Analysis of Structural Properties of Complex and Networked Systems

Over the past decades, science and society have been experiencing systems that tend to be increasingly sophisticated and interconnected. Although it would be challenging to understand and control complex systems fully, the analysis and control of such systems can be partially realized only after applying some reasonable simplifications. In particular, for the analysis of certain control properties, such as controllability, a complex system can be simplified to a linear structured system capturing an essential part of the structural information in that system, such as the existence or absence of relations between components of the system. This thesis has studied the effect of the interconnection structure of complex systems on their control properties following a structural analysis approach. More explicitly, we have analyzed strong structural properties of complex systems. The main contributions have been split into two parts:1. We have introduced a new framework for linear structured systems in which the relations between the components of the systems are allowed to be unknown. This kind of systems has been formalized in terms of pattern matrices whose entries are either fixed zero, arbitrary nonzero, or arbitrary. We have dealt with strong structural controllability and the solvability of the FDI problem of this kind of linear structured systems.2. We have introduced a novel framework for linear structured systems in which a priori given entries in the system matrices are restricted to take arbitrary but identical values. Several sufficient algebraic and graph theoretic conditions were established under which these systems are strongly structurally controllable.Finally, in the outlook subsection, we have suggested some future research problems concerning the analysis of strong structural properties of complex systems

Strong Structural Controllability of Systems on Colored Graphs

This paper deals with structural controllability of leader-follower networks. The system matrix defining the network dynamics is a pattern matrix in which a priori given entries are equal to zero, while the remaining entries take nonzero values. The network is called strongly structurally controllable if for all choices of real values for the nonzero entries in the pattern matrix, the system is controllable in the classical sense. In this paper we introduce a more general notion of strong structural controllability which deals with the situation that given nonzero entries in the system's pattern matrix are constrained to take identical nonzero values. The constraint of identical nonzero entries can be caused by symmetry considerations or physical constraints on the network. The aim of this paper is to establish graph theoretic conditions for this more general property of strong structural controllability.Comment: 13 page

Vibration signal de-noising based on empirical wavelet transform autocorrelation analysis

In diesel engine fault diagnosis, non-stationary vibration signal is easily disturbed by strong noise. In view of the shortcomings of empirical mode decomposition (EMD) and wavelet transform in de-noising, a de-noising method is proposed, which is Empirical Wavelet Transform (EWT) autocorrelation analysis. Taking advantages of EMD and wavelet transform, the Fourier spectrum is adaptively divided by EWT, and the intrinsic mode components of different frequency are extracted through constructed wavelet filter, and the method can effectively eliminate modal aliasing and solve adaptive problems in wavelet de-noising. At the same time, autocorrelation analysis can make the random noise decay to zero, and the modal components with high frequency random noise are dealt by autocorrelation analysis. The method is used to de-noising and compared the de-noising effect of EWT and EMD. Results show that the method can effectively decompose the intrinsic mode component with less number, and there is no false mode, and the de-noising effect is better than EMD de-noising. The method is feasible and effective in de-noising by vibration signals of diesel engine

A Unifying Framework for Strong Structural Controllability

This paper deals with strong structural controllability of linear systems. In contrast to existing work, the structured systems studied in this paper have a so-called zero/nonzero/arbitrary structure, which means that some of the entries are equal to zero, some of the entries are arbitrary but nonzero, and the remaining entries are arbitrary (zero or nonzero). We formalize this in terms of pattern matrices whose entries are either fixed zero, arbitrary nonzero, or arbitrary. We establish necessary and sufficient algebraic conditions for strong structural controllability in terms of full rank tests of certain pattern matrices. We also give a necessary and sufficient graph theoretic condition for the full rank property of a given pattern matrix. This graph theoretic condition makes use of a new color change rule that is introduced in this paper. Based on these two results, we then establish a necessary and sufficient graph theoretic condition for strong structural controllability. Moreover, we relate our results to those that exists in the literature, and explain how our results generalize previous work.Comment: 11 pages, 6 Figure

Engine fault feature extraction based on order tracking and VMD in transient conditions

A method based on order tracking and Variational Mode Decomposition was proposed to solve the problem of non-stationarity and background noise in the vibration signal of engine. For the vibration signal of diesel engine crankshaft bearing fault and Connecting rod bearing of gasoline engine, the non-stationary signal in the time domain was converted into a pseudo stationary signal on the angular domain based on order tracking. Then the reconstructed signal was decomposed by several components by VMD, and the component that contains fault information was selected. The three-dimensional spectral array of order, speed and power spectrum was calculated, and the fault feature was extracted. The effectiveness of the proposed method is verified by simulation and experiment

Fault detection and isolation for linear structured systems

This paper deals with the fault detection and isolation (FDI) problem for linear structured systems in which the system matrices are given by zero/nonzero/arbitrary pattern matrices. In this paper, we follow a geometric approach to verify solvability of the FDI problem for such systems. To do so, we first develop a necessary and sufficient condition under which the FDI problem for a given particular linear time-invariant system is solvable. Next, we establish a necessary condition for solvability of the FDI problem for linear structured systems. In addition, we develop a sufficient algebraic condition for solvability of the FDI problem in terms of a rank test on an associated pattern matrix. To illustrate that this condition is not necessary, we provide a counterexample in which the FDI problem is solvable while the condition is not satisfied. Finally, we develop a graph-theoretic condition for the full rank property of a given pattern matrix, which leads to a graph-theoretic condition for solvability of the FDI problem.Comment: 6 pages, 1 figure, 1 tabl

CCD photometric study of the W UMa-type binary II CMa in the field of Berkeley 33

The CCD photometric data of the EW-type binary, II CMa, which is a contact star in the field of the middle-aged open cluster Berkeley 33, are presented. The complete R light curve was obtained. In the present paper, using the five CCD epochs of light minimum (three of them are calculated from Mazur et al. (1993)'s data and two from our new data), the orbital period P was revised to 0.22919704 days. The complete R light curve was analyzed by using the 2003 version of W-D (Wilson-Devinney) program. It is found that this is a contact system with a mass ratio $q=0.9$ and a contact factor $f=4.1$. The high mass ratio ($q=0.9$) and the low contact factor ($f=4.1$) indicate that the system just evolved into the marginal contact stage

Strong structural controllability of systems on colored graphs

This article deals with strong structural controllability of leader-follower networks. The system matrix defining the network dynamics is a pattern matrix, in which a priori given entries are equal to zero, while the remaining entries take nonzero values. These nonzero entries correspond to edges in the network graph. The network is called strongly structurally controllable if for all choices of real values for the nonzero entries in the pattern matrix, the system is controllable in the classical sense. The novelty of this article is that we consider the situation that prespecified nonzero entries in the system's pattern matrix are constrained to take identical (nonzero) values. These constraints can be caused by symmetry properties or physical constraints on the network. Restricting the system matrices to those satisfying these constraints yields a new notion of strong structural controllability. The aim of this article is to establish graph-theoretic conditions for this more general property of strong structural controllability