Abstract Summary
In this paper surrogate models of the performance metrics of early-stage design of aerostructures are created to optimize a subset of design parameters based on some prescribed limits of the intended real system response. The designed system is that of an aircraft wing that is subjected to a design of experiments to collect data for training of the surrogate models. There are two quantities of interest for this problem related to the load distribution on the wing and its aerodynamic performance for which surrogate models have been built covering the entire design space. Priors have been chosen for the high-dimensional design space which includes both uncertain design parameters and stochastic covariates with which the inverse design problem of optimizing a subset of design parameters is defined. Gaussian processes have been used for surrogate models wherein the uncertainty due to lack of data and model form error can be quantified and propagated. The approach taken requires novel formulation of the likelihood function to tackle the following issues: (1) the output of the surrogate model is dependent on the remaining unoptimized design parameters and therefore their influence must be marginalized out each time the likelihood function is evaluated in the Markov chain; (2) ensuring that the posterior distribution over the quantities of interest is within the 95% confidence interval of the constraints; (3) ensuring that the optimization process does not favor one quantity of interest over the other or fail completely due to compromise. Latin hyper cube sampling of the remaining unoptimized parameters is used to solve (1). As Gaussian process surrogate models are used it is possible to solve (2) given the predictions are in the form of the first two moments of a normal distribution. Finally, as the likelihood is the joint likelihood of both systems remaining within their constraints given the same set of parameters, their marginal likelihoods take on similar forms based around the CDF of a standard normal distribution. Markov Chain Monte Carlo is used to obtain the posterior distribution over the parameters, and subsequently the posterior distribution over the quantities of interest, given the constraints. Several case studies are presented that study how the likelihood function can be manipulated to address issue (3), it is found that the optimization is sensitive to decreases and increases of the variances of the marginal standard normal CDF’s such that it can be used as a weight to direct the optimization towards a quantity of interest, therefore adjustment of this parameter is used to balance the optimization.
