Removal of Multivariate Environmental Influences in Structural Health Monitoring through Conditional Covariances and Supervised Learning

2026-06-03

AI Summary

This study addresses the challenge that environmental and operational variations not only perturb the mean of structural health monitoring data but also substantially alter its covariance and correlation structure, rendering conventional mean-correction approaches inadequate. To overcome this limitation, the paper introduces, for the first time, a systematic framework for conditional covariance modeling, leveraging supervised learning to estimate the influence of environmental variables on the covariance of multi-sensor outputs. The approach integrates diverse strategies, including nonparametric kernel methods, random forests, semi-parametric additive models, and deep neural networks. Experimental validation on synthetic datasets, load-testing data from the Vahrendorfer Bridge in Germany, and modal frequency measurements from the KW51 railway bridge in Belgium demonstrates that the proposed method effectively removes higher-order statistical interference, significantly enhancing the accuracy and robustness of damage identification.

Abstract

In structural health monitoring (SHM) systems, data is collected from a multitude of sensors measuring, for example, vibration or strain in the structure, along with additional features that capture environmental or operational information. It is well known that changes in the measured sensor outputs do not necessarily originate from structural damage but are often induced by environmental changes. One popular approach to account for these effects is regressing the system outputs on the confounding factors, also known as "response surface modeling". Afterward, the predicted values are subtracted from the observed ones to obtain corrected data with the environmental effects (supposedly) removed. However, the evaluation of real-world SHM data shows that environmental conditions may affect not only the expected output values but also higher-order statistical moments, particularly the variances of and the covariances and correlations between the output quantities, such as eigenfrequencies of different modes or strain sensors at different locations. By construction, the (supervised) machine learning techniques commonly used for response surface modeling cannot account for those higher-order effects. To address these issues, we present and discuss several approaches for identifying and quantifying multivariate confounding effects on output covariances and correlations: a nonparametric, kernel-based estimator, a random forest, a semiparametric additive model, and a deep learning approach. Furthermore, we show how the resulting conditional covariance matrices can be used in an SHM pipeline. We compare the competing methods on both artificial data and real-world load test data from the Vahrendorfer Stadtweg bridge in Hamburg, Germany, as well as eigenfrequency data from the railway bridge KW51 near Leuven, Belgium.

Problem

• structural health monitoring
• environmental influences
• conditional covariances
• multivariate confounding
• higher-order statistics

Innovation

• conditional covariance
• structural health monitoring
• environmental compensation
• supervised learning
• multivariate confounding