An Adaptive Response Surface Method Using Bayesian Metric and Model Bias Correction Function

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Lei Shi ◽  
Ren-Jye Yang ◽  
Ping Zhu

The Bayesian metric was used to select the best available response surface in the literature. One of the major drawbacks of this method is the lack of a rigorous method to quantify data uncertainty, which is required as an input. In addition, the accuracy of any response surface is inherently unpredictable. This paper employs the Gaussian process based model bias correction method to quantify the data uncertainty and subsequently improve the accuracy of a response surface model. An adaptive response surface updating algorithm is then proposed for a large-scale problem to select the best response surface. The proposed methodology is demonstrated by a mathematical example and then applied to a vehicle design problem.

2003 ◽  
Vol 125 (2) ◽  
pp. 210-220 ◽  
Author(s):  
G. Gary Wang

This paper addresses the difficulty of the previously developed Adaptive Response Surface Method (ARSM) for high-dimensional design problems. ARSM was developed to search for the global design optimum for computation-intensive design problems. This method utilizes Central Composite Design (CCD), which results in an exponentially increasing number of required design experiments. In addition, ARSM generates a complete new set of CCD points in a gradually reduced design space. These two factors greatly undermine the efficiency of ARSM. In this work, Latin Hypercube Design (LHD) is utilized to generate saturated design experiments. Because of the use of LHD, historical design experiments can be inherited in later iterations. As a result, ARSM only requires a limited number of design experiments even for high-dimensional design problems. The improved ARSM is tested using a group of standard test problems and then applied to an engineering design problem. In both testing and design application, significant improvement in the efficiency of ARSM is realized. The improved ARSM demonstrates strong potential to be a practical global optimization tool for computation-intensive design problems. Inheriting LHD points, as a general sampling strategy, can be integrated into other approximation-based design optimization methodologies.


2012 ◽  
Vol 16 (2) ◽  
pp. 305-318 ◽  
Author(s):  
I. Haddeland ◽  
J. Heinke ◽  
F. Voß ◽  
S. Eisner ◽  
C. Chen ◽  
...  

Abstract. Due to biases in the output of climate models, a bias correction is often needed to make the output suitable for use in hydrological simulations. In most cases only the temperature and precipitation values are bias corrected. However, often there are also biases in other variables such as radiation, humidity and wind speed. In this study we tested to what extent it is also needed to bias correct these variables. Responses to radiation, humidity and wind estimates from two climate models for four large-scale hydrological models are analysed. For the period 1971–2000 these hydrological simulations are compared to simulations using meteorological data based on observations and reanalysis; i.e. the baseline simulation. In both forcing datasets originating from climate models precipitation and temperature are bias corrected to the baseline forcing dataset. Hence, it is only effects of radiation, humidity and wind estimates that are tested here. The direct use of climate model outputs result in substantial different evapotranspiration and runoff estimates, when compared to the baseline simulations. A simple bias correction method is implemented and tested by rerunning the hydrological models using bias corrected radiation, humidity and wind values. The results indicate that bias correction can successfully be used to match the baseline simulations. Finally, historical (1971–2000) and future (2071–2100) model simulations resulting from using bias corrected forcings are compared to the results using non-bias corrected forcings. The relative changes in simulated evapotranspiration and runoff are relatively similar for the bias corrected and non bias corrected hydrological projections, although the absolute evapotranspiration and runoff numbers are often very different. The simulated relative and absolute differences when using bias corrected and non bias corrected climate model radiation, humidity and wind values are, however, smaller than literature reported differences resulting from using bias corrected and non bias corrected climate model precipitation and temperature values.


Author(s):  
G. Gary Wang

Abstract This paper addresses the difficulty of the previously developed Adaptive Response Surface Method (ARSM) for high-dimensional design problems. The ARSM was developed to search for the global design optimum for computation-intensive design problems. This method utilized the Central Composite Designs (CCD), which resulted in an exponentially increasing number of required design experiments. In addition, the ARSM generates a complete new set of CCDs in a gradually reduced design space. These two factors greatly undermine the efficiency of the ARSM. In this work, the Latin Hypercube Designs (LHD) were utilized to generate saturated design experiments. Because of the use of Latin Hypercube Designs, the historical design experiments can be inherited in later iterations. The improved ARSM has been tested using a group of standard testing problems and then applied to an engineering design. In both testing and design application, significant efficiency improvement of the ARSM was observed. The ARSM at the current stage demonstrated strong potential to be an efficient global optimization tool for computation-intensive design problems.


2016 ◽  
Vol 42 ◽  
pp. 05003
Author(s):  
Miguel A. Panesso ◽  
Camilo J. Cruz ◽  
Juan C. Bohorquez ◽  
Luis E. Muñóz ◽  
Néstor M. Peña ◽  
...  

AIAA Journal ◽  
2018 ◽  
Vol 56 (2) ◽  
pp. 862-873 ◽  
Author(s):  
Teng Long ◽  
Xin Li ◽  
Renhe Shi ◽  
Jian Liu ◽  
Xiaosong Guo ◽  
...  

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