Hybrid Representations of Coupled Nonparametric and Parametric Models for Dynamic Systems

Ghanem, Roger; Das, Sonjoy

doi:10.2514/1.39591

Cited by 12 publications

(8 citation statements)

References 30 publications

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“…Such a positive-definite and bounded random matrix is naturally encountered in determining the effective material property of a heterogeneous material. In contrast to the parametric model where a form of the governing equations are pre-selected, the nonparametric models [2,3] relax the structure of the governing equations to a certain extent and rely directly on some mathematical representation of available information to yield a well-posed mathematical problem. Specifically, in the context of our work, the nonparametric notion of C eff stems from the fact that the entire matrix, C eff , is simultaneously characterized by the nonparametric model.…”

Section: Introductionmentioning

confidence: 99%

A Bounded Random Matrix Approach for Stochastic Upscaling

Das¹,

Ghanem²

2009

Multiscale Model. Simul.

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A maximum entropy (MaxEnt) based probabilistic approach is developed to model mechanical systems characterized by symmetric positive-definite matrices bounded from below and above. These matrices are typically encountered in the constitutive modeling of heterogeneous materials, where the bounds are deduced by employing the principles of minimum complementary energy and minimum potential energy. Current random matrix based nonparametric approach is only adapted to the Wishart or matrix-variate Gamma probability model supported over the entire space of the symmetric positive-definite matrices, and therefore, unable to exploit additional information available through the lower and upper bounds when appropriate. Specifically, for a given material, the constitutive matrix is construed as a random matrix. A probability measure that reflects the constraints consistent with the energybased bounds, together with an associated sampling scheme, are constructed to synthesize realizations of this random matrix. An additional constraint of the ensemble mean matrix is also considered, and an appropriate probability model and sampling scheme are developed and illustrated numerically for this case.

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Section: Introductionmentioning

confidence: 99%

A Bounded Random Matrix Approach for Stochastic Upscaling

Das¹,

Ghanem²

2009

Multiscale Model. Simul.

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“…For example, the sample of the mass matrix may be not positive definite. Furthermore, samples in RM-based analysis are drawn from well-known Wishart distribution for which efficient and accurate sampling algorithms have been developed (see for example [12]). MATLAB also provides the built-in function wishrnd for sampling from Wishart distribution.…”

Section: Simulations and Resultsmentioning

confidence: 99%

“…Then, using the constructed probability model, samples of the perturbation matrices are drawn from optimal Wishart distribution using Eq. (12) and (14). Substituting the samples in Eq.…”

Section: B MC Simulations 1) Rv-based Mc Analysismentioning

confidence: 96%

“…In fact, maximizing the entropy measure of uncertainty helps to pick from amongst the set of all admissible density functions (that satisfy the prior information and constraints). This method has been frequently used to obtain the density function of the systems random variables e.g., Soize [6], [7], [10], Adhikari [11] and Ghanem and Das [12] used the maximum entropy method to derive the probability model of the structural system matrices (mass, damping, stiffness and frequency response function matrices). Das and Ghanem [13], [14] further addressed this problem by incorporating additional upper and lower bound constraints on the system matrices.…”

Section: Random Matrix Formulationmentioning

confidence: 99%

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Random matrix based uncertainty model for complex robotic systems

Sovizi

Alamdari

Das

et al. 2014

2014 IEEE International Conference on Robotics and Automation (ICRA)

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In this paper, we generalize our random matrix based (RM-based) uncertainty model for manipulator Jacobian matrix to the dynamic model of the robotic systems. Conventional random variable based (RV-based) schemes require a detailed knowledge of the system parameters variation and may be not able to fully characterize the uncertainties of the complex dynamic systems. However, the proposed RM-based approach provides a probabilistic framework for systematic characterization of the uncertainties in the complex systems with limited available information. Moreover, RM-based uncertainty model is an efficient mathematical tool that ensures the kinematic and dynamic consistency and takes into account the system complexity, configuration, structural inter-dependencies, etc. The application of the RM-based uncertainty model is investigated using an example of kinematically redundant planar parallel manipulator (3-(P)RRR). The simulation results are compared with those obtained through conventional RV-based approach and the effectiveness of the proposed method is discussed.

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“…[26][27][28][29][30][31][32][33][34][35] The resulting probability models are capable of accounting for the effects of modeling uncertainties associated with the meso-scopic material heterogeneities. 34,35 Off late, micro-damage analysis based on macroscale response has drawn the attention of researchers in the field of structural health monitoring.…”

Section: Introductionmentioning

confidence: 99%