Validating Surrogate models and incorporating Uncertainty Quantification in Aerospace Engineering Design Optimization

Multi-objective and multi-disciplinary design optimisation tools are becoming a necessity for the development of innovative and more efficient advanced aerodynamic configurations. The highly complex flow-field that develops around such airfoils especially in high lift configuration and the computational cost to accurately simulate and extract the crucial flow metrics represents a challenging task for the design optimisation process. Benefits can be obtained by replacing the original model with CPU inexpensive mathematical functions, called metamodels or surrogates. However, many challenging issues remain unresolved. In fact, one of the criticisms of the traditional engineering design optimisation process is that it often produces optimal designs that are not robust to perturbations in the design parameters or other uncertain parameters. The problem with uncertainty can be exacerbated in multi-disciplinary optimisation whereby the models for several disciplines are coupled and the propagation of uncertainty has to be accounted for within and across disciplines. The uncertainties in this process arise principally from the aerodynamic data (approximations and errors from CFD code). In addition, since a surrogate model is an approximation to an unknown function, prediction errors are generally present in the estimated function values. Being approximations, they will necessarily introduce additional uncertainty that must be accounted for. Statistical measures, such as mean value, standard deviation, and probability of failure can provide such information. These statistical measures are available to the engineer through the various types of uncertainty quantification and reliability estimation software tools that are now available. Thus, it is a natural extension for engineers to incorporate statistical measures directly into the design optimisation process. Few studies have been conducted on studying the accuracy of using metamodels for optimisation under uncertainty. Surrogate-based optimisation under uncertainty formulations shows promise both in reducing the number of function evaluations required and in mitigating the effects of non-smooth response variations. There is a need to automate stochastic uncertainty quantification codes in the digital age. Problems in wing Computational Fluid Dynamics (CFD) are characterised by non-linear and discontinuous responses and long run times. Ensuring the reliability of Uncertainty Quantification (UQ) codes under such conditions, in an autonomous way, is a challenging problem. There is consequently a great need for systematic and automatic ways to quantify design uncertainties. The accuracy for optimisation under uncertainty also relies on how accurate the metamodel is in capturing the performance variations, which could be affected by small perturbations of design parameters. Knowledge on the accuracy of various metamodelling techniques in this context will thus be very valuable. This project relies on the sophisticated development of validated surrogate models, as well as their integration with optimisation algorithms and other computational design tools in order to define and develop a better design methodology, combining optimisation methods with uncertainty quantification and reliability estimation methods. The test case under consideration is a section of a Multi Element Wing for which an aerodynamic optimisation under uncertainty will be performed and preliminary results presented.