This article proposes a fast adaptive S-transform (FAST) to improve the time-frequency resolution and computational efficiency of power quality disturbances (PQDs) feature extraction. By directly controlling the standard deviation instead of other parameters, FAST can reduce the difficulty of optimizing time-frequency resolution. Based on the frequency spectrum of PQD signals, FAST only needs to calculate characteristic frequency points determined by maximum envelope curve, which can eliminate redundant calculation without losing effective feature information. In fact, the computational complexity of parameter optimization step is often higher than that of S-transform (ST) calculation step. To address this problem, a window matching spectrum (WMS) method is proposed to optimize the time-frequency resolution. Matching the effective window width with the main spectrum energy interval of signals, WMS determines the standard deviation without iterative calculation. Based on the time-frequency representation of FAST, four features are extracted as the feature vectors and applied to the support vector machine, probabilistic neural network, extreme learning machine (ELM), convolutional neural network, decision tree (DT-C4.5) and random forest classifiers. Classification results of the six classifiers show that FAST has better time-frequency resolution and lower computational complexity than that of generalized S-transform and ST. In addition, the FAST-ELM method has stronger noise immunity and better performance than other combination methods with the simulation signals and experimental signals.

中文翻译：

---

用于复杂质量扰动特征提取的快速自适应S变换


本文提出了一种快速自适应 S 变换（FAST）来提高电能质量扰动（PQD）特征提取的时频分辨率和计算效率。通过直接控制标准差而不是其他参数，FAST可以降低优化时频分辨率的难度。 FAST基于PQD信号的频谱，只需计算最大包络曲线确定的特征频点，可以消除冗余计算，且不会丢失有效的特征信息。事实上，参数优化步骤的计算复杂度往往高于S变换（ST）计算步骤的计算复杂度。为了解决这个问题，提出了一种窗口匹配频谱（WMS）方法来优化时频分辨率。 WMS将有效窗宽与信号的主频谱能量区间相匹配，无需迭代计算即可确定标准差。基于FAST的时频表示，提取四种特征作为特征向量，应用于支持向量机、概率神经网络、极限学习机（ELM）、卷积神经网络、决策树（DT-C4.5）和随机森林分类器。 6个分类器的分类结果表明，FAST比广义S变换和ST具有更好的时频分辨率和更低的计算复杂度。此外，FAST-ELM方法比其他模拟信号和实验信号的组合方法具有更强的抗噪性和更好的性能。