Du, H. and Yu, M., 2020. Probability distribution of nonlinear wave surface slope based on Copula function. In: Yang, Y.; Mi, C.; Zhao, L., and Lam, S. (eds.), Global Topics and New Trends in Coastal Research: Port, Coastal and Ocean Engineering. Journal of Coastal Research, Special Issue No. 103, pp. 839–842. Coconut Creek (Florida), ISSN 0749-0208.

In order to improve the reliability of nonlinear wave surface, a mathematical model of probability distribution of nonlinear wave surface slope based on Copula function is proposed. Using the structure of nonlinear wavefront slope statistical model of fuzzy Smith neural network, the probability distribution function of nonlinear wavefront slope is analyzed under the condition of gradient linear complementarity, and the convergence constraint function of nonlinear wavefront control is realized. According to the weights of the nonlinear wavefront slope statistical model, a delayed hyperbolic proportional differential adjustment feedback element is constructed for implicit layer weight learning of nonlinear wavefront. The robustness of nonlinear wavefront reliability output is trained on the nodes of generalized gradient distribution, and the convergence is judged in the gradient distribution space. According to the learning method of nonlinear wave surface slope statistical model, the optimal solution of nonlinear wave surface slope statistical model is obtained, and the nonlinear Jakobi matrix is constructed to analyze the control stability. The simulation results show that the simulation reliability of probability distribution of nonlinear wave surface slope is good, and the steady-state convergence is good, which improves the reliability of probability simulation of nonlinear wave surface slope.