Spectral analysis of non-stationary signals and applications

光谱分析是科学家可用的最基本的分析工具之一。尽管它无处不在，但这个工具存在固有的困难。传统的频谱分析工具可能难以处理频谱随时间快速变化的信号。 在频谱分析领域的一个最近的主要进展是希尔伯特黄变换（HHT）。该算法使用称为经验模式分解（EMD）的启发式算法，将信号分解为“窄带”信号的总和，对于该窄带信号，存在频谱分析问题的良好解决方案，即希尔伯特变换。该算法有几个重要的局限性。这在计算上是昂贵的。该算法不能分离频率差小于10%的信号。该算法不能分离出相对能量较低的信号。伪影在端点处被引入信号中。研究人员已经开发出一种替代的分解方法，克服了这些限制。最重要的是，这种方法在计算上并不比快速傅立叶变换（FFT）昂贵，并且对于具有稀疏频谱分量的信号，可以比FFT有效得多。然而，这种方法目前也受到限制。这些限制包括可以存在于信号中的谱线的数量以及该局部收敛算法的良好初始化的必要性。本研究的两个主要目标是减少和消除现有的限制，这种算法尽可能大，并应用这种新的方法，如电力系统的频率和阻抗测量和电阻点焊电阻测量的应用。这项研究的结果将是一个强大的频谱分析工具的HHT，但更大的频率分离能力，和FFT的计算成本。它的应用将解决长期以来汽车电阻点焊焊接电压测量的难题。这有可能提高汽车的质量和安全性，每年节省数百万美元，并使加拿大制造厂在国际竞争中具有竞争优势。

Spectral analysis is one of the most fundamental analysis tools available to scientists. Despite its ubiquity, there are inherent difficulties with this tool. Traditional spectral analysis tools can have difficulty with signals whose spectrum changes quickly with time. A recent major advance in the field of spectral analysis is the Hilbert Huang transform (HHT). This algorithm uses a heuristic algorithm called empirical mode decomposition (EMD), to decompose the signal into sums of 'narrowband' signals for which a good solution to the spectral analysis problem, the Hilbert Transform, exists. Several significant limitations have been identified with the algorithm. It is computationally expensive. The algorithm is not able to separate signals with frequency differences of less than 10%. The algorithm can fail to separate signals with low relative energy. Artifacts are introduced into the signal at the end points. The researcher has developed an alternative means of decomposing that overcomes these limitations. Most significantly, this approach is not computationally more expensive than the fast Fourier transform (FFT), and for signals with sparse spectral components, can be significantly more efficient than the FFT. This approach, however, also presently suffers from limitations. These include a limit on the number of spectral lines that can be present in the signal and the necessity of good initialization of this locally convergent algorithm. The two main goals of this research are to reduce and eliminate the existing limitations of this algorithm as greatly as possible and apply this new approach to applications such as power systems frequency and impedance measurements and resistance measurement in resistance spot welding. The results of this research will be a spectral analysis tool as powerful as the HHT but with much greater frequency separating power, and the computational cost of the FFT. Its application will solve the long standing problem of measuring weld voltage for resistance spot welding of vehicles. This has the potential of increasing the quality and safety of automobiles, of creating savings of millions of dollars per year and giving Canadian manufacturing plants a competitive advantage against international competition.