Keywords: structural identification, penalty function, modal space, stochastic response.

System identification directed at verification of structural models or to assess damage in structures is certainly one of most active fields in structural dynamics. In the framework of parametric identification techniques [1], least square methods are to date one of the most utilized approaches. The basic idea of the least square method stays in the minimization of the so called penalty function representing the error squared between selected measured response parameters and the correspondent quantities determined through the study of a pertinent finite element model. Traditionally, modal response parameters are the preferred quantities for defining the penalty function. Specifically, natural frequencies and/or mode shapes are commonly used. Clearly, from the experimental tests only lower modes can be accurately estimated. Furthermore, in the case of high damping and for closely spaced modes the estimation of modal parameters can be quite challenging. To overcome this drawback, frequency response functions (FRF) have been proposed for defining a more suitable penalty function [2]. This choice possesses the advantage that FRF data contains information from all the modes of the structure. On the other hand for lightly damped structures it is very difficult to accurately predict the peaks of the FRF. Alternative strategies have been proposed following a time-domain approach. Critical comparisons can be found in reference [3].

In this paper a bounded variable time domain least square identification procedure is proposed. The procedure is directed at the identification of structural parameters of linear behaving structures vibrating under either deterministic or stochastic excitations. To this aim a state space approach is suitably employed. Unbounded results are avoided introducing two-sided inequality constraints to the structural parameters. By this approach rank deficiency is avoided, so reducing biasing [2,3,4] in the evaluation of structural parameters. Computational effort for determining the pertinent sensitivity matrix is drastically reduced using a modal approach for determining the response sensitivity [5]. Various numerical examples including the ASCE benchmark [6] show the effectiveness of the proposed method also for determining deteriorating structural parameters simulating damage.

1

Imai H., Yun C.-B., Maruyama O., Shinozuka M., "Fundamentals of system identification in structural dynamics", Prob. Eng. Mech., 4(4), 162-173, 1989. doi:10.1016/0266-8920(89)90022-2

2

Yu E., Taciroglu E., Wallace J.W., "Parameter identification of framed structures using an improved finite element model-updating method -Part I: Formulation and verification", Earthquake Engineering and Structural Dynamics, 36, 619-639, 2007. doi:10.1002/eqe.646

3

Petsounis K.A., Fassois S.D., "Parametric time-domain methods for the identification of vibrating structures - a critical comparison and assessment", Mechanical Systems and Signal Processing, 15(6), 1031-1060, 2001. doi:10.1006/mssp.2001.1424

4

Friswell M.I., Mottershead J.E., "Finite Element model updating in structural dynamics", Kluwer Academic Publishers, 1995.

5

Cacciola P., Colajanni P., Muscolino G., "A modal approach for the evaluation of the response sensitivity of structural systems subjected to non-stationary random process", Comp. Meth. Appl. Mech. Eng. , 194, 4344-4361, 2005. doi:10.1016/j.cma.2004.11.006

6

Johnson E.A., Lam H.F., Katafygiotis L.S., Beck J.L., "Phase I IASC-ASCE, Structural Health Monitoring Benchmark Problem Using Simulated Data", Journal of Engineering Mechanics, ASCE, 130(1), 3-15. doi:10.1061/(ASCE)0733-9399(2004)130:1(3)

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