## 1 Introduction  
As technology development progresses and improved living standards are promoted, there is a corresponding and growing demand for power quality in human society. As an essential facility in all sections of industries, a power system influences economic growth or human's daily life, from something as little as a power outage, to something far more serious, such as severe damage to power generation and transmission equipment, or even an entire power network shut down, which would be a tremendous thread to the power system [1; 2]. For the sake of maintaining a quality power system, the performance as well as the reliabilities of a power transmission line and high low voltage equipments is a critical issue. A power system is mainly made up of conductors, ferrite materials and insulators, namely the key component for a well maintained power system, simply for the reason that a deteriorated insulator is commonly seen in an overloaded or aged facility. In addition, human errors or construction not following a standard operating procedure are also found as further cause for a damage to an insulator. Statistics show that a large number of accidents in the course of power system operation are attributed to aged or malfunctioned insulators [3; 4]. According to the literature [5; 6], the different types of partial discharge (PD) sources can generate different discharge patterns. The discharge pattern is represented by a set of characteristic features, which can be extracted from a PD signal. In the early days, a partial discharge signal was recognized by seasoned specialists according to the features revealed on an elliptical trajectory. However, as a consequence of a long term technology progress made over years, commercial instruments have been made to accurately sense partial discharge signals [7; 8; 9] emanating from an insulation facility, analyze the dielectric punch through process, provide a maintenance message and prevent catastrophe. Yet, such commercial instruments, valued as high as a million dollars, preprocess field detected signals in their front end circuits, and as a results, part of the intrinsic physical meaning contained is lost. For this reason, a detected signal is transformed into a time-frequency-energy 3D spectrum through the improved Hilbert-Huang Transformation (HHT), combined with a fractal theory to extract fractal features embedded. Finally, an extension method is adopted so as to identify defect modes out of a partial discharge signal. Subject to the defect types of an insulator, a partial discharge process is a highly complicated phenomenon, that is, distinct defect models bring about distinct discharge spectrums as expected. In a bid to accurately recognize insulation conditions of a power cable, a data base is built for diagnosis purposes by successively measuring partial discharge signals from a sequence of defect models. This work aims to analyze a detected discharge signal through the Hilbert-Huang transform, an approach with a high resolution to a nonlinear as well as non-stationary signal. Yet, there exist two inherent problems, degrading the accuracy in signal analysis and hence a barrier to an automatic defect mode identification. The first problem is lacking a decision criterion to precisely specify the optimal shifting number. In the case of an excessive shifting number, the intrinsic physical meaning carried in extracted intrinsic mode function (IMFs) will be unintentionally removed, that is, any instant frequency cannot be viewed out of all the IMFs accordingly. The second is that illusive components may be seen in the course of empirical mode decomposition (EMD) process as a result of the use of the extrema interpolation, i.e., a cause for a mode confusion problem. For this sake, combined with a K-S test and an energy ratio sorting, an improved HHT, abbreviated as IHHT hereafter, is proposed as an effective approach to specify the optimal shifting number and as a decision criterion in the identification of illusive components.