Development of 4S BEPU Method and Application in CAP1400 Containment Response Analysis

Compared with conservation evaluation model, best estimate plus uncertainty (BEPU) method can obtain more realistic results and gain larger license margins with respect to the safety criteria. In view of this, a BEPU method named 4S (SNERDI Statistical Solution for Safety) has been developed, according to the basic principles of evaluation model development and assessment of RG 1.203. The characteristics of 4S method are as follows: The output uncertainty is quantified by using random sampling and propagation of input uncertainties. Global sensitivity analysis is used to support PIRT establishment. Uncertainties of model parameters are calibrated and validated by using separate effects tests considering measuring uncertainties. DAKOTA code is used for uncertainty and sensitivity analysis. An automatic BEPU analysis platform has been developed by coupling DAKOTA and different reactor safety analysis codes, and code calculations can be performed in parallel. BEPU analysis of mass and energy release and containment pressure response of CAP1400 under a postulated double-ended cold leg break loss of coolant accident (DECL LOCA) has been carried out by coupling DAKOTA, a mass and energy release analysis code and a containment analysis code. In total, 21 uncertain input parameters are considered. To make the results more stable, the sample size is 124 and the third highest peak pressure is used as the pressure upper bound (with 95%/95% probability/confidence) based on Wilks’ formula. The calculated results show that the peak pressure upper bound is obviously lower than the present conservation method used in license application, with more than 10% analysis margin. Influences of input parameter uncertainties on the containment peak pressure have been analyzed, according to the partial rank correlation coefficients calculated by DAKOTA. The results show that the input parameters mainly affecting the peak pressure are the containment condensation heat transfer multiplier, initial containment temperature, break resistance, decay heat, initial containment pressure, Core Makeup Tank (CMT) resistance multiplier and initial containment humidity.

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Linking biogeochemistry to hydro-geometrical variability in tidal estuaries: a generic modeling approach

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-12-6351-2015 ◽

2015 ◽

Vol 12 (7) ◽

pp. 6351-6435

Author(s):

C. Volta ◽

G. G. Laruelle ◽

S. Arndt ◽

P. Regnier

Keyword(s):

Sensitivity Analysis ◽

World Ocean ◽

Reaction Network ◽

Co2 Exchange ◽

Model Parameters ◽

Parameter Uncertainties ◽

Tidal Estuaries ◽

Biogeochemical Indicators ◽

C And N ◽

Co2 Sink

Abstract. This study applies the Carbon-Generic Estuary Model (C-GEM) modeling platform to simulate the estuarine biogeochemical dynamics – in particular the air-water CO2 exchange – in three idealized end-member systems covering the main features of tidal alluvial estuaries. C-GEM uses a generic biogeochemical reaction network and a unique set of model parameters extracted from a comprehensive literature survey to perform steady-state simulations representing average conditions for temperate estuaries worldwide. Climate and boundary conditions are extracted from published global databases (e.g. World Ocean Atlas, GLORICH) and catchment model outputs (GlobalNEWS2). The whole-system biogeochemical indicators Net Ecosystem Metabolism (NEM), C and N filtering capacities (FCTC and FCTN, respectively) and CO2 gas exchanges (FCO2) are calculated across the three end-member systems and are related to their main hydrodynamic and transport characteristics. A sensitivity analysis, which propagates the parameter uncertainties, is also carried out, followed by projections of changes in the biogeochemical indicators for the year 2050. Results show that the average C filtering capacities for baseline conditions are 40, 30 and 22% for the marine, mixed and riverine estuary, respectively. This translates into a first-order, global CO2 outgassing flux for tidal estuaries between 0.04 and 0.07 Pg C yr−1. N filtering capacities, calculated in similar fashion, range from 22% for the marine estuary to 18 and 15% for the mixed and the riverine estuary, respectively. Sensitivity analysis performed by varying the rate constants for aerobic degradation, denitrification and nitrification over the range of values reported in the literature significantly widens these ranges for both C and N. Simulations for the year 2050 indicate that all end-member estuaries will remain net heterotrophic and while the riverine and mixed systems will only marginally be affected by river load changes and increase in atmospheric pCO2, the marine estuary is likely to become a significant CO2 sink in its downstream section. In the decades to come, such change of behavior might strengthen the overall CO2 sink of the estuary-coastal ocean continuum.

