Damping Identification Using a Robust FRF-Based Model Updating Technique (original) (raw)

A Robust FRF-based technique for Model Updating

Frequency Response Functions (FRFs) residues have been widely used in time to update Finite Element models . Major reasons for this is that FRFs are very sensitive to damping properties at resonance peaks, local modes influence is included and no modal analysis is required. Nevertheless, it is well known that due to their nature, the frequency responses may change its order of magnitude very rapidly for small parameter or frequency changes. This situation may cause serious discontinuities in the topology of the objective function, causing the updating strategy to diverge or to find a local non-physical minimum . A primary tool for the correlation of FRFs is the Frequency Domain Assurance Criterion . This technique introduces the concept of frequency shift between the frequency response shapes of a reference model (the experimental structure) and a perturbed model (an initial non-updated FE model). Such a concept opens the way for using residues at different frequencies. For instance, in reference [6] the residue is composed by point FRFs at anti-resonances. This paper introduces a general FRF-based model-updating technique, which is focused in using stable residues during the interactive optimization procedure. A benchmark case from the Cost F3 action is used to assess the goodness of the method compared to other well known methods.

Robust parameter identification using forced responses

Mechanical Systems and Signal Processing, 2007

In this paper, a new model updating scheme is introduced to adjust the system matrices of a finite-element model by using experimental operating deflection shapes (ODS). An ODS is defined here as the response vector when the system is driven at a given degree of freedom with a unit force of fixed frequency. The proposed algorithm adjusts the numerical model in an iterative way. The matrix equilibrium equation is solved by first taking into account the frequency shift that appears between the non-updated finite element model and the experimental structure. In this way, numerical instabilities observed in state-of-the-art methods are avoided. We present results on two well-known numerical and experimental benchmark cases. They show the good convergence properties of the proposed approach. r (R. Pascual).

Estimation of damping model correctness using experimental modal analysis

This paper is dedicated to the damping identification problem. Short outlook of damping identification methods is given in the first part of the paper. All these methods can successfully identify internal damping of free-moving structures but it becomes problematically to correctly estimate damping forces when the structure is fixed and there are some joints. The recent methods of structural damping identification don’t give a full understanding of dissipation problem too. An explanation of damping-frequency relation features based on the existence of another damping nature, external damping for example, is proposed in this paper. These assumptions are demonstrated by the modal parameters identification of a turbine blade.

Structural model updating using frequency response function and quasi-linear sensitivity equation

Journal of Sound and Vibration, 2009

A method is presented for structural mass and stiffness estimation including damping effects and using vibration data. It uses the frequency response function (FRF) and natural frequencies data for finite element model updating. The FRF data are compiled using the measured displacement, velocity or acceleration of the damaged structure. A least-square algorithm method with appropriate normalization is used for solving the over-determined system of equations with noise-polluted data. Sensitivity equation normalization and proper selection of measured frequency points improved the accuracy and convergence in finite element model updating. Using simulated measurements shows that this method can detect, locate and quantify the severity of damage within structures.

Structural finite element model updating using transfer function data

Computers & Structures, 2010

A new method is presented for the finite element model updating of structures at the element level utilizing Frequency Response Function data. Response sensitivities with respect to the change of mass and stiffness parameters are indirectly evaluated using the decomposed form of the FRF. Solution of these sensitivity equations through the Least Square algorithm and weighting of these equations has been addressed to achieve parameter estimation with a high accuracy. Numerical examples using noise polluted data confirm that the proposed method can be an alternative to conventional model updating methods even in the presence of mass modeling errors.

