scholarly journals gPCE-Based Stochastic Inverse Methods: A Benchmark Study from a Civil Engineer’s Perspective

2021 ◽  
Vol 6 (11) ◽  
pp. 158
Author(s):  
Filippo Landi ◽  
Francesca Marsili ◽  
Noemi Friedman ◽  
Pietro Croce
Keyword(s):  
Structural Model ◽  
Polynomial Chaos ◽  
Minimum Mean Square Error ◽  
Polynomial Chaos Expansion ◽  
Inverse Methods ◽  
Complex Case ◽  
Fe Model ◽  
Chaos Expansion ◽  
One Dimensional ◽  
Uncertain Input

In civil and mechanical engineering, Bayesian inverse methods may serve to calibrate the uncertain input parameters of a structural model given the measurements of the outputs. Through such a Bayesian framework, a probabilistic description of parameters to be calibrated can be obtained; this approach is more informative than a deterministic local minimum point derived from a classical optimization problem. In addition, building a response surface surrogate model could allow one to overcome computational difficulties. Here, the general polynomial chaos expansion (gPCE) theory is adopted with this objective in mind. Owing to the fact that the ability of these methods to identify uncertain inputs depends on several factors linked to the model under investigation, as well as the experiment carried out, the understanding of results is not univocal, often leading to doubtful conclusions. In this paper, the performances and the limitations of three gPCE-based stochastic inverse methods are compared: the Markov Chain Monte Carlo (MCMC), the polynomial chaos expansion-based Kalman Filter (PCE-KF) and a method based on the minimum mean square error (MMSE). Each method is tested on a benchmark comprised of seven models: four analytical abstract models, a one-dimensional static model, a one-dimensional dynamic model and a finite element (FE) model. The benchmark allows the exploration of relevant aspects of problems usually encountered in civil, bridge and infrastructure engineering, highlighting how the degree of non-linearity of the model, the magnitude of the prior uncertainties, the number of random variables characterizing the model, the information content of measurements and the measurement error affect the performance of Bayesian updating. The intention of this paper is to highlight the capabilities and limitations of each method, as well as to promote their critical application to complex case studies in the wider field of smarter and more informed infrastructure systems.

Heat Transfer Modeling of Spent Nuclear Fuel Using Uncertainty Quantification and Polynomial Chaos Expansion

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Imane Khalil ◽  
Quinn Pratt ◽  
Harrison Schmachtenberger ◽  
Roger Ghanem
Keyword(s):  
Heat Transfer ◽  
Fuel Assembly ◽  
Uncertainty Quantification ◽  
Nuclear Fuel ◽  
Polynomial Chaos ◽  
Spent Nuclear Fuel ◽  
Polynomial Chaos Expansion ◽  
Complex Case ◽  
Chaos Expansion ◽  
Input Parameters

A novel method that incorporates uncertainty quantification (UQ) into numerical simulations of heat transfer for a 9 × 9 square array of spent nuclear fuel (SNF) assemblies in a boiling water reactor (BWR) is presented in this paper. The results predict the maximum mean temperature at the center of the 9 × 9 BWR fuel assembly to be 462 K using a range of fuel burn-up power. Current related modeling techniques used to predict the heat transfer and the maximum temperature inside SNF assemblies rely on commercial codes and address the uncertainty in the input parameters by running separate simulations for different input parameters. The utility of leveraging polynomial chaos expansion (PCE) to develop a surrogate model that permits the efficient evaluation of the distribution of temperature and heat transfer while accounting for all uncertain input parameters to the model is explored and validated for a complex case of heat transfer that could be substituted with other problems of intricacy. UQ computational methods generated results that are encompassing continuous ranges of variable parameters that also served to conduct sensitivity analysis on heat transfer simulations of SNF assemblies with respect to physically relevant parameters. A two-dimensional (2D) model is used to describe the physical processes within the fuel assembly, and a second-order PCE is used to characterize the dependence of center temperature on ten input parameters.

scholarly journals Generalized Polynomial Chaos Expansion for Fast and Accurate Uncertainty Quantification in Geomechanical Modelling

Algorithms ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 156
Author(s):  
Claudia Zoccarato ◽  
Laura Gazzola ◽  
Massimiliano Ferronato ◽  
Pietro Teatini
Keyword(s):  
Sensitivity Analysis ◽  
Data Assimilation ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Fe Model ◽  
Chaos Expansion ◽  
Generalized Polynomial Chaos ◽  
Hydrocarbon Reservoir ◽  
Generalized Polynomial ◽  
Major Interest

Geomechanical modelling of the processes associated to the exploitation of subsurface resources, such as land subsidence or triggered/induced seismicity, is a common practice of major interest. The prediction reliability depends on different sources of uncertainty, such as the parameterization of the constitutive model characterizing the deep rock behaviour. In this study, we focus on a Sobol’-based sensitivity analysis and uncertainty reduction via assimilation of land deformations. A synthetic test case application on a deep hydrocarbon reservoir is considered, where land settlements are predicted with the aid of a 3-D Finite Element (FE) model. Data assimilation is performed via the Ensemble Smoother (ES) technique and its variation in the form of Multiple Data Assimilation (ES-MDA). However, the ES convergence is guaranteed with a large number of Monte Carlo (MC) simulations, that may be computationally infeasible in large scale and complex systems. For this reason, a surrogate model based on the generalized Polynomial Chaos Expansion (gPCE) is proposed as an approximation of the forward problem. This approach allows to efficiently compute the Sobol’ indices for the sensitivity analysis and greatly reduce the computational cost of the original ES and MDA formulations, also enhancing the accuracy of the overall prediction process.

scholarly journals Deep Neural Network and Polynomial Chaos Expansion-Based Surrogate Models for Sensitivity and Uncertainty Propagation: An Application to a Rockfill Dam

Water ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 1830
Author(s):  
Gullnaz Shahzadi ◽  
Azzeddine Soulaïmani
Keyword(s):  
Polynomial Chaos ◽  
Complex Structure ◽  
Uncertainty Propagation ◽  
Surrogate Models ◽  
Polynomial Chaos Expansion ◽  
Soil Parameters ◽  
Chaos Expansion ◽  
Rockfill Dam ◽  
Parametric Studies ◽  
The Impact

Computational modeling plays a significant role in the design of rockfill dams. Various constitutive soil parameters are used to design such models, which often involve high uncertainties due to the complex structure of rockfill dams comprising various zones of different soil parameters. This study performs an uncertainty analysis and a global sensitivity analysis to assess the effect of constitutive soil parameters on the behavior of a rockfill dam. A Finite Element code (Plaxis) is utilized for the structure analysis. A database of the computed displacements at inclinometers installed in the dam is generated and compared to in situ measurements. Surrogate models are significant tools for approximating the relationship between input soil parameters and displacements and thereby reducing the computational costs of parametric studies. Polynomial chaos expansion and deep neural networks are used to build surrogate models to compute the Sobol indices required to identify the impact of soil parameters on dam behavior.

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