Response surface methodology using a prior knowledge and its application to pin fin heat sink design

Abstract

Large number of simulations or experiments is needed for optimization and uncertainty quantification of a mechanical system. Therefore, if simulations or experiments are numerically expensive and time consuming, it is difficult to execute optimization and uncertainty quantification in practical cost and time. To reduce the cost and time, a surrogate model is often used. The surrogate model is a mathematical model which represents a relationship between control variables and corresponding response value. The surrogate model is constructed from sampling data; a set of results of simulations or experiments with different values of control variables. When the surrogate model is used for optimization and uncertainty quantification, its result depends greatly on an accuracy of the surrogate model. Hence, it is important to construct an accurate surrogate model. Generally, an accuracy of the surrogate model increases as a number of sampling data increases. However, if a number of sampling data increase, the cost and time to make them also increase, which should be avoided. Therefore, it is necessary to develop a methodology which can construct an accurate surrogate model with fewer number of sampling data. In mechanical design problems, there often exist experimental equations which represent relationships between control variables and response values. In this study, we proposed a method which uses the experimental equations to improve an accuracy of the surrogate surface. In the proposed method, the experimental equation and its parameters are used as priori knowledge for constructing a surrogate model, and values of parameters and an offset between the experimental equation and true values are estimated simultaneously based on sampling data. We applied the proposed method to construct surrogate models for a heat resistance and a pressure drop of a pin-fin heat sink. As a result, it is shown that the proposed method can construct surrogate models which gives better estimation than conventional methods and has robustness to accuracies of priori knowledges.

Keywords

• surrogate model
• response surface
• a prior knowledge
• bayesian estimation
• pin-fin heat sink