Journal
STRUCTURAL HEALTH MONITORING-AN INTERNATIONAL JOURNAL
Volume 20, Issue 6, Pages 3436-3452Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1475921721993381
Keywords
Structural health monitoring; missing data; distribution regression; warping function; confidence estimation; bootstrap; functional data analysis
Funding
- National Natural Science Foundation of China [51908166, 51638007, U1711265]
- China Postdoctoral Science Foundation [2019M661287]
- National Key Research and Development Program of China [2018YFB1600202]
- Open Funding of State Key Laboratory of Safety and Health for In-service Long Bridges [2020SJKHIT001]
- Fundamental Research Funds for the Central Universities
- Postdoctoral Science Foundation of Heilong Jiang province
Ask authors/readers for more resources
This article focuses on uncertainty quantification for the distribution-to-warping function regression method used in reconstructing distributions of missing data. Through functional transformation and functional principal component analysis, warping functions are successfully transformed into a vector space, and confidence estimation for the regression operator is conducted. The confidence region of the conditional expectation of missing distribution caused by data loss can be further estimated and visualized.
Data loss is a common problem of structural health monitoring and adversely affects many structural health monitoring applications. Tremendous progress in missing structural health monitoring data imputation has been made in recent years, forming an important part of sensor validation. Most of the imputed data are based on estimates obtained by data-driven statistical or machine learning models; quantifying their estimation uncertainties is significant in terms of being able to perform accuracy assessments and providing more insights into the imputed data. However, this procedure has been surprisingly neglected in the structural health monitoring community. This article focuses on uncertainty quantification for the distribution-to-warping function regression method (an indirect distribution-to-distribution regression method) used in reconstructing distributions of missing data. The distribution-to-warping function regression method belongs to the framework of functional data analysis as both the predictor and response are continuous functions. The challenge of performing uncertainty quantification for the distribution-to-warping function regression method comes not only from the functional nature of warping functions but also from their inherent constraints. To this end, a functional transformation is employed to transform warping functions into a vector space, and the confidence estimation for the regression operator is conducted in the vector space based on functional principal component analysis and bootstrapping. Then, the confidence region of the conditional expectation of missing distribution (caused by data loss) can be further estimated and visualized. In addition, a calibration processing procedure is also considered to obtain improved estimates of the confidence intervals with a better coverage accuracy under the desired probability. Simulation studies are conducted to validate and illustrate the proposed method, and then, it is applied to field strain monitoring data.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available