An alternative solution to the model structure selection problem

An alternative solution to the model structure selection problem is introduced by conducting a forward search through the many possible candidate model terms initially and then performing an exhaustive all subset model selection on the resulting model. An example is included to demonstrate that this approach leads to dynamically valid nonlinear model

Vibration-based methods for structural and machinery fault diagnosis based on nonlinear dynamics tools

This study explains and demonstrates the utilisation of different nonlinear-dynamics-based procedures for the purposes of structural health monitoring as well as for monitoring of robot joints

Vibration-based damage detection in structures using time series analysis

The paper considers some possibilities to use pure time series analysis for damage diagnosis in vibrating structures. It introduces the basics of the state space methodology and discusses a number of possible methods to extract damage sensitive features from the state space representation of the attractor of a vibrating system. The discussed methods can be divided into two groups: methods that use non-linear dynamics characteristics and methods based on the statistical characteristics of the distribution of points on the attractor. Each possible damage feature is introduced separately and the advantages and shortfalls of its application are discussed. The application of the suggested techniques is demonstrated on a test case of a reinforced concrete plate

Symbolic Toolkit for Chaos Explorations

New computational technique based on the symbolic description utilizing kneading invariants is used for explorations of parametric chaos in a two exemplary systems with the Lorenz attractor: a normal model from mathematics, and a laser model from nonlinear optics. The technique allows for uncovering the stunning complexity and universality of the patterns discovered in the bi-parametric scans of the given models and detects their organizing centers -- codimension-two T-points and separating saddles.Comment: International Conference on Theory and Application in Nonlinear Dynamics (ICAND 2012

Recurrence-based time series analysis by means of complex network methods

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos (2011

On the predictability of time series by metric entropy

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2006Includes bibliographical references (leaves: 48-49)Text in English; Abstract: Turkish and Englishxi, 55 leavesThe computation of the metric entropy, a measure of the loss of information along the attractor, from experimental time series is the main objective of this study. In this study, replacing the current warning systems (simple threshold based, on/off circuits), a new and promising prognosis system is tried to be achieved by the metric entropy, i.e. Kolmogorov . Sinai entropy, from chaotic time series. Additional to metric entropy, correlation dimension and time series statistical parameters were investigated.Condition monitoring of ball bearings and drill bits was achieved in the light of practical considerations of time series applications. Two different accelerated bearing run-to-failure test rigs were constructed and the prediction tests were performed.However, as a reason of shaft failure in both structures during the experiments, none of them is completed. Finally, drill bit breakage experiments were carried out. In the experiments, 10 small drill bits (1 mm ) were tested until they broke down, while vibration data were consecutively taken in equal time intervals. After the analysis, a consistent decrement in variation of metric entropy just before the breakage was observed. As a result of the experiment results, metric entropy variation could be proposed as an early warning system