Copula-Based Uncertainty Quantification (Copula-UQ) for Multi-Sensor Data in Structural Health Monitoring.

Han-Teng Liu,Ji-Hui Shen,He-Qing Mu

doi:10.3390/s20195692

Abstract

The problem of uncertainty quantification (UQ) for multi-sensor data is one of the main concerns in structural health monitoring (SHM). One important task is multivariate joint probability density function (PDF) modelling. Copula-based statistical inference has attracted significant attention due to the fact that it decouples inferences on the univariate marginal PDF of each random variable and the statistical dependence structure (called copula) among the random variables. This paper proposes the Copula-UQ, composing multivariate joint PDF modelling, inference on model class selection and parameter identification, and probabilistic prediction using incomplete information, for multi-sensor data measured from a SHM system. Multivariate joint PDF is modeled based on the univariate marginal PDFs and the copula. Inference is made by combing the idea of the inference functions for margins and the maximum likelihood estimate. Prediction on the PDF of the target variable, using the complete (from normal sensors) or incomplete information (due to missing data caused by sensor fault issue) of the predictor variable, are made based on the multivariate joint PDF. One example using simulated data and one example using temperature data of a multi-sensor of a monitored bridge are presented to illustrate the capability of the Copula-UQ in joint PDF modelling and target variable prediction.

Highlights

The problem of uncertainty quantification (UQ) for multi-sensor data has been one of the main concerns in nondestructive testing and structural health monitoring (SHM) over the years [1,2,3,4,5,6,7,8,9].One important task is multivariate joint probability density function (PDF) modelling
Modelling of the proposed Copula-UQ and (3) the performance of the proposed Equation (23) for prediction on the target variable given complete or incomplete information
2 Note that the yellow dots correspond to incomplete information of the predictor variable due to missing data caused by a sensor fault issue

Summary

Introduction

The problem of uncertainty quantification (UQ) for multi-sensor data has been one of the main concerns in nondestructive testing and structural health monitoring (SHM) over the years [1,2,3,4,5,6,7,8,9]. This paper attempts to break through this limitation by conducting computation of marginalization and conditioning based on the copula-based joint PDF, for prediction on the PDF of the target variable using the complete (from normal sensors) or incomplete information (due to missing data caused by sensor fault issue) of the predictor variable. This paper proposes the copula-based UQ (Copula-UQ), composing multivariate joint PDF modelling, inference on model class selection and parameter identification, and probabilistic prediction using incomplete information, for multi-sensor data measured from a SHM system. One example using simulated data and one example using temperature data of multi-sensor of a monitored bridge are presented to illustrate the capability of the proposed Copula-UQ in joint PDF modelling and target variable prediction

Copula-Based Multivariate Joint PDF Modelling

Univariate Marginal PDFs

Copula

Inference on Univariate Marginal PDFs and Copula n m o m

Illustrative Examples

Simulation Data

Temperature Data of Multi-Sensor of a Monitored Bridge

Findings

Conclusions