Geometrical Optimization of Solar Concentrating Collectors Through Quasi-Monte Carlo Simulation

Abstract

Monte Carlo (MC) ray-tracing simulation coupled with stochastic programming has recently been shown to be a powerful technique for optimizing the design of solar concentrating collectors, but this procedure is complicated by the statistical uncertainty that MC introduces into the objective function. This paper shows how using quasi-Monte Carlo (QMC) methods instead of MC to simulate radiation heat transfer reduces these uncertainties, allowing the Kiefer-Wolfowitz technique to perform required gradient estimations using much smaller sample sizes. Consequently, QMC greatly increases the computational speed of the overall concentrating collector design optimization algorithm. In an attempt to ensure that the minimum required sample size is used at each design iteration, a novel condition-based iterative approach is introduced which starts at a low sample size and increases in a logarithmic manner until the estimate reaches the required degree of accuracy.