A new reliability based optimization of tuned mass damper parameters using energy approach

In this work a reliability based optimization (RBO) strategy of Tuned Mass Damper (TMD) parameters is presented. The strategy is based on an energetic approach. The strategy consists to optimize the TMD parameters so that we minimize the failure probability (objective function) characterized by the exceedence of the power dissipated in the primary structure of a certain threshold value during some interval time. The evaluation of the objective function is carried out using the classical Rice’s formula. The strategy is, firstly, applied to linear single-degree of freedom (SDOF) system, subjected to seismic motion, and then extended to linear multi-degree of freedom (MDOF) system. The use of the Rice’s formula requires the knowledge of the joint probability density function (PDF) of the considered processes; to this end, exact expression of the joint PDF is presented for the SDOF system and an approximation is presented for the evaluation of the failure probabilities for the MDOF system. By making use of the obtained joint PDF, for the SDOF system, as the a priori joint PDF, the approximation of the joint PDF, for the MDOF system, has been performed using the Minimum cross-entropy method (MinxEnt). To highlight the good effectiveness of the proposed strategy, a ten-story shear building, subjected to different earthquakes, is considered. The obtained results are compared with other from literature, and it has been shown the superiority of the proposed strategy.

On Rice's Formula for Stationary Multivariate Piecewise Smooth Processes

Let X = {Xt: t ≥ 0} be a stationary piecewise continuous Rd-valued process that moves between jumps along the integral curves of a given continuous vector field, and let S ⊂ Rd be a smooth surface. The aim of this paper is to derive a multivariate version of Rice's formula, relating the intensity of the point process of (localized) continuous crossings of S by X to the distribution of X0. Our result is illustrated by examples relating to queueing networks and stress release network models.

On Rice's Formula for Stationary Multivariate Piecewise Smooth Processes

LetX= {Xt:t≥ 0} be a stationary piecewise continuousRd-valued process that moves between jumps along the integral curves of a given continuous vector field, and letS⊂Rdbe a smooth surface. The aim of this paper is to derive a multivariate version of Rice's formula, relating the intensity of the point process of (localized) continuous crossings ofSbyXto the distribution ofX0. Our result is illustrated by examples relating to queueing networks and stress release network models.

Assessment of Full-Scale Measurements With Regard to Extreme Hogging and Sagging Condition of Container Ships

In the design of a vessel’s ultimate strength the extreme hogging condition is of great concern. Due to special properties of container ship structures, such as large bow flare and overhanging stern, wave-induced slamming makes the ship responses more skewed to sagging conditions. In particular in large sea states, the ratio between maximum sagging and hogging can be quite high. Hence, the sagging condition might be very crucial with respect to a ship’s ultimate strength. In this study, the extreme response caused by hogging and sagging is derived from upcrossing spectrums of ship responses. The Weibull fitting method and Rice’s formula for the computation of the upcrossing spectrum are discussed using full-scale measurements from a container vessel on the North Atlantic trade. The extreme ship responses are therefore predicted using the long-term upcrossing spectrum. In the case where the ship response can be approximately treated as a series of stationary Gaussian processes, the corresponding upcrossings are computed by the explicit Rice’s formula. For the non-Gaussian ship response, it is shown that the 4-moment Hermite transformation is an efficient approach to compute the corresponding upcrossing spectrums. The parameters in the transformation mainly depend on the wave environments and operation profiles. The relations between these parameters and the wave environments are needed if no measurement is available. However, according to the full-scale measurements, it is not possible to find general formulas to estimate the parameters in terms of wave environments or operation profiles for the practical applications.