Abstract
The current thesis main topic of discussion is the problem of vibration data-based damage detection for a population of nominally identical structures. Vibration data-based damage detection as part of the broader Structural Health Monitoring family of methods, receives significant academic and industrial attention over the last several years, since random vibrations are typically naturally available during the structures normal operation, while the corresponding data acquisition and processing equipment is mature and of relatively low cost. The respective vibration-based damage detection methods main concept is based on the fact that a damage changes the structural dynamics. Then, damage detection is based on tracking these changes via proper features that represent some of the modal characteristics of the structure. Nevertheless, such changes may occur due to a multitude of damage irrelevant factors, such as varying Environmental and Operational Conditions (EOCs), thus potentially ``m ...
The current thesis main topic of discussion is the problem of vibration data-based damage detection for a population of nominally identical structures. Vibration data-based damage detection as part of the broader Structural Health Monitoring family of methods, receives significant academic and industrial attention over the last several years, since random vibrations are typically naturally available during the structures normal operation, while the corresponding data acquisition and processing equipment is mature and of relatively low cost. The respective vibration-based damage detection methods main concept is based on the fact that a damage changes the structural dynamics. Then, damage detection is based on tracking these changes via proper features that represent some of the modal characteristics of the structure. Nevertheless, such changes may occur due to a multitude of damage irrelevant factors, such as varying Environmental and Operational Conditions (EOCs), thus potentially ``masking'' the changes due to damage on the dynamics and jeopardizing effective vibration-based damage detection.This issue is further amplified when the vibration-based damage detection problem is considered from an asset management viewpoint. In such a case, damage detection is not implemented on a single structure, but, rather, on a population of similar or nominally-identical structures. Of-course, this cannot be pursued by means of training using a single member of the population, as even nominally identical structures are not truly identical due to variability in the materials, manufacturing, assembly, boundary conditions, and so forth, thereby featuring variability or uncertainty in their dynamics that compounds the uncertainty originating from the varying EOCs. The problem of damage detection for a population of nominally identical structures is effectively unexplored, with a very limited number of studies being available. Yet, the uncertainty in the population dynamics, may be simplistically treated, along with the EOCs stemming uncertainty, into a robustness setting using proper methods to account for this uncertainty. Such robust methods are typically of the machine-learning-type, with their main idea being the construction of a subspace, within a proper feature space, which contains the healthy state dynamics for all the population, under any EOC (Healthy Subspace). In this context, several methods have been proposed over the last two decades, exhibiting very good damage detection performance, yet they are subject to a number of limitations, including: (a) the requirements for relatively high numbers of signal records during the training phase; (b) the selection, often subjective, by the user of a number of hyper-parameters; (c) optimization procedures of significant complexity within high-dimensional spaces and/or non-convex problems; (d) assumptions regarding the Healthy Subspace distribution or geometry; (e) user expertise for the construction of the Healthy Subspace, which is not based on a simple and automated procedure. Therefore, the problem is herein considered and for the first time systematically investigated through a proper benchmark experimental application study, employing a population sample of 31 nominally identical composite aerostructures that feature significant material, manufacturing, and assembly variability, affecting their dynamics. Each population member represents one of the tail booms of a commercial twin tail Unmanned Aerial Vehicle (UAV), while the considered invisible and barely visible damage scenarios are characterized by a combination of delamination, small cracks, and broken fibres, caused by impact at two distinct energy levels.What is more, the above-mentioned limitations are addressed in the present thesis by postulating a number of novel robust damage detection methods, while using only a single vibration sensor and a limited frequency bandwidth. Toward this end, proper unsupervised Multiple Model (MM) methods, which increase detection performance and require limited vibration response signal records from the healthy structural state, are postulated and experimentally assessed by means of the benchmark application study in Chapter 3. The damage detection results indicate that among the considered methods a PCA enhanced MM based method is the most prominent, achieving very good damage detection performance, at 96.3% correct damage detection rate for 3% false alarm rate, even under the significant uncertainty effects of the considered benchmark study. Yet, this performance is pertinent to proper hyper--parameters selections, requiring user judgment and experience, in the method's training phase. Toward addressing this limitation, a supervised version of the PCA-enhanced MM based method is postulated in Chapter 4. This method employs vibration response signals from healthy as well damaged structures in its training phase, in order to automatically - that is without user intervention - determine its hyper-parameters. The respective damage detection results, for the herein considered population of nominally identical structures, indicate that the supervised method yields improved performance compared to most of its unsupervised counterparts, while it relieves the user from critical selections during its implementation. However, damaged structures are typically not available during the methods training phase. Thus, a novel unsupervised method is postulated instead in Chapter 5, which features automated training requiring only vibration response signals from healthy structures. This method constructs a Healthy Subspace representation, by means of the union of a number of deterministic hyper-spheres with distinct centres and radii, thereby providing a good approximation of any Healthy Subspace geometry. The postulated method's damage detection performance is assessed by means of the benchmark application study, as well as an additional experimental case study considering damage detection on a single composite aerostructure under simulated local stiffness reduction type of damage and varying EOCs. The method is additionally compared with three well known robust damage detection methods, with the aggregate assessment results indicating the postulated method's very good detection performance, which exceeds that of the alternative methods, while using limited signal records for its automated training and featuring robustness to any Healthy Subspace geometry.The latter method's performance and characteristics are achieved at the cost of increased computational complexity. This issue is addressed in Chapter 6, where a novel crude Gaussian mixture model based damage detection method is postulated. The method is formulated within a probabilistic framework, featuring a very simple convex estimation procedure, thereby improving the computational complexity issues of the previous method. The crude Gaussian mixture based method approximates the Healthy Subspace, through the superposition of a proper set of isotropic Gaussian distributions, with distinct, properly defined, means and covariances. The latter method is assessed by means of the two experimental application studies of the previous chapter and through comparisons with its predecessors, as well as other powerful state-of-the-art methods. The assessment results indicate the crude Gaussian mixture based method excellent performance, which is superior to all the other methods, given its unsupervised and automated operation under limited training signals records and any Healthy Subspace geometry.
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