A new instantaneous frequency extraction method for nonstationary response signals in civil engineering structures

Civil engineering structures in essence belong to time-varying and nonlinear structures and the resultant dynamic responses are usually nonstationary signals. A new method is proposed to extract instantaneous frequency of such nonstationary signals. The new method combines the extended analytical mode decomposition, normalization scheme, and improved arccosine function algorithm. In this method, a multicomponent response signal is first decomposed into several mono-components signals by the extended analytical mode decomposition theorem, and then the extracted mono-components are demodulated into purely frequency modulated signals by a repeated normalization scheme. After that, the improved arccosine function is presented to compute the instantaneous phase and instantaneous frequency. A numerical example and an experimental study of a cable with time-varying tension force are provided to illustrate the working of the method. The results demonstrate that the proposed method can extract instantaneous frequencies from multicomponent signals more accurately than Hilbert-Huang transform.