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Title: Advanced functional and sequential statistical time series methods for damage diagnosis in mechanical structures
Other Titles: Εξελιγμένες συναρτησιακές και επαναληπτικές στατιστικές μέθοδοι χρονοσειρών για την διάγνωση βλαβών σε μηχανολογικές κατασκευές
Authors: Κοψαυτόπουλος, Φώτης
Issue Date: 2013-02-01
Keywords: Damage diagnosis
Damage detection
Damage identification
Damage localization
Damage quantification
Structural health monitoring
System identification
Stochastic models
Time series models
Multiple operating conditions
ARX/ARMAX models
Structural identification
Keywords (translated): Διάγνωση βλαβών
Ανίχνευση βλαβών
Εντοπισμός βλαβών
Παρακολούθηση υγείας κατασκευών
Στοχαστικά μοντέλα
Στατιστικές μέθοδοι χρονοσειρών
Αναγνώριση συστημάτων
Δυναμικά συστήματα
Ταλαντωτικές μέθοδοι
Μορφική ανάλυση
Πολλαπλά σημεία λειτουργίας
Abstract: The past 30 years have witnessed major developments in vibration based damage detection and identification, also collectively referred to as damage diagnosis. Moreover, the past 10 years have seen a rapid increase in the amount of research related to Structural Health Monitoring (SHM) as quantified by the significant escalation in papers published on this subject. Thus, the increased interest in this engineering field and its associated potential constitute the main motive for this thesis. The goal of the thesis is the development and introduction of novel advanced functional and sequential statistical time series methods for vibration based damage diagnosis and SHM. After the introduction of the first chapter, Chapter II provides an experimental assessment and comparison of vibration based statistical time series methods for Structural Health Monitoring (SHM) via their application on a lightweight aluminum truss structure and a laboratory scale aircraft skeleton structure. A concise overview of the main non-parametric and parametric methods is presented, including response-only and excitation-response schemes. Damage detection and identification are based on univariate (scalar) versions of the methods, while both scalar (univariate) and vector (multivariate) schemes are considered. The methods' effectiveness for both damage detection and identification is assessed via various test cases corresponding to different damage scenarios, multiple experiments and various sensor locations on the considered structures. The results of the chapter confirm the high potential and effectiveness of vibration based statistical time series methods for SHM. Chapter III investigates the identification of stochastic systems under multiple operating conditions via Vector-dependent Functionally Pooled (VFP) models. In many applications a system operates under a variety of operating conditions (for instance operating temperature, humidity, damage location, damage magnitude and so on) which affect its dynamics, with each condition kept constant for a single commission cycle. Typical examples include mechanical structures operating under different environmental conditions, aircrafts under different flight conditions (altitude, velocity etc.), structures under different structural health states (various damage locations and magnitudes). In this way, damage location and magnitude may be considered as parameters that affect the operating conditions and as a result the structural dynamics. This chapter's work is based on the novel Functional Pooling (FP) framework, which has been recently introduced by the Stochastic Mechanical Systems \& Automation (SMSA) group of the Mechanical Engineering and Aeronautics Department of University of Patras. The main characteristic of Functionally Pooled (FP) models is that their model parameters and innovations sequence depend functionally on the operating parameters, and are projected on appropriate functional subspaces spanned by mutually independent basis functions. Thus, the fourth chapter of the thesis addresses the problem of identifying a globally valid and parsimonious stochastic system model based on input-output data records obtained under a sample of operating conditions characterized by more than one parameters. Hence, models that include a vector characterization of the operating condition are postulated. The problem is tackled within the novel FP framework that postulates proper global discrete-time linear time series models of the ARX and ARMAX types, data pooling techniques, and statistical parameter estimation. Corresponding Vector-dependent Functionally Pooled (VFP) ARX and ARMAX models are postulated, and proper estimators of the Least Squares (LS), Maximum Likelihood (ML), and Prediction Error (PE) types are developed. Model structure estimation is achieved via customary criteria (Bayesian Information Criterion) and a novel Genetic Algorithm (GA) based procedure. The strong consistency of the VFP-ARX least squares and maximum likelihood estimators is established, while the effectiveness of the complete estimation and identification method is demonstrated via two Monte Carlo studies. Based on the postulated VFP parametrization a vibration based statistical time series method that is capable of effective damage detection, precise localization, and