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Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4041622 ◽

2019 ◽

Vol 14 (2) ◽

Cited By ~ 1

Author(s):

Souransu Nandi ◽

Tarunraj Singh

Keyword(s):

Sensitivity Analysis ◽

Linear Systems ◽

Global Sensitivity Analysis ◽

Benchmark Problems ◽

Model Parameters ◽

Parameter Uncertainties ◽

Sobol Indices ◽

Global Sensitivity ◽

Time Invariant ◽

The Impact

The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

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Global Sensitivity Analysis of Attenuation Zones of 2D Periodic Foundations

10.3233/atde210167 ◽

2021 ◽

Author(s):

Xinnan Liu ◽

Yuan Tian ◽

Yihe Wang ◽

Yiqiang Ren ◽

Xiaoruan Song

Keyword(s):

Sensitivity Analysis ◽

Lower Bound ◽

Initial Stress ◽

Upper Bound ◽

Filling Ratio ◽

Sensitivity Analyses ◽

Relative Importance ◽

Global Sensitivity ◽

Input Parameters ◽

Periodic Constant

In this paper, global sensitivity analyses of attenuation zones of 2D periodic foundations are conducted. Global sensitivity analyses of upper bound frequency and lower bound frequency of the 1st attenuation zone of 2D periodic foundation are conducted considering four input parameters, i.e., initial stress ratio, filling ratio of core, filling ratio of resonator and periodic constant. Interactions and relative importance of input parameters are calculated.

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Global sensitivity analysis of a pure steam dropwise condensation heat transfer model

Journal of Physics Conference Series ◽

10.1088/1742-6596/2116/1/012012 ◽

2021 ◽

Vol 2116 (1) ◽

pp. 012012

Author(s):

Jakob Sablowski ◽

Simon Unz ◽

Michael Beckmann

Keyword(s):

Heat Transfer ◽

Sensitivity Analysis ◽

High Sensitivity ◽

Nucleation Site ◽

Heat Transfer Model ◽

Model Parameters ◽

Transfer Model ◽

Dropwise Condensation ◽

Input Parameters ◽

Pure Steam

Abstract Established heat transfer models for dropwise condensation (DWC) consider wetting behavior, surface structure and nucleation dynamics to calculate the heat flux. However, model results often deviate from experiments, in part due to uncertainties of the model input parameters. In this study, we apply quantitative sensitivity analysis to a pure steam DWC heat transfer model in order to attribute the variation of the model result to its input parameters. Four scenarios with different variations of the model parameters are discussed and sensitivity coefficients for each parameter are calculated. Our results show a high sensitivity of the model result towards the coating thickness, the contact angle and the nucleation site density, underlining the need to accurately determine these parameters in DWC experiments.

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A meta-model assisted framework of optimization of the Hydrological model parameters for accurate calibration

10.5194/egusphere-egu2020-21083 ◽

2020 ◽

Author(s):

Ammara Nusrat ◽

Hamza Farooq Gabriel ◽

Sajjad Haider ◽

Muhammad Shahid

Keyword(s):

