Robust Vibration-Based damage diagnosis under varying environmental and operating conditions and uncertainty via stochastic functional model methods

Abstract

Random vibration-based Structural Health Monitoring (SHM), which aims at damage diagnosis based on measured vibration signals, has rapidly progressed over the past several years, reaching high levels of technological maturity. Yet, a major challenge relating to effective damage diagnosis (including damage detection and localization) under varying Environmental and Operating Conditions (EOCs) still remains. The fundamental reason behind it has to do with the fact that such factors may affect the underlying structural dynamics in a specific way that may be similar to that caused by damage, and as such changes are at the core of damage diagnosis, the latter may become ineffective. Thus, overcoming this challenge requires the development of robust damage diagnosis methods. Robust damage detection has received remarkable attention with numerous methods achieving impressive performance. These methods typically attempt, in their training phase, the modeling of the considered healthy structural dynamics under varying EOCs and uncertainty. Such modeling may assume various forms and be broadly classified as `implicit' or `explicit'. `Implicit' methods focus on the selection of features of the dynamics that are insensitive to changes due to the varying EOCs, assuming that they are sensitive to damage. On the contrary, explicit' methods attempt to model the effect of the varying EOCs on the dynamics via explicit deterministic or stochastic modeling techniques. However, methods of both categories are subject to a number of important limitations. For example, some may require the continuous, in operation, measurement of the actual EOCs, which may be cost-inefficient or not feasible, complex modeling, or the requirement of a high number of signals / experiments for their training, while others may `depend' on the subjective selection of parameters, critical for their performance. Despite the wide variety of robust damage detection methods, robust damage localization is still scarce in the literature. In addition to that, most available methods typically treat localization as a rough classification problem. According to this, the discretization of the considered structural topology into a number of regions, each one uniquely specified by a sensor, is performed, so as there is a one-to-one correspondence between sensors and examined regions. Based on the this, the training of such methods includes the modeling of the healthy dynamics under varying EOCs through vibration signals obtained from each sensor (representing a distinct region), leading to a `pool of baseline models' (each one corresponding to a distinct sensor / region). Damage detection and conceptually rough localization are accomplished, based on fresh vibration signals obtained from all employed sensors, by checking for discrepancies between the current and all baseline models' dynamics. In case of deviation from a specific model, damage detection and rough localization to the specific region have been achieved. As evident, such a (restrictive) treatment is accompanied by additional disadvantages as for instance the dense sensor network needed for the complete coverage of the structure, which is impractical and cost-inefficient. Over the past years, the data-based Functional Model Based Methods (FMBMs) have been developed and assessed by the Stochastic Mechanical Systems and Automation (SMSA) Laboratory of the University of Patras, focusing on the problem of damage precise localization and magnitude estimation. This family of methods is uniquely characterized by the fact that it may provide estimates of the exact damage magnitude and / or the damage coordinates on the considered structural topology, along with a precise confidence region. The cornerstone of the FMBMs is a special form of stochastic data-based Functional Models (FMs), which are capable of representing the structural dynamics under damage of any magnitude and / or at different locations on the considered topology. Yet, they have been only developed for structures operating under constant EOCs, which may be considered as an ideal / non-realistic approach. It is worth noting that FMs have been also employed within a robust damage detection framework, also developed by the SMSA Laboratory, yet it `suffers' from limitations such as the requirement for the continuous measurement of the varying EOCs throughout its operation, which, in practice, may not be feasible or it may require further sensing systems, leading thus to additional costs. The current thesis focuses on the robust, to varying EOCs and other