A Bayesian statistical method for quantifying model form uncertainty and two model combination methods

Park, Inseok; Grandhi, Ramana V.

doi:10.1016/j.ress.2014.04.023

Cited by 48 publications

(17 citation statements)

References 19 publications

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“…If Μ¼{M 1 ,…,M K } denotes the set of all models being considered and if δ is the quantity of interest, then the posterior distribution of δ given the data D is [39,54,44] Pr Δj D ð Þ¼…”

Section: Proposed Methodologymentioning

confidence: 99%

Predicting water main failures using Bayesian model averaging and survival modelling approach

Kabir

Tesfamariam

Sadiq

2015

Reliability Engineering & System Safety

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Section: Proposed Methodologymentioning

confidence: 99%

Predicting water main failures using Bayesian model averaging and survival modelling approach

Kabir

Tesfamariam

Sadiq

2015

Reliability Engineering & System Safety

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“…Free vibration and dynamic stability analysis of rotating thin-walled composite beams (Saraviaa et al, 2011) and nonlinear thermal stability of eccentrically stiffened functionally graded truncated conical shells are recently reported (Duc and Cong, 2015). In contrast, many numerical investigations are carried out using response surface methods such as moving least square (MLS) method and other methods for structural analysis (Choi et al, 2004;Wu et al, 2005;Park and Grandhi, 2014;Shu et al, 2007;Kang et al, 2010). Some researchers studied specifically on the moving least squares (MLS) approximation for the regression analysis (Lancaster and Salkauskas, 1981;Breitkpf et al, 2005) instead of the conventional least squares (LS) approximation in conjunction to traditional response surface method (RSM) techniques (Mukhopadhyay et al, 2015, Dey et al, 2015a.…”

Section: A N U S C R I P Tmentioning

confidence: 99%

Stochastic dynamic stability analysis of composite curved panels subjected to non-uniform partial edge loading

Dey

Mukhopadhyay

Sahu

et al. 2018

European Journal of Mechanics - A/Solids

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The stochastic dynamic stability analysis of laminated composite curved panels under nonuniform partial edge loading is studied using finite element analysis. The system input parameters are randomized to ascertain the stochastic first buckling load and zone of resonance. Considering the effects of transverse shear deformation and rotary inertia, first order shear deformation theory is used to model the composite doubly curved shells. The stochasticity is introduced in Love's and Donnell's theory considering dynamic and shear deformable theory according to the Sander's first approximation by tracers for doubly curved laminated shells. The moving least square method is employed as a surrogate of the actual finite element model to reduce the computational cost. The results are compared with those available in the literature. Statistical results are presented to show the effects of radius of curvatures, material properties, fibre parameters, and non-uniform load parameters on the stability boundaries.

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“…Therefore, the expected value of the adjusted model, E ln (y) , is calculated as shown in Eq. (16), as the sum of the natural logarithm of the prediction of the "best" model and the expected value of the multiplicative adjustment factor, E ln E * m , as shown in Eq. (14).…”

Section: American Institute Of Aeronautics and Astronauticsmentioning

confidence: 99%

Effectiveness of Different Model-Form Quantification Techniques as Applied to Thermal Physics-Based Simulations

Fischer

Deaton

Grandhi

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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In the past, the majority of work in the uncertainty quantification field has focused on parametric uncertainties inherent in design parameters within engineering problems. Current work has begun to incorporate model form uncertainties into the uncertainty quantification process. Model form uncertainty arises as a result of the uncertainty present in not knowing which model within a model set used to predict a system response is the best approximating model. Thus it becomes necessary to develop and utilize techniques for quantifying this uncertainty. This work presents a design scenario in which multiple models defining a single model set are used for predicting the same system response, and thus representing the presence of model form uncertainty. Four different model form uncertainty techniques are presented and applied to the model set consisting of three models, each used for predicting the transient temperature response at different locations within a corrugated-core sandwich panel used in thermal protection systems subject to thermal loading and boundary conditions to demonstrate the challenges inherent in each of the quantification techniques. The effectiveness of each technique is weighted against those of the other techniques. Nomenclaturê ε k = predictive uncertainty of model k (σ k ) 2 k = maximum likelihood estimator of variance x i = parameter set i ρ * = material density of homogenized section ρ i = material density of section i θ = angle between BFS and web f k = function of model k ε k,i = error between ith data point and prediction of model k A * = cross-sectional area of homogenized section A i = cross-sectional area of section i C * = material specific heat of homogenized section C i = material specific heat of section i D = experimental data d = distance from center BFS to center TFS E * a = additive adjustment factor E * m = multiplicative adjustment factor E * pa f a = probabilistic adjustment factor K = number of models in model set k = model index k i = material thermal conductivity of homogenized section k i = material thermal conductivity of section i M k = model k N = number of experimental data points p = length of 1/2 unit cell/length of symmetric portion of unit cell t b = thickness of bottom face sheet (BFS) section t t = thickness of top face sheet (TFS) section t w = thickness of web section

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A Bayesian statistical method for quantifying model form uncertainty and two model combination methods

Cited by 48 publications

References 19 publications

Predicting water main failures using Bayesian model averaging and survival modelling approach

Predicting water main failures using Bayesian model averaging and survival modelling approach

Stochastic dynamic stability analysis of composite curved panels subjected to non-uniform partial edge loading

Effectiveness of Different Model-Form Quantification Techniques as Applied to Thermal Physics-Based Simulations

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