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Shaikh Faruque Ali
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Shaikh Faruque Ali
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Shaikh Faruque Ali
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Faruque Ali, Shaikh
Ali, S. F.
Ali, S. Faruque
Ali, Shaikh Faruque
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9 results
Now showing 1 - 9 of 9
- PublicationUncertainty quantification of bladed disc systems using data driven stochastic reduced order models(15-01-2021)
;Kumar, Rahul; ;Jeyaraman, SankarkumarThis study focusses on the development of stochastic reduced order model for probabilistic characterisation of bladed disc systems with random spatial inhomogeneities. High fidelity finite element modelling is used to mathematically model the system. A two step reduction strategy is applied involving reduction in the state space dimension and reduction in the stochastic dimensions. Information of the spatial inhomogeneities are assumed to be available from limited in situ measurements across the spatial extent and are modelled as non-Gaussian random fields. The stochastic version of the finite element matrices are developed using a polynomial chaos based framework, which optimizes the stochastic dimensionality of the problem. The uncertainties in the input propagates through the system into the response, which are also random. Surrogate models for these response quantities are obtained as PCE and are constructed using the method of stochastic collocations. Challenges involved in application of PCE on complex geometrically irregular spatial domains are addressed. The efficacy of the proposed framework is demonstrated through two numerical examples -an academic bladed disc system and an industrial turbine rotor blade. - PublicationStochastic reduced order modelling and analysis of rotating bladed discs(01-01-2022)
;Kumar, Rahul; A computational finite-element (FE)-based technique is proposed for developing a stochastic reduced order model for rotating bladed disc with spatial random inhomogeneities. The spatial inhomogeneities imply the system to be randomly mistuned. The formulation assumes the availability of a high fidelity FE model for the tuned system. The corresponding FE matrices are antisymmetric on account of the Coriolis forces due to rotation. The spatial inhomogeneities, available from limited point measurements on the blades, are modelled as non-Gaussian random fields with arbitrary distributions. A low order stochastic computational model is developed by projecting the FE model onto a reduced dimensional state space defined in terms of specified observable nodal points and expressing the stochasticity through an arbitrary polynomial chaos (aPC) basis. This model enables probabilistic quantification of the variabilities in the system response and estimating failure probabilities. The methodology enables drastic reduction in the state space and stochastic dimensions, addresses the practical difficulties with having limited measurable data points, antisymmetric FE matrices, aPC representation in complex irregular geometries and carrying out probabilistic analyses on industrial systems, at significantly reduced computational costs. The methodology is illustrated through an academic rotor and an industrial rotor blade. - PublicationEnergy harvesting from chaos in base excited double pendulum(01-06-2019)
;Kumar, Rahul; This study focusses on exploiting the dynamics of a base excited double pendulum to generate electricity in small scale. The system consists of two pendulum attached in series with rigid massless links. The mass of the double pendulum is assumed to be concentrated at the bobs. A magnet is rigidly attached to the tip of second (lower) pendulum. A series of equally spaced coils are placed near the arc of the trajectory of the magnet. Small amplitude oscillations result in fluctuating magnetic field, generating electricity in the coils. The harvested power is significantly increased when the magnet undergoes chaotic motion. Parametric studies are carried out to optimize the system and excitation parameters that lead to enhancing the harvested energy. The proof-of-concept has been demonstrated through experiments. This involved recording the motion of the bobs, subsequent video processing, followed by time series analyses to establish the chaotic dynamics and correlating the dynamical behavior with the harvested energy. The experimental observations reveal good qualitative match with the numerical simulations. - PublicationAnalysis of Stepped Beam Using Reduced Order Models(01-01-2021)
;Kumar, Rahul; Damage detection in complicated engineering systems from vibration measurements typically involves the use of algorithms that are built on the principles of bayesian dynamic state estimation. These methods invariably required the solution of the forward problem a fairly large number of times. For complex engineering systems that are numerically modeled using Finite Element (FE), this can be computationally intensive especially when a single FE run for the problem takes a large time. To alleviate this problem, there is a need for the development of Reduced Order Models (ROMs) that significantly reduce the computational cost associated with solving the forward problem, for a given measure without sacrificing the accuracy. The present study discusses three ROM methods with specific reference to a simple problem. These methods include well-known Component Mode Synthesis (CMS) and System Equivalent Reduction Expansion Process (SEREP) which are applicable only for linear systems, as well as Principal Component Analysis (PCA)—the method which is more general and can be used for nonlinear systems as well. A comparison of the performance of all these methods is carried out for a stepped beam. The FE based results obtained from the full model is treated as the benchmark. - PublicationStatic condensation based reduced order modelling of stochastically parametered large ordered systems(01-10-2021)
;Kumar, Rahul; A surrogate stochastic reduced order model is developed for the analysis of randomly parametered structural systems with complex geometries. It is assumed that the mathematical model is available in terms of large ordered finite element (FE) matrices. The structure material properties are assumed to have spatial random inhomogeneities and are modelled as non-Gaussian random fields. A polynomial chaos expansion (PCE) based framework is developed for modelling the random fields directly from measurements and for uncertainty quantification of the response. Difficulties in implementing PCE due to geometrical complexities are circumvented by adopting PCE on a geometrically regular domain that bounds the physical domain and are shown to lead to mathematically equivalent representation. The static condensation technique is subsequently extended for stochastic cases based on PCE formalism to obtain reduced order stochastic FE models. The efficacy of the method is illustrated through two numerical examples. - PublicationSEREP integrated control of flexible structures(01-01-2020)
