Dynamic structural system identification using observability techniques
Correu electrònic de l'autorballester.ramirez.davidgmail.com
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Structures are complex systems with several stages within their service life. Firstly, engineers have to design the structure with some of the many available mathematical and computational tools. In most cases, the designed structures are discretized within finite elements method (FEM). The equations implemented in this method relate the external actions (e.g. forces, accelerations, imposed displacements) with the output response of the structure (e.g. nodal displacements) by means of the geometric and mechanical parameters of the structural elements (e.g. beams' areas, inertias, Young's Modulus), leading to large systems of equations. Generally, for a given structure in a design stage, the structural parameters are assumed as known, allowing thus to compute a direct solution for the structure. Nevertheless, during the following stages of construction and operation, the structures are subjected to different elements (e.g. humidity, temperature, chemical products) and actions (construction errors, loads, earthquakes) that in most cases can be assumed as random and unknown. These, may lead to a change in the value of the structural parameters and turn them to be uncertain too. Thus, for the sake of security and structural control, the actual uncertain parameters must be identified. In order to identify them, many techniques are available. Particularly, this paper deals with an inverse analysis called Structural System Identification (SSI). Within all the techniques inside the SSI techniques, this paper is implementing the observability technique. This technique is nailed to the null space theory for a given system of equations in order to determine which of the unknowns can be assessed uniquely. Meaning that a unique solution can be found for each of them. Also, in this paper, an algebraic matricial methodology in order to allow the identification of the unknown parameters is proposed. In order to do so, a set of experimental measurements taken from the structure must be input into the method. The observability technique has been implemented in many fields of engineering and for many different equations. A special mention is deserved to the implementation of this technique to the stiffness matrix method which observes the static parameters of a given structure from static measurements of load test. In this thesis, the observability technique is going to be applied on the eigenvalue equation and an algorithm is going to be developed in order to carry out the computations. The dynamic character of the method requires the inputs measurements to be the modal displacements and the eigenfrequencies for the different natural modes of vibration. These data is assessed through the implementation of modal experimental analysis over the structures which computes the actual modal data. Finally, the method is applied within a symbolical approach, obtaining for the first time in the literature the symbolic equations of the identified parameters and their numerical errors for a dynamic approach.