Chapter 31 Online Systems Parameters Identification for Structural Monitoring Using Algebraic Techniques L.G. Trujillo-Franco, G. Silva-Navarro, and F. Beltrán-Carbajal Abstract Nowadays, with the modern techniques and developments on sensors and actuators technologies, disciplines like Operational Modal Analysis (OMA), Structural Health Monitoring (SHM) and Non-Destructive Evaluation (NDE), among others, are now basic parts of the study, modeling and monitoring for modern civil structures and vibrating mechanical systems. The most important system parameters of a given mechanical system, including civil structures, like modal parameters, mass and stiffness matrices are indicatives of the inherent nature and dynamical behavior of it, and, at the same time, a possible way to detect failures by comparing two different sets of such parameters, before and after any failure happens. In this work, a novel fast and online system parameter identification scheme, based on module theory and algebraic techniques for structural monitoring and vibration absorption purposes or model updating for mechanical systems under nominal operation conditions is proposed, that is, in an operational fashion, where only system output information is available. The proposed scheme is evaluated with experimental data. Keywords Algebraic identification • Operational modal analysis • Real time structure monitoring • Structural health monitoring • System identification 31.1 Introduction On the area of mechanical design and modeling (civil structures inclusive), the process called modal parameter identification or modal analysis has become into a basic technological tool, which allows having a correct knowledge and sometimes a prediction of the system response under harmonic excitation. In this information era, modal analysis can specially count on the newest and powerful data analyzers for storing and processing the data under study. In this order of ideas, the task of analyzing engineering structures response and behavior, when the system is working on its nominal operation conditions is a natural consequence [1, 2] (e.g., via the OMA approach). Most of the times, real world systems work under a completely random and hard to measure excitation; furthermore, in some special cases, it is desirable to monitor some interest output in a real-time fashion. Certainly, the actual state of the art for modal analysis has a robust background, consisting of plenty of identification algorithms in time or frequency domain, mainly for off-line estimation of modal parameters. However, it is important to consider that, most of these techniques are essentially asymptotic, recursive, complex and slow for on-line parameter estimation implementations, which could be required for efficient adaptive active noise and vibration control and monitoring applications on dynamic mechanical structures [3–5]. As reported in Refs. [4–7], here we apply a theoretical framework for the algebraic parameter identification on continuoustime linear systems. This identification approach platform consists of powerful mathematical tools as module theory, differential algebra and operational calculus. It is important to remark that, the operational calculus is a quite general approach based on different integral transformations of functions and generalized functions (e.g., Fourier, Laplace, Stieltjes, Hilbert, Bessel) [4–7]. The application of operational calculus in mechanical engineering is quite common for the transformation of functions from time to frequency domain and solving differential equations. L.G. Trujillo-Franco ( ) • G. Silva-Navarro Departamento de Ingeniería Eléctrica, Sección de Mecatrónica, Centro de Investigación y de Estudios Avanzados del I.P.N., Av. IPN No. 2508, Col. S.P. Zacatenco, C.P. 07360, Mexico, D.F., Mexico e-mail: ltrujillo@cinvestav.mxgsilva@cinvestav.mx F. Beltrán-Carbajal Departamento de Energía, Universidad Autónoma Metropolitana, Unidad Azcapotzalco, Av. San Pablo No. 180, Col. Reynosa Tamaulipas, C.P. 02200, Mexico, D.F., Mexico e-mail: fbeltran@correo.azc.uam.mx © The Society for Experimental Mechanics, Inc. 2017 J. Caicedo, S. Pakzad (eds.), Dynamics of Civil Structures, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-54777-0_31 251
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