Advanced functional and sequential statistical time series methods for damage diagnosis in mechanical structures

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 arapid increase in the amount of research related to Structural Health Monitoring (SHM) as quantifiedby the significant escalation in papers published on this subject. Thus, the increased interest in thisengineering 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 andsequential statistical time series methods for vibration based damage diagnosis and SHM. After theintroduction of the first chapter, Chapter II provides an experimental assessment and comparisonof vibration based statistical time series methods for Structural Health Monitoring (SHM) via theirapplication 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, includingresponse-only and excitation-response schemes. Damage detection and identification are based onunivariate (scalar) versions of the methods, while both scalar (univariate) and vector (multivariate)schemes are considered. The methods' effectiveness for both damage detection and identification isassessed via various test cases corresponding to different damage scenarios, multiple experiments andvarious sensor locations on the considered structures. The results of the chapter confirm the highpotential and effectiveness of vibration based statistical time series methods for SHM.Chapter III investigates the identification of stochastic systems under multiple operating conditionsvia Vector-dependent Functionally Pooled (VFP) models. In many applications a system operatesunder 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 fora single commission cycle. Typical examples include mechanical structures operating under differentenvironmental conditions, aircrafts under different ight conditions (altitude, velocity etc.), structuresunder different structural health states (various damage locations and magnitudes). In this way, damagelocation and magnitude may be considered as parameters that affect the operating conditions andas 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 ofPatras. The main characteristic of Functionally Pooled (FP) models is that their model parametersand innovations sequence depend functionally on the operating parameters, and are projected on appropriatefunctional subspaces spanned by mutually independent basis functions. Thus, the fourthchapter of the thesis addresses the problem of identifying a globally valid and parsimonious stochasticsystem model based on input-output data records obtained under a sample of operating conditionscharacterized by more than one parameters. Hence, models that include a vector characterization ofthe operating condition are postulated. The problem is tackled within the novel FP framework thatpostulates proper global discrete-time linear time series models of the ARX and ARMAX types, datapooling techniques, and statistical parameter estimation. Corresponding Vector-dependent FunctionallyPooled (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. Modelstructure estimation is achieved via customary criteria (Bayesian Information Criterion) and a novelGenetic Algorithm (GA) based procedure. The strong consistency of the VFP-ARX least squares andmaximum likelihood estimators is established, while the effectiveness of the complete estimation andidentification method is demonstrated via two Monte Carlo studies.Based on the postulated VFP parametrization a vibration based statistical time series methodthat is capable of effective damage detection, precise localization, and magnitude estimation withina unified stochastic framework is introduced in Chapter IV. The method constitutes an importantgeneralization 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 localizationon continuous structural topologies. More precisely, the proposed method can accuratelylocalize damage anywhere on properly defined continuous topologies on the structure, instead of predefined specific locations. Estimator uncertainties are taken into account, and uncertainty ellipsoidsare provided for the damage location and magnitude. To achieve its goal, the method is based onthe extended class of Vector-dependent Functionally Pooled (VFP) models, which are characterizedby parameters that depend on both damage magnitude and location, as well as on proper statisticalestimation and decision making schemes. The method is validated and its effectiveness is experimentallyassessed via its application to damage detection, precise localization, and magnitude estimationon a prototype GARTEUR-type laboratory scale aircraft skeleton structure. The damage scenariosconsidered 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 magnitudeestimation based on even a single pair of measured excitation-response signals.Chapter V presents the introduction and experimental assessment of a sequential statistical timeseries 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 combinationof 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 thehealthy structure. In this work the full list of properties and capabilities of the SPRT are for the firsttime presented and explored in the context of vibration based damage detection, identification andquantification. The method is shown to achieve effective and robust damage detection, identificationand quantification based on predetermined statistical hypothesis sampling plans, which are both analyticallyand experimentally compared and assessed. The method's performance is determined a priorivia the use of the analytical expressions of the Operating Characteristic (OC) and Average SampleNumber (ASN) functions in combination with baseline data records, while it requires on average aminimum number of samples in order to reach a decision compared to most powerful Fixed SampleSize (FSS) tests. The effectiveness of the proposed method is validated and experimentally assessedvia its application on a lightweight aluminum truss structure, while the obtained results for threedistinct vibration measurement positions prove the method's ability to operate based even on a singlepair of measured excitation-response signals.

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