A Numerical Study of the Compositional Static Aeroelastic Analysis Method

Data-driven analysis techniques have recently emerged for solving nonlinear static aeroelasticity problems that leverage parallel computation to reduce computational time relative to conventional loosely-coupled schemes that iteratively exchange displacement and traction field information between independent fluid and structural models. One approach in particular, the compositional static aeroelastic analysis method, relies upon statistical exploration of shape parameters characterizing a reduced-order representation of the structural deformations, which is followed by a set of independent one-way fluid and structure model evaluations used to construct an aeroelastic surrogate model whose fixed-point parametrically represents the static aeroelastic solution. This works seeks to examine the trade-offs between solution accuracy, computational time, and computational cost of the compositional method relative to a conventional loosely-coupled analysis and considers a range of problem dimensions, shape parameter sampling domain sizes, number of surrogate training samples, and surrogate model types. Additionally, an adaptive sampling scheme is proposed that combines the parallelization capabilities and surrogate information of the compositional method with the superior convergence properties of iterative methods. The results from this study suggest that the compositional method with non-adaptive sampling is adequate for low-to-moderate fidelity analysis as solution error ranges on the order of 0.1% to 1% for moderately sized sampling domains with 20 or less shape parameters. Incorporating adaptive sampling considerably improves solution accuracy compared to non-adaptive sampling for the same total number of fluid-structure evaluations while improving the rate of convergence of fixed-point iteration up to four orders of magnitude. Depending upon analysis requirements, use of adaptive sampling improves computational time by a factor of 5 to 15 and computational cost up to a factor of 4 relative to fixed-point iteration.