Abstract
The noise problem is crucial in modeling ship maneuvering motion function based on sampling tracks by conducting self-propulsion model tests. In general, the normal noise in the data is tolerated and deposed properly. While abnormal noise and outliers might accumulate errors, they are not accepted during the ship motion function training. In this paper, we show that the problems of variant Gaussian noise and outliers can be overcome using a support vector regression (SVR) method. The solution of SVR is given as a formula using sequential minimal optimization training algorithm. Simulations were conducted to validate the SVR method in dealing with variant Gaussian noise polluted ship tracks compared to polynomial and Fourier regression methods based on the known maneuvering motion function of the ship Mariner. Finally, the promising performance of the SVR method in deposing outliers and regressing polluted ship tracks is demonstrated. Here, the polluted ship tracks were recorded using an ultrasonic positioning system by conducting set-sail and circular tests in a towing tank.
Highlights
Ship maneuvering motion function plays a significant role in track prediction and dynamic positioning control
Ε-support vector regression (SVR) method is proposed to regress sampling tracks, which are generated by known maneuvering motion function of ship Mariner and polluted by variant Gaussian noise
OF ε-SUPPORT VECTOR REGRESSION AND sequential minimal optimization (SMO) ε-support vector regression (ε-SVR) derives its origin from support vector machine (SVM) [11]
Summary
OF ε-SUPPORT VECTOR REGRESSION AND SMO ε-SVR derives its origin from support vector machine (SVM) [11]. Because a few support vectors constitute separating hyperplane, SVM is sensitive to noises and outliers. The introduction of slack variable C decreased the influence of noises and outliers to the optimal separating hyperplane in C-SVM [13]. Owing to an ε-insensitive error function that determines noises insensitiveness of separating hyperplane, C-SVR was successfully applied to solve the regression problem based on C-SVM. Ε-SVR achieved the optimal regression based on support vectors with noises and outliers punished by adjusting slack variable C and setting insensitive error ε. Chunking algorithm [11] is reported by Boser et al decomposition algorithm [15], [16], SMO algorithm [17]–[19], and modified algorithms were proposed to solve SVR.
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