Keywords: non-linear systems, structural identification, structural diagnostics, dynamic testing, Volterra series, pattern recognition.

Dynamic system identification is a major tool for monitoring and diagnosis of structures: experimental results from dynamic testing give knowledge about global structural behaviour and could be used in calibrating numerical models, in forecasting the response to dynamic and earthquake loading and can help in evaluating the safety conditions. Structural diagnosis can be performed according to two different strategies: a) knowledge of the undamaged linear state and comparisons with current conditions; b) detection of symptoms of the fault that are contained in the structural response.

In civil engineering applications the problem of identifying the dynamic properties is characterized by uncertainty, which may be ascribed to different causes, as, for example, the mechanical behaviour of material, almost always nonlinear to some extent, and the test conditions, which are never completely controllable when the tests are carried out in situ. Structures are often tested in operational conditions (i.e., subjected to ambient excitation) not to break off the normal activities and, or to avoid introducing damage: output-only identification techniques are really flexible and powerful for identifying modal parameters, but sometimes cannot allow a reliable identification: the major uncertainties are related to the estimation of damping characteristics and when the system's vibration is nonlinear to some extent.

In the identification of structures characterised by localized nonlinearities, the definition of instantaneous time-frequency estimators [1] may result particularly useful: more specifically, its extension to nonlinear systems, whose input, output relationship is depicted as a Volterra series, as is described in the first part of this paper. Following this approach, the determination of the parameters of a nonlinear dynamic system characterised by quadratic stiffness was conducted by approximating system response through a second degree Volterra polynomial and by introducing the time-frequency representation of the signals detected. Instantaneous estimates of system parameters can be defined through the use of the linear time-frequency representation, by introducing "time data" in parallel with the frequency content data. The definition of punctual estimates makes it possible to assess the stability over time, the mean value and the coefficient of variation of the estimates obtained: this improves the confidence level of the estimates, compared to the determination obtained through non-instantaneous parameter estimation methods. Though it is the most sensitive to the presence of noise, the instantaneous estimator of a nonlinear parameter is characterised by good stability and robustness. A less burdensome testing stage is matched by increased computational costs of post-processing operations, especially for the generation of the synthetic response as a Volterra polynomial system and the solution of a large number of optimisation processes.

The information obtained from a nonlinear identification session may both offer a clue in choosing reliable structural models, and forecast the dynamic behaviour in non-operational conditions (e.g. during a seismic event). When the detection of non-linear behaviour and its qualitative classification may prove very difficult, symptom based procedures may be employed in order to perform a fault classification, thus supporting a further model-based identification stage [2]. The second part of the paper reports about a pattern recognition strategy applicable to non-linearity classification. In more detail, special neural networks are trained to recognize non-linearity from free decay structural response. Feature extraction is based on statistical moments of the analytical representation of the response signals, as resulting from a conventional Hilbert transform.

1

G.V. Demarie, R. Ceravolo and A. De Stefano, "Instantaneous Identification of Polynomial Nonlinearity Based on Volterra Series Representation", Key Engineering Materials, 293-294, 703-710, 2005. doi:10.4028/www.scientific.net/KEM.293-294.703

2

A. De Stefano, D. Sabia and L. Sabia, "The Use of Hilbert Transform and Neural Intelligence in Structural Non-Linearity Detection", J. Structural Control, 1, 89-105, 1997. doi:10.1002/stc.4300040109

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