On the orthogonalised reverse path method for nonlinear system identification

Abstract

Abstract. The problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general Multi-Degree-of-Freedom (MDOF) system can be solved using the Conditioned Reverse Path (CRP) method introduced by Richards and Singh (1998 Journal of Sound and Vibration, 213(4): p. 673-708). The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion. Although the CRP has proved extremely useful in the context of nonlinear system identification, it has a number of small issues associated with it. One of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti-resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors. The first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm. The results are demonstrated on numerically-simulated responses from MDOF systems. In the second part of the paper, a more radical suggestion is made, to replace the conditioned spectral analysis (which is the basis of the CRP method) with an alternative time domain decorrelation method. The suggested approach -the Orthogonalised Reverse Path (ORP) method -is illustrated here using data from simulated Single-Degree-of-Freedom (SDOF) and MDOF systems.

Complex dynamics of a nonlinear aerospace structure: Experimental identification and modal interactions

“…Quite surprisingly, a review of the technical literature about parameter estimation [5] reveals that basesine excitations have so far received little attention in the nonlinear system identification community. This is manifestly because a measure of the force is a common requirement of most existing techniques, as is the case for nonlinear auto-regressive [34], frequencydomain feedback [35], reverse path [36,37] or subspace methods [38,39]. It turns out from this survey that the RFS method is one of the only approaches compatible with unmeasured base-sine excitations.…”

An Optimization-Based Framework for Nonlinear Model Selection and Identification

“…Different numerical methods may be used to solve the nonlinear algebraic equations. Here, in this study, the resultant nonlinear algebraic equations of Equation (26) are solved using the arc-length continuation method. The amplitude-frequency response of the system obtained from the numerical method is used in the optimization process to identify the nonlinear system.…”

“…In this approach, the nonlinear elements are considered as feedback forces on the underlying linear system. The application of this method can be found in References [12][13][14][15]26]. Kerschen and Golinval [14] utilized the aforementioned method to introduce a two-step identification approach to generate accurate finite element models of nonlinear structures.…”

A forward selection reverse path method for spatial location identification of nonlinearities in MDOF systems

“…The RP method was firstly proposed by Bendat [30,31] and then developed by Rice and Fitzpatric [32], Richards and Singh [33], Muhamad et al [34] and Magnevall et al [35]. The forward selection formulation of the RP method in this paper is described in the following part.…”

“…However, although CRP method only needs a single excitation point, the formulation of the problem is complex and increases computational complexity. Muhamad et al [34] proposed orthogonalized reverse path method (ORP) which provides a simpler formulation for the problem of characterizing the underlying linear system by removing the effects of nonlinearities in the time domain. Another method modifying the RP method proposed by Magnevall et al [35] only needs a single broadband excitation.…”