, 12]. It has been widely used in time series forecasting. ARIMA is a general form of several time series processes, such as pure autoregressive (AR), pure moving average (MA), combination of AR and MA (ARMA), and ARMA with differencing (ARIMA). Since ARIMA is a linear model, it is assumed that the data follows a linear pattern. However, the data in real problems does not always follow linear pattern only. The linear approximation is not always satisfactory to forecast with good performance as well. Artificial neural network (ANN) is an alternative nonlinear model that has been extensively studied and used in time series forecasting [24]. Their capability in nonlinear modeling is the major advantage of ANN model. It is not necessary to specify a particular model form. ANN model is adaptively formed based on the features presented from the data. For many empirical data sets where no theoretical guidance is available to suggest an appropriate data generating process, this data-driven approach is the suitable one [17]. Researches in prediction of ship motion have been studied by using several time series models. Zhang and Ye [26] used ARIMA model to predict the roll motion. Nicolau et al. [13] in their research used ANN model to predict the roll motion of a conventional ship. Different training data sets and noise conditions were used to analyze the neural architecture. The results showed that the predictor of ANN model worked well for different levels of the input noise. Khan et al. [8] have used both ARIMA and ANN models to predict the roll motion. The ARIMA model used was ARIMA(15,0,1) and the ANN model used was feedforward neural network with the combination of conjugate gradient (CG) algorithm and genetic algorithm (GA). The results showed that ANN model had a better performance than ARIMA model in predicting the roll motion. Several recent researches also shown that the roll prediction using ANN based model is still satisfactory and powerful [20, 23].