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...e essentially nonparametric methodology of the virtual distortion method (VDM) [4]. The monitored structure is characterized in a purely experimental way, by means of its impulse response functions. As a result, no parametric numerical modelling is required, which obviates the need for model updating and fine-tuning that is typical for other model-based methods. Most of the low-frequency identification methods used in global structural health monitoring (SHM) can be classified into two general groups: (1) Model-based methods that rely on a parametric numerical model of the monitored structure [5,6]. Their appealing feature is the physicality of the model and its identified modifications. However, an accurate parametric model is not easy to obtain and update. (2) Pattern recognition methods, which rely on a database of numerical fingerprints that are extracted from the experimentally measured responses [7]. No parametric modeling is required. The identification rarely goes beyond detection or approximate localization of the modification. The developed approach exploits the advantages of both groups: it makes use of a nonparametric model of the monitored structure based on experimentally ...

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...red. The identification rarely goes beyond detection or approximate localization of the modification. The developed approach exploits the advantages of both groups: it makes use of a nonparametric model of the monitored structure based on experimentally measured data, but it allows parametrically expressed modifications to be identified. In [1], a time-domain version of the approach has been proposed and experimentally verified. It proved to be accurate, and thanks to the iterative CGLS solution scheme, provided a good control over numerical regularization of the computed time-domain response [8]. However, the fundamental equation is a system of linear integral equations of the Volterra type, whose solution is significantly time-consuming. This paper develops and verifies a frequency-domain approach, which uses the fast Fourier transform (FFT) to solve the equations. A significant reduction in computation time is attained (up to four orders of magnitude). However, this is at the cost of losing the control of the process of numerical regularization: regularization in frequency domain seems to be relatively weakly researched and understood. The aim of this study is to test the accuracy ...

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...e essentially nonparametric methodology of the virtual distortion method (VDM) [4]. The monitored structure is characterized in a purely experimental way, by means of its impulse response functions. As a result, no parametric numerical modelling is required, which obviates the need for model updating and fine-tuning that is typical for other model-based methods. Most of the low-frequency identification methods used in global structural health monitoring (SHM) can be classified into two general groups: (1) Model-based methods that rely on a parametric numerical model of the monitored structure [5,6]. Their appealing feature is the physicality of the model and its identified modifications. However, an accurate parametric model is not easy to obtain and update. (2) Pattern recognition methods, which rely on a database of numerical fingerprints that are extracted from the experimentally measured responses [7]. No parametric modeling is required. The identification rarely goes beyond detection or approximate localization of the modification. The developed approach exploits the advantages of both groups: it makes use of a nonparametric model of the monitored structure based on experimentally ...

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...t. The verification uses a finite element model of the same real structure that was tested with the time-domain version of the approach. A natural further step is a lab verification based on experimental data. IPPT Reports 4f/2013 2 Introduction This paper presents a derivation and reports on a numerical verification of a frequency-domain version of a nonparametric approach to identification of added masses in truss structures. The general approach has been recently developed in IPPT PAN [1–3], and it is based on the essentially nonparametric methodology of the virtual distortion method (VDM) [4]. The monitored structure is characterized in a purely experimental way, by means of its impulse response functions. As a result, no parametric numerical modelling is required, which obviates the need for model updating and fine-tuning that is typical for other model-based methods. Most of the low-frequency identification methods used in global structural health monitoring (SHM) can be classified into two general groups: (1) Model-based methods that rely on a parametric numerical model of the monitored structure [5,6]. Their appealing feature is the physicality of the model and its identified ...

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...ng that is typical for other model-based methods. Most of the low-frequency identification methods used in global structural health monitoring (SHM) can be classified into two general groups: (1) Model-based methods that rely on a parametric numerical model of the monitored structure [5,6]. Their appealing feature is the physicality of the model and its identified modifications. However, an accurate parametric model is not easy to obtain and update. (2) Pattern recognition methods, which rely on a database of numerical fingerprints that are extracted from the experimentally measured responses [7]. No parametric modeling is required. The identification rarely goes beyond detection or approximate localization of the modification. The developed approach exploits the advantages of both groups: it makes use of a nonparametric model of the monitored structure based on experimentally measured data, but it allows parametrically expressed modifications to be identified. In [1], a time-domain version of the approach has been proposed and experimentally verified. It proved to be accurate, and thanks to the iterative CGLS solution scheme, provided a good control over numerical regularization of t...

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...s. However, an accurate parametric model is not easy to obtain and update. (2) Pattern recognition methods, which rely on a database of numerical fingerprints that are extracted from the experimentally measured responses [7]. No parametric modeling is required. The identification rarely goes beyond detection or approximate localization of the modification. The developed approach exploits the advantages of both groups: it makes use of a nonparametric model of the monitored structure based on experimentally measured data, but it allows parametrically expressed modifications to be identified. In [1], a time-domain version of the approach has been proposed and experimentally verified. It proved to be accurate, and thanks to the iterative CGLS solution scheme, provided a good control over numerical regularization of the computed time-domain response [8]. However, the fundamental equation is a system of linear integral equations of the Volterra type, whose solution is significantly time-consuming. This paper develops and verifies a frequency-domain approach, which uses the fast Fourier transform (FFT) to solve the equations. A significant reduction in computation time is attained (up to fou...

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...s impulse response functions. As a result, no parametric numerical modelling is required, which obviates the need for model updating and fine-tuning that is typical for other model-based methods. Most of the low-frequency identification methods used in global structural health monitoring (SHM) can be classified into two general groups: (1) Model-based methods that rely on a parametric numerical model of the monitored structure [5,6]. Their appealing feature is the physicality of the model and its identified modifications. However, an accurate parametric model is not easy to obtain and update. (2) Pattern recognition methods, which rely on a database of numerical fingerprints that are extracted from the experimentally measured responses [7]. No parametric modeling is required. The identification rarely goes beyond detection or approximate localization of the modification. The developed approach exploits the advantages of both groups: it makes use of a nonparametric model of the monitored structure based on experimentally measured data, but it allows parametrically expressed modifications to be identified. In [1], a time-domain version of the approach has been proposed and experimentall...

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...ms of the finite element method. The unmodified structure is assumed to be linear and to satisfy the equation of motion: (1) where M, C and K denote respectively the structural matrices of mass, damping and stiffness, f(t) is the external testing excitation and x L (t) denotes the corresponding response of the unmodified structure (reference response). In frequency domain, (1) takes the following quasi-static form: (2) where is the angular frequency, and denote respectively the complex amplitudes of the reference response and the excitation, and D( ) is the complex dynamic stiffness matrix, , (3) whose inverse is called the dynamic compliance matrix and allows (2) to be represented in the direct form: . (4) The added masses, , are represented in terms of the modification (m) to the original mass matrix . The mass matrix of the modified structure is thus given by , (5) while its dynamic stiffness matrix can be expressed as (6) As a result, the response of the modified structure (the original structure with added masses) satisfies the following counterpart of (2): , (7) where the vector denotes the pseudo-loads that act in the involved DOFs of the unmodified structure to model the inert...