Recently proposed Hilbert-Huang transform (HHT), consisting of empirical mode decomposition (EMD) and Hilbert spectrum analysis (HSA), has been proved to be an effective approach in both scientific researches and engineering applications. However, this method is still empirical because of lacking rigorously mathematical foundation. This paper primarily focuses on providing a mathematical contribution on its sifting characteristics and instantaneous features. Firstly, the theory of the original methods as well as their advantages and restrictions are briefly reviewed. Secondly, we conduct indepth investigations of the instantaneous parameters (IPs) and sifting ability. Thirdly, we proposed a new EMD stopping criterion, determined an optimal number of sifting iterations, employed a new masking signal to fix the mode mixing problem and investigated into the sifting property according to the extremum distribution. Finally, comparative studies, simulations and real data analyses depending on the proposed method are presented to demonstrate the validity of the novel research. The simulations illustrate that the typically defined intrinsic mode functions (IMFs) are not perfectly symmetric with zero-mean, there is still no rigorous mathematical standard to determine the "watershed" between mono and multi-component IMFs. The comparative researches indicate that unlike the prism property of the Fourier transform (FT) and the mathematical microscope property of the wavelet transform (WT), the ultimate goal of the HHT is to work as raindrops.

Cable termination is a weak point in an underground cable system. The transient earth voltage (TEV) method is an effective and nonintrusive method for estimating the insulation condition of cable termination. However, the practical application of TEV detection is mainly focused on switchgears, generators, and transformers with a flat and conductive shell. A flexible sensor array based on the TEV method is presented for online partial discharge (OLPD) monitoring of the cable termination. Each sensing element is designed with a dual-capacitor structure made of flexible polymer material to obtain better and more stable sensitivity. Based on the electromagnetic (EM) wave propagation theory, the partial discharge (PD) propagation model in the cable termination is built to analyze and verify the rationality and validity of the sensor unit. Some influencing factors are discussed regarding the response characteristics of sensors. Finally, the performance of the sensor array is verified by simulations and experiments. Besides, an OLPD monitoring system is introduced. The monitoring system is composed of the on-site monitoring device and the remote monitoring host. The two parts of the system exchange the data through wireless networks using a wireless communication module. The experiment results show that the monitoring device could supply the PD condition monitoring demand for cable termination.

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