Higher-Order Multivariate Environmental Influences in Structural Health Monitoring

2026-03-24

AI Summary

This study addresses the challenge that environmental factors not only affect the mean response of structural health monitoring (SHM) systems but also significantly distort higher-order statistical characteristics—such as covariance and correlation—thereby obscuring genuine damage signatures. To overcome the limitations of conventional approaches that correct only the mean, this work presents the first systematic modeling framework for environmental effects on multivariate output higher-order statistical moments. Two novel methods are proposed: one based on random forest regression and another leveraging nonparametric kernel techniques, both designed to capture the complex relationship between environmental conditions and output covariance structures. Experiments on both synthetic and real-world SHM data demonstrate that the kernel-based method achieves higher accuracy, while the random forest approach offers superior robustness and interpretability, effectively elucidating the mechanisms by which environmental variability interferes with higher-order statistics.

Technology Category

• Machine Learning: Kernel Methods
• Intelligent Robots: State Estimation
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

System outputs such as eigenfrequencies or strain data, often used in structural health monitoring (SHM), not only react to damage but also depend on environmental conditions. When trying to correct for these confounding effects, it is often (at least implicitly) assumed that only the expected, i.e., mean, output values are affected by environmental conditions. However, the evaluation of real-world SHM data indicates that environmental conditions may influence not only the mean output 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. To address these issues, we discuss two approaches for identifying and quantifying multivariate confounding effects on output covariances and correlations: a random forest and a nonparametric, kernel-based approach. We compare the two competing methods on both artificial and real-world SHM data, finding that the kernel-based approach achieves higher accuracy, but the random forest produces estimates that are more robust and sometimes easier to interpret.

Problem

• structural health monitoring
• environmental influences
• higher-order statistics
• covariance
• multivariate effects

Innovation

• higher-order statistics
• multivariate environmental effects
• covariance modeling
• structural health monitoring
• nonparametric kernel method