Determination of loads and boundary conditions causing deformations of concentrating solar mirrors using non-derivative optimization methods and finite element analysis

Mirror shape optimization is a major part of improving the performance of concentrating solar power (CSP) collectors. Loads and boundary conditions of different origin and with varying influence on shape deviation need to be understood and quantified, e.g., in order to give specifications for the design of new collector generations. Finite element analysis (FEA) has proven to be a suitable method for evaluating mirror shape. An optimization process is presented that utilizes finite element models (FEM) of mirrors and a subsequent evaluation of the slope deviation to approximate a reference, e.g., a measured mirror shape, and determine the load values causing the mirror panel to deform. In this paper, the suggested approach is proven to be feasible: Two optimization algorithms are implemented: BOBYQA and CMA-ES. A simulated reference created in ANSYS Workbench and a reference from a deflectometry measurement are investigated. The determined geometrical parameters are compared to the reference values. For BOBYQA an absolute minimum and maximum deviation of 0.02 % and 0.3 %, and for CMA-ES of 0.0001 % and 0.004 % relative to the reference values is found. With the measured mirror shape as reference, the optimization algorithm was again capable of reproducing the mirror shape in FEA. However, the geometrical load parameters found were only partially in agreement with the measured values. Yet, it is concluded that the proposed method for reproducing mirror shape works.