Mathematical morphology, used extensively in image processing, tracks the support domains for the operation of convolution and deconvolution. Morphology is also important in the modelling of signals on time scales. Time scale theory provides a generalization tent under which the operations of discrete and continuous time signal and Fourier analysis rest as special cases. The time scale paradigm provides modelling under which a rich class of hybrid signals and systems can be analyzed. We begin with introductory material on mathematical morphology which is foundational to the development of time scale theory. The support of convolution is related to the operation of dilation in mathematical morphology. Mathematical morphology is most commonly associated with image processing. Applications of morphology was initially applied to binary black and white images by Matheron [966]. The field is richly developed [506, 578]. Here, we outline the fundamentals. In N dimensions, let X and H denote a set of vectors or, in the degenerate case of one dimension, a set of real numbers.
In the last fifty years, approximately, advances in computers and the availability of images in digital form have made it possible to process and to analyze them in automatic (or semi-automatic) ways. Alongside with general signal processing, the discipline of image processing has acquired a great importance for practical applications as well as for theoretical investigations. Some general image processing references are (Castleman, 1979) (Rosenfeld & Kak, 1982) (Jain, 1989) (Pratt, 1991) (Haralick & Shapiro, 1992) (Russ, 2002) (Gonzalez & Woods, 2006). Mathematical Morphology, which was founded by Serra and Matheron in the 1960s, has distinguished itself from other types of image processing in the sense that, among other aspects, has focused on the importance of shapes. The principles of Mathematical Morphology can be found in numerous references such as (Serra, 1982) (Serra, 1988) (Giardina & Dougherty, 1988) (Schmitt & Mattioli, 1993) (Maragos & Schafer, 1990) (Heijmans, 1994) (Soille, 2003) (Dougherty & Lotufo, 2003) (Ronse, 2005).
The shape characteristic of the axis orbit plays an important role in the fault diagnosis of rotating machinery. However, the original signal is typically messy, and this affects the identification accuracy and identification speed. In order to improve the identification effect, an effective fault identification method for a rotor system based on the axis orbit is proposed. The method is a combination of ensemble empirical mode decomposition (EEMD), morphological image processing, Hu invariant moment feature vector, and back propagation (BP) neural network. Experiments of four fault forms are performed in single-span rotor and double-span rotor test rigs. Vibration displacement signals in the X and Y directions of the rotor are processed via EEMD filtering to eliminate the high-frequency noise. The mathematical morphology is used to optimize the axis orbit including the dilation and skeleton operation. After image processing, Hu invariant moments of the skeleton axis orbits are calculated as the feature vector. Finally, the BP neural network is trained to identify the faults of the rotor system. The experimental results indicate that the time of identification of the tested axis orbits via morphological processing corresponds to 13.05 s, and the identification accuracy rate ranges to 95%. Both exceed that without mathematical morphology. The proposed method is reliable and effective for the identification of the axis orbit and aids in online monitoring and automatic identification of rotor system faults.
Application of Axis Orbit Image Optimization in Fault Diagnosis for Rotor System