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The Uncertainty Laboratory

Location:  MSB 108
Mechanical Science Block
Department of Applied Mechanics
Indian Institute of Technology Madras

Email: uncertaintylab.iitm@gmail.com
Phone: +91 44 2257 5071

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Present Members

Postdocs

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Dr. Mahashweta Patra
PhD (IISER, Kolkata)

Smooth discontinuous maps


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PhD Students

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Aasifa Rounak
PhD Student 

Stochastic analysis of systems with discontinuous nonlinearities
Personal website

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Rahul Kumar
PhD Student

Stochastic reduced order modelling in mistuned rotors

Co-guide: Prof S Faruque Ali, Applied Mechanics

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Saranya Biswas
PhD Student

The effect of noise on the stability of nonlinear dynamical systems

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Vineeth Reddy
PhD Student (External)

Stochastic methods in modelling and predicting material behaviour and life estimation

Co-guide:  Prof Ilaksh Adlakha, Applied Mechanics

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Rajanya Chatterjee
PhD Student

Bladeless wind energy harvesters

Co-guide: Prof Sunetra Sarkar, Aerospace Engg

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Rahul Das
PhD Student

Targeted energy transfer in nonlinear dynamical systems

Co-guide: Prof Anil K Bajaj, Purdue University

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Dhrubajyoti Biswas
PhD Student (Physics)

Nonlinear dynamics of networks

Personal website
Co-guide: Prof Vaibhav Madhok, Physics

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Samana P
PhD Student

Dynamics of complex networked systems


Former Postdocs

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Jithin Jith
Post-doctoral Researcher (2018-2019)

Stochastic modelling of buffeting in fin structures

Placement: Schlumberger

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Dheelibun W Remigius
Post-doctoral Researcher (2018)

Intermittency in rotating discs in compresisble bounded fluid medium

Co-guide: Prof Sunetra Sarkar, Aerospace Engg

Placement Post-doctoral Researcher
Technical University of Denmark


Graduated PhD Students

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S Krishnakumar
PhD (2020)
Multiplicative noise induced intermittency in fluid-elastic dynamical systems

 This thesis studies the phenomenon of mul- tiplicative noise induced intermittency (mNII) arising due to the streamwise flow velocity fluctuations, which appear in the governing equations of motion as parametric or multi- plicative noise. The conditions for the onset and disappearance for mNII are developed analytically. The role of correlation in the flow fluctuations is investigated. The theoretical developments proposed in this thesis are investigated numerically through a set of progressively complex mathematical models. The importance of mNII is demonstrated through experimental investigations on a flow induced oscillations based energy harvester.
Publications

Post PhD: Post-doc at Center for Atmospheric Science, Indian Institute of Science Bangalore

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Chandan Bose
PhD (2019)
Dynamical analysis of unsteady flow phenomena around flapping wings 

The primary aim of this dissertation is to investigate the transitional wake dynamics and nonlinear fluid-structure interaction (FSI) behavior of flapping wings in low Reynolds number (Re) regime through high-fidelity numerical simulations. The study focusses on identifying the dynamical transition routes to chaos in the unsteady flow-field of rigid and flexible flapping wings and on examining the underlying flow-physics behind the chaotic transition.
Publications 

Co-guide:  Prof Sunetra Sarkar, Aerospace Engg
Post PhD: Post-doc at University of Leige, Belgium
Personal website
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Jithin Jith 
PhD (2018)
Acousto-elastic interactions in high pressure centrifugal compressors  Download

The study develops a computationally efficient numerical framework for accurate acousto-elastic eigenanalysis of high-pressure centrifugal compressors. CO2 is chosen as the working fluid because of its various applications in the oil and gas industry. Under high-pressure conditions, CO2 transitions into a supercritical fluid and brings about large changes in its thermophysical properties. The first part of the thesis studies the effect of these changes on the eigenfrequencies and eigenmodes of an idealised centrifugal compressor. Following this, the acousto-elastic computational framework is augmented to account for viscous and thermal dissipative phenomena  in the acoustic boundary layers of the working fluid. Conventional acousto- elastic analyses of centrifugal compressors do not consider the visco-thermal effects, and therefore fail to capture the impact of these losses on the frequency response of the compressor. A novel computationally efficient numerical framework, using the Boundary Layer Impedance (BLI) model, is proposed to account for the visco-thermal effects.
Publications

Co-guide: Prof Sunetra Sarkar, Aerospace Engg 

Post PhD: Schlumberger

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Hridya P
PhD (2018)
Reduced order modelling in stochastically parametered vibrating fluid structure interaction systems Download

