Novel optimisation of bicoherence estimation for fatigue monitoring

The higher order spectra of order 3, ie the bispectrum and the normalised bispectrum, the bicoherence, are widely used for many engineering applications for nonlinearity and non-Gaussianity monitoring[1-9]. In particular, the bicoherence method has been applied for detection of nonlinearity and the quadratic phase coupling in waves[1], speech signals[2], control loops[3], fluids[4] and for condition monitoring of different types of machinery and structures[5-9] including damage monitoring in many aerospace applications, for example fatigue monitoring in aircraft structures and gear teeth analysis in helicopter transmissions[10, 11]. The most important advantages of the bicoherence are high sensitivity to the presence of system nonlinearity and nonGaussianity and capability to suppress the Gaussian noise. One of the main disadvantages of bicoherence is a relatively high variance of bicoherence estimate; it is much higher than the variance of estimate of the power spectral density[12]. A common way to reduce the variance of bicoherence estimate is splitting signal duration into the segments, followed by averaging of the bicoherence over segments. For finite signal duration segment size defines the bias and the variance of bicoherence estimate. Following the literature[13], the usual practice for defining the optimal segment size is the square root of signal length. Usually, this rule is used for bicoherence estimation in damage monitoring tasks but some authors use rather empiric approaches to segment size selection[1, 6, 8, 9]. However, this rule is based on the optimal trade-off between the bias and the variance of bicoherence estimate and has been developed for the linearity test[13], which involves only one class of signals. For damage monitoring, optimisation of segment size should be performed for two or multi-class diagnostics and should be based on optimisation criterion for monitoring effectiveness rather than on a trade-off between the bias and the variance of bicoherence estimate. Optimisation of the main bicoherence parameters for damage monitoring involving two or multi-class signals has been investigated in literature only to a limited extent. In particular, it is believed that no-one has optimised the segment size of bicoherence estimate for fatigue monitoring. In addition, no-one has investigated the influence of damage level on optimal segment size for fatigue monitoring. The purpose of this paper is to investigate optimisation of segment size for bicoherence estimation for fatigue monitoring. It is important to investigate this problem for fatigue monitoring for many engineering applications including aerospace applications.