uncertainties, SHM, attempting to overcome all the aforementioned limitations of the state-of-the-art methods. Thus, the main goal is the development of a robust damage diagnosis method, including damage detection and precise localization on continuous structural topologies, via the proper use of FMs. Chapter II addresses the problem of railway vertical random vibration-based dynamic analysis under normal varying operating conditions and constitutes a preliminary study and part of the fundamental basis of the next chapters. The main goal here is twofold: (i) the selection of a proper, robust to varying EOCs, characteristic quantity for the monitoring of the varying structural dynamics and (ii) the healthy dynamics' compact representation via global modeling techniques. The analysis is based on various data-based non-parametric and parametric estimation methods including Welch-type power spectral density (PSD) and transmittance function (TF) estimates, AutoRegressive (AR), Vector AutoRegressive (VAR) and Transmittance (Function) type AutoRegressive with eXogenous (ARX) excitation modeling, as well as Functionally Pooled (FP)-ARX representations. Based on the results, it is concluded that the Transmittance type FP-ARX model may be considered as a proper selection for the problem of robust damage diagnosis, and thus employed in the next chapters. The proposed novel stochastic Functional Model based method for robust fault detection is introduced in Chapter III. The method, in this chapter, is developed considering structures operating under a single varying operating condition, constituting thus a first approach to the specific problem. The method aims at high detection performance levels, while eliminating the aforementioned limitations of other available, state-of-the-art, methods. Its cornerstone is the representation of the healthy structural dynamics under any EOCs in a parameter space, referred to as the `healthy subspace'. This subspace is constructed in an initial, baseline phase, using signal records obtained from controlled experiments (allowing - only in this phase - for measurement of the EOCs) and a data-based FM. Fault detection is then based upon determining, at a certain risk level, whether or not the current dynamics resides within the healthy subspace. The method's effectiveness along with the concept validation are confirmed via an application case study pertaining to fault detection in railway vehicle suspension systems under varying payload - a major engineering problem that has not yet been seriously addressed - achieving high detection performance. A comparison demonstrating the performance improvement attained over an alternative robust damage detection method is also made. Chapter IV includes the extension of the FM based method, as presented in Chapter III, within a more realistic context, considering now multiple varying EOCs and other exogenous uncertainties. For this reason, a Vector-dependent FM equipped with a scheduling vector that incorporates multiple EOCs, is employed. In addition, a new version of the method with a new statistical hypothesis testing procedure is also introduced. This version is based on the residual variance of the FM (compared to that presented in Chapter III which is based on the residual uncorrelatedness), reducing the user intervention in subjective parameters' selection. The present chapter constitutes, a systematic, proof-of-concept study through the robust damage detection in an Unmanned Aerial Vehicle (UAV) tail structure via hundreds of physical experiments, validating thus the reliable method's performance. The method achieves ideal detection performance via its (new) residual variance version and also quite good, yet degraded, for the residual uncorrelatedness version (Chapter III). Comparisons with other robust state-of-the-art methods are also made. After postulating and successfully validating the FM based method for robust damage detection (Chapters III and IV), Chapter V addresses the problem of vibration-based robust and precise damage localization under varying operating conditions, constituting thus the final step of the proposed damage diagnosis framework. In this chapter, the extension of the FM based method for robust damage precise localization is now presented, with the employed FM characterized by parameters that depend on a proper scheduling vector including the varying operating conditions and the damage location coordinates. Unlike most available vibration-based methods, the current one approaches the problem from a damage precise localization perspective. This implies the estimation of the damage's exact coordinates, assuming that the damage may occur anywhere on the considered topology. The