Systematic Strategy for Modeling and Optimization of Thermal Systems with Design Uncertainties

Abstract

Thermal systems play significant roles in the engineering practice and our lives. To improve those thermal systems, it is necessary to model and optimize the design and the operating conditions. More importantly, the design uncertainties should be considered because the failures of the thermal systems may be very dangerous and produce large loss. This review paper focuses on a systematic strategy of modeling and optimizing of the thermal systems with the considerations of the design uncertainties. To demonstrate the proposed strategy, one of the complicated thermal systems, Chemical Vapor Deposition (CVD), is simulated, parametrically modeled, and optimized. The operating conditions, inlet velocities and susceptor temperatures, are the most significant factors in the CVD and are chosen as the design variables. Several responses - including the percentage of the working area, the mean of the deposition rate, the root mean square of the deposition, and the surface kurtosis - are chosen based on the physical needs and statistical foundations, and are utilized to represent the productivity and the quality of the thin-film deposition. One of the Response Surface Method (RSM), the Radial Basis Function (RBF), is employed to formulate the objective and constraint functions for the optimization. However, it is not until the design uncertainties are considered that the thermal system designs have high risk of the violations of the performance constraints. The Reliability-Based Design Optimization (RBDO) algorithms are used to solve the optimization problems with the design uncertainties. The most famous RBDO methods are the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). In RBDO, probabilistic constraints are established with respect to either normally or non-normally distributed random variables. The optimal solutions are found subjected to the allowable level of the failure probabilities. The Monte Carlo Simulation (MCS) results can be used to evaluate the failure probabilities. As a result, the proposed systematic strategy of parametrically modeling and optimizing with design uncertainties can be applied to either experiments or simulations of other thermal systems to quantitatively represent the performances, improve their productivity, maintain the quality control, and reduce the probability of the system failure.