Performance Assessment of a Naca-2412 Surrogate Model Using Non-Intrusive Polynomial Chaos Method

2021 ◽  
Author(s):  
Fayssal Fayssal ◽  
Houssam El Dine Matbouli
Keyword(s):  
Performance Assessment ◽  
Surrogate Model ◽  
Polynomial Chaos

System Uncertainty Effects on the Wave Frequency Response Of Floating Vessels Based on Polynomial Chaos Expansion

2021 ◽  
Author(s):  
Gowtham Radhakrishnan ◽  
Xu Han ◽  
Svein Sævik ◽  
Zhen Gao ◽  
Bernt Johan Leira
Keyword(s):  
Sensitivity Analysis ◽  
Surrogate Model ◽  
Polynomial Chaos ◽  
Response Spectrum ◽  
Uncertainty Propagation ◽  
Wave Spectrum ◽  
Frequency Domain Analysis ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Polynomial Coefficients

Abstract From a mathematical viewpoint, the frequency domain analysis of vessel motion responses due to wave actions incorporates the integration of system dynamics idealized in terms of response amplitude operators (RAOs) for 6 DOF rigid body motions and an input wave spectrum to yield the response spectrum. Various quantities of interest can be deduced from the response spectrum and further used for decision support in marine operations, extreme value and fatigue analysis. The variation of such quantities, owing to the uncertainties associated with the vessel system parameters, can be quantified by performing uncertainty propagation (UP) and consequent sensitivity analysis (SA). This study, emphasizes and proposes a computational-efficient way of assessing the sensitivity of the system model output with respect to the uncertainties residing in the input parameters by operating on a surrogate model representation. In this respect, the global sensitivity analysis is effectively carried out by deploying an efficient non-intrusive polynomial chaos expansion (PCE) surrogate model built using a point collocation strategy. Successively, the coherent and effective Sobol’ indices are obtained from the analytical decomposition of the polynomial coefficients. The indices, eventually, are employed to quantitatively gauge the effects of input uncertainties on the output 6 DOF vessel responses.

scholarly journals Towards predictive data-driven simulations of wildfire spread – Part I: Reduced-cost Ensemble Kalman Filter based on a Polynomial Chaos surrogate model for parameter estimation

2014 ◽  
Vol 14 (11) ◽  
pp. 2951-2973 ◽  
Author(s):  
M. C. Rochoux ◽  
S. Ricci ◽  
D. Lucor ◽  
B. Cuenot ◽  
A. Trouvé
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Surrogate Model ◽  
Polynomial Chaos ◽  
Computational Cost ◽  
Fire Spread ◽  
Data Driven ◽  
Fire Front ◽  
Wildfire Spread

Abstract. This paper is the first part in a series of two articles and presents a data-driven wildfire simulator for forecasting wildfire spread scenarios, at a reduced computational cost that is consistent with operational systems. The prototype simulator features the following components: an Eulerian front propagation solver FIREFLY that adopts a regional-scale modeling viewpoint, treats wildfires as surface propagating fronts, and uses a description of the local rate of fire spread (ROS) as a function of environmental conditions based on Rothermel's model; a series of airborne-like observations of the fire front positions; and a data assimilation (DA) algorithm based on an ensemble Kalman filter (EnKF) for parameter estimation. This stochastic algorithm partly accounts for the nonlinearities between the input parameters of the semi-empirical ROS model and the fire front position, and is sequentially applied to provide a spatially uniform correction to wind and biomass fuel parameters as observations become available. A wildfire spread simulator combined with an ensemble-based DA algorithm is therefore a promising approach to reduce uncertainties in the forecast position of the fire front and to introduce a paradigm-shift in the wildfire emergency response. In order to reduce the computational cost of the EnKF algorithm, a surrogate model based on a polynomial chaos (PC) expansion is used in place of the forward model FIREFLY in the resulting hybrid PC-EnKF algorithm. The performance of EnKF and PC-EnKF is assessed on synthetically generated simple configurations of fire spread to provide valuable information and insight on the benefits of the PC-EnKF approach, as well as on a controlled grassland fire experiment. The results indicate that the proposed PC-EnKF algorithm features similar performance to the standard EnKF algorithm, but at a much reduced computational cost. In particular, the re-analysis and forecast skills of DA strongly relate to the spatial and temporal variability of the errors in the ROS model parameters.

