For the purpose of constructing the backbone of nonlinear systems, the Interpolated Short Time Fourier Transform (ISTFT) is proposed as a means to improve the estimation accuracy of the instantaneous amplitudes and frequencies of response signals. It is shown that the backbone curves estimated by the ISTFT agree with theoretical backbone curves very well. Additionally, the restoring force can be reconstructed to specify the type of nonlinear stiffness. A curve-fitting technique is introduced to estimate the parameters of nonlinear systems on the basis of theoretical backbone curves. It is shown that a number of typical nonlinear stiffness functions such as cubic, bilinear and pre-compressed springs can be identified accurately using this new method.

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