A New Framework for Reduced Order Model Development
Long-time numerical simulations of large-scale mechanistic models of complex systems (e.g., molecular/multi-body/computational fluid dynamics or structural finite element models) are still problematic, either due to numerical instabilities or excessive, yet necessary computational resources. Therefore, reduced models that can be simulated for a long-time and provide truthful approximations to the actual long-time dynamics are needed. A new framework, based on new concepts of dynamical consistency and subspace robustness, for identifying subspaces suitable for reduced-order model development is developed. The new framework identifies subspaces that provide accurate model reductions for a range of forcing parameters, and that only four and higher dimensional models could be dynamically consistent.
Optimal Motion Path Planning and Control
The problem of motion planing and control for an unmanned ocean surface vessel is considered from dynamical systems perspective. Motion path planning takes into account the vessel’s dynamical model and uses meta-heuristics approach. Dynamic obstacle avoidance, multi-agent task planning in various constraint scenarios is also considered.
SMOOTH ORTHOGONAL DECOMPOSITION
a new multivariate data analysis tool. current research focus is on its applications to: (1) experimental vibration modal analysis; (2) nonlinear model reduction; (3) nonlinear normal mode identification; (4) nonlinear noise reduction.
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.