Session: 07-12-01: Optimization, Uncertainty and Probability

Paper Number: 112546

112546 - Reliability-Based Design Optimization of Uncertain Linear Systems Subjected to Random Vibrations 

In the area of random vibrations, the probability of first-passage failure is defined as the probability that a response of a system subjected to a stochastic load reaches a certain threshold. For instance, this response can be represented by a stress response and the threshold by the yield strength of the system material. This probability is calculated using the failure rate and a service life. In the case of linear systems and Gaussian stochastic random processes, well-established results exist to compute the probability of first-passage failure.

In most random vibration problems, the system’s parameters are assumed to be deterministic, leaving the loads as the only source of uncertainty. However, although it is sometimes assumed that uncertainties in the system parameters have negligible effects on the response of a system subjected to a random excitation, particularly when the excitation is a wide-band process such as an earthquake ground motion, it has been demonstrated that the uncertainty in those parameters may have an equal or greater influence on the response than the uncertainty in the excitation.

In this work, the computation of the first-passage failure probability with uncertain system parameters is computed as the total probability, which does not only account for the stochastic excitation, but also for the distributions of random parameters such as material properties. This quantity is in general difficult to compute for complex problems involving finite element analyses due to its dependency on the computation of the failure rate, which depends on the root-mean-square response of the displacement and velocity. This difficulty becomes even more pronunced in the case of design optimization under uncertainty.

This work proposes to solve the reliability-based design optimization problem using surrogate models and a dedicated adaptive sampling scheme. Gaussian Processes (GPs) are used as surrogates and the adaptive sampling scheme leverages the availability of the prediction variance while accounting for the joint distribution of the system’s random parameters, enabling the scheme to focus on regions of the space in high probabilistic content. In particular, a GP is used to approximate the failure rate over the extended space which includes design and random parameters. In addition, the proposed method uses a classification scheme based on a support vector machine to account for several failure modes simultaneously, which makes the computation of the total probability markedly more efficient.

The method is applied to the reliability-based design optimization of several random vibrations problems involving finite element models. In particular, a payload adaptor in a launcher subjected to a specific random excitation defined through a power spectral density is used. The geometry and material properties of the payload are used as design variables. Uncertainties in the material properties are selected as the random parameters. Several failure modes are used in the computation of the total probability of failure.

Presenting Author: Luis Enrique Ballesteros Martinez University of Arizona

Presenting Author Biography: Luis Enrique Ballesteros Martinez is a PhD candidate in the Aerospace and Mechanical Engineering Department at the University of Arizona.

Authors:

Luis Enrique Ballesteros Martinez University of Arizona
Samy Missoum University Of Ariz