magnitude estimation within a unified stochastic framework is introduced in Chapter IV. The method constitutes an important generalization of the recently introduced Functional Model Based Method (FMBM) in that it allows, for the first time in the statistical time series methods context, for complete and precise damage localization on continuous structural topologies. More precisely, the proposed method can accurately localize damage anywhere on properly defined continuous topologies on the structure, instead of pre-defined specific locations. Estimator uncertainties are taken into account, and uncertainty ellipsoids are provided for the damage location and magnitude. To achieve its goal, the method is based on the extended class of Vector-dependent Functionally Pooled (VFP) models, which are characterized by parameters that depend on both damage magnitude and location, as well as on proper statistical estimation and decision making schemes. The method is validated and its effectiveness is experimentally assessed via its application to damage detection, precise localization, and magnitude estimation on a prototype GARTEUR-type laboratory scale aircraft skeleton structure. The damage scenarios considered consist of varying size small masses attached to various continuous topologies on the structure. The method is shown to achieve effective damage detection, precise localization, and magnitude estimation based on even a single pair of measured excitation-response signals. Chapter V presents the introduction and experimental assessment of a sequential statistical time series method for vibration based SHM capable of achieving effective, robust and early damage detection, identification and quantification under uncertainties. The method is based on a combination of binary and multihypothesis versions of the statistically optimal Sequential Probability Ratio Test (SPRT), which employs the residual sequences obtained through a stochastic time series model of the healthy structure. In this work the full list of properties and capabilities of the SPRT are for the first time presented and explored in the context of vibration based damage detection, identification and quantification. The method is shown to achieve effective and robust damage detection, identification and quantification based on predetermined statistical hypothesis sampling plans, which are both analytically and experimentally compared and assessed. The method's performance is determined a priori via the use of the analytical expressions of the Operating Characteristic (OC) and Average Sample Number (ASN) functions in combination with baseline data records, while it requires on average a minimum number of samples in order to reach a decision compared to most powerful Fixed Sample Size (FSS) tests. The effectiveness of the proposed method is validated and experimentally assessed via its application on a lightweight aluminum truss structure, while the obtained results for three distinct vibration measurement positions prove the method's ability to operate based even on a single pair of measured excitation-response signals. Finally, Chapter VI contains the concluding remarks and future perspectives of the thesis.
Abstract (translated): Κατά τη διάρκεια των τελευταίων 30 ετών έχει σημειωθεί σημαντική ανάπτυξη στο πεδίο της ανίχνευσης και αναγνώρισης βλαβών, το οποίο αναφέρεται συνολικά και σαν διάγνωση βλαβών. Επίσης, κατά την τελευταία δεκαετία έχει σημειωθεί σημαντική πρόοδος στον τομέα της παρακολούθησης της υγείας (δομικής ακεραιότητας) κατασκευών. Στόχος αυτής της διατριβής είναι η ανάπτυξη εξελιγμένων συναρτησιακών και επαναληπτικών μεθόδων χρονοσειρών για τη διάγνωση βλαβών και την παρακολούθηση της υγείας κατασκευών υπό ταλάντωση. Αρχικά γίνεται η πειραματική αποτίμηση και κριτική σύγκριση των σημαντικότερων στατιστικών μεθόδων χρονοσειρών επί τη βάσει της εφαρμογής τους σε πρότυπες εργαστηριακές κατασκευές. Εφαρμόζονται μη-παραμετρικές και παραμετρικές μέθοδοι που βασίζονται σε ταλαντωτικά σήματα διέγερσης και απόκρισης των κατασκευών. Στη συνέχεια αναπτύσσονται στοχαστικά συναρτησιακά μοντέλα για την στοχαστική αναγνώριση κατασκευών υπό πολλαπλές συνθήκες λειτουργίας. Τα μοντέλα αυτά χρησιμοποιούνται για την αναπαράσταση κατασκευών σε διάφορες καταστάσεις βλάβης (θέση και μέγεθος βλάβης), ώστε να είναι δυνατή η συνολική μοντελοποίσή τους για όλες τις συνθήκες λειτουργίας. Τα μοντέλα αυτά αποτελούν τη βάση στην οποία αναπτύσσεται μια συναρτησιακή μέθοδος η οποία είναι ικανή να αντιμετωπίσει συνολικά και ενιαία το πρόβλημα της ανίχνευσης, εντοπισμού και εκτίμησης βλαβών σε κατασκευές. Η πειραματική αποτίμηση της μεθόδου γίνεται με πολλαπλά πειράματα σε εργαστηριακό σκελετό αεροσκάφους. Στο τελευταίο κεφάλαιο της διατριβής προτείνεται μια καινοτόμος στατιστική επαναληπτική μέθοδο για την παρακολούθηση της υγείας κατασκευών. Η μέθοδος κρίνεται αποτελεσματική υπό καθεστώς λειτουργικών αβεβαιοτήτων, καθώς χρησιμοποιεί επαναληπτικά και στατιστικά τεστ πολλαπλών υποθέσεων. Η αποτίμηση της μεθόδου γίνεται με πολλαπλά εργαστηριακά πειράματα, ενώ η μέθοδος κρίνεται ικανή να λειτουργήσει με τη χρήση ενός ζεύγους ταλαντωτικών σημάτων διέγερσης-απόκρισης.
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