scholarly journals Bayesian inference of earthquake rupture models using polynomial chaos expansion

2018 ◽  
Vol 11 (7) ◽  
pp. 3071-3088 ◽  
Author(s):  
Hugo Cruz-Jiménez ◽  
Guotu Li ◽  
Paul Martin Mai ◽  
Ibrahim Hoteit ◽  
Omar M. Knio
Keyword(s):  
Bayesian Inference ◽  
Surrogate Model ◽  
Polynomial Chaos ◽  
Fault Plane ◽  
Dominant Role ◽  
Prediction Equation ◽  
Peak Ground Velocity ◽  
Earthquake Rupture ◽  
Physical Constraints ◽  
Rupture Model

Abstract. In this paper, we employed polynomial chaos (PC) expansions to understand earthquake rupture model responses to random fault plane properties. A sensitivity analysis based on our PC surrogate model suggests that the hypocenter location plays a dominant role in peak ground velocity (PGV) responses, while elliptical patch properties only show secondary impact. In addition, the PC surrogate model is utilized for Bayesian inference of the most likely underlying fault plane configuration in light of a set of PGV observations from a ground-motion prediction equation (GMPE). A restricted sampling approach is also developed to incorporate additional physical constraints on the fault plane configuration and to increase the sampling efficiency.

scholarly journals Uncertainty quantification for the Hokkaido Nansei-Oki tsunami using B-splines on adaptive sparse grids

2021 ◽  
Vol 62 ◽  
pp. C30-C44
Author(s):  
Michael Rehme ◽  
Stephen Roberts ◽  
Dirk Pflüger
Keyword(s):  
Uncertainty Quantification ◽  
Surrogate Model ◽  
Polynomial Chaos ◽  
Spline Interpolation ◽  
Sparse Grids ◽  
Stochastic Collocation ◽  
B Splines ◽  
Spatially Adaptive ◽  
Modeling Uncertainties ◽  
Run Up

