Post by Steve Yenisch on May 13, 2009 23:34:05 GMT -5
Paper: www.mae.ufl.edu/nkim/ISSMO/FenfenXiongPaper.pdf
Presentation:www.mae.ufl.edu/nkim/ISSMO/FenfenXiongPresentation.ppt
Enhanced Probabilistic Analytical Target Cascading with Application to Multiscale Design
Fenfen Xiong1, Xiaolei Yin2, Wei Chen3* and Shuxing Yang4
1 School of Aerospace Science and Engineering, Beijing Institute of Technology, 100081 & Predoctoral Visiting Fellow, Department of Mechanical Engineering, Northwestern University, IL 60208
2,3 Integrated Design Automation Laboratory (IDEAL), Mechanical Engineering, Northwestern University, IL 60208
4 School of Aerospace Science and Engineering, Beijing Institute of Technology, 100081
ABSTRACT
Probabilistic Analytical Target Cascading (PATC) is an approach for multilevel multidisciplinary design optimization under uncertainty. In the existing PATC approach, only the mean and variance of each individual interrelated response and linking variable are matched in a multilevel hierarchy. However, due to the existence of random linking variables or parameters, the interrelated responses from lower-level subsystems are statistically correlated and have a direct influence on the statistical performance of an upper-level subsystem. The ignorance of response correlation introduces difficulties in finding optimal solutions especially when the covariance of interrelated responses has a significant impact. In this paper, an enhanced PATC (EPATC) approach is proposed to improve the performance of PATC by considering the correlations in optimization cycles. With the EPATC approach, in addition to matching the first two statistical moments, the covariance between the interrelated responses is also considered by applying a modified updating strategy for estimating the statistical performance of an upper-level subsystem. A mathematical example and a multiscale design problem are used to demonstrate the effectiveness and efficiency of the proposed EPATC approach. The results using the Probabilistic All-In-One (PAIO) method are used as references to verify the accuracy of the EPATC approach. It is observed that the effectiveness of EPATC highly depends on the impact strength of the covariance on optimal solutions. Our study shows that the EPATC approach outperforms the original PATC by providing more accurate optimal solutions; the multilevel optimization that allows distributed design activities is highly applicable to multiscale design problems.
Keywords: Probabilistic analytical target cascading, Multilevel optimization, Uncertainty, Correlated response, Multiscale design
*Corresponding author, weichen@northwestern.edu
Presentation:www.mae.ufl.edu/nkim/ISSMO/FenfenXiongPresentation.ppt
Enhanced Probabilistic Analytical Target Cascading with Application to Multiscale Design
Fenfen Xiong1, Xiaolei Yin2, Wei Chen3* and Shuxing Yang4
1 School of Aerospace Science and Engineering, Beijing Institute of Technology, 100081 & Predoctoral Visiting Fellow, Department of Mechanical Engineering, Northwestern University, IL 60208
2,3 Integrated Design Automation Laboratory (IDEAL), Mechanical Engineering, Northwestern University, IL 60208
4 School of Aerospace Science and Engineering, Beijing Institute of Technology, 100081
ABSTRACT
Probabilistic Analytical Target Cascading (PATC) is an approach for multilevel multidisciplinary design optimization under uncertainty. In the existing PATC approach, only the mean and variance of each individual interrelated response and linking variable are matched in a multilevel hierarchy. However, due to the existence of random linking variables or parameters, the interrelated responses from lower-level subsystems are statistically correlated and have a direct influence on the statistical performance of an upper-level subsystem. The ignorance of response correlation introduces difficulties in finding optimal solutions especially when the covariance of interrelated responses has a significant impact. In this paper, an enhanced PATC (EPATC) approach is proposed to improve the performance of PATC by considering the correlations in optimization cycles. With the EPATC approach, in addition to matching the first two statistical moments, the covariance between the interrelated responses is also considered by applying a modified updating strategy for estimating the statistical performance of an upper-level subsystem. A mathematical example and a multiscale design problem are used to demonstrate the effectiveness and efficiency of the proposed EPATC approach. The results using the Probabilistic All-In-One (PAIO) method are used as references to verify the accuracy of the EPATC approach. It is observed that the effectiveness of EPATC highly depends on the impact strength of the covariance on optimal solutions. Our study shows that the EPATC approach outperforms the original PATC by providing more accurate optimal solutions; the multilevel optimization that allows distributed design activities is highly applicable to multiscale design problems.
Keywords: Probabilistic analytical target cascading, Multilevel optimization, Uncertainty, Correlated response, Multiscale design
*Corresponding author, weichen@northwestern.edu