Multi-Fidelity Construction of Explicit Boundaries: Application to Aeroelasticity

• Main Author: Dribusch, Christoph
• Other Authors: Missoum, Samy
• Language: en
• Published: The University of Arizona. 2013
• Subjects: Mechanical Engineering
• Online Access: http://hdl.handle.net/10150/293482

Wings, control surfaces and rotor blades subject to aerodynamic forces may exhibit aeroelastic instabilities such as flutter, divergence and limit cycle oscillations which generally reduce their life and functionality. This possibility of instability must be taken into account during the design process and numerical simulation models may be used to predict aeroelastic stability. Aeroelastic stability is a design requirement that encompasses several difficulties also found in other areas of design. For instance, the large computational time associated with stability analysis is also found in computational fluid dynamics (CFD) models. It is a major hurdle in numerical optimization and reliability analysis, which generally require large numbers of call to the simulation code. Similarly, the presence of bifurcations and discontinuities is also encountered in structural impact analysis based on nonlinear dynamic simulations and renders traditional approximation techniques such as Kriging ineffective. Finally, for a given component or system, aeroelastic instability is only one of multiple failure modes which must be accounted for during design and reliability studies. To address the above challenges, this dissertation proposes a novel algorithm to predict, over a range of parameters, the qualitative outcomes (pass/fail) of simulations based on relatively few, classified (pass/fail) simulation results. This is different from traditional approximation techniques that seek to predict simulation outcomes quantitatively, for example by fitting a response surface. The predictions of the proposed algorithm are based on the theory of support vector machines (SVM), a machine learning method originated in the field of pattern recognition. This process yields an analytical function that explicitly defines the boundary between feasible and infeasible regions of the parameter space and has the ability to reproduce nonlinear, disjoint boundaries in n dimensions. Since training the SVM only requires classification of training samples as feasible or infeasible, the presence of discontinuities in the simulation results does not affect the proposed algorithm. For the same reason, multiple failure modes such as aeroelastic stability, maximum stress or geometric constraints, may be represented by a single SVM predictor. Often, multiple models are available to simulate a given design at different levels of fidelity and small improvements in accuracy may increase simulation cost by an order of magnitude. In many cases, a lower-fidelity model will classify a case correctly as feasible or infeasible. Therefore a multi-fidelity algorithm is proposed that takes advantage of lower-fidelity models when appropriate to minimize the overall computational burden of training the SVM. To this end, the algorithm combines the concepts of adaptive sampling and multi-fidelity analysis to iteratively select not only the training samples, but also the appropriate level of fidelity for evaluation. The proposed algorithm, referred to as multi-fidelity explicit design space decomposition (MF-EDSD), is demonstrated on various models of aeroelastic stability to either build the stability boundary and/or to perform design optimization. The aeroelastic models range from linear and nonlinear analytical models to commercial software (ZAERO) and represent divergence, flutter, and limit cycle oscillation instabilities. Additional analytical test problems have the advantage that the accuracy of the SVM predictor and the convergence to optimal designs are more easily verified. On the other hand the more sophisticated models demonstrate the applicability to real aerospace applications where the solutions are not known a priori. In conclusion, the presented MF-EDSD algorithm is well suited for approximating stability boundaries associated with aeroelastic instabilities in high-dimensional parameter spaces. The adaptive selection of training samples and use of multi-fidelity models leads to large reductions of simulation cost without sacrificing accuracy. The SVM representation of the boundary of the feasible design space provides a single differentiable constraint function with negligible evaluation cost, ideal for numerical optimization and reliability quantification.