Frequency Based Spatial Damping Identification—Theoretical and Experimental Comparison

Conference proceedings of the Society for Experimental Mechanics, 2017

This research compares spatial damping identification methods, both theoretically and experimentally. In contrast to the commonly used damping methods (modal, proportional) the spatial damping information improves structural models with a known location of the damping sources. The real case robustness of full FRF matrix and local equation of motion methods were tested against: modal and spatial incompleteness, differences in viscous and hysteretic damping models and the effect of damping treatments. To obtain accurate results, a careful analysis of measurements in terms of reciprocity in the raw measurements, and in terms of how to preserve symmetry has to be done. It was found that full FRF matrix needs to be symmetrisized due to small deviations in reciprocity before the damping identification. Full frequency response function (FRF) matrix methods (e.g.: Lee-Kim) can identify the spatial damping if spatial and modal incompleteness are carefully evaluated, but the measurement effort increases with second order and, consequently, the size of the FRF matrix. Keywords Spatial damping • Inverse identification • Frequency response • Modal incompleteness • Spatial incompleteness 3.1 Introduction Numerical and analytical prediction of the structural responses depends on the identified spatial damping throughout the structure. Good damping prediction is important for validation of analytical/numerical models in civil, mechanical and aerospace engineering. Damping in linear mechanical systems is usually identified using one of the methods such as logarithmic decay [1] in time domain, continuous wavelet transform [2], the Morlet wave method [3] or the synchrosqueezed wavelet [4] in time-frequency domain or half-power point [1] and first order perturbation [5] in frequency domain. Damping identification methods form the basis of several model updating methods [6, 7], where accurate damping identification can further improve numerical models [8, 9]. Two other examples where exact damping spatial location is needed are: identification of damping sources on existing structures and precise application of damping treatment. However, typically used damping identification methods [1, 8] do not provide spatial information (damping distribution throughout the structure). An alternative approach is to use direct damping identification methods that were developed for identification of damping distribution directly from the frequency response functions (FRF) without the transformation to the modal coordinates. One of the typically used direct methods is the Lee and Kim's dynamic stiffness method [10]. The core of the method is a inverse identification of linear damping model from the complex part of the measured data which have been found to be very sensitive to real world problems in most follow-on studies, e.g. phase error [11], noise when the modal overlap is low [5] and leakage [12]. Ozgen and Kim [12] proposed a new experimental procedure with simultaneous excitation of all nodes to overcome described measurement errors, but the procedure is not practical with lots of measurement degrees of freedom because demands as many shakers as there are measurement degrees of freedom. Some direct methods, not considered in this research, are reviewed in [5, 11, 13]. This research focuses on the modal and spatial incompleteness effect on the identification of spatial damping. Modal incompleteness deals with limited frequency span over number of modes whereas spatial incompleteness covers effects of non-measured points on the structure [14]. Modal and spatial incompleteness for spatial damping have been studied numerically [5, 15] and experimentally [11] on low DOF models.

Structural Finite Element Model Updating Using FRF of Incomplete Modal Data

A structural finite element model updating technique is proposed using Frequency Response Function (FRF) data and extracted natural frequencies of the damaged structure. To decrease non-linearity of the model updating process, the change of FRF of a structure is correlated to the change of stiffness and mass through sensitivity equations, which have been derived using the change of eigenvectors and extracted natural frequencies of the damaged structure. Eigenvector participation factor is expressed as a function of the perturbation of the stiffness and mass. The set of sensitivity equations is solved by the least square algorithm. Numerical example using a beam structure confirms that the procedure is an effective model updating technique for structural health monitoring purposes.

Frequency domain identification of structural dynamics using the pole/residue parametrization

1996

The pole/residue parametrization has been traditionally used in single and multiple degree of freedom identification methods for structural dynamics. By considering residues as secondary unknowns that are solution of a least-squares problems, the nonlinear optimization linked to this parametrization can be performed with the poles as only unknowns. An ad hoc optimization scheme, based on the use of gradient information and allowing simultaneous update of all poles, is proposed and shown to work in many situations. The iterative nature of the algorithm and the use of poles as only unknowns permits simple user interactions and generally allows the construction of models that contain all physical modes of the test bandwidth and no other modes. Models of structures generally verify many constraints (minimality, reciprocity, properness, positiveness) which are not necessarily verified by pole/residue models (which only assume linearity and diagonalizability). It is shown that constrained pole/residue models can be easily constructed as approximations of unconstrained pole/residue models and that this approach gives good representations of the initial data set. Difficulties, that a few years of experience with the proposed algorithms have shown to be typical, are highlighted using examples on experimental data sets.