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.

中文翻译：

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从零交叉到时间序列的分位数频率分析及其在无损评估中的应用

由本杰明·凯德姆（Benjamin Kedem）教授的开创性工作代表，时间序列数据的零交叉已被证明可用于表征语音识别和脑电波分析等许多应用中的振荡模式。与传统的频谱分析技术相比，针对异常值和非线性失真的鲁棒性是零交叉的优势之一。本文介绍了一种频谱分析的新工具，该工具可用于超越零交叉的时间序列数据。这称为分位数频率分析（QFA）。QFA由三角分位数回归构造而成，可将时间序列转换为分位数水平和频率变量的双变量函数。对于每个固定的分位数水平，它对应于类似于周期图的函数，称为分位数周期图，它表征了分位数周围时间序列的振荡行为。通过将QFA与功能主成分分析相结合，提出了新的降维特征用于时间序列的判别分析。通过对现实世界中的超声信号进行分类以进行飞机面板无损评估的案例研究，证明了这些功能的实用性。通过交叉验证对各种机器学习分类器进行了培训和测试。结果表明，与基于普通周期图的方法相比，QFA方法具有明显的优势，可以提供更高的样本外分类精度。通过对现实世界中的超声信号进行分类以进行飞机面板无损评估的案例研究，证明了这些功能的实用性。通过交叉验证对各种机器学习分类器进行了培训和测试。结果表明，与基于普通周期图的方法相比，QFA方法具有明显的优势，可以提供更高的样本外分类精度。通过对现实世界中的超声信号进行分类以进行飞机面板无损评估的案例研究，证明了这些功能的实用性。通过交叉验证对各种机器学习分类器进行了培训和测试。结果表明，与基于普通周期图的方法相比，QFA方法具有明显的优势，可以提供更高的样本外分类精度。