Design optimization under uncertainty for rotor blades of horizontal axis wind turbines

2016-06-23This dissertation is motivated by challenges involved in the design optimization under uncertainty for the structures undergoing fluid structure interaction phenomena. In particular, this study focuses on the aerodynamic simulation and optimization under uncertainty for rotor blades of Horizontal Axis Wind Turbines (HAWT). To that end, a reliability‐based design framework integrating the aeroelastic computation based on the blade element method with a stochastic optimization, is developed. The wind model is a stochastic process which accounts for the variation in time and space. The aeroelastic calculation determines the aerodynamic forces on the blade. The uncertainty propagated in the aerodynamic forces stems from the uncertain characteristics of the wind. Another source of uncertainty is introduced in the material property of the blade which results in random structural parameters such as stiffness and capacity. These sources of uncertainty lead to a random objective function and constraints. The objective function is the generated power subjected to the constraints on stresses in the blade. The reliability is defined based on the probability of the safety in the system. The design variables are considered to be shape parameters, namely twist angles along the blade. In order to show the effect of uncertainty in the design, the result of the deterministic optimization is obtained and compared with the optimization results under uncertainty. Polynomial chaos expansion is used in various parts of this work as a mathematical tool for the uncertainty propagation. In particular, polynomial chaos expansion can be used to characterize the solution of stochastic differential equations such as the governing equation of the motion of the blade. Significant computational challenges are associated with the polynomial chaos expansion approach for problems with high dimensional parameter space. This challenge is addressed in the present dissertation by developing a methodology for convergence acceleration of polynomial chaos‐based stochastic Galerkin solutions. Specifically, Nonlinear sequence transformations are adapted to these expansions, viewed as a one‐parameter family of functions with the parameter being the polynomial degree of the expansion. Stochastic Galerkin approach yields polynomial chaos representations that have the requisite analytical properties to ensure suitable convergence of these nonlinear sequence transformations. In particular, the properties of Shanks and Levin transformations are explored in the context of a stochastic initial value problem and a stochastic elliptic problem