Residual frequency autocorrelation as an indicator of non-linearity

Abstract

A new temporal analysis approach using discrete frequency models has recently been introduced by the authors. These models relate the steady-state output of non-linear vibrating systems at each frequency to the excitation at that frequency and the output at other frequencies. The discrete frequency modeling approach is used here to derive an experimental frequency domain indicator function for non-linear vibrations. These indicator functions are autocorrelation functions of residuals from multiple input, multiple output frequency response function estimates. Unlike ordinary spectral coherence functions, which only indicate input–output linearity locally at a single frequency, the autocorrelation functions relate the error at each frequency to the errors at frequencies across the frequency band of interest. This feature enables residual autocorrelation functions to distinguish between system non-linearities and bias errors localized in frequency. Non-linearities in a simulated single-degree-of-freedom system, an analog computer system, and a complicated multiple-degree-of-freedom system are detected using the new indicator function.