286 A. delli Carri and D.J. Ewins Method Excitation Response D C L Q E Notes Hg any (2) any SDOF only HT any any Indirect detection. May fail in experimental tests RP broadband disp [2] Subject to numerical issues. Frequency domain SVD any disp, vel, acc Massive request of input data CFRF stepped sine disp (any) SDOF only. Many test runs required NNM harmonic(n) disp (acc) SDOF only. Complex theory. Peculiar test RFS any disp, vel, acc SDOF only. Massive request of input data NOFRFs broadband (2) acc Complex theory. Only works for inline DOF FNSI broadband any [3] Frequency domain Fig. 28.1 Considered methods and their categorisation: detection (D), characterisation (C), localisation (L), quantification (Q), and experimental evidence (E) Figure 28.1 collects all the different methods that have been gathered since the start of this work. It represents a nonexhaustive database of all the different nonlinear analysis methods currently available in literature. The scope of this paper is to widen the number of considered methods and to select the best ones for inclusion in a future nonlinear modal testing toolbox for use in an industrial environment. The criteria for the inclusion in this toolbox are generally linked to the requirements of the industrial framework, which demands reliable performance and low cost. This consideration leads to the exclusion of methods that use many test runs or require non-standard setups or measurements as well as ones that are too simple to be of any use for a complex MDOF dynamical system. Based on these assumptions, two of the methods from Fig. 28.1 were chosen for inclusion in the toolbox: (a) the Reverse Path method (RP) has all the capabilities to identify the nonlinear phenomena but it performs poorly in the quantification step, and (b) the Frequency-domain Nonlinear Subspace Identification (FNSI) which is able to quantify the nonlinear coefficients but it needs knowledge about the location and functional form of the nonlinearities, so the two methods complement each other. 28.2 A Review of the Selected Methods In this section, two of the methods presented in Fig. 28.1 will be reviewed in a little more detail: the Reverse Path method has already been covered in the previous iteration of this work [1] but it is now presented with more insight, while the Frequency-domain Nonlinear Subspace Identification is a recent addition. These two methods together are able to cover many of the different aspects of the nonlinear phenomenon—from detection to quantification—using common test practices, without requiring exotic excitation or setups. More important, they both require time histories data but exploit the frequency domain which leads generally to faster estimation and lower computing burden. 28.2.1 Reverse Path Method (RP) The Reverse Path method was initially proposed by Bendat in 1990 [4]. The method is known as Reverse Path since the input and output quantities are reversed (Fig. 28.3). The processing is performed in the frequency domain using conventional Multiple-Input-Single-Output (MISO) techniques and estimates of both the Underlying Linear Model and the nonlinearity locations and types are obtained from a single analysis.
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