The dynamic analysis of a deepwater floating production systems has many complexities, such as the dynamic coupling between the vessel and the riser, the coupling between the first-order and second-order wave forces, and several sources of nonlinearities. Moreover, the sea state is random. Hence, there is a need of stochastic dynamic analysis for such systems. In this paper, the evaluation of the
... [Show full abstract] non-Gaussian distributions of the responses of these systems is developed through a novel method of stochastic equivalent linearization, called Tail Probability Equivalent Linearization Method (TPELM). The Tail Probability Equivalent Linear System (TPELS) is the Equivalent Linear System (ELS) obtained by minimizing the difference between the tail probability of the equivalent system and the original nonlinear system. The TPELS is defined through a machine learning algorithm providing the hyperplane capable of correctly classifying the highest number of sample data. TPELM has several attractive features: (i) it gives a good approximation of the tail probability with reduced computational cost, (ii) it works well in high dimensions and it is not affected by the presence of multiple design points, (iii) it gives information about the achieved accuracy, and (iv) it does not require the evaluation of the design point, which is challenging in high dimensional spaces. The accuracy and efficiency of TPELM is shown through the application to a simplified model of a marine riser