Composites of Surrogate Models with Data Uncertainty

• Main Authors: Dian-YunWu, 吳典運
• Other Authors: Kuei-Yuan Chan
• Format: Others
• Language: en_US
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/60189409575563959082

碩士 === 國立成功大學 === 機械工程學系碩博士班 === 101 === Surrogate modeling, also known as response surface or meta modeling, is an important methodology in product design and development process. By fitting measurement data and testing outcomes with some types of basis functions, surrogate models can be created as a substitute of the original underlying physical phenomena of the data. Common practice of surrogate modeling is to replace expensive in-field tests and time-consuming computer simulations. Data fitting will inevitably associated with errors regardless of the basis being used. Researchers in the past have used polynomial functions as surrogate models to observe the trend of a given data set. With the increase of polynomial terms, one is able to provide a better fit. Among other nonlinear basis, neural network and Kriging are two of the most commonly applied surrogate models in engineering practice. The main advantage of using these surrogate models lies in the reduction of time and cost in `predicting' a design that has not been tested or even before its production. A better surrogate model fits the data `well'. However, different views on the data might affect the types of method used to quantify wellness of a surrogate model. In the past, the root mean square errors (RMSE) between measurements and predictions have been used as the most important index in selecting a good surrogate model. By reducing the RMSE, one is able to find the optimal parameters of a surrogate model given its basis forms. However, not all data at hands are perfect. They might contain important information as well as useless measuring errors or even wrongful biased outcomes. Unfortunately these uncertainties have primarily been omitted in surrogate modeling with RMSE. In other words, the data used in fitting are assumed to be in accordance with the main function trends, no significant variations exist. Another important index in quantifying the goodness-of-fit of a surrogate model is the evidence based on Bayesian theory. Evidence considers data with some form of underlying uncertainty in nature. Each set of model parameters is obtained with the most likely set to reproduce the data given existing prior information at hand. In this thesis we combine the RMSE and the Bayesian evidence in selecting the best surrogate model. We denote the RMSE as the deterministic metric while the evidence the probabilistic metric. The best surrogate model in this research is considered to have a form from all possible sources, therefore it is a composite surrogate model. An RMSE-evidence contour is proposed to form the region of trust. Comparing different RMSE-evidence contours enables us to balance between deterministic and probabilistic metrics of a surrogate. Optimal composition of all available surrogate models, in this work polynomial, neural network, and Kriging, is obtained by systematically tuning the parameters until no compositions outperforms the other one in both aspects. Several mathematical cases are used to demonstrate the process and usefulness of the proposed method. A cantilever beam with time-variant aging data is used to demonstrate the proposed method in predicting product reliability.