Robust Statistical Methods for Analysis of Ship Motion Simulation Results

摘要

Simulation of ship motion is becoming increasingly more viable as a method for estimating the value of parameters that can be used for design, life-cycle management, risk analysis, developing and validating operational tactics, training, etc. It is vitally important to be able to draw sound conclusions from the simulation results. An examination of the process for obtaining parameter estimates and the means of determining their reliability is key to evaluating the confidence that can be placed in the results and avoiding drawing inappropriate conclusions from the simulation results. An extension of Chebyshev's Theorem was developed to provide a robust general tool to provide a conservative estimate of the probability that the parameter is within a specific interval. In addition, a method for determining the number of simulation runs required is suggested. A : wave amplitude; k : wave number; x : position; t : time; ε : phase angle; Η : wave height; ω : wave frequency; a : small change in sample mean; c : coefficient of v in half-interval of the Extended; Chebyshev's Inequality; E[·] : expected value; k : coefficient of σ (standard deviation) in half-interval; of the standard Chebyshev's Inequality; l : center of the interval in the Chebyshev's; Inequalities; n : number of simulations required; P(·) : probability; p(x) : probability density function; p(x_i) : probability density function evaluated at x_i; Q : 1 - P; X : random variable; x : Sample mean; i.e., expected value of X based on the; sample; x_i : specific value of the random variable; x_(n+1) : next value to be added; μ : population mean; σ : population standard deviation