Advances in Bayesian Probabilistic Modeling for Industrial Applications

Ghosh, Sayan; Pandita, Piyush; Atkinson, Steven; Subber, Waad; Zhang, Yiming; Kumar, Navneet; Chakrabarti, Saswat; Wang, Liping

doi:10.1115/1.4046747

Cited by 25 publications

(15 citation statements)

References 18 publications

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“…Recently, Gastaldi et al [17] experimentally investigated the effect of surface finish on the function of underplatform dampers, showing a large impact of the contact interface conditions on the dynamic response. Comparisons between measured data and predictions from nonlinear models also showed the uncertainty in the dynamic performance of underplatform dampers due to the contact interface [31][32][33]. These different works demonstrate the high influence of friction contact uncertainties from the contact interface on the dynamic response of structures with friction, and highlight the necessity to take them into consideration.…”

Section: Introductionmentioning

confidence: 85%

Propagation of friction parameter uncertainties in the nonlinear dynamic response of turbine blades with underplatform dampers

Yuan

Fantetti

Denimal

et al. 2021

Mechanical Systems and Signal Processing

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Underplatform dampers are widely used in turbomachinery to mitigate structural vibrations by means of friction dissipation at the interfaces. The modelling of such friction dissipation is challenging because of the high variability observed in experimental measurements of contact parameters. Although this variability is not commonly accounted for in state-of-the-art numerical solvers, probabilistic approaches can be implemented to include it in dynamics simulations in order to significantly improve the estimation of the damper performance. The aim of this work is to obtain uncertainty bands in the dynamic response of turbine blades equipped with dampers by including the variability observed in interfacial contact parameters. This variability is experimentally quantified from a friction rig and used to generate uncertainty bands by combining a deterministic state-of-the-art numerical solver with stochastic Polynomial Chaos Expansion (PCE) models. The bands thus obtained are validated against experimental data from an underplatform damper test rig. In addition, the PCEs are also employed to perform a variance-based global sensitivity analysis to quantify the influence of contact parameters on the variation in the nonlinear dynamic response via Sobol indices. The analysis highlights that the influence of each contact parameter in vibration amplitude strongly varies over the frequency range, and that Sobol indices can be effectively used to analyse uncertainties associated to structures with friction interfaces providing valuable insights into the physics of such complex nonlinear systems.

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Section: Introductionmentioning

confidence: 85%

Propagation of friction parameter uncertainties in the nonlinear dynamic response of turbine blades with underplatform dampers

Yuan

Fantetti

Denimal

et al. 2021

Mechanical Systems and Signal Processing

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“…In the forward modeling step, a probabilistic multi-fidelity Gaussian Process (MFGP) regression model for the expensive experiments is constructed using the GE Bayesian Hybrid Modeling (GEBHM) [24,25]. To reduce the cost associated with the design of the computer experiments [26,27,28,29,30] required by the GEBHM, a multi-fidelity adaptive sampling [26] is used to adaptively determine the experiment and level of fidelity that are needed to enhance the performance.…”

Section: Pmi Frameworkmentioning

confidence: 99%

“…al. [24] for more details, which is a fully Bayesian approach to estimates the posterior distribution of the parameters based on the observed data and prior distribution.…”

Section: Multi-fidelity Gaussian Process (Mfgp)mentioning

confidence: 99%

“…With the goal of achieving less than 10% of nRMSE, a total of 249 low-fidelity and 231 high-fidelity CFD simulation were required. The parameters of MFGP are estimated using MCMC [24], which is a fully Bayesian approach to estimates the posterior distribution of the parameters based on the observed data and prior distribution. Therefore, it quantifies the uncertainty on the MFGP parameters associated with the sparse data and performs robustly in terms of predictive capability.…”

Section: Forward Modelingmentioning

confidence: 99%

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Inverse Aerodynamic Design of Gas Turbine Blades using Probabilistic Machine Learning

Ghosh¹,

Padmanabha²,

Cheng³

et al. 2021

Preprint

Self Cite

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One of the critical components in Industrial Gas Turbines (IGT) is the turbine blade. Design of turbine blades needs to consider multiple aspects like aerodynamic efficiency, durability, safety and manufacturing, which make the design process sequential and iterative. The sequential nature of these iterations forces a long design cycle time, ranging from several months to years. Due to the reactionary nature of these iterations, little effort has been made to accumulate data in a manner that allows for deep exploration and understanding of the total design space. This is exemplified in the process of designing the individual components of the IGT resulting in a potential unrealized efficiency. To overcome the aforementioned challenges, we demonstrate a probabilistic inverse design machine learning framework (PMI), to carry out an explicit inverse design. PMI calculates the design explicitly without excessive costly iteration and overcomes the challenges associated with ill-posed inverse problems. In this work, the framework will be demonstrated on inverse aerodynamic design of three-dimensional turbine blades.

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“…The Gaussian Process (GP) surrogate model is widely used for engineering problems as a cost-effective alternative to costly computer simulator [18]. In the authors' previous work [19], a fully-Bayesian industrial-level implementation for GP-based metamodeling and model calibration has been exhaustively covered. This implementation, called GE's Bayesian hybird modeling (GEBHM), has been rigorously tested and validated on numerous benchmark problems and the impact of using Bayesian surrogate modeling has been demonstrated on several challenging industrial problems.…”

Section: Surrogate Modelingmentioning

confidence: 99%

Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

Subber¹,

Ghosh²,

Pandita³

et al. 2020

Preprint

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Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem

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Advances in Bayesian Probabilistic Modeling for Industrial Applications

Cited by 25 publications

References 18 publications

Propagation of friction parameter uncertainties in the nonlinear dynamic response of turbine blades with underplatform dampers

Propagation of friction parameter uncertainties in the nonlinear dynamic response of turbine blades with underplatform dampers

Inverse Aerodynamic Design of Gas Turbine Blades using Probabilistic Machine Learning

Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

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