A Kriging-PGD Algorithm to Couple Enriched Multifidelity Metamodels and Reduced-order Model to Handle Multiparametric Problem
Résumé
The advent of Virtual Testing and industry's willingness for hyper fine structural optimization impose technical constraints for computational mechanics community. Optimize mechanical criterion for a turbine blade with classical techniques costs around months of CPU computation. To handle this issue, many cost-killer methods have been developed and two major families can be distinguished: surrogate models for an optimal approximation of mechanical criteria in the whole design space or around global optimum; and reduced-order models to approximate mechanical fields and allows evaluation of criteria in real-time. Our contribution is to unify these strategies around an nonlinear solver, well-designed for multiparametric problem: the LATIN-PGD method [Ladevèze, 1999]. It has two key features: each LATIN iteration gives an MOR-approximation of mechanical fields at each time step, known as time-space PGD modes; and it can be (re)started with fields from another solution. With these features, we can consider low-fidelity data from a non-converged LATIN solution, and harness the possibility to create a spatial modes basis for (re)start computation with other parameters set from design space, which drastically cut time computation. Our algorithm relies on building a initial surrogate model of the mechanical criterion with multi-fidelity data observations from a non-converged LATIN solution [Forrester, 2007]. This surrogate model will be enriched with well-choosed points from MSE or EI criterion and spatial modes arising from previous computations will be used to accelerate LATIN convergence. Attention will be focused towards the number of initial points on design space, and the way to choose low-fidelity data. This new algorithm will be presented on an elasto-visco-plastic case, using parallel computing.