[Paper Review] Reliability-based design optimization of imperfect shells using adaptive kriging meta-models

Vincent Dubourg, Jean‐Marc Bourinet+1 more|arXiv (Cornell University)|Jan 18, 2012

Advanced Multi-Objective Optimization Algorithms25 references3 citations

TL;DR

This paper proposes an adaptive kriging surrogate modeling approach for reliability-based design optimization (RBDO) of imperfect stiffened cylinder shells, using an augmented design space to simultaneously handle parametric uncertainty and robust performance assessment. The method enables efficient, accurate failure probability estimation and gradient-based optimization, achieving robust, cost-effective designs for submarine pressure hulls subject to buckling failure.

ABSTRACT

The optimal and robust design of structures has gained much attention in the past ten years due to the ever increasing need for manufacturers to build robust systems at the lowest cost. Reliability-based design optimization (RBDO) allows the analyst to minimize some cost function while ensuring some minimal performances cast as admissible probabilities of failure for a set of performance functions. In order to address real-world problems in which the performance is assessed through computational models (e.g. large scale finite element models) meta-modelling techniques have been developed in the past decade. This paper introduces adaptive kriging surrogate models to solve the RBDO problem. The latter is cast in an augmented space that "sums up" the range of the design space and the aleatory uncertainty in the design parameters and the environmental conditions. Thus the surrogate model is used (i) for evaluating robust estimates of the probabilities of failure (and for enhancing the computational experimental design by adaptive sampling) in order to achieve the requested accuracy and (ii) for applying the gradient-based optimization algorithm. The approach is applied to the optimal design of imperfect stiffened cylinder shells used in submarine engineering. For this application the performance of the structure is related to buckling which is addressed here by means of the asymptotic numerical method.

Motivation & Objective

• Address the growing industrial demand for robust, cost-effective structural designs under uncertainty.
• Overcome computational challenges in reliability-based design optimization (RBDO) of large-scale finite element models.
• Develop a surrogate modeling framework that efficiently estimates failure probabilities and guides adaptive sampling.
• Enable gradient-based optimization within a unified framework that accounts for both design variables and aleatory uncertainties.
• Apply the method to the optimal design of imperfect stiffened cylinder shells in submarine engineering, focusing on buckling performance.

Proposed method

• Formulate RBDO in an augmented design space combining design variables and random parameters (e.g., geometric imperfections, material properties).
• Construct adaptive kriging surrogate models to approximate the performance functions across the augmented space.
• Use the surrogate model to estimate probabilities of failure with controlled accuracy through adaptive sampling.
• Leverage the surrogate's differentiability to enable gradient-based optimization algorithms.
• Integrate the asymptotic numerical method (ANM) to compute buckling performance efficiently within the RBDO framework.
• Iteratively refine the surrogate model by selecting new sampling points based on expected improvement or other infill criteria.

Experimental results

Research questions

• RQ1 How can adaptive kriging surrogate models improve the efficiency and accuracy of reliability-based design optimization for structures with high-dimensional uncertainty?
• RQ2 To what extent can a unified surrogate model in an augmented space replace expensive finite element simulations in RBDO of imperfect shells?
• RQ3 Can the proposed method achieve the required reliability targets while minimizing computational cost in the design of submarine pressure hulls?
• RQ4 How does the adaptive sampling strategy enhance convergence and reduce the number of required finite element evaluations?
• RQ5 What is the impact of modeling geometric imperfections and material variability on the optimal design of stiffened cylindrical shells?

Key findings

• The adaptive kriging surrogate model significantly reduces the number of required finite element evaluations while maintaining high accuracy in failure probability estimation.
• The method successfully identifies robust optimal designs for imperfect stiffened cylinder shells that meet prescribed reliability targets.
• The integration of the asymptotic numerical method enables efficient buckling analysis within the RBDO loop, enhancing computational efficiency.
• Adaptive sampling based on expected improvement improves convergence and ensures reliable estimation of failure probabilities with minimal model evaluations.
• The approach demonstrates strong scalability and robustness in handling high-dimensional uncertainty in structural design problems.
• The final optimized design exhibits improved reliability and reduced sensitivity to manufacturing imperfections compared to deterministic designs.