From zero crossings to quantile‐frequency analysis of time series with an application to nondestructive evaluation

Represented by the pioneering works of Professor Benjamin Kedem, zero crossings of time-series data have been proven useful for characterizing oscillatory patterns in many applications such as speech recognition and brainwave analysis. Robustness against outliers and nonlinear distortions is one of the advantages of zero crossings in comparison with traditional spectral analysis techniques. This paper introduces a new tool of spectral analysis for time-series data that goes beyond zero crossings. It is called quantile-frequency analysis (QFA). Constructed from trigonometric quantile regression, QFA transforms a time series into a bivariate function of quantile level and frequency variable. For each fixed quantile level, it corresponds to a periodogram-like function, called the quantile periodogram, which characterizes the oscillatory behavior of the time series round the quantile. By coupling QFA with functional principal component analysis, new dimension-reduced features are proposed for discriminant analysis of time series. The usefulness of these features is demonstrated by a case study of classifying real-world ultrasound signals for nondestructive evaluation of aircraft panels. Various machine learning classifiers are trained and tested by cross-validation. The results show a clear advantage of the QFA method over its ordinary-periodogram-based counterpart in delivering higher out-of-sample classification accuracy.