Modeling uncertainties in the input parameters of computer simulations is an established way to account for inevitably limited knowledge. To overcome long run-times and high demand for computational resources, a surrogate model can replace the original simulation. We use spatially adaptive sparse grids for the creation of this surrogate model. Sparse grids are a discretization scheme designed to mitigate the curse of dimensionality, and spatial adaptivity further decreases the necessary number of expensive simulations. We combine this with B-spline basis functions which provide gradients and are exactly integrable. We demonstrate the capability of this uncertainty quantification approach for a simulation of the Hokkaido Nansei–Oki Tsunami with anuga. We develop a better understanding of the tsunami behavior by calculating key quantities such as mean, percentiles and maximum run-up. We compare our approach to the popular Dakota toolbox and reach slightly better results for all quantities of interest.  References B. M. Adams, M. S. Ebeida, et al. Dakota. Sandia Technical Report, SAND2014-4633, Version 6.11 User’s Manual, July 2014. 2019. https://dakota.sandia.gov/content/manuals. J. H. S. de Baar and S. G. Roberts. Multifidelity sparse-grid-based uncertainty quantification for the Hokkaido Nansei–Oki tsunami. Pure Appl. Geophys. 174 (2017), pp. 3107–3121. doi: 10.1007/s00024-017-1606-y. H.-J. Bungartz and M. Griebel. Sparse grids. Acta Numer. 13 (2004), pp. 147–269. doi: 10.1017/S0962492904000182. M. Eldred and J. Burkardt. Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification. 47th AIAA. 2009. doi: 10.2514/6.2009-976. K. Höllig and J. Hörner. Approximation and modeling with B-splines. Philadelphia: SIAM, 2013. doi: 10.1137/1.9781611972955. M. Matsuyama and H. Tanaka. An experimental study of the highest run-up height in the 1993 Hokkaido Nansei–Oki earthquake tsunami. National Tsunami Hazard Mitigation Program Review and International Tsunami Symposium (ITS). 2001. O. Nielsen, S. Roberts, D. Gray, A. McPherson, and A. Hitchman. Hydrodymamic modelling of coastal inundation. MODSIM 2005. 2005, pp. 518–523. https://www.mssanz.org.au/modsim05/papers/nielsen.pdf. J. Nocedal and S. J. Wright. Numerical optimization. Springer, 2006. doi: 10.1007/978-0-387-40065-5. D. Pflüger. Spatially Adaptive Sparse Grids for High-Dimensional Problems. Dr. rer. nat., Technische Universität München, Aug. 2010. https://www5.in.tum.de/pub/pflueger10spatially.pdf. M. F. Rehme, F. Franzelin, and D. Pflüger. B-splines on sparse grids for surrogates in uncertainty quantification. Reliab. Eng. Sys. Saf. 209 (2021), p. 107430. doi: 10.1016/j.ress.2021.107430. M. F. Rehme and D. Pflüger. Stochastic collocation with hierarchical extended B-splines on Sparse Grids. Approximation Theory XVI, AT 2019. Springer Proc. Math. Stats. Vol. 336. Springer, 2020. doi: 10.1007/978-3-030-57464-2_12. S Roberts, O. Nielsen, D. Gray, J. Sexton, and G. Davies. ANUGA. Geoscience Australia. 2015. doi: 10.13140/RG.2.2.12401.99686. I. J. Schoenberg and A. Whitney. On Pólya frequence functions. III. The positivity of translation determinants with an application to the interpolation problem by spline curves. Trans. Am. Math. Soc. 74.2 (1953), pp. 246–259. doi: 10.2307/1990881. W. Sickel and T. Ullrich. Spline interpolation on sparse grids. Appl. Anal. 90.3–4 (2011), pp. 337–383. doi: 10.1080/00036811.2010.495336. C. E. Synolakis, E. N. Bernard, V. V. Titov, U. Kânoğlu, and F. I. González. Standards, criteria, and procedures for NOAA evaluation of tsunami numerical models. NOAA/Pacific Marine Environmental Laboratory. 2007. https://nctr.pmel.noaa.gov/benchmark/. J. Valentin and D. Pflüger. Hierarchical gradient-based optimization with B-splines on sparse grids. Sparse Grids and Applications—Stuttgart 2014. Lecture Notes in Computational Science and Engineering. Vol. 109. Springer, 2016, pp. 315–336. doi: 10.1007/978-3-319-28262-6_13. D. Xiu and G. E. Karniadakis. The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24.2 (2002), pp. 619–644. doi: 10.1137/S1064827501387826.

scholarly journals Surrogate Model Development of Spent Fuel Degradation for Repository Performance Assessment.

2020 ◽  
Author(s):  
Paul Mariner ◽  
Timothy Berg ◽  
Kyung Chang ◽  
Bert Debusschere ◽  
Rosemary Leone ◽  
...  
Keyword(s):  
Performance Assessment ◽  
Surrogate Model ◽  
Model Development ◽  
Spent Fuel

Novel Performance-Oriented Tolerance Design Method Based on Locally Inferred Sensitivity Analysis and Improved Polynomial Chaos Expansion

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Guodong Sa ◽  
Zhenyu Liu ◽  
Chan Qiu ◽  
Xiang Peng ◽  
Jianrong Tan
Keyword(s):  
Sensitivity Analysis ◽  
Surrogate Model ◽  
Polynomial Chaos ◽  
Design Method ◽  
Polynomial Chaos Expansion ◽  
Product Performance ◽  
Tolerance Design ◽  
Chaos Expansion ◽  
Performance Requirements ◽  
Electromechanical Products

Abstract Tolerance design is becoming increasingly important for electromechanical products. Reasonable tolerance design can reduce production costs and improve product performance. However, as the complexity of the coupling of tolerances and performance increases, it becomes difficult for designers to establish accurate tolerance design models, leading to experience-based design. This study proposes a novel performance-oriented tolerance design method. First, the main tolerance variables affecting the product performance are rapidly determined based on the proposed locally inferred sensitivity analysis method. Then, based on the improved approximate polynomial chaos expansion, a surrogate model of the product performance and main tolerance variables is established. Finally, the geometric tolerances of the electromechanical products are optimized based on the surrogate model with performance requirements. The proposed tolerance design method is computationally efficient and accurate, and it can be implemented with a small number of samples. To demonstrate its performance, the proposed method is validated with a spaceborne active-phased array antenna. The optimal tolerance design of the antenna for the electrical performance requirements is performed successfully.

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