A Novel Adaptive Weighted Least Square Support Vector Regression Algorithm-Based Identification of the Ship Dynamic Model

This study contributes to developing a novel hybrid identification method based on intelligent algorithms, i.e. the least support vector regression algorithm (LS-SVR) and the artificial bee colony algorithm (ABC), to deal with the identification of the simplified ship dynamic model while the outliers exist in the measurements. The ship dynamic model is directly derived from our previous work which has been well verified and validated. The outliers are detected by introducing the robust estimation method namely the <inline-formula> <tex-math notation="LaTeX">$3\sigma $ </tex-math></inline-formula> principle and then deleted from the training data. The weighted version of LS-SVR (WLS-SVR) with spareness and robustness ability is used as the fundamental identification approach. To improve the performance of the WLS-SVR, the structural parameters involved in it are optimized by utilizing the artificial bee colony algorithm (ABC), and the weights of it are adaptively set with the use of the adaptive weight method. Two case studies including the simulation study on a container ship and the experimental study on an Unmanned Surface Vessel (USV) are carried out to test the proposed hybrid intelligent identification method. The simulation study demonstrates the effectiveness and the acceptable time complexity in terms of the engineering application of the proposed identification method through the comparison with the cross-validation method and particle swarm optimization algorithm optimized LS-SVR. In the experimental study, ABC-LSSVR, ABC-LSSVR with the <inline-formula> <tex-math notation="LaTeX">$3\sigma $ </tex-math></inline-formula> principle (D-ABC-LSSVR), ABC-LSSVR with the adaptive weight (ABC-AWLSSVR), and ABC-LSSVR with both the <inline-formula> <tex-math notation="LaTeX">$3\sigma $ </tex-math></inline-formula> principle and the adaptive weight (D-ABC-AWLSSVR) are applied to identify the steering model for the USV. The results indicate that the influence of the outliers on model identification is effectively diminished by the robust <inline-formula> <tex-math notation="LaTeX">$3\sigma $ </tex-math></inline-formula> principle and the adaptive weight method and that the D-ABC-AWLSSVR outperforms over the other three identification methods in terms of the mean squared error (MSE) of the model predictions.

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