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Le principe de la maintenance conditionnelle consiste à évaluer en permanence l’intégrité des machines industrielles, à partir des mesures et de traitements du signal appropriés, afin d’intervenir uniquement au moment le plus opportun. Dans ce contexte, l’objectif de cette thèse est de développer une technique de détection, aussi précoce que possible, de l’amorce de dégradation lente d’une structure vibrante, telle que les fissures de fatigue, pour éviter toute défaillance inattendue des machines. Notre approche se base sur les données mesurées à l’aide de deux moyens expérimentaux mis en œuvre au laboratoire. L’étude a démarré avec une poutre encastrée-libre sollicitée en flexion et s’est poursuivie sur un banc d’essais plus représentatif de la problématique industrielle. Dans les deux cas, l'endommagement de la structure a été naturel et progressif, depuis un état réputé sain jusqu’à l’apparition de la fissure. Le comportement dynamique a été suivi à l’aide d’accéléromètres. Ainsi, afin d’identifier des indicateurs sensibles au phénomène d’endommagement, plusieurs pistes ont été envisagées. Nous avons examiné les indicateurs scalaires descriptifs des signaux mesurés, qui sont les moments statistiques, fréquences moyennes et médianes. Ces indicateurs sont utilisés avec succès pour la détection de défaut sur les éléments de machines tournantes, mais ils se sont montrés peu sensibles pour détecter des défaillances structurales. Les fréquences propres identifiées automatiquement à partir des signaux temporels acquis sous chargements opérationnels ont également été étudiées. Ensuite, nous nous sommes orientés vers une approche plus globale pour surveiller les changements spectraux causés par l’apparition d’un défaut sur une structure. En se basant sur les matrices spectrales, fonctions et matrices de transmissibilité, des indicateurs multi-capteurs ont été développés et testés pour les deux cas d’étude. Une Analyse en Composantes Principales a permis d’identifier, entre les indicateurs analysés, ceux qui sont les plus pertinents pour la surveillance de l’intégrité des structures. / The principle of the conditional maintenance consists in continuously evaluating the health state of industrial machines, from measurements and appropriate signal processing, in order to carry out maintenance operations only at the most convenient time. In this context, the objective of this PhD thesis is to implement a technique for detecting as soon as possible slow damage initiation in vibrating structures, such as the fatigue cracks, to avoid the unexpected failure of machines. We have conducted empirical investigations with two experimental setups built in the laboratory. The study started with a cantilever beam subjected to dynamic bending loads, and continued on a test-bench more representative of the industrial problem. In both cases, the structure was naturally and progressively damaged, from a state considered to be healthy, until the crack occurs. Its dynamical behavior was monitored using accelerometers. Therefore, in order to identify damage-sensitive features, many leads were investigated. We have examined the features describing the measured signals waveform, which are statistical moments, mean frequencies and median frequencies. They are successfully used for fault detection on rotating machinery, but they did not demonstrate enough sensitiveness to detect structural damage. The natural frequencies automatically identified from the measured time signals under operational loads have also been studied. Thus, we oriented our work towards a more global approach to monitor the spectral changes caused by the appearance of damage on a structure. Based on the spectral matrices and transmissibility quantities, multi-sensor indicators were developed and tested for the two cases of study. A Principal Component Analysis allowed us to identify, between the surveyed features, the ones most relevant for monitoring the integrity of structures.

Analysis of vibration of systems with uncertainty in material properties under the influence of a random forcing function is an active area of research. Especially the characterization based on mode shapes and frequencies of linear vibrating systems leads to much discussed random eigenvalue problem, which repeatedly appears while analyzing a number of engineering systems. Such analyses with conventional schemes for significant variation of system parameters for large systems are often not viable because of the high computational costs involved. Appropriate tools to reduce the size of stochastic vibrating systems and efficient response calculation are yet to mature. Among the mathematical tools used in this case, polynomial chaos formulation of uncertainties shows promise. But this comes with the implementation issue of solving large systems of nonlinear equations arising from Bubnov-Galerking projection in the formulation. This dissertation reports the study of such dynamic systems with uncertainties characterized by the probability distribution of eigen solutions under a stochastic finite element framework. In the context of structural vibration, the determination of appropriate modes to be considered in a stochastic framework is not straightforward. In this dissertation, at first the choice of dominant modes in stochastic framework is studied for vibration problems. A relative measure, based on the average energy contribution of each mode to the system, is developed. Further the interdependence of modes and the effect of the shape of the load on the choice of dominant modes are studied. Using these considerations, a hybrid algorithm is developed based on polynomial chaos framework for the response analysis of a structure with random mass and sickness and under the influence of random force. This is done by using modal truncation for response analysis with in a Monte Carlo loop. The algorithm is observed to be more efficient and achieves a high degree of accuracy compared to conventional techniques. Considering the fact that the Monte Carlo loops within the above mentioned hybrid algorithm is easily parallelizable, the efficient implementation of it depends on the SFE solution. The set of nonlinear equations arising from polynomial chaos formulation is solved using matrix-free Newton’s iteration using GMRES as linear solver. Solution of a large system using a iterative method like GMRES necessitates the use of a good preconditioner. Keeping focus on the par-allelizability of the algorithm, a number of efficient but cheap-to-construct preconditioners are developed and the most effective among them is chosen. The solution process is parallelized for large systems. The scalability of solution process in conjunction with the preconditioner is studied in details.