The First Integral Approach in Stability Problem of Large Scale Nonlinear Dynamical Systems

In analyzing large scale nonlinear dynamical systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solutions properties of the large scale system are then deduced from the solution properties of the individual subsystems and the nature of the interconnections. In this paper a new approach is proposed for the stability analysis of large scale systems, which is based upon the concept of vector Lyapunov functions and the decomposition methods. The present results make use of graph theoretic decomposition techniques in which the overall system is partitioned into a hierarchy of strongly connected components. We show then, that under very reasonable assumptions, the overall system is stable once the strongly connected subsystems are stables. Finally an example is given to illustrate the constructive methodology proposed.

Stability of Interconnected Systems under Structural Perturbation: Decomposition-Aggregation Approach

In this paper, the decomposition-aggregation method is used to carry out connective stability criteria for general linear composite system via aggregation. The large scale system is decomposed into a number of subsystems. By associating directed graphs with dynamic systems in an essential way, we define the relation between system structure and stability in the sense of Lyapunov. The stability criteria is then associated with the stability and system matrices of subsystems as well as those interconnected terms among subsystems using the concepts of vector differential inequalities and vector Lyapunov functions. Then, we show that the stability of each subsystem and stability of the aggregate model imply connective stability of the overall system. An example is reported, showing the efficiency of the proposed technique.

Weld Defect Detection in Industrial Radiography Based Digital Image Processing

Industrial radiography is a famous technique for the identification and evaluation of discontinuities, or defects, such as cracks, porosity and foreign inclusions found in welded joints. Although this technique has been well developed, improving both the inspection process and operating time, it does suffer from several drawbacks. The poor quality of radiographic images is due to the physical nature of radiography as well as small size of the defects and their poor orientation relatively to the size and thickness of the evaluated parts. Digital image processing techniques allow the interpretation of the image to be automated, avoiding the presence of human operators making the inspection system more reliable, reproducible and faster. This paper describes our attempt to develop and implement digital image processing algorithms for the purpose of automatic defect detection in radiographic images. Because of the complex nature of the considered images, and in order that the detected defect region represents the most accurately possible the real defect, the choice of global and local preprocessing and segmentation methods must be appropriated.

Quantitative Analysis of Weld Defect Images in Industrial Radiography Based Invariant Attributes

For the characterization of the weld defect region in the radiographic image, looking for features which are invariant regarding the geometrical transformations (rotation, translation and scaling) proves to be necessary because the same defect can be seen from several angles according to the orientation and the distance from the welded framework to the radiation source. Thus, panoply of geometrical attributes satisfying the above conditions is proposed and which result from the calculation of the geometrical parameters (surface, perimeter, etc.) on the one hand and the calculation of the different order moments, on the other hand. Because the large range in values of the raw features and taking into account other considerations imposed by some classifiers, the scaling of these values to lie between 0 and 1 is indispensable. The principal component analysis technique is used in order to reduce the number of the attribute variables in the aim to give better performance to the further defect classification.