Onboard Tuning and Uncertainty Estimation of Vessel Seakeeping Model Parameters

Abstract

The accurate prediction of critical vessel motions is essential for safe and cost-efficient marine operations. Compared with the difference-frequency responses that can be compensated by mooring and dynamic positioning systems, first-order wave-induced responses are very challenging to control and therefore become increasingly important to accurately predict. Marine operations are usually executed at moderate seas where the rigid body dynamics of conventional vessels can be well represented by linear transfer functions in 6 degrees of freedom, also called response amplitude operators (RAOs). The accuracy of these RAOs depends on the confidence in the vessel loading condition at operation. During the design of marine operations, vessel loading conditions are normally specified according to the best available information on operational arrangement and planning. However, the real condition on board can be different from the planned condition. Therefore, improving knowledge about onboard vessel conditions can increase the motion prediction accuracy, reduce conservatism, and consequently increase cost efficiency. Unfortunately, some critical vessel parameters describing the loading condition and dynamics (e.g., related to inertia distribution and viscous damping) are difficult to measure directly.

The present PhD thesis therefore focuses on how to improve the knowledge about onboard vessel conditions by tuning important vessel parameters and estimating their uncertainties based on available vessel response measurements and wave information for a very limited number of sea states. Consequently, the tuned vessel parameters can improve the accuracy of the corresponding RAOs and the motion prediction for unobserved future sea states, and the quantified uncertainties can be applied to quantitative reliability and risk assessment for real-time onboard applications.

First, the important vessel parameters mostly affecting the critical vessel responses are identified by parametric sensitivity studies. The sensitivity varies with the quantities and locations of the interesting responses, vessel loading conditions, and wave conditions in terms of wave direction and period. Then, an algorithm based on discrete Bayesian inference (DBI) is proposed for tuning these important vessel parameters. Likelihood functions are estimated based on inverse distance weighting. The DBI-based tuning can fully capture the nonlinear and multimodal behavior within the entire predefined parametric uncertainty domain. Sensitivities of the hyperparameters of this DBI-based model are also studied.

The tuning results are influenced by the quality of lowpass filtering of signal noise. A novel algorithm is thus developed to find the sea state dependent optimal cutoff frequency without the need to know sea state information. The optimal cutoff frequency can be found based on the criteria of two newly introduced parameters and , which describe the relationship of cutoff frequency with the energy and zero-upcrossing period of filtered vessel response signals. An improved tuning of vessel parameters is also demonstrated by applying this adaptive lowpass filter.

Due to linearization, some important hydrodynamic parameters become sea state dependent, such as the linearized viscous damping coefficient. Those tuned parameters and the associated RAOs at the present sea state cannot be applied directly for motion prediction at other sea states. Therefore, a predictive model is required to be implemented in the tuning loop so that the tuned parameter can improve the accuracy of the predictive model, and in return, this model can provide improved prior information for prediction or tuning in the next sea states. Consistent with uncertainty updating in the tuning process, the predictive model should also be able to carry and update the associated uncertainties. To address this challenge, a model based on Gaussian process regression is proposed and applied to tune and predict sea state dependent parameters as part of the DBI-based tuning process. The feasibility of the modified tuning algorithm is demonstrated by numerical simulations. With doubled computational cost, the 2-step tuning algorithm is found to be more promising as a compromise between the different preferred tuning rates for sea state dependent and independent parameters.

For the DBI-based tuning algorithm, the computational cost increases exponentially with the number of considered uncertain vessel parameters. Therefore, a new algorithm inspired by unscented Kalman filter (UKF) is proposed to solve this curse of dimensionality. Only the mean and covariance of the joint probability distribution of uncertain vessel parameters are accounted for in the tuning process. The computational cost of the UKF-based algorithm increases linearly with the number of uncertain parameters and is thus preferred for real applications. The UKF-based tuning algorithm becomes even more attractive because it is also proven to be able to simultaneously reduce uncertainties of the corresponding sea state characteristics. Numerical simulations are first performed to demonstrate the algorithm.

Furthermore, the UKF-based tuning algorithm is tested based on seakeeping model tests for an offshore construction vessel with open moonpools. Coupling and nonlinear effects from moonpool resonance on vessel motions are significant. Consequently, simplifications of the applied numerical seakeeping simulation introduce significant systematic errors of the estimated RAOs around those resonance frequencies. Unbiased tuning is achieved by carefully designing the measurement space of the UKF model, accounting for such systematic errors.