title: Advances of Mathematical Morphology and Its Applications in Signal Processing
Creators: name: Zhang, Jinfei
Publisher: name: University of Liverpool Repository
Year: 2023

description: This thesis describes some advances of Mathematical Morphology (MM), in order to improve the performance of MM filters in I-D signal processing, . especially in the application to power system protection. MM methodologies are founded on set-theoretic concepts and nonlinear superpositions of signals and images. The morphological operations possess outstanding geometrical properties which make it undoubted that they are efficient image processing methods. However in I-D signal processing, MM filters are not widely employed. To explore the applications of MM for I-D signal processing, our contributions in this area can be summarized in the following two aspects. Firstly, the fram.ework of the traditional signal processing methods is based on the frequency domain representation of the signal and the analysis of the operators' transfer function in the frequency domain. But to the morphological operations, their representations in the frequency domain are uncertain. In order to tackle this problem, this thesis presents our attempt to describe the weighted morphological dilation in the frequency domain. Under certain restrictions to the signal and the structuring element, weighted dilation is transformed to a mathematical expression in the frequency domain. Secondly, although the frequency domain analysis plays an important role in signal processing, the geometrical properties of a signal such as the shape of the signal cannot be ignored. MM is an effective method in dealing with such problems. In this thesis, based on the theory of Morphological Wavelet (MW), three multi-resolution signal decomposition schemes are presented. They are Multiresolution Morphological Top-Hat scheme (MMTH), Multi-resolution Morphov logical Gradient scheme (MMG) and Multi-resolution Noise Tolerant Morphological Gradient scheme (MNTMG). The MMTH scheme shows its significant effect in distinguishing symmetrical features from asymmetrical features on the waveform, which owes to its signal analysis operator: morphological Top-Hat transformation, an effective morphological technique. In this thesis, the MMTH scheme is employed in the identification of transformer magnetizing inrush curr~nt from internal fault. Decomposing the signal by MMTH, the asymmetrical features of the inrush waveform are exposed, and the other irrelevant components are attenuated. The MMG scheme adopts morphological gradient, a commonly used operator for edge detection in image and signal processing, as its signal analysis / operator. The MMG scheme bears significant property in characterizing and recognizing the sudden changes with sharp peaks and valleys on the waveform. Furthermore, to the MMG scheme, by decomposing the signal into different levels, the higher the level is processed, the more details of the sudden changes are revealed. In this thesis, the MMG scheme is applied for the design of fault locator of power transmission lines, by extracting the transient features directly from fault-generated transient signals. The MNTMG decomposition scheme can effectively reduce the noise and extract transient features at the same time. In this thesis, the MNTMG scheme is applied to extract the fault generated transient wavefronts from noise imposed signals in the application of fault location of power transmission lines. The proposed contributions focus on the effect of weighted dilation in the frequency domain, constructions of morphological multi-resolution decomposition schemes and their applications in power systems.