;Patel, Hiren ;Kumar, RahulFlexible structures are continuum modeled as infinite degrees of freedom. Most of the time finite element models are made with large number of degrees-of-freedom to analyse flexible structures. Continuous monitoring, analysis and control of dynamics of flexible structures need simulation of large degrees of freedom in real time. This is computationally expensive and realtime control fails. This study focuses on the development of a reduced order framework for dynamics of flexible structures and use the reduced order model for controlling the structure. Essentially, in the proposed framework, full order state space obtained from finite element modeling of the flexible structure has been reduced to lower subspace using a reduced order algorithm keeping the dynamical characteristic intact. The transformation matrix for reduction has been calculated using system equivalent reduction expansion process (SEREP). Traditionally, full order dynamical system is being used to find the gain matrix to suppress the uncontrolled dynamics associated with the dynamical system. Here in this methodology, the reduced dimension of state space of the system is used for estimating the gain matrix using optimal linear quadratic regulator (LQR). The gain obtained through the reduced system is subsequently used as a feedback to the attached actuators which produce the required force to control the system. A numerical example of a flexible cantilever beam has been shown to investigate the effectiveness of the algorithm. - PublicationROM integrated vibration control of stochastically parametered flexible structures(23-09-2020)
;Patel, Hiren ;Kumar, RahulThis study focusses on the vibration control of linear large scale engineering structures, modelled as continuous system, with varying system parameters. Because of manufacturing limitations or/and measurement errors, system parameters need to be modelled as random variables. Here, system parameters are modelled as non-Gaussian random variables. Mathematically, continuous system is governed by partial differential equations and solved using approximation methods. High fidelity finite element model is the starting point of the analysis. Since numerical approximation involves large number of degrees-of-freedom, solving the system in real time is computationally expensive and application of control algorithm is cumbersome. In this study, a reduced order model is developed to reduce the state space dimension of the problem and further integrated with the control algorithm. Next, controller gain is obtained using linear quadratic regulator in reduced subspace which is used as a feedback to the actuators to produce the required control force for vibration control. A numerical example of flexible cantilever beam is solved to demonstrate the efficacy of the algorithm and probabilistic characterisation is carried out using Monte Carlo simulation. - PublicationRandom field modeling and analysis of rotor bladed disc sector using a data driven PCE based approach(01-01-2019)
;Kumar, Rahul; Bladed disc systems, are designed to be rotationally periodic i.e. each sector repeats itself in an angular manner. This ensures that the response characteristics preserve this rotational periodicity and is defined as a tuned system. However, due to manufacturing limitations, there are invariably random spatial variations in the sectors which constitute the rotor. This in turn destroys the periodicity (angular symmetry) of the rotor. Such a system is defined as a mistuned system, leads to energy localization and makes the rotor susceptible to damage leading to a loss of its service life. This study focusses on developing a methodology for modeling the random spatial inhomogeneities and integrating with finite element analysis for estimating the behavior of a sector of a rotor blade assembly. Approximations for the non-Gaussian random fields for the spatial inhomogeneities are directly developed from the data set of measurements available from coordinate measuring machine (CMM). Subsequently, Rosenblatt’s transformations are applied to each component of the discrete measurement data set for polynomial chaos (PC) representation of the parameter to get the estimated probability density function (pdf). Spearman’s rank correlation coefficient (SRCC) is calculated to obtain the correlation parameter. Kullback – Liebler entropy (KLE) is used as a metric to compare the estimated pdf obtained through the PC representation of the measured data. The in-house PC based developed codes are subsequently integrated with commercially available finite element software which enable quantifying the propagation of the spatial random uncertainties into the response characteristics. Statistical processing of the response quantities is carried out to estimate probabilistic measures of the corresponding response quantities. - PublicationStochastic modelling and analysis of rotating bladed discs(01-01-2020)
;Kumar, Rahul; This study focusses on probabilistic modelling of the bladed disc system and numerical estimation of the distributions of the response quantities of the system. Stochastic finite element model of the system consisting of all the assemblies and the hub is developed and reported. The spatial inhomogeneity of mistuned structures is modelled as non-Gaussian random field. Experimentally, the system parameters can be measured at the specified locations of the bladed disk structure. In this analysis, a synthetic data is generated which represent this measured data set. Further, Nataf transformation is implemented to each component of the data set to get the polynomial chaos expansion framework of the system parameters. Since, the random field of the system parameter is approximated as correlated random variables, Spearman's rank correlation coefficient is used in this manuscript to obtain that correlation among the random parameters across the domain. The approximated probability density function obtained through the aforementioned methodology is compared with the target probability density function of the parameter using Kullback - Liebler (KL) entropy as a metric. Also, the same KL entropy is used as a metric to check the convergence of polynomial chaos terms in the expansion. Next, the proposed polynomial chaos method is integrated with commercial finite element software to quantify the propagation of randomness associated with system parameters into the response quantities. Subsequently, the statistical processing helps in estimating the probabilistic measure of the required response quantities. The results obtained through the conventional Monte Carlo (MC) simulations have been used as the benchmark to compare the response characteristics obtained through the proposed algorithm.