Singular value decomposition and unsupervised machine learning for virtual strain sensing: Application to an operational railway bridge

Abstract

Metal fatigue is a major concern in civil, mechanical, and offshore structures. As a result, inspections are frequently directed to critical, fatigue prone locations using visual inspections, nondestructive evaluations, or sensor data. However, fatigue assessment may be hampered if access to these fatigue-prone areas is difficult or impossible. Furthermore, when comprehensive sensor use as part of a bridge health monitoring system is desired, cost and power requirements can be prohibitive. These identified limitations have motivated studies examining virtual sensing methods that estimate strains at unmeasured locations using indirect measurements. Kalman filtering (KF) and modal expansion (ME) are two popular strain estimation processes. However, both processes are model-based, requiring calibration of a finite element (FE) model of the structure of interest, which can be time-consuming, particularly for complex structures. This constraint has spurred the need for data-driven strain estimation methods, which depends solely on data from the structure, typically provided by sensors, without any additional a priori knowledge of the structure, such as what could be provided by a FE model. This study investigated the use of a novel, data-driven, Singular Value Decomposition (SVD) based method for strain estimation on an operational railroad bridge. Left singular vector (LSV) SVD modes, also known as Proper Orthogonal Modes (POMs), were employed for strain estimation. Machine learning (ML) was implemented to reduce POM variability and subsequently increase estimation accuracy using two classification methods: k-means clustering and root mean square (RMS); and self-organizing maps (SOM) and POMs. Strains were predicted using strain time-history POMs from snapshot matrices from clustered groups of train passages to estimate unmeasured time-histories from the same group. The method was applied to operational strain measurements from approximately 300 train passages over a steel, truss, railway bridge. Results showed that use of the data driven SVD technique in conjunction with ML could predict suitable strain time signals at unmeasured locations, data that can subsequently be utilized when performing fatigue assessment.