Towards simulteaneous meta-modeling for both the output and input spaces in the context of design shape optimization unsin asynchronous high-performance computing
Balaji Raghavan, Piotr Breitkopf, Pierre Villon · 2012
Industrial-size structural optimization frequently ends up a far more formidable task than was originally envisioned by the research and development teams involved. It is, by now, common knowledge that high-fidelity function evaluations can prohibitively increase the CPU time, and this led to the wide-spread use of computing clusters, research on increasing the scalability of numerical solvers, parallel optimization algorithms, etc. The problem of CPU time for a sufficiently realistic result also gave birth to tomes of research on model reduction strategies to get an approximate function evaluation in a fraction of the CPU time needed for a high fidelity result. The multi-disciplinary optimization community now boasts of an array of impressive physics-based meta-models to choose from, a series of optimization algorithms to consider and everything from workstations to computing clusters/grids to perform the simulations. However, as far as development in high performance computing for optimization assisted by surrogate meta-modeling, we have seen but the tip of the iceberg. While literature shows that research exists specific to certain genres of problems in order to speed up computation, three main issues need to be targeted before we can develop a truly holistic and reliable meta-modeling protocol for industrial structural optimization. The first is the problem of cluster/server failures, outages or delays due to a large number of competing users. Given that a dedicated cluster to run simulations for several hours is hardly realistic, it has been observed that the absence of or delays in function evaluations due to server issues can casily derail an evolutionary optimization procedure. We first present a novel and elegant protocol that combines our asynchronous and future paradigm with a high-quality surrogate meta-mode! that is adaptively refined in the neighborhood of the optimal solutions to continue the optimization in the absence of exact solutions. The second aspect of our work is an issue that has, thus far, never been broached in the context of structural optimization in the literature surveyed : that of design domain dimensionality, which we observed is linked with the phenomenon of CAO failures due to the generation of inadmissible geometries. High dimensionality is by itself, quite understandably, an impediment to efficient optimization, since it greatly affects the efficiency of gradient-based optimizers unless the gradients arc available analytically. More importantly, geometric parameterization methods used in traditional CAO are seen to have a high failure rate of generating admissible shapes, as we have observed with the three industrial test-cases presented by Renault. To this end, we introduce a novel space-reduction meta-model that maps an optimization problem into space using a unique representation of structural shape (the indicator function) and then identifies the manifold of admissible shapes for the given problem and finally performs constrained shape interpolation between admissible geometries to reduce the size of the optimization problem while guaranteeing feasibility of the shapes generated. The third aspect of our work concerns a foray into the usual POO-based techniques to develop an improved reduced order model for the physics of a system. In the usual manner, we attack the ever-present problem of improving the precision of a surrogate meta model without compromising the evaluation time. We build up on the previously-introduced concept of constrained proper orthogonal decomposition to conserve linear functions of the field variables. We introduce a constrained projector that works on the coefficients obtained by projecting the snapshots on to a basis that guarantees the conservation of linear quantities by design, and then adjust these coefficients to satisfy quadratic constraints, in order to further augment the precision. Three industrial performance optimization test-cases were provided by Renault for use in the OM02 project : a 20 air-conditioning duct and 30 air-conditioning duct with 2 performance objectives each : the flow permeability and exit flow uniformity and a 30 engine intake with a single performance objective : the mass flow rate. One or more of these test-cases were used to develop, refine and finally demonstrate each of these protocols : the ask and future tell paradigm, the modified POO protocol and the diffuse morphing methodology. In addition, a variety of academic test-cases have been used to illustrate the methodology as and when required. Some development has also been initiated to use the diffuse-morphing space-reduction approach for the optimization of a distributed parameter : hood thickness optimization for vehicle-pedestrian head impact. Summing up, this thesis combines our research on the three subjects listed above, asynchronous surrogate-assisted optimization on a busy/loaded cluster, constrained shape interpolation for input-space reduction and an energy-preserving constrained POO-Iike projector for quadratic constraints. We believe that this thesis introduces concepts that work towards developing a robust meta modeling protocol for surrogate-assisted optimization. While we do focus mostly on shape optimization problems in the bulk of the narrative, we include a full extension of the space-reduction protocol for optimization of a distributed parameter (density, thickness, etc) with application to a simplified industrial problem.