Types Of System Behaviors Research Articles

Enhanced multiresolution wavelet analysis of complex dynamics in nonlinear systems.

Multiresolution wavelet analysis (MWA) is a powerful data processing tool that provides a characterization of complex signals over multiple time scales. Typically, the standard deviations of wavelet coefficients are computed depending on the resolution level and such quantities are used as measures for diagnosing different types of system behavior. To enhance the capabilities of this tool, we propose a combination of MWA with detrended fluctuation analysis (DFA) of detail wavelet coefficients. We find that such an MWA&DFA approach is capable of revealing the correlation features of wavelet coefficients in independent ranges of scales, which provide more information about the complex organization of datasets compared to variances or similar statistical measures of the standard MWA. Using this approach, we consider changes in the dynamics of coupled chaotic systems caused by transitions between different types of complex oscillations. We also demonstrate the potential of the MWA&DFA method for characterizing different physiological conditions by analyzing the electrical brain activity in mice.

IMER-FM: Iterative Process of System Feature Model Extraction from the Requirements

Software product line engineering (SPLE) is a paradigm to promote systematic software reuse. A Feature Model (FM) is a common means to illustrate the commonality and variability of software products in a family. In most existing FM extraction approaches, keywords in the requirement document or certain types of system behavior or external events are considered features. The resulting FM is a combination of user activities and system actions (SAs), making it hard to understand. In this paper, we present an automatic approach to generate a product line FM from multiple requirement documents. We consider user activity and SAs separately in our approach and focus on the expected behaviors of the software system, together with the data being processed. The resulting FM clearly illustrates the expected functionalities of the software system and their variability in the product line. We also compared our approach with existing techniques by processing the same textual documents, and noted improvements in our results.

Sound Over-Approximation of Probabilities

Safety analysis of high confidence systems requires guaranteed bounds on the probability of events of interest. Establishing the correctness of algorithms that compute such bounds is challenging. We address this problem in three steps. First, we use monadic transition systems (MTS) in the category of sets as a general framework for modeling discrete time systems. MTS can capture different types of system behaviors, but here we focus on a combination of non-deterministic and probabilistic behaviors that arises often when modeling complex systems. Second, we use the category of posets and monotonic maps as general setting to define and compare approximations. In particular, for the MTS of interest, we consider approximations of their configurations based on complete lattices of interval probabilities. Third, we obtain an algorithm that computes over-approximations of system configurations after a finite number of steps, by restricting to finite lattices.

THE CONSTRUCTION OF SOLUTIONS OF PIECEWISE-LINEAR PHASE SYSTEMS

The creation of methods for the study of nonlinear phase systems has a long history, since the 60s of the last century (V.I. Tikhonov, V. Lindsay, M.V. Kapranov, B.I. Shakhtarin, etc.). By now, rigorous and approximate analysis methods of such systems have been developed. However, most methods are limited to the analysis of low order systems. Only in recent years attempts have been made to create methods, which allow to carry out the analysis of high-order phase systems. The material of this article deals with these methods. The article considers the construction of solutions of phase systems on the example of phase-locked frequency of arbitrary dimension with piecewise linear approximation of the nonlinear function. This approximation allowed to use an explicit form of solutions in the linearity and to obtain analytical conditions for the existence of various types of system behavior. The analytical conditions for the existence of solutions leading to the emergence of complex limit sets of the trajectories of phase systems and their bifurcations are obtained. These are homoclinic trajectories in the case of the saddle-focus equilibrium state, which play a decisive role in the occurrence of chaos. It is also shown that it is possible to obtain analytical conditions for the bifurcation of the birth and the existence of multi-pass rotational cycles in a piecewise linear phase system, on the basis of which a criterion for the transition to chaos through bifurcations cascade of doubling the stable cycle period can be obtained; in accordance with the Sharkovsky theorem it ends with the bifurcation of the cycle birth of the period three and the occurrence of developed chaos. It should be noted that the research methods of piecewise linear systems described in the paper were applied by the authors not only to phase systems, but, for example, to the Chua system, allowing various chaotic behavior.

