Damping identification from non-linear random responses using a multi-triggering random decrement technique

Ibrahim, S. R.; Wentz, Kenneth R.; Lee, J.

doi:10.1016/0888-3270(87)90096-3

Cited by 8 publications

(3 citation statements)

References 3 publications

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“…The original publications of the RD technique were quite sparse on the theoretical analysis of the technique itself and they were consequently supported by a mathematical basis in 1982 by Vandiver et al 40 Notably, in the mathematical basis by Vandiver et al, 40 a proportional relationship to the correlation function was derived, which was later generalised by Brincker et al 41 in 1992. Ibrahim et al 19,42 also contributed to the development of the RD technique in the late 1970s and 1980s by extending the method to multiple-input multiple-output (MIMO) systems by defining cross RD signatures. The latter enables the estimation of full RD signature matrices similarly to full correlation function matrices in MIMO OMA.…”

Section: Method: Nonlinearity Optimised Random Decrementmentioning

confidence: 99%

“…which results in the following matrix form with multiple measuring channels and multiple triggering channels: 19,42 D co yy ðτÞ ¼…”

Section: Step 3-computation Of Rd Signaturesmentioning

confidence: 99%

“…The approach of evaluating nonlinear systems by estimating quasi-linear ones using OMA has already been established by preceding studies. In the 1980s Ibrahim et al 18,19 introduced the concept of quasi-linear identification of nonlinear structures, where the RD technique and parameter estimation methods are applied to several modal tests with different response intensities in order to characterise the nonlinearities in a test-wise quasi-linear manner. Consecutively, this idea of analysing nonlinear structures in a quasi-linear manner has been further explored from the early 1990s to the present time.…”

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confidence: 99%

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Conditional linear approximation of nonlinear systems using Operational Modal Analysis

Friis

Vesterholm

Katsanos

et al. 2021

Struct Control Health Monit

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Dynamic characteristics of structures in operational conditions are commonly identified from measured responses using Operational Modal Analysis (OMA). The OMA techniques are, however, confined to the principle of linearity. To overcome some of this limitation, this paper proposes a method for an OMAbased conditional linear approximation of a type of nonlinear systems, by which two or more sets of linear modes are estimated that together describe the behaviour of the true system. These sets of modes can be used to update a nonlinear numerical model that fits each linear estimate in relation to the associated conditions. Additionally, the method can alleviate the issue of varying approx. natural frequencies of nonlinear systems, when employing Structural Health Monitoring to detect damages based on changes of these. The method is demonstrated on both a numerical and an experimental study. Specifically, the numerical study consists of a cantilever beam with a clearance and a stopper at the tip, and it is shown, based on a single response measurement with multiple channels, that the method enables identification of both the underlying linear system and a linear system with modal properties affected by the nonlinearity. The experimental study consists of two simple, friction-coupled, offshore platform-like models, for which two sets of modes are estimated from one measurement, each set characterising the dynamic behaviour in coupled and uncoupled state, respectively. The paper also demonstrates that the proposed method can relieve the said complications of conducting Structural Health Monitoring of structures with changing natural frequencies due to nonlinearity.

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