 This study focuses on the development of reduced order models that enable enhancing the computational efficiency of the solution of stochastically parametered large ordered linear dynamical systems. The finite element (FE) discretized equations of motion are assumed to be the starting point of the analysis with the distributed parameter uncertainties being assumed to be represented in the weak form as a vector of random variables with specified probability density function (pdf). A two step procedure is adopted to develop the reduced order models for these systems. A reduction in the state space dimension is first achieved by adopting modal truncation along with the system equivalent reduction expansion process (SEREP). These developments are extended to the stochastic case by applying Polynomial Chaos Expansion (PCE) to bring about further reduction in the stochastic dimensions by retaining only the dominant stochastic modes in the basis space. The proposed developments enable building surrogate models for complex large ordered stochastically parametered fluid-structure interaction (FSI) systems which lead to accurate predictions at significantly reduced computational costs.
Publications

Co-guide: Prof Sunetra Sarkar, Aerospace Engg

Post PhD: Post doctoral researcher, Civil Engineering, Indian Institute of Science

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J Venkatramani
PhD (2018)
Intermittency in pitch-plunge aeroleastic systems Download

This thesis focuses on investigating the phenomenon of intermittency in the dynam- ical behavior of aeroelastic systems. Wind tunnel experiments on a NACA 0012 profile reveal the rpesence of fluctuations in the flow lead to an earlier onset of flutter. Stochastic bifurcation analysis is carried out to estimate the dynamical stability boundaries. The physical mechanisms for the intermittent oscillations that presage loss of stability have been investigated. A set of precursor measures based on recurrence quantification analysis, Hurst exponents, statsitical entropy and complexity based measures have been developed to predict the onset of flutter.
Publications

Co-guide: Prof Sunetra Sarkar, Aerospace Engineering

Post PhD: Assistant Professor, 
Mechanical Engg, Shiv Nadar University, Noida.
website

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Pankaj Kumar
PhD (2017) 
Investigations into the bifurcation of stochastically excited nonlinear oscillators  Download

The focus of the study undertaken in this dissertation has been on the development of numerical techniques for the dynamical stability analysis of nonlinear oscillators sub- jected to random excitations, and to gain an understanding on the dynamical behaviour of such systems at different parameter regimes. Essentially, the study builds on the established ideas of dynamic stability analysis of deterministic systems and extends these concepts in interpreting the behaviour of stochastically excited nonlinear oscillators. The crux in this approach lies in writing the corresponding Fokker-Planck (FP) equation for these nonlinear oscillators and developing numerical techniques for their solution. Inferences about the stochastic stability are made based on the topological changes in the structure of the joint probability density function (pdf) of the associated state variables, at different parameter regimes as well as the topological changes associated with the phase plane trajectories.  The use of various non-smooth coordinate transformations has been investigated for analysing problems involving discontinuities in the vector field, for developing the corresponding Fokker-Planck-Kolmogorov equations.
Publications

Co-guide: Prof S Narayanan, Mechanical Engg

Post PhD: Senior Scientist
Bharat Heavy Electrical Limited, India (External Registrant)

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Y Appalanaidu
PhD (2016)
Stochastic damage growth in circular pipes carruing high temperature fluids Download  thesis

The work reported in this thesis investigated the problem of predicting the damage growth in structural components in industrial installations that carry liquids at high tem- peratures, and estimating the risk of failure. The investigations were limited to the damage growth mechanisms due to thermal creep and fatigue only. The dmaage processes and the material properties were modelled as random inhomgeneities in space and time. Stochastic finite element frameworks have been used for developing a weak formulation of the problem. Probabilistic analsyes have been carried out to estimate the risk of failures in these components.
Publications

Post PhD: Associate Professor
Mechanical Engg, Vellore Institute of Technology
Website

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P Sasikumar
PhD (2015)
Uncertainty quantification and reliability analysis of laminated composite structures with spatial random inhomogeneities Download

 The work reported in this thesis is aimed towards the development of methodologies for quantification of the uncertainties associated with laminated CFRP composite struc- tures and estimating their failure probability. Most of the studies available in composite literature have focussed on developing models for the structural system that ignore the effects of spatial random inhomogeneities in the material properties. This is primarily due to the complexities involved in modelling the spatially random inhomogeneities in the material properties of composite structural systems and their subsequent analysis. The present study has focussed on the development of a stochastic finite element methodology that enables incorporating non-Gaussian models for the spatial random inhomogeneities in the material properties in laminated CFRP composites. 

