18—22.10.2021, Belgrade, Serbia
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Umaaran Gogilan and Tamara Nestorović

Implementation of state observer-based conditioned reverse path method to the identification of a nonlinear system


A method to extract the properties of an underlying linear model (ULM) is the conditioned reverse path (CRP) method. The CRP method parameterizes the nonlinearities of the system by using spectral techniques and recovers the frequency response function (FRF) of the nonlinear model. However, applying the CRP method is challenging if the system states are not accessible for measurement. In large-scale structures, the frequency range of operation may encompass several hundreds of states, so that the measurement of all system states may become impossible due to the deficiency of appropriate sensors. For this reason, a state estimation process is integrated with the CRP method resulting into the observer-based conditioned reverse path (OBCRP) method. The state estimation based on the Kalman filter technique provides the access to all required system states resulting in turn into the reduction of the required number of sensors. Applying spectral techniques with the CRP/OBCRP method, the resulting nonlinear spectra consist of real and imaginary parts. Since imaginary parts have no physical meaning, the nonlinear coefficients based only on the real parts of the spectra are thus distorted. To minimize the distortion of nonlinear coefficients the OBCRP method is extended by a novel weighting scheme. The OBCRP method successfully recovered the FRF of the ULM and accurately parameterized the nonlinearities of the system.