Response CDF sensitivity and its solution based on sparse grid integration

Abstract

The sensitivity of the cumulative distribution function (CDF) of the response with respect to the input parameters is studied in this work, to quantify how the model output is affected by input uncertainty. To solve the response CDF sensitivity more efficiently, a novel method based on the sparse grid integration (SGI) is proposed. The response CDF sensitivity is transformed into expressions involving probability moments, which can be efficiently estimated by the SGI technique. Once the response CDF sensitivity at one percentile level of the response is obtained, the sensitivity values at any other percentile level can be immediately obtained with no further call to the performance function. The proposed method finds a good balance between the computational burden and accuracy, and is applicable for engineering problems involving implicit performance functions. The characteristics and effectiveness of the proposed method are demonstrated by several engineering examples. Discussions on these examples have also validated the significance of the response CDF sensitivity for the purpose of variable screening and ranking.

Keywords:

• distribution parameter
• input variable
• output response
• CDF sensitivity
• sparse grid

Acknowledgements

The authors would like to thank the reviewers and the associate editor for their very helpful comments and suggestions, which have greatly improved the presentation of this paper.

Additional information

Funding

This work is supported by the Nature Science Foundation of China [grant number 51175425] and Research Fund for the Doctoral Program of Higher Education of China [grant number 20116102110003].

Notes on contributors

Chang-Cong Zhou

Chang-Cong Zhou received his BS degree in flight vehicle design from the School of Aeronautics at Northwestern Polytechnical University, Xi'an, China, in 2009. He has been a PhD candidate at Northwestern Polytechnical University since September 2009, majoring in flight vehicle design. His research interests include aircraft design, structural reliability and sensitivity analysis. He is the author and co-author of nearly 20 journal and conference papers.

Zhen-Zhou Lu

Zhen-Zhou Lu is a professor in the School of Aeronautics at Northwestern Polytechnical University, Xi'an, China. She received her BS and PhD degrees from Northwestern Polytechnical University, both in flight vehicle design, in 1988 and 1993, respectively. During January 1994 to May 1996, she was a post-doctoral research associate in the Department of Engineering Mechanics at Northwestern Polytechnical University. Since December 1995, she has been teaching and researching in the School of Aeronautics at Northwestern Polytechnical University, first as an associate professor and then, since December 1998, as a professor. Her current research interests include aircraft design, structural reliability, sensitivity analysis and robust design. She has published a book and more than 150 journal and conference papers.

Ji-Xiang Hu

Ji-Xiang Hu was born in Jiangsu Province, China, in 1989. He received his BS degree in flight vehicle design from the School of Aeronautics at Northwestern Polytechnical University, Xi'an, China, in 2012. He has been an MS candidate at Northwestern Polytechnical University since 2012. His current research interests include aircraft design, structural reliability and engineering optimisation.

Ming Yuan

Ming Yuan is a postgraduate from Northwestern Polytechnical University and is mainly engaged in the research of mechanical and electrical hydraulic servo control system. He got his bachelor degree from Chong Qing University in 2009.