A Damage Detection Approach for Axially Loaded Beam-like Structures Based on Gaussian Mixture Model

Abstract

Axially loaded beam-like structures represent a challenging case study for unsupervised learning vibration-based damage detection. Under real environmental and operational conditions, changes in axial load cause changes in the characteristics of the dynamic response that are significantly greater than those due to damage at an early stage. In previous works, the authors proposed the adoption of a multivariate damage feature composed of eigenfrequencies of multiple vibration modes. Successful results were obtained by framing the problem of damage detection as that of unsupervised outlier detection, adopting the well-known Mahalanobis squared distance (MSD) to define an effective damage index. Starting from these promising results, a novel approach based on unsupervised learning data clustering is proposed in this work, which increases the sensitivity to damage and significantly reduces the uncertainty associated with the results, allowing for earlier damage detection. The novel approach, which is based on Gaussian mixture model, is compared with the benchmark one based on the MSD, under the effects of an uncontrolled environment and, most importantly, in the presence of real damage due to corrosion.

Unsupervised Learning Methods for Data-Driven Vibration-Based Structural Health Monitoring: A Review

“…For univariate outlier analysis, a statistical significance test (e.g., z-test or t -test) is commonly used. A threshold can be set using confidence intervals [ 83 , 108 , 130 , 136 ], significance [ 62 , 73 , 88 , 102 , 120 ], percentiles [ 58 , 63 , 64 , 66 , 74 ], or other data statistics. For multidimensional features, MD, or MSD, is often used [ 59 , 67 , 72 , 82 , 89 , 90 , 99 , 116 , 132 ].…”

“…Using the Z-24 bridge benchmark as a validation, it was shown that introducing the genetic algorithm improved the stability of the EM method, especially in minimizing type 2 errors. Addressing tie-rods evolutive damage, such as corrosion, Lucà et al [ 66 ] proposed a tie-rod damage detection method by fitting a GMM using eigenfrequencies. The existence of damage can be detected based on the likelihood values of two GMM hypotheses, which are single versus double Gaussian densities.…”

“…For example, model parameters, which are commonly used as damage-sensitive features, can drastically change due to temperature variations [ 185 ]. In the past decade, many researchers focused on developing damage-sensitive features and novelty detection techniques that are less sensitive to environmental variability [ 66 , 67 , 81 , 82 , 83 , 96 , 105 , 125 ]. Others considered a probabilistic novelty detection method that would incorporate uncertainties including environmental variations and measurement noise [ 72 , 132 ].…”

Short-Training Damage Detection Method for Axially Loaded Beams Subject to Seasonal Thermal Variations

“…Before entering into details of the two compared approaches, it is worth mentioning that the initial damage feature is a collection of eigenfrequencies of the monitored tie-rod. This starting point comes from previous research works where it has been proved that the eigenfrequencies of an axially-loaded beam-like structure, used as a multivariate damage feature, can be effectively adopted to spot damage in operating tie-rods [ 18 , 49 , 50 , 54 ].…”

“…Moreover, as already mentioned, a change of the axial load cannot be directly related to the presence of a crack in the tie-rod, due to the axial load sensitivity to physical variables, not correlated to the state of health of the tie-rod, and due to environmental effects, e.g., temperature. Only recently, the problem of detecting damage in tie-rods has been faced, with a focus on cracks [ 17 ] or corrosion [ 49 , 50 ], and this is an important aspect when SHM of larger structures where tie-rods are in use must be carried out (e.g., [ 51 ]). Lucà et al showed that tie-rod eigenfrequencies can be used as synthetic damage features that are representative of all physical variables which affect the system behaviour, included the axial load.…”