A novel Kalman smoothing (Ks) − Long Short-Term Memory (LSTM) hybrid model for filling in short- and long-term missing values in significant wave height

Abstract

Continuous recordings of significant wave height (SWH) are of significant importance to facilitate the development and application of wave energy assessments. However, SWH recording is often interrupted by a variety of factors, including severe weather, apparatus failure, etc. The presence of short-term intermittent and long-term continuous missing values is recognized as a significant challenge for the accurate analysis and energy assessment of wave data. To effectively fill in the short- and long-term missing values simultaneously, a hybrid Kalman smoothing (KS) − Long Short-Term Memory (LSTM) model, which is applied to fill in SWH for the first time, is proposed. Initially, the short-term intermittent missing values, with missing ratios of 10%-50%, are filled by using the KS method, achieving a root mean square error (RMSE) as low as 0.082. Based on short-term missing values addressed by KS, the LSTM model is introduced to effectively predict the long-term continuous missing values. The maximum RMSE reduction rate of KS-LSTM is reduced by 49.6%, 59.4%, and 57.8% compared to KS-ARIMA, LSTM, and ARIMA, respectively, within the short-term intermittent missing ratios of 10%-50%. The maximum reduction in mean square error (MSE) is observed to be 71.4%, 83.6%, and 82.1%. Similarly, the maximum reduction in mean absolute error (MAE) is 74.6%, 61.1%, and 55.5%. The lowest prediction RMSE of long-term missing values by KS-LSTM is only 0.091, which demonstrates that the effectiveness of filling in both short-term and long-term missing values simultaneously by the KS-LSTM.