Improving Ship Motion Forecasts by Combining Measurement Data with Physical Model Forecasts

This paper compares models to improve ship motion forecasting performance on 4, 8 and 12 hours ahead forecasts by combining time series measurement data with the currently used physical model forecasts. The first is a simple component model which serves as a basic benchmark. The second is a local level model where the physical model forecast is included as a component in the state equation of which we consider two variants: one where the weighting coefficients for the components in the state equation are estimated upfront and kept fixed and one where these coefficients are re-estimated during the forecasting exercise. The third is a dynamic mixture model where the physical model is included in the same way as in the local level model, but this specification allows for level shifts in order to react to peak responses. In both the second and the third model the parameters are estimated by the Bayesian technique of Gibbs sampling. The performance is measured by the average root mean square error over the forecasting exercise. The simple component model does not improve the performance compared to the physical model forecasts. The local level model with re-estimated coefficients leads to improvements in the 4 and 8 hour forecasting horizons but fails to do so for 12 hours ahead. The strongest forecasting improvements of 14-44% are found using the local level model with pre-estimated coefficients. This model performs better than both the dynamic mixture model with fixed and with varying coefficients, which find improvements of 11-41% and 11-36% respectively. The performances of the models hold when tested on multiple subsets of data, which indicates that finding the improvement is not a coincidence. The local level model is also more suitable for implementation due to advantages in computing time, sensitivity to prior parameters and the data length needed to evaluate the model than the dynamic mixture models. Therefore it is the recommended method to use as basis when considering implementation in the on-board software to improve the ship motion forecasting performance.