Session: 01-06-01: AI and Machine Learning in Acoustics and Vibrations

Paper Number: 173384

Local Failure Domain Approximation for the Stochastic Optimization of Random Vibration Problems 

When analyzing or optimizing structures under random vibrations, inherent uncertainties which are typically linked to material properties, can significantly impact the structure’s dynamic behavior. Consequently, these uncertainties, along with the randomness of the applied loads, must be incorporated when performing stochastic optimization.

Probabilistic constraints related to first passage failure and fatigue estimates under random vibrations depend on the computation of the root mean square (RMS) responses (e.g., displacement, acceleration, or stress RMS response). These quantities are often difficult to compute in complex problems that involve finite element analysis. The difficulty is further intensified by the need for repeated function evaluations in optimization problems.

A recent study addressed these challenges by employing Gaussian processes as surrogate models for failure rates, combined with a specialized adaptive sampling scheme to efficiently estimate the RMS responses of general systems. Probabilistic constraints related to first-passage failure were determined using established random vibration theory and by propagating inherent system uncertainties to calculate the total probability of first-passage failure. However, in this approach, the number of failure modes directly influences the number of required surrogates and function evaluations. This is, as the number of failure modes increases, so does the demand for surrogate models and computationally expensive function evaluations.

Therefore, this work proposes an adaptive classification-based approach that employs a Support Vector Machine (SVM) to approximate the boundaries of the local failure domain defined by a set of failure modes or limit state functions (LSF). Shifting the optimization approach from a regression to a classification scheme allows for a significant reduction in the number of function evaluations, as it eliminates the need to assess all failure modes or probabilistic constraints at every point in the design space. To refine the SVM and its approximation of the failure domain, an adaptive sampling scheme based on a Generalized Max-Min (GMM) sampling is employed. The GMM efficiently refines the SVM by selecting new samples along the failure boundary that are as far away as possible from the existing samples, while also considering the statistical distributions of both design variables and random parameters.

The proposed methodology is applied to the stochastic optimization of a cantilever beam with a tip mass and a launcher payload adapter to a specific random excitation defined through its power spectral density. Both problems are modeled through finite elements. The beam and the payload adapter geometries are used to define the design variables, whereas the material properties are selected as the random parameters. High dimensional optimization problems with multiple failure modes such as first-passage and fatigue are presented.

Presenting Author: Luis Enrique Ballesteros Martinez University of Arizona

Presenting Author Biography: Luis Enrique Ballesteros Martínez is a PhD candidate in the Aerospace and Mechanical
Engineering Department at the University of Arizona. He is part of the Computational Optimal Design of Engineering Systems (CODES) laboratory under the supervision of Dr. Samy Missoum.

Authors:

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