The harmonic probing method for output-only nonlinear mechanical systems

Abstract

Most engineering applications involving vibrating structures are nonlinear in nature and many techniques have been recently investigated to provide a better understanding of such problems. Among the large variety of methods, the harmonic probing has presented useful properties for identification and dynamic analysis of nonlinear systems. The method is conventionally described by the multi-dimensional Fourier transform of the Volterra kernels and it depends on the knowledge of the equations of motion and the respective input and output data. However, this white-box methodology is limited to applications where the input signal is either unknown or even unmeasured. Thus, the present paper is concerned with the development of an extended version of the harmonic probing method to deal with applications where only the outputs are available. The algebraic expressions of the extended Volterra kernels transform and their theoretical properties are provided. The main advantages, novelties and drawbacks of this new approach are discussed and compared with the conventional approach. It is verified that the new kernels can be expressed as a combination of the conventional ones. Numerical tests based on a classical 2DOF Duffing oscillator are carried out and the results reveal the effectiveness and potential of the extended harmonic probing method based on a nonparametric model using new kernels to describe a prediction of vibrating systems in nonlinear regime of motion.