arXiv:2001.09884v1 [math.NA] 27 Jan 2020 Adaptive Importance Sampling based Neural Network framework for Reliability and Sensitivity Prediction for Variable Stiffness Composite Laminates with hybrid uncertainties Tittu Varghese Mathew a , P Prajith a , R. O. Ruiz b , E. Atroshchenko c , S Natarajan a,∗ a Integrated Modelling and Simulation Lab, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai-600036, India. b Department of Civil Engineering, Universidad de Chile, Av. Blanco Encalada 2002, Santiago,Chile c School of Civil and Environmental Engineering, University of New South Wales, Sydney, Australia Abstract In this work, we propose to leverage the advantages of both the Artificial Neural Net- work (ANN) based Second Order Reliability Method (SORM) and Importance sampling to yield an Adaptive Importance Sampling based ANN, with specific application towards fail- ure probability and sensitivity estimates of Variable Stiffness Composite Laminate (VSCL) plates, in the presence of multiple independent geometric and material uncertainties. The performance function for the case studies is defined based on the fundamental frequency of the VSCL plate. The accuracy in both the reliability estimates and sensitivity studies using the proposed method were found to be in close agreement with that obtained using the ANN based brute-force MCS method, with a significant computational savings of 95%. Moreover, the importance of taking into account the randomness in ply thickness for failure probability estimates is also highlighted quantitatively under the sensitivity studies section. Keywords: Adaptive Importance Sampling, Artificial Neural Network, Global Reliability Sensitivity Analysis, Monte Carlo Simulations, Probability of failure, Second Order Reliability Method, Variable Stiffness Composites. 1. Introduction None of the above mentioned parameters are deterministic in nature, thanks to the in- herent statistical nature of material properties of the constituents and the unavoidable fab- rication inaccuracies in ply layup and fiber placements. Composite materials are used extensively both in primary as well as secondary structures of aerospace and mechanical structures. During the course of a product lifetime, such compo- nents are exposed to harsh environments, including mechanical vibration. They are found to exhibit superior strength-to-weight and strength-to-stiffness ratios. Since composites are an ∗ Corresponding author 1 Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai-600036, India. E-mail: [email protected]; [email protected] Preprint submitted to Elsevier January 28, 2020
Adaptive Importance Sampling based Neural Network framework for Reliability and Sensitivity Prediction for Variable Stiffness Composite Laminates with hybrid uncertainties
Jun 26, 2023
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