Session: 07-13-01 Optimization, Uncertainty and Probability I

Paper Number: 71092

Start Time: Tuesday, 03:30 PM

71092 - A Sensitivity-Based Approach for Interval Reliability Analysis of Structures Under Random Excitation 

It is now widely recognized by the scientific community that the classical probabilistic reliability theory may fail to provide accurate structural safety assessment when available experimental data are insufficient to define the Probability Density Function (PDF) of the uncertain parameters. Indeed, the probabilities of failure are highly sensitive to small variations of the assumed probabilistic models, especially in the tails [1]. To cope with this issue, Ben-Haim [1] first introduced a non-probabilistic concept of reliability using the convex model of uncertainty. Since then, several studies have been devoted to structural safety assessment based on non-probabilistic uncertainty models.

The present paper addresses reliability analysis of linear discretized structures subjected to stationary Gaussian multi-correlated random excitation. Both mass and stiffness parameters are assumed to be uncertain and are modeled as interval variables [2]. The formulation is developed in the context of the first-passage theory, under the Poisson assumption of independent up-crossings of a prescribed threshold [3]. It is assumed that the structure fails as soon as a selected stress process at a critical location firstly exceeds a prescribed safe domain. Due to uncertainties, the reliability function for the extreme value stress process turns out to have an interval nature. The main challenge is to limit the overestimation due to the so-called dependency phenomenon, which affects stress-related quantities more than displacements. To this aim, a sensitivity-based procedure relying on the Improved Interval Analysis via Extra Unitary Interval [4] is proposed. By analyzing the sign of sensitivities, this procedure allows us to detect suitable combinations of the endpoints of the uncertain mass and stiffness parameters which yield accurate estimates of the lower bound and upper bound of the interval reliability function for the extreme value stress process. Furthermore, sensitivity analysis enables to identify the most influential parameters on structural reliability. To enhance the computational efficiency, only the most influential uncertain parameters can be conveniently modeled as interval variables while the remaining parameters can be set to their nominal values.

For validation purpose, a frame structure with uncertain mass of the floors and Young’s moduli of the columns subjected to wind excitation is analyzed.

References

[1]  Ben-Haim, Y., 1994, “A non-probabilistic concept of reliability,” Struct. Saf., 14(4), 227-245.

[2]  Moore, R.E., Kearfott, R.B., and Cloud, M.J., 2009, Introduction to Interval Analysis, SIAM, Philadelphia.

[3] Lutes, L.D, Sarkani, S., 1997, Stochastic Analysis of Structural and Mechanical Vibrations, Prentice-Hall, Upper Saddle River.

[4]  Muscolino, G., and Sofi, A., 2012, “Stochastic analysis of structures with uncertain-but-bounded parameters via improved interval analysis,” Probab. Eng. Mech., 28, pp. 152-163.

Presenting Author: Alba Sofi University "Mediterranea" of Reggio Calabria

Authors:

Filippo Giunta University of Messina
Giuseppe Muscolino University of Messina
Alba Sofi University "Mediterranea" of Reggio Calabria