温州大学数理学院2025年第21期数理大讲堂

报告题目：Recent Advances in Signal Separation: Theory and Applications in Rotating Machinery Fault Diagnosis

报告人：蒋庆堂

主持人：高利新

报告时间：12月30日上午10：30

报告地点：3B205

摘要 ：In the natural world, physical phenomena existing in the form of signals (or data collected as time series) are typically influenced by multiple factors. These ultimately manifest as multi-component signals that overlap in the time domain. To gain a deeper understanding of these phenomena and facilitate subsequent signal processing, it is necessary to extract the unknown individual components of a target multi-component signal from "blind source" data.

This is an inverse problem with a long history, dating back to 1795 when the French engineer Gaspard de Prony developed a computational technique known as Prony's Method for separating stationary signals.

However, for non-stationary signals (signals where the component frequencies change over time), a rigorous mathematical treatment was lacking until just over a decade ago, when Ingrid Daubechies and her collaborators introduced research on the synchrosqueezing transform (SST). Despite the efforts of many researchers, SST can only be applied under strict conditions.

This report will introduce two major improvements to the SST:

Time-varying parameters: We introduce time-varying parameters into the original SST to eliminate certain constraints (specifically those related to frequency separation), resulting in more robust signal component separation.

Chirplet transform: We will discuss our recently developed chirplet transform, which is capable of separating multi-component signals even when their instantaneous frequency curves cross.

Unlike traditional 2D time-frequency spaces, the chirplet transform maps signals into a 3D space of time-frequency-chirp rate. Furthermore, we will address a key challenge facing this method: the problem of "slow decay" along the chirp rate direction. We will present our latest research results showing how combining the X-ray transform with the chirplet transform resolves this issue. Finally, we will discuss the practical application of these chirplet-based methods in the fault diagnosis of rotating machinery.

报告人简介：

蒋庆堂教授于北京大学获得博士学位，并曾在该校数学系先后担任讲师和副教授。2002年加入美国 University of Missouri-St. Louis（UMSL）之前，他曾在新加坡国立大学从事NSTB博士后等研究工作，并曾先后在加拿大University of Alberta和美国 West Virgina University 担任访问学者。2005年至2024年，他担任UMSL数学与计算机系的教授。目前，他是浙江师范大学的杰出教授。他曾合著一部学术著作，并已发表九十余篇学术论文。

蒋教授的研究领域包括：小波分析及其在图像恢复和信号分类中的应用；时频分析；稀疏数据表示；数学成像；以及近期的信号分解与混合信号分离、基于深度学习的视频识别和机械振动故障诊断。