Post PhD: Scientist
 Vikram Sarabhai Space Center
Trivandrum, India (External Registrant)


Graduated MS students

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Avisha Ghorpade
MS S

Stochastic Modelling and analysis of fin buffeting

This study aims to model buffeting in tail fin of delta-wing combat aircraft for estimation of premature failure due to fatigue damage. Buffeting occurs when the tail fin is subjected to irregular oscillations due to the flow from aircraft wings striking its surface. This phenomenon impacts the aerodynamic performance of the aircraft and may also affect the fatigue life of the fin. The separated flow from a delta wing is stochastic in nature and is known to be Gaussian. The present study quantifies the forces on the tail fin from CFD analyses with random boundary conditions and its response have been obtained from FE analyses. A solver that couples Navier-Stokes solver with Finite Element structural solver has been developed to find the response of the fin using a one-way fluid-structure interaction approach. Further, random vibration analysis was done to estimate the random stresses developed in the fin due to buffeting. The rainflow fatigue damage and the expected life of the fin were calculated based on analytico-computational algorithms. The predictions have been validated using Monte Carlo simulations. 

Co-guide:Prof Sunetra Sarkar, Aerospace Engg
Placement: Eaton

Short video

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N Ganesh
MS (2013)
A spectral approach to time variant reliability analysis of randomly excited nonlinear vibrating systems  Download

 The focus of this study is on the development of a methodology by which one can derive analytical/numerical approximations for the crossing statistics of the response of nonlinear structures subjected to random vibrations. This involves transforming the problem into a mathematical subspace spanned by the basis vectors obtained from the projections of the spectral content of the input process. The present study investigates the use of a special class of stochastic collocation technique- the sparse grid approach based on Smolyak’s algorithm, for computing these multi-dimensional inte- grals. The usefulness of this method lies in its computational efficiency in comparison to other existing techniques.

Placement: Design Engineer
 TVS Motors, Bangalore

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Rangaraj Pandurangan
MS (2013)
Polynomial chaos in bootstrap particle filtering for system identification  Downalod

This study focuses on the use of particle filters, more specifically the bootstrap particle filter, for identification of the system parameters of dynamical systems from measurement data. The underlying principle of the bootstrap particle filters is based on Bayesian framework. The implementation of the bootstrap particle filter involves solving the forward problem a large number of times using Monte Carlo simulations. This is computationally intensive, especially in dealing with com- plex systems where the solution of a single forward problem requires significant com- putational time. The present study focuses on the development of a new approach of coupling the bootstrap particle filter with Polynomial Chaos Expansion to reduce the computational effort. Polynomial Chaos based methods are spectral uncertainty quantification tools based on projecting the uncertain parameters along random basis functions, which are in the form of polynomials. The central idea of the proposed method lies in projecting the forward problem into a space spanned by orthogonal functions and performing filtering in this space. This ensures an accelerated solution of the forward problem, requiring significantly less computational efforts. Moreover, performing the filtering in the random space bypasses the requirement of constructing the polyno- mial chaos expansion at later time steps in the identification algorithm. This further reduces the required computational effort.

Co-guide: Prof Abhijit Chaudhuri, Applied Mechanics
Placement: General Electric, Bangalore.
Currently in Benz,  Bangalore

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Bharat Pokale
MS (2013)
An experimental study on system identification in beams for vibration measurements  Download

A particle filter based methodology is developed for damage identification from ambient vibration measurements obtained from physical experiments. The focus of the study has been primarily on identifying vibration induced fatigue cracks. To demonstrate the applicability of the proposed method, small scale laboratory experiments have been conducted and the time history of the response obtained from accelerometer readings has been assumed to be the inputs to the particle filter algorithm. It has been demon- strated that the method is useful not only for identifying the presence of damage but also for estimating the severity and the approximate location of what are essentially localized damages. 

Placement: Assistant Professor
Hindustan Univeristy, Chennai.

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R Rangaraj
MS (2012)
Identification of fatigue cracks in vibrating beams using particle filtering algorithm  Download

The focus of this study is on the development of a methodology for identifying fatigue cracks in beams from vibration measurements. This constitutes an inverse problem. A particle filter based methodology is developed to address the problem. This method is built on the principles of dynamic state estimating within a Bayesian frame work. The beam is modeled using finite elements with crack parameters to be identified be- ing modeled as random variables with assumed probability density function. As more measurements become available, the probability density functions of these variables are updated following Bayesian framework. Thus the variability associated with these variables decrease with time as more measurements are assimilated. This leads to iden- tification of the fatigue cracks with reasonable accuracy levels. The performance of the proposed method is demonstrated through numerical case studies.

