Projects in Nonlinear Dynamics Laboratory


	matlab software archives
	in this archive we have collected all the programs written in our lab for nonlinear time series analysis, multivariate data analysis and phase space warping based analysis. all the code is distributed for free under the gnu public license, and we would appreciate acknowledgement of our work.
	research projects
	SMOOTH ORTHOGONAL DECOMPOSITION a new multivariate data analysis tool. current research focus is on its applications to: - experimental vibration modal analysis - nonlinear model reduction - nonlinear normal mode identification
	PHASE SPACE WARPING current research is focused on investigating new nonlinear short-time statistics that quantify phase space warping (psw), which describes a process of change in dynamical system's flow due to the change in system's parameters.
	DAMAGE IDENTIFICATION IN VARAIBLE OPERATING CONDITIONS methods that can identify multidimensional damage states based on readily available measurements from system of interest and are suitable for on-line, real-time applications are developed. current focus is on tracking multidimensional damage variables in a hierarchical dynamical systems with variable loading and environmental conditions.
	DATA DRIVEN DAMAGE PROGNOSIS this project addresses practical aspects of machinery health monitoring systems development. the main accent is on already developed algorithm refinement for implementation in on-line, real-time applications.
	DYNAMICAL SYSTEMS APPROACH TO FATIGUE DAMAGE MODELING damage is a complex phenomenon and we make no attempt to theorize about the "hidden" physical nature of damage, but aim to develop appropriate concepts and procedures for identifying phenomenological regularities that establish the needed experimental links between the measurements and the complex damage phenomena.
	TRACKING FATIGUE RELATED CHANGES IN HUMAN COORDINATION the dynamical and stochastic systems methods are used to probe how pathological changes at the cellular/tissue levels affect behavior at the observable (i.e., biomechanical) level during fatigue progression. the applicability of the psw-based techniques to tracking and predicting pathological developments in patients is investigated.
	MEASUREMENT NOISE AND NONLINEAR STATISTICS the correlation entropy and correlation dimension are measures of the predictability and structure of a chaotic system. measurement noise, when present, creates difficulties in extracting these quantities from a time series. this project is focused on detecting and evaluating measurement noise effects.