The generalized empirical interpolation method (GEIM) can be used to estimate the physical field by combining observation data acquired from the physical system itself and a reduced model of the underlying physical sy...
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The generalized empirical interpolation method (GEIM) can be used to estimate the physical field by combining observation data acquired from the physical system itself and a reduced model of the underlying physical system. In presence of observation noise, the estimation error of the GEIM is blurred even diverged. We propose to address this issue by imposing a smooth constraint, namely, to constrain the H-1 semi-norm of the reconstructed field of the reduced model. The efficiency of the approach, which we will call the H-1 regularization GEIM (R-GEIM), is illustrated by numerical experiments of a typical IAEA benchmark problem in nuclear reactor physics. A theoretical analysis of the proposed R-GEIM will be presented in future works.
In this paper, we apply the so-called generalized empirical interpolation method (GEIM) to address the problem of sensor placement in nuclear reactors. This task is challenging due to the accumulation of a number of d...
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In this paper, we apply the so-called generalized empirical interpolation method (GEIM) to address the problem of sensor placement in nuclear reactors. This task is challenging due to the accumulation of a number of difficulties like the complexity of the underlying physics and the constraints in the admissible sensor locations and their number. As a result, the placement, still today, strongly relies on the know-how and experience of engineers from different areas of expertise. The present methodology contributes to making this process become more systematic and, in turn, simplify and accelerate the procedure. (c) 2018 Elsevier Inc. All rights reserved.
Sensor positioning and real-time estimation of non -observable fields is an open question in the nuclear sector, especially for advanced nuclear reactors. In Circulating Fuel Reactors (CFR), liquid fuel and coolant ar...
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Sensor positioning and real-time estimation of non -observable fields is an open question in the nuclear sector, especially for advanced nuclear reactors. In Circulating Fuel Reactors (CFR), liquid fuel and coolant are homogeneously mixed, and thus these reactors will not have internal structures, making sensor positioning in the primary circuit, including the core, an unresolved problem, making most of the core blind to sensors. Thus, the possibility of estimating the system state in the whole domain using a few local measurements has important implications for safety, monitoring, and control both in nominal and accidental conditions. In this context, the integrated Model Order Reduction and Data Assimilation framework offers intriguing opportunities to reliably combine experimental data and background knowledge from a reduced mathematical model. This work discusses and applies innovative methods within this framework, based on the generalizedempiricalinterpolation and the Indirect Reconstruction algorithms, to a proposed concept of CFR. This work aims to identify the optimal sensor positioning within the core and assess the feasibility of reconstructing the quantities of interest starting only from transient sparse data on fuel temperature, possibly noisy, and testing the predictive capabilities of the discussed methods.
The need for accelerating the repeated solving of certain parametrized systems motivates the development of more efficient reduced order methods. The classical reduced basis method is popular due to an offline-online ...
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The need for accelerating the repeated solving of certain parametrized systems motivates the development of more efficient reduced order methods. The classical reduced basis method is popular due to an offline-online decomposition and a mathematically rigorous a posterior error estimator which guides a greedy algorithm offline. For nonlinear and nonaffine problems, hyper reduction techniques have been introduced to make this decomposition efficient. However, they may be tricky to implement and often degrade the offline and online computational efficiency. To avoid this degradation, reduced residual reduced over-collocation (R2-ROC) was invented. It integrates the empiricalinterpolation techniques on the solution snapshots and the well-chosen residuals, the collocation philosophy, and the simplicity of evaluating the hyper-reduced well-chosen residuals. In this paper, we introduce an adaptive enrichment strategy for R2-ROC rendering it capable of handling parametric fluid flow problems. Built on top of an underlying Marker and Cell (MAC) scheme, a novel hyper-reduced MAC scheme is therefore presented and tested on lid-driven cavity and flow past a backward -facing step problems demonstrating its high efficiency, stability and accuracy. (C) 2022 Elsevier Inc. All rights reserved.
The need for multiple interactive, real-time simulations using different parameter values has driven the design of fast numerical algorithms with certifiable accuracies. The reduced basis method (RBM) presents itself ...
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The need for multiple interactive, real-time simulations using different parameter values has driven the design of fast numerical algorithms with certifiable accuracies. The reduced basis method (RBM) presents itself as such an option. RBM features a mathematically rigorous error estimator which drives the construction of a low-dimensional subspace. A surrogate solution is then sought in this low-dimensional space approximating the parameter-induced high fidelity solution manifold. However when the system is nonlinear or its parameter dependence nonaffine, this efficiency gain degrades tremendously, an inherent drawback of the application of the empiricalinterpolationmethod (EIM). In this paper, we augment and extend the EIM approach as a direct solver, as opposed to an assistant, for solving nonlinear partial differential equations on the reduced level. The resulting method, called Reduced Over-Collocation method (ROC), is stable and capable of avoiding the efficiency degradation. Two critical ingredients of the scheme are collocation at about twice as many locations as the number of basis elements for the reduced approximation space, and an efficient error indicator for the strategic building of the reduced solution space. The latter, the main contribution of this paper, results from an adaptive hyper reduction of the residuals for the reduced solution. Together, these two ingredients render the proposed R2-ROC scheme both offline- and online-efficient. A distinctive feature is that the efficiency degradation appearing in traditional RBM approaches that utilize EIM for nonlinear and nonaffine problems is circumvented, both in the offline and online stages. Numerical tests on different families of time-dependent and steady-state nonlinear problems demonstrate the high efficiency and accuracy of our R2-ROC and its superior stability performance. (C) 2021 Elsevier Inc. All rights reserved.
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