Robust LQR and LQI control with actuator failure of a 2DOF unmanned bicycle robot stabilized by an inertial wheel

Abstract Essential ingredients for robust control are the ability to cope with different types of system behavior following modeling imperfections and the ability to assure a certain performance level. In this paper, we propose to use an actuator fault-tolerant control law to govern, during experiments, the stabilization of a bicycle robot with an inertial wheel in order to take into account unmodeled uncertainty introduced by using a linearized model in an LQR fashion. Our proposal is illustrated by signal plots and the values of performance indices obtained from a set of experiments.

Asymptotic solutions for Mathieu instability under random parametric excitation and nonlinear damping

A theoretical analysis is presented of the response of a lightly and nonlinearly damped mass–spring system in which the spring constant contains a small randomly fluctuating component. Damping is represented by a combination of linear and nonlinear power-law damping. System response to some initial disturbance at time zero is described by a sinusoidal wave whose amplitude and phase vary slowly and randomly with time. Leading order formulations for the equations of amplitude and phase are obtained through the application of methods of stochastic averaging of Stratonovich. The equations of amplitude and phase are given in two versions: Fokker–Planck equations for transient probability and Langevin equations for response in the time-domain. Solutions in closed-form of these equations are derived by methods of mathematical and theoretical physics involving higher transcendental functions. They are used to study the behavior of system response for ever increasing time applying asymptotic methods of analysis such as the method of steepest descent or saddle-point method. It is found that system behavior depends on the power density of the parametric excitation at twice the natural frequency and on the magnitude and form of the damping. Depending on these parameters different types of system behavior are found to be possible: response which decays exponentially to zero, response which leads to a stationary state of random behavior, and response which can either grow unboundedly or which approaches zero in a finite time.

Architectural support for mode-driven fault tolerance in distributed applications

Many distributed applications exhibit different types of system behaviors, or modes , during the course of their operation. Each such mode may have different functional and non-functional requirements (such as fault tolerance, availability, and security). A static software fault-tolerance solution can not cater to the needs of every mode, and also does not utilize system resources intelligently. A flexible architecture is required to provide dependability that can be tailored for such applications. We propose a novel mode-driven fault-tolerance approach that includes: (i) a generic framework to extend the specification of modes with fault-tolerance requirements, and (ii) a software architecture that uses this description to provide the appropriate fault tolerance for each mode at runtime. We also present a case study using a distributed multi-modal CORBA application to demonstrate the effectiveness of our approach.

On the geometry of space- and time-equivalent catastrophes

The geometrical nature of the Elementary catastrophes ( Thom, 1969 ) is reviewed. Histories of the movement of catastrophe manifolds and bifurcation sets are presented for some of the space-equivalent unfoldings described by Wassermann (1975) . These unfoldings provide descriptions of the variation with time of the stability of stationary states of associated potential energy functions. Identification of these stationary energy states with stationary states of a system therefore provides a description of its behavior with time. Qualitative descriptions of this type are particularly useful when the complexity of a system prevents a detailed quantitative description. Histories of bifurcation set movements suggest different types of system behavior at different space-like coordinates. This type of theory may be a useful model for the processes leading to differentiation of cells and to emergence of adult forms of a biological organism.

Vibration Analysis of Large High-Speed Rotating Equipment

This paper discusses the application of mobility methods to the lateral vibration analysis of coupled machinery. Some effects of bearing and/or casing structural mobility on the rotational system behavior are shown. In particular, the various types of system behavior and their interrelations are shown to be closely tied to the response of the rotor-support structure. The effect of hydrodynamic oil films are also shown. Lateral vibrational problems have been encountered when connecting drive and driven equipment produced by different manufacturers. Generally, these are caused by natural frequencies in the operating-speed range which result directly from the method of coupling. Methods of solving this problem are presented with emphasis on flexible couplings and their proper inclusion in system response calculations.