Co-guide: Prof Anuradha Banerjee, Applied Mechanics

Placement: Senior Engineer
Asok Leyland Motors, Chennai. (External Registrant)


Graduated M.Tech/ Dual Degree Students

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Devarkonda Chandrasekhar Yashwant
M.Tech Student (2019) Applied Mechanics

Numerical investigations into fluid-structure interactions 

Placement: K12 Techno Service Private Limited, Bangalore


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Siddhesh Godbole
Dual Degree (2015): Civil & Applid Mechanics
Parallelization in uncertainty quantification analysis in large order dynamical systems  Download

Placement:  PhD Student,
University of Melbourne, Australia

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Vighnesh Ambetkar
Dual Degree (2015): Naval Architecture & Applied Mechanics
A saddlepoint approach to estimating crossing statistics for random processes Download

Placement:  Indian Register for Shipping
At present: DNV GL

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Jainendra Dubey
M.Tech (2015): Applied Mechanics
Interfacing comercial softwares for uncertainty quantification in fluid structure interaction problems

Placement: Scientist F,
Indira Gandhi Center for Atomic Research, Kalpakkam (External Registrant)

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Anindya Roy
M. Tech (2014): Applied Mechanics

Development of stochastic FEM based methodlogy for uncertainty quantification in structures with non-Gaussian inhomogenieties

Placement:  PhD Student,
Technical University of Delft, The Netherlands.

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T Sravan Kumar
Dual Degree (2014): Civil Engg & Applied Mechanics

Numerical studies on noisy Lorentz attractor

Placement:  Risk Analyst,
Nomura Services India Pvt Ltd

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Abhishek Ghiya
M. Tech (2013): Applied Mechanics

Energy harvesting from wind vibrations

Placement:  Scientist,
Defence Research Development Organization, Pune (External Registrant)

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Kaushik Mohan
Dual Degree (2013): Naval Architecture & Applied Mechanics

Multivariate extreme value distributions for vector LMA processes

Placement:  Deutsche Bank
Later: New York University

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Abhishek Venketesweran
Dual Degree (2013): Aerospace Engineering

Polynomial chaos in multiscale modelling of uncertainties in composite structures Download

Placement:  PhD Student,
State Univeristy of New York, Buffalo

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Jithin Jith
Dual Degree (2012): Naval Architecture & Applied Mechanics

Crossing statistics of second order response of structures subjected to LMA loadings Download

Placement: PhD Student, IIT Madras

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Yash Vyas
Dual Degree (2012): Civil Engg & Applied Mechanics

Modelling of uncertainties and analysis os stochastic damage growth in structural systems Download

Placement:  Wipro Technologies,
Financial and banking sector
Later: Stanford University

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Lokeshwar Rao M
M.Tech (2011): Applied Mechanics

Parameter estimation in vibrating structures using particle filtering algorithm

Placement: General Electric, Bangalore

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Radhika Nair
M.Tech  (2010): Applied Mechanics

Damage detection in aging vibrating structures using a probabilistic method.

Placement:  PhD Student, IISc Bangalore
At present: Faculty at LBS Institute of Technology for Women, Trivandrum

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Rajasekhar Reddy
Dual Degree (2009): Mechanical Engineering

Stochastic Hopf bifurcation of a 2-dimensional turbine blade in randomly fluctuating flow 

Placement:  Headstrong, Hyderabad
At present: HealthLucid, Bangalore

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Manoj Kattaminchi
M. Tech (2009): Applied Mechanics

Uncertainty quantification of natural frequencies of jointed segments of aerospace vehicles 

Placement:  Scientist,
Defence Research Development Organization, Hyderabad (External Registrant)

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Naajein Cherat
M. Tech (2009): Applied Mechanics

Stochastic fatigue crack growth in randomly vibrating structures

Placement:  General Electric, Bangalore


Former Students & Research Associates

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Ramakrishna Kuppa
2011-2019
Crossing statistics of non-Gaussian random processes
Affiliation: Sreenidhi Institute of Technology, Hyderabad (External Registrant)

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Bidhayak Goswami
2017-2018
Placement:
PhD Student, IIT Kanpur

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Indranil Hazra
2016-2017
Placement: PhD Student, University of Waterloo, Canada

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Sreelekha Etikyala
2015-2017
Placement: PhD Student, Chalmers University, Sweden

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V Srinivasan
2008-2010
Placement:  Eaton
At present: Aptiv Technical Center India