Sensitivity Analysis ◽

Parameter Optimization ◽

Hydrological Modeling ◽

Hydrological Model ◽

Flood Forecasting ◽

Large River ◽

Model Parameters ◽

Distributed Hydrological Model ◽

Dimensional Parameter ◽

Input Parameters

&#160;Increase in frequency of the floods is one of the noticeable climate change impacts. The efficient and optimized flood analysis system needs to be used for the reliable flood forecasting. The credibility and the reliability of the flood forecasting system is depending upon the framework used for its parameter optimization. Comprehensive framework has been presented to optimize the input parameters of the computationally extensive distributed hydrological model. A large river basin has the high spatio-temporal heterogeneity of aquifer and surface properties. &#160;Estimating the parameters in fully distributed hydrological model is a challenging task. The parameter optimization becomes computationally more demanding when the model input parameters (30 to 100 even greater) have multi-dimensional parameter space, many output parameters which make the optimization problem multi-objective and large number of model simulations requirement for the optimization. Aforementioned challenges are met by introducing the methodology to optimize the input parameters of fully distributed hydrological model, following steps are included (1) screening of the parameters through Morris sensitivity analysis method in different flow periods, so that optimization would be performed for sensitive parameters, different scalar output functions are used in this regard (2) to emulate the hydrologic response of the dynamic model, surrogate models or meta-models are used (3) sampling of parameters values using the optimized ranges obtained from the meta-models; the results are evident that the parameter optimization using the proposed framework is efficient can be effectively performed.&#160; The effectiveness and efficiency of the proposed framework has been demonstrated through the accurate calibration of the model with fewer model runs. This study also demonstrates the importance and use of scalar functions in calculating sensitivity indices, when the model output is temporally variable. In addition, the parameter optimization using the proposed framework is efficient and present study can be used as reference for optimization of distributed hydrological model.&#160;&#160;Keywords: Calibration, parameter ranking, Sensitivity analysis, Hydrological modeling, optimization

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Linking biogeochemistry to hydro-geometrical variability in tidal estuaries: a generic modeling approach

Hydrology and Earth System Sciences ◽

10.5194/hess-20-991-2016 ◽

2016 ◽

Vol 20 (3) ◽

pp. 991-1030 ◽

Cited By ~ 6

Author(s):

Chiara Volta ◽

Goulven Gildas Laruelle ◽

Sandra Arndt ◽

Pierre Regnier

Keyword(s):

Sensitivity Analysis ◽

World Ocean ◽

Reaction Network ◽

Co2 Exchange ◽

Model Parameters ◽

Parameter Uncertainties ◽

Tidal Estuaries ◽

Biogeochemical Indicators ◽

C And N ◽

Co2 Sink

Abstract. This study applies the Carbon-Generic Estuary Model (C-GEM) modeling platform to simulate the estuarine biogeochemical dynamics – in particular the air–water CO2 exchange – in three idealized tidal estuaries characterized by increasing riverine influence, from a so-called "marine estuary" to a "riverine estuary". An intermediate case called "mixed estuary" is also considered. C-GEM uses a generic biogeochemical reaction network and a unique set of model parameters extracted from a comprehensive literature survey to perform steady-state simulations representing average conditions for temperate estuaries worldwide. Climate and boundary conditions are extracted from published global databases (e.g., World Ocean Atlas, GLORICH) and catchment model outputs (GlobalNEWS2). The whole-system biogeochemical indicators net ecosystem metabolism (NEM), C and N filtering capacities (FCTC and FCTN, respectively) and CO2 gas exchanges (FCO2) are calculated across the three idealized systems and are related to their main hydrodynamic and transport characteristics. A sensitivity analysis, which propagates the parameter uncertainties, is also carried out, followed by projections of changes in the biogeochemical indicators for the year 2050. Results show that the average C filtering capacities for baseline conditions are 40, 30 and 22 % for the marine, mixed and riverine estuary, respectively, while N filtering capacities, calculated in a similar fashion, range from 22 % for the marine estuary to 18 and 15 % for the mixed and the riverine estuaries. Sensitivity analysis performed by varying the rate constants for aerobic degradation, denitrification and nitrification over the range of values reported in the literature significantly widens these ranges for both C and N. Simulations for the year 2050 suggest that all estuaries will remain largely heterotrophic, although a slight improvement of the estuarine trophic status is predicted. In addition, our results suggest that, while the riverine and mixed systems will only marginally be affected by an increase in atmospheric pCO2, the marine estuary is likely to become a significant CO2 sink in its downstream section. In the decades to come, such a change in behavior might strengthen the overall CO2 sink of the estuary–coastal ocean continuum.

