Towards reliability analysis by adaptive sampling with multiple fidelity levels by the use of reduced basis methods
Résumé
Running a reliability analysis on complex numerical models can be very expensive, requiring advanced simulation methods to reduce the numerical cost. Distinct approaches have been proposed to reduce the problem of numerical costs. Adaptive sampling based reliability analysis methods are one way for reducing the computational cost. These methods consist in building a Kriging surrogate model (Gaussian process interpolation) of a performance function and using the uncertainty structure of Kriging to enrich iteratively this surrogate model. However these methods may remain expensive as the numerical model's complexity is increased in order to reproduce the real response of the mechanical systems. Another way to reduce computationally expensive full system resolutions related to numerical models consists in model order reduction. Here, we focus on the model order reduction techniques classified as reduced basis methods [1]. These methods rely on the projection of the system's equation onto a subspace of subsequently reduced dimensionality compared to the initial space. A combination of adaptive sampling based reliability analysis and reduced-basis modeling is then a potential way to further reduce the computational costs, which will be investigated here. The resulting method can be seen as a reliability analysis method with multiple fidelities. That means the model's fidelity is chosen at each iteration of the reliability analysis. The residual of the reduced solution can be computed to evaluate its accuracy and decide whether a basis enrichment is necessary [2]. We will explore however a more advanced technique, based on a preconditioned residual to have a better estimation of the error behavior. This work will present the development of the coupling between adaptive sampling and reduced-basis modeling and the use of a preconditioner to increase the knowledge of the fidelity of reduced basis solutions. Application of the method to the estimation of the probability of failure of a laminated plate under complex loading will be presented as an application example. References [1] Benner P., Gugercin S., Willcox K. (2015). A survey of projection-based model reduction methods for parametric dynamical systems. SIAM review, 57(4), 483-531. [2] Christian Gogu and Jean-Charles Passieux. Efficient surrogate construction by combining response surface methodology and reduced order modeling. Structural and Multidisciplinary Optimization, 47(6): 821-837, June 2013. Powered by TCPDF (www.tcpdf.org)