State-space formulation for the chain parameters of nonuniform transmission lines

1970 ◽  
Vol 6 (13) ◽  
pp. 422
Author(s):  
C. Toker ◽  
N. Yildirim
Keyword(s):  
State Space ◽  
Transmission Lines ◽  
Space Formulation ◽  
Nonuniform Transmission Lines

Cylindrically Anisotropic Tubes Containing a Line Dislocation

2006 ◽  
Author(s):  
Chung-Hao Wang
Keyword(s):  
State Space ◽  
Dislocation Line ◽  
Longitudinal Axis ◽  
The State ◽  
Fourier Series Expansion ◽  
General Solutions ◽  
Mixed Dislocation ◽  
Line Dislocation ◽  
Space Formulation ◽  
Cylindrically Anisotropic

An analytical solution of the problem of a cylindrically anisotropic tube which contains a line dislocation is presented in this study. The state space formulation in conjunction with the eigenstrain theory is proved to be a feasible and systematic methodology to analyze a tube with the existence of dislocations. The state space formulation which expediently groups the displacements and the cylindrical surface traction can construct a governing differential matrix equation. By using Fourier series expansion and the well developed theory of matrix algebra, the asymmetrical solutions are not only explicit but also compact in form. The dislocation considered in this study is a kind of mixed dislocation which is the combination of edge dislocations and a screw dislocation and the dislocation line is parallel to the longitudinal axis of the tube. The degeneracy of the eigen relation and the technique to determine the inverse of a singular matrix are thoroughly discussed, so that the general solutions can be applied to the case of isotropic tubes, which is one of the novel features of this research. The results of isotropic problems, which are belong to the general solutions, are compared with the well-established expressions in the literature. The satisfied correspondences of these comparisons indicate the validness of this study. A cylindrically orthotropic tube is also investigated as an example and the numerical results for the displacements and tangential stress on the outer surface are displayed. The effects on surface stresses due to the existence of a dislocation appear to have a characteristic of localized phenomenon.

Leak detection and localization for pipelines using multivariable fuzzy learning backstepping

2021 ◽  
pp. 1-12
Author(s):  
Farzin Piltan ◽  
Jong-Myon Kim
Keyword(s):  
Transmission Lines ◽  
Leak Detection ◽  
Support Vector ◽  
Robust Learning ◽  
Regression Techniques ◽  
Space Formulation ◽  
Points Of View ◽  
Detection And Localization ◽  
Fuzzy Learning ◽  
Backstepping Algorithm

Pipelines are a nonlinear and complex component to transfer fluid or gas from one place to another. From economic and environmental points of view, the safety of transmission lines is incredibly important. Furthermore, condition monitoring and effective data analysis are important to leak detection and localization in pipelines. Thus, an effective technique for leak detection and localization is presented in this study. The proposed scheme has four main steps. First, the learning autoregressive technique is selected to approximate the flow signal under normal conditions and extract the mathematical state-space formulation with uncertainty estimations using a combination of robust autoregressive and support vector regression techniques. In the next step, the intelligence-based learning observer is designed using a combination of the robust learning backstepping method and a fuzzy-based technique. The learning backstepping algorithm is the main part of the algorithm that determines the leak estimation. After estimating the signals, in the third step, their classification is performed by the support vector machine algorithm. Finally, to find the size and position of the leak, the multivariable backstepping algorithm is recommended. The effectiveness of the proposed learning control algorithm is analyzed using both experimental and simulation setups.

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