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Ongoing Research

The Uncertainty Lab

My research interests are primarily in stochastic mechanics and stochastic nonlinear dynamics. The origin of stochasticity lies in the inherent uncertainties that exists in nature; for example,   in the randomness in the loadings, such as earthquakes, wind and sea waves,  in the variations of the  micro-structure  in materials and in the variations of atmospheric conditions. An additional source of uncertainty lies in the insufficient knowledge in modelling or measuring nature. For example, simplifying assumptions in mathematical models, errors in acquiring measurement data also contribute to uncertainties. The focus of our studies is on modelling these uncertainties and quantifying how these uncertainties propagate through the analysis and manifest into the response.

My interests in uncertainty analysis are primarily focussed on dynamical applications and vibrations with emphasis on understanding the nonlinear dynamical characteristics arising due to complexities resulting from geometric nonlinearities, coupled multi-physics problems (like fluid-structure interactions) and non-smooth dynamical systems. However, I also investigate on problems involving uncertainty quantification in materials and composites. 

Complex Systems and Dynamics 

I am also a member of the Complex Systems and Dynamics group - an informal initiative involving about 32 faculty members from 10 departments across the Institute. The objective of this group is to initiate discussions on interdisciplinary problems involving complex networks, coupled problems and dynamical systems and build up multi-disciplinary teams to investigate complex and challenging problems.

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Stochastic bifurcations

Stochastic bifurcations in nonlinear dynamical systems are defined in terms of  D-bifurcations and  P-bifurcations. While the former is characterized in terms of the largest Lyapunov exponents, P-bifurcation analysis as discussed in the literature have been primarily qualitative. Through our studies, we have developed new quantitative measures for characetrzing P-bifurcations. Additionally, our studies have revealed that P-bifurcation essentially involves basin hopping of the trajectories between co-existing attractors due to the effect of noise. Investigations to gain further insights are currently being actively pursued in the group.

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Noise induced intermittency

Noise induced intermittency is a nonlinear dynamical phenomenon in which the system trajectories randomly move between the basins of different attractors in the presence of noise in the excitations.

 Our studies on aeroelastic systems in gusty flows have revealed that the scales of the random fluctuations play a crucial role in the qualitative natire of intermittency. Noise induced intermittency has been observed in several different applications involving nonlinear dynamical systems. Investigations are currently in progress to understand this phenomenon in more general settings through nonlinear maps

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Nonlinear dynamics of flapping wings

This is a collaborative study being carried out with Prof Sunetra Sarkar from Department of Aerospace Engineering and her group - The Biomimetics and Dynamics Laboratory.

The motivation of this study is on understanding the physics associated with futuristic biomimetic flapping devices. This study requires extensive computational modelling of the flow and the fluid-structure interaction effects and resolving the associated nonlinear dynamical behaviour and the routes to instability and chaos for both the flapping wing and the flow. Both computational as well as wind tunnel experiments are in progress to gain further insights into the behaviour of these systems.

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Non-smooth systems and noise

Dynamical systems with discontinuities in the time evolution of their state space trajectories - due to such phenomena as impact, friction or state dependent switches - are defined as non-smooth systems. The inherent nonlienar nature of such systems lead to phenomenologically rich dynamical behvaiour characterised by bifurcations and routes to chaos which could be significantly different from continuous nonlinear dynamical systems.  Additionally, we are investigating the effects of noise on the behaviour of such systems. These studies involve both computational as well as experimental investigations.

The motivation of our study in this field arise due to the need for investigating the mechanism of flapping wings which involve discontinuous nonlinearities, as well as the need for studying the behaviour of air heat exchangers for the nuclear industry. 

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Energy harvesting from flows

Complementary to our studies on flexible flapping wings, we have also initiated studies on possibilities of harvesting energy from flexible structures flapping in flows. This has led to a three way collaborative research with Prof Sunetra Sarkar, Department of Aerospace Engineering and Prof Shaikh Faruque Ali, Department of Applied Mechanics. This has led to a concept design of a vortex induced based wind energy harvester. Numerical investigations, as well as wind tunnel experiments, reveal that the dynamics of the flapper - made of smart materials - is governed by the spatio-temporal behaviour of the vortices impinging on it and plays a crucial role in the energy efficiency of the harvester. Investigations are currently in progress for understanding the flapper dynamics so that the efficiency of the harvester may be optimized.


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Stochastic reduced order modelling 

Computational studies on flexibile structure-fluid interaction problems require development of high fidelity numerical models for the structure (using finite elements) as well as for the fluid (using computational fluid dynamics) along with coupling interfaces. Thus, the weak form numerical models typically contain thousands of state variables arising from the discretization used in finite elements and computational fluid mechanics. The stochasticity in the system leads to additional unknowns in the system arising from the stochastic dimension of the problem.

In order to alleviate the computational costs associated with the numerical analysis, stochastic reduced order models are being developed that reduce the dimensionality of the problem in terms of the state variables as well as in the stochastic dimension without affecting the accuracy of the analysis. 

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Stochastic material modelling

The focus of this study is to develop stochastic models for predicting material behaviour and life estimation, with particular attention on predicting the first stage of crack initiation. Probabilistic random field models are being developed for the micro-structure heterogeneity. Next, the corresponding uncertainties will be propagated across multi-scales with an aim to predict the macro scale behaviour. Novel probabilistically equivalent models for the material are being developed that can be used to characterise the damage growth in a computationally efficient manner.

This study is being carried out in collaboration with Prof Ilaksh Adlakha, Department of Applied Mechanics, IIT Madras.

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Inverse problems: system identification

The problem of parameter identification from experimental measurement data is being carried out using theories of dynamic Bayesian techniques. Our studies in this field, which are both numerical as well as experimental, have led to the development of novel particle filtering techniques. The computational costs have been mitigated by transorming the filtering to a mathematical subspace through polynomial chaos expansions.  

The developments have been used for identifying the presence of fatigue cracks, their locations and size from vibration measurements. Recently, these techniques have been used for identifying extra-terrestrial terramechanical parameters from measurements obtained from rovers remotely.

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Crossing statistics & time variant reliability

Failures in structural systems could be (a) due to overloading (when the response exceeds specified safe levels), and (b) due to gradual material degradation (such as fatigue, creep etc). My interests encompasses both these failure modes.

Our studies focus on using non-Gaussian models for the loadings (wind and ocean waves) and developing analytical/numerical techniques using the theories of random vibrations and random processes that enable computing the crossing statistics of the filtered non-Gaussian processes. The crux in these studies lie in approximating the joint probability density function of the response and its instantaneous time derivative. These results have been used in estimating first passage statistics as well as the rain-flow fatigue damage rate in randomly excited systems such as offshore platforms subjected to stormy seas, vehicles travelling in rough roads and wind turbine blades.

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Stochastic finite element method

Structural reliability studies require development of frameworks that enable incoprorating the uncertainties in the loading and material properties into a finite element model and developing methodologies for their analyses. Current research efforts are in the development of efficient stochastic finite element methods. These studies are intensely analytical and/or computational.

Based on the requirements from the space industry and their need for building a reusable launch vehicle, we started working on uncertainty quantification in laminated composites taking into account the spatial variabilities. The salient features of this study include extensive experimental investigations for the first time to develop stochastic models for the spatial inhomogeneities, incorporating limited measurement data directly in the numerical model and a novel stochastic reduced order model. 

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We have developed spectral stochastic finite element based methods for estimating the residual life of pipelines in nuclear power plants against thermal creep, thermal fatigue and thermal creep-fatigue interaction effects as well.