Higher order numerical integration scheme for stochastic Hamiltonian dynamics on manifold with geometry preservation of manifold structure.

A new framework has been developed to solve geometric stochastic differential equations (SDEs) arising from stochastic Hamiltonian dynamics. This framework takes into account the interaction of geometry, nonlinearity, and stochasticity while preserving the geometry of the manifold where the system evolves.

Accurate estimation of the response with lower-order errors is a crucial aspect of closing the fundamental gap in the advancement of non-Euclidean statistics. The use of this framework enables a better understanding of the behavior of complex systems under uncertain conditions, and has the potential to revolutionize the field of non-Euclidean statistics.

In addition, a symplectic numerical integration scheme for the non-linear stochastic oscillators evolving on a manifold is developed to preserve Hamiltonian’s drift arising from the stochastic nature of the system along with the manifold’s geometry. This will enable the simulation of the Hamiltonian systems over long time intervals without loosing its accuracy. 

Blind modal identification of structures with complex modes, IMPRINT IIC with VSSCISRO.

A cutting-edge real-time modal identification algorithm has been developed, based on first-order eigen-perturbation and second-order separation techniques for linear vibrating systems with complex modes. The effectiveness of the algorithm is demonstrated through the use of both numerically simulated and benchmark case studies.

These case studies take into account various scenarios such as the formation of complex modes with closely spaced modes, non-proportional damping, dynamic changes in the damping matrix, and the addition of a secondary system over the primary structure. This work provides accurate, real-time identification of complex modes, even when system properties change dynamically.

This new algorithm represents a major advancement in the field of modal identification, providing valuable tools for understanding and managing the behavior of complex vibrating systems.

A framework for finding out the response statistics for nonlinear vibrating systems.

A stochastic bi-directional formulation for structural systems based on the concepts of correlated Wiener process is developed in this project. The framework enables the exploration of the effect of different levels of correlation in the input excitation on the structural response and its statistics. This is particularly important in the presence of torsional coupling, where the rotation of one component of the structure can have significant impacts on the behavior of other components. By taking into account these complex interactions, the framework provides a more comprehensive understanding of the structural behavior under uncertain conditions. 

A new approach for estimating the mean square solution of nonlinear structural systems has been developed using a framework based on the Adomian method. This framework allows for easy calculation of second-order response statistics of stochastic nonlinear dynamical systems, eliminating the need for computationally intensive Monte Carlo simulations. 

By enabling the estimation of the second-order response statistics, this framework provides important information about the behavior of nonlinear structural systems under uncertain conditions. This information can be used to improve the design and performance of these systems, and to make informed decisions about their operation and maintenance. 

Error-adapted FOEP techniques for modal identification and damage detection of dynamical systems under stochastic excitation.

A FOEP-based algorithm has been developed to address the challenge of real-time modal identification and damage detection in complex dynamical systems. This algorithm boasts quick convergence, providing reliable and efficient results for dynamic analysis and system health monitoring. The implementation of this cutting-edge technology allows for accurate and prompt identification of changes in system behavior, enabling proactive measures to be taken to address any potential issues. 

The unique feature of the FOEP-based algorithm is its quick convergence, allowing for near-instantaneous identification and assessment of the system's behavior, even in complex and challenging situations. This significantly improves the efficiency of the overall modal identification and damage detection process, providing timely and accurate results.