Model-based structural damage identification using vibration measurements

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Antti Huhtala Name of the doctoral dissertation Model-based structural damage identification using vibration measurements Publisher School of Science Unit Department of Mathematics and Systems Analysis Series Aalto University publication series DOCTORAL DISSERTATIONS 30/2015 Field of research Mechanics Manuscript submitted 15 December 2014 Date of the defence 20 March 2015 Permission to publish granted (date) 3 February 2015 Language English Monograph Article dissertation (summary + original articles) Abstract In structural health monitoring (SHM), a structure is continuously monitored with a set of embedded sensors. Damage identification is the part of a SHM system, in which the damage state of the structure is determined from obtained measurements. More specifically, the presence of damage is detected, and its location and severity are estimated. Even if the measured quantities are known to be sensitive to damage, the reconstruction of damage from the measurement is generally not well-posed, since significantly different damage states may still produce similar measurement results. Damage identification is thus an inverse problem. In this thesis, a model-based approach using vibration measurements is taken. The vibration of the structure is measured using several sensors, which can be for instance strain gauges, gyroscopes or accelerometers. A model of the structure, including a model of how the damage affects the structure and a model of the measurement sensors, is then used to simulate the measurements. Damage identification is achieved through finding a plausible damage state of the model which reproduces the actual measurements as simulated measurements. Most of the work in this thesis is on damage identification using Bayesian inference, while taking the measurements as mode frequencies and mode shapes of the structure. A multivariate normal distributed noise term is included in the measurement model, which allows taking into account the measurement error and also a large part of the model error. The knowledge of plausible damage states is described using a prior distribution, which is merged with the information obtained through measurement using Bayesian inference. Other approaches to the damage identification problem are also discussed in the work. The Kalman filter can be used for damage identification by augmenting the state vector of the vibrating structure with parameters of the damage state. The state estimate then gives the damage parameters along with the other state components. While this approach is more sensitive to model errors, it could be used for real-time damage identification for a continuous assessment of the damage state. The method of sigma algebras on contour maps (SACOM) uses the same noise distribution as the Bayesian approach, and like the Bayesian approach also gives a probability distribution for the damage state. However, in this approach the distribution is obtained by mapping the noise distribution through the set-valued inverse of the structure model. Finally, a brief discussion is given on the possibility of formulating the damage identification problem as an inverse source problem. As the resulting problem is linear, it gives greater opportunity for a thorough mathematical analysis.