Novel reliability method for multidimensional nonlinear dynamic systems

Abstract

The paper describes a novel structural reliability method, particularly suitable for multi-dimensional structural responses, either measured or numerically simulated over sufficient period of time, resulting in sufficiently long ergodic time series. Unlike other reliability methods the new method does not require to re-start simulation each time system fails, in case of numerical simulation. In case of measured structural response, an accurate prediction of system failure probability is also possible as illustrated in this study. Moreover, classic reliability methods, dealing with time series do not have an advantage of dealing easily with system high dimensionality and cross-correlation between different dimensions.As an example for this reliability study was chosen container ship subjected to large deck panel stresses and extreme roll angles occurring during sailing in harsh weather. Risk of losing containers due to extreme motions is primary concern for ship transport. Due to non-stationarity and complicated nonlinearities of both waves and ship motions, it is a considerable challenge to model such a phenomenon. In case of extreme motions, the role of nonlinearities dramatically increases, activating effects of second and higher order. Moreover, laboratory tests may also be questioned because of the scaling and the sea state choice. Therefore, data measured on actual ships during their voyages in harsh weather provides a unique insight into statistics of ship motions.The aim of this work is to benchmark state of art method, which makes it possible to extract the necessary information about the extreme response from onboard measured time histories. The method proposed in this paper opens up the possibility to predict simply and efficiently failure probability for nonlinear multi-dimensional dynamic system as a whole.