Structural Safety of the Steel Hall under Dynamic Excitation Using the Relative Probabilistic Entropy Concept

Abstract

This work aimed to analyze the reliability of a steel hall that was recently erected in central Poland subjected to dynamic wind excitation using the stochastic finite element method. Reliability analysis was completed using the relative entropy concept delivered by Bhattacharyya and contrasted with the first-order reliability method recommended by the engineering design codes. Bhattacharyya probabilistic relative entropy was additionally rescaled in this study to fit the demands and recommended admissibility intervals given in Eurocode 0. The finite element method study was carried out thanks to a discrete model created in the system ABAQUS 2019, while all further statistical and probabilistic computations were programmed and completed in the symbolic environment of MAPLE 2019. Contrary to most engineering analyses in steel structure areas, this study included the important warping effect while designing the hall ridges and the purlins. Dynamic structural responses were determined via the Hilber-Hughes-Taylor algorithm and their series were numerically obtained for a series of input uncertainty parameters representing several mechanical and environmental quantities. The generalized 10th order iterative stochastic perturbation technique was contrasted in this context with statistical estimators from the Monte Carlo simulations and numerical integration resulting from the semi-analytical approach. The key research finding of this study was an extremely good coincidence between the FORM indices and the rescaled relative probabilistic entropies for the given stochastic excitations, which additionally did not depend on a choice of one of the three proposed numerical approaches.

On Bhattacharyya relative entropy in a homogenization of composite materials

“…A choice of the Bhattacharyya entropy model has been motivated by its recent successful applications to study the reliability of some engineering structures under static environmental loads 11 as well as under dynamic wind excitation. 12 This relative entropy (divergence) has been derived assuming that both initial moduli, as well as homogenized characteristics, have Gaussian distribution, which has been demonstrated before. 8,13 This distribution has been chosen due to its popularity in various mechanical and physical applications, according to the brevity of the presentation, and because of its importance in the view of the maximum entropy principle.…”

“…An application of the relative entropy to study this distance seems to be more adequate than the traditional comparison of the basic probabilistic moments (or their various combinations) of the original and homogenized material tensors. A choice of the Bhattacharyya entropy model has been motivated by its recent successful applications to study the reliability of some engineering structures under static environmental loads 11 as well as under dynamic wind excitation 12 …”

Selected Problems of Random Free Vibrations of Rectangular Thin Plates with Viscoelastic Dampers

“…In the case of any mathematical difficulties with computer algebra integration, the iterative generalized stochastic perturbation technique implemented as the SFEM is recommended. Further uncertainty analysis may be alternatively completed by the application of probabilistic entropy or its relative version presented recently in the literature [ 17 , 18 ].…”

Research on Intelligent Detection Algorithm of the Single Anchored Mooring Area for Maritime Autonomous Surface Ships

“…It enjoys characteristics of the simple method and easy programming, and provides a relatively accurate answer. The Monte-Carlo stochastic simulation is widely used in research on Structural Safety [14], risk assessing workers' unsafe behavior [15], working space analyses of Robotic Arms [16], efficient long-term extreme analysis [17], helicopter maritime search and rescue response plans [18] and the dynamic process simulation of ship pilotage risk [19]. The above engineering problems share the same scientific principle with the mooring area detection problem, and act as a significant reference.…”