method is experimentally assessed using hundreds of experiments via damage precise localization on a thin aluminum plate under varying boundary conditions and early-stage damage scenarios. The performance of the method under two different case studies, depending on the availability of the excitation signal, is also investigated. Despite the minor nature of the damage scenarios, the limited number of the employed sensors and the low frequency bandwidth, the obtained results indicate impressive accuracy for both case studies, highlighting the method's capability to be based solely on vibration response signals, yet still achieving performance of high accuracy. Finally, Chapter VI contains the concluding remarks and future perspectives of the thesis.

Η παρακολούθηση της υγείας (δομικής ακεραιότητας) των κατασκευών βάσει σημάτων ταλάντωσης, η οποία στοχεύει στη διάγνωση βλαβών με αποκλειστική χρήση ταλαντωτικών σημάτων, έχει σημειώσει σημαντική πρόοδο τα τελευταία χρόνια, φτάνοντας σε υψηλά επίπεδα τεχνολογικής ωριμότητας. Ωστόσο, μια σημαντική πρόκληση που σχετίζεται με την αποτελεσματική διάγνωση βλαβών (συμπεριλαμβανομένης της ανίχνευσης βλαβών και της ακριβούς χωροθέτησής τους) υπό μεταβαλλόμενες περιβαλλοντικές και λειτουργικές συνθήκες (ΠΛΣ), παραμένει μέχρι και σήμερα. Ο θεμελιώδης λόγος πίσω από αυτό, σχετίζεται με το γεγονός ότι τέτοιοι παράγοντες (ΠΛΣ) μπορούν να επηρεάσουν τα δυναμικά χαρακτηριστικά μιας κατασκευής με παρόμοιο τρόπο όπως μια ενδεχόμενη βλάβη. Καθώς τέτοιες αλλαγές βρίσκονται στον πυρήνα της διάγνωσης βλαβών, αυτή μπορεί να καταστεί αναποτελεσματική. Με γνώμονα την αντιμετώπιση της πρόκλησης αυτής, στόχος της παρούσας διατριβής είναι η ανάπτυξη μίας μεθόδου για την εύρωστη διάγνωση βλαβών (ανίχνευση και ακριβής χωροθέτηση) βάσει σημάτων ταλάντωσης υπό μεταβαλλόμενες ΠΛΣ και αβεβαιότητα μέσω μεθόδων στοχαστικών συναρτησιακών μοντέλων. Αρχικά, στο Κεφάλαιο ΙΙ αντιμετωπίζεται το πρόβλημα της δυναμικής ανάλυσης σιδηροδρομικών οχημάτων, μέσω ταλαντωτικών σημάτων, υπό κανονικές μεταβαλλόμενες συνθήκες λειτουργίας. Η ανάλυση βασίζεται σε διάφορες μη-παραμετρικές και παραμετρικές μεθόδους και αποτελεί μια προκαταρκτική μελέτη και μέρος της βάσης των επόμενων κεφαλαίων. Η προτεινόμενη μεθοδολογία για την εύρωστη ανίχνευση βλαβών μέσω στοχαστικών συναρτησιακών μοντέλων παρουσιάζεται στο Κεφάλαιο III. Η μέθοδος, σε αυτό το κεφάλαιο, αναπτύσσεται για κατασκευές οι οποίες λειτουργούν υπό μία μεταβαλλόμενη συνθήκη λειτουργίας, αποτελώντας έτσι μια πρώτη προσέγγιση στο πρόβλημα και στοχεύει σε υψηλά επίπεδα απόδοσης, ενώ εξαλείφει διάφορους περιορισμούς άλλων διαθέσιμων μεθόδων της βιβλιογραφίας. Η αποτίμηση της μεθόδου γίνεται μέσω μελέτης προσομοιώσεων και αφορά στην ανίχνευση σφαλμάτων σε συστήματα ανάρτησης σιδηροδρομικών οχημάτων υπό μεταβαλλόμενο ωφέλιμο φορτίο. Επιτυγχάνεται υψηλή απόδοση ενώ τέλος, πραγματοποιείται και σύγκριση έναντι μιας εναλλακτικής μεθόδου. Το Κεφάλαιο IV περιλαμβάνει την επέκταση της μεθόδου, όπως παρουσιάζεται στο Κεφάλαιο III, μέσα σε ένα πιο ρεαλιστικό πλαίσιο, λαμβάνοντας υπόψη πολλαπλές μεταβαλλόμενες ΠΛΣ και άλλες εξωγενείς αβεβαιότητες. Επιπλέον, εισάγεται μια νέα έκδοσή της, η οποία μειώνει την παρέμβαση του χρήστη στην επιλογή υποκειμενικών παραμέτρων. Το κεφάλαιο αυτό αποτελεί, μια συστηματική μελέτη για την πειραματική αποτίμηση της προτεινόμενης μεθοδολογίας, η οποία πραγματοποιείται μέσω εκατοντάδων πειραμάτων σε κομμάτι της ουράς ενός μη-επανδρωμένου αεροσκάφους (UAV). Τα αποτελέσματα παρουσιάζουν ιδανική απόδοση ανίχνευσης μέσω της νέας έκδοσης, καθώς επίσης πραγματοποιούνται και συγκρίσεις με άλλες μεθόδους της βιβλιογραφίας. Το τελευταίο κεφάλαιο (Κεφάλαιο V) αντιμετωπίζει το πρόβλημα της εύρωστης και ακριβούς χωροθέτησης βλαβών για κατασκευές που λειτουργούν υπό μεταβαλλόμενες συνθήκες λειτουργίας, αποτελώντας έτσι και το τελικό στάδιο του προτεινόμενου πλαισίου διάγνωσης βλαβών. Σε αντίθεση με τις περισσότερες διαθέσιμες μεθόδους της βιβλιογραφίας, η παρούσα έχει την δυνατότητα εκτίμησης των ακριβών συντεταγμένων της βλάβης, υποθέτοντας ότι μπορεί να συμβεί οπουδήποτε στην εξεταζόμενη τοπολογία. Η μέθοδος αξιολογείται πειραματικά μέσω πολλαπλών πειραμάτων για τον ακριβή εντοπισμό βλάβης σε μια λεπτή πλάκα αλουμινίου υπό μεταβαλλόμενες συνοριακές συνθήκες και σενάρια βλαβών πρώιμης φάσης. Εξετάζεται επίσης η απόδοσή της σε δύο διαφορετικές περιπτωσιολογικές μελέτες, ανάλογα με τη διαθεσιμότητα του σήματος διέγερσης. Παρά τη μικρή φύση των εξεταζόμενων βλαβών, τον περιορισμένο αριθμό των χρησιμοποιούμενων αισθητήρων και το εύρος ζώνης χαμηλής συχνότητας, η μέθοδος παρουσιάζει εντυπωσιακή ακρίβεια και για τις δύο περιπτώσεις, υπογραμμίζοντας την ικανότητά της να λειτουργεί αποκλειστικά με ταλαντωτικά σήματα απόκρισης.