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TOWARDS OVERCOMING THE CURSE OF DIMENSIONALITY IN PREDICTIVE MODELLING AND UNCERTAINTY QUANTIFICATION

EPJ Web of Conferences ◽

10.1051/epjconf/202124720005 ◽

2021 ◽

Vol 247 ◽

pp. 20005

Author(s):

Dan G. Cacuci

Keyword(s):

Sensitivity Analysis ◽

Uncertainty Quantification ◽

Predictive Modeling ◽

Curse Of Dimensionality ◽

Current Data ◽

Model Parameters ◽

Mathematical Framework ◽

Response Distribution ◽

Parameter Uncertainties ◽

Adjoint Sensitivity

This invited presentation summarizes new methodologies developed by the author for performing high-order sensitivity analysis, uncertainty quantification and predictive modeling. The presentation commences by summarizing the newly developed 3rd-Order Adjoint Sensitivity Analysis Methodology (3rd-ASAM) for linear systems, which overcomes the “curse of dimensionality” for sensitivity analysis and uncertainty quantification of a large variety of model responses of interest in reactor physics systems. The use of the exact expressions of the 2nd-, and 3rd-order sensitivities computed using the 3rd-ASAM is subsequently illustrated by presenting 3rd-order formulas for the first three cumulants of the response distribution, for quantifying response uncertainties (covariance, skewness) stemming from model parameter uncertainties. The use of the 1st-, 2nd-, and 3rd-order sensitivities together with the formulas for the first three cumulants of the response distribution are subsequently used in the newly developed 2nd/3rd-BERRU-PM (“Second/Third-Order Best-Estimated Results with Reduced Uncertainties Predictive Modeling”), which aims at overcoming the curse of dimensionality in predictive modeling. The 2nd/3rd-BERRU-PM uses the maximum entropy principle to eliminate the need for introducing a subjective user-defined “cost functional quantifying the discrepancies between measurements and computations.” By utilizing the 1st-, 2nd- and 3rd-order response sensitivities to combine experimental and computational information in the joint phase-space of responses and model parameters, the 2nd/3rd-BERRU-PM generalizes the current data adjustment/assimilation methodologies. Even though all of the 2nd- and 3rd-order are comprised in the mathematical framework of the 2nd/3rd-BERRU-PM formalism, the computations underlying the 2nd/3rd-BERRU-PM require the inversion of a single matrix of dimensions equal to the number of considered responses, thus overcoming the curse of dimensionality which would affect the inversion of hessian and higher-order matrices in the parameter space.

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TOWARDS OVERCOMING THE CURSE OF DIMENSIONALITY IN PREDICTIVE MODELLING AND UNCERTAINTY QUANTIFICATION

EPJ Web of Conferences ◽

10.1051/epjconf/202124700002 ◽

2021 ◽

Vol 247 ◽

pp. 00002

Author(s):

Dan G. Cacuci

Keyword(s):

Sensitivity Analysis ◽

Uncertainty Quantification ◽

Predictive Modeling ◽

Curse Of Dimensionality ◽

Current Data ◽

Model Parameters ◽

Mathematical Framework ◽

Response Distribution ◽

Parameter Uncertainties ◽

Adjoint Sensitivity

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A Sensitivity Analysis of the SPACSYS Model

Agriculture ◽

10.3390/agriculture11070624 ◽

2021 ◽

Vol 11 (7) ◽

pp. 624

Author(s):

Yan Shan ◽

Mingbin Huang ◽

Paul Harris ◽

Lianhai Wu

Keyword(s):

Sensitivity Analysis ◽

Wheat Yield ◽

Climatic Conditions ◽

Water Dynamics ◽

Ecological Modelling ◽

Soil Conditions ◽

Model Parameters ◽

Nutrient Inputs ◽

Nutrient Pool ◽

Wheat Field

A sensitivity analysis is critical for determining the relative importance of model parameters to their influence on the simulated outputs from a process-based model. In this study, a sensitivity analysis for the SPACSYS model, first published in Ecological Modelling (Wu, et al., 2007), was conducted with respect to changes in 61 input parameters and their influence on 27 output variables. Parameter sensitivity was conducted in a ‘one at a time’ manner and objectively assessed through a single statistical diagnostic (normalized root mean square deviation) which ranked parameters according to their influence of each output variable in turn. A winter wheat field experiment provided the case study data. Two sets of weather elements to represent different climatic conditions and four different soil types were specified, where results indicated little influence on these specifications for the identification of the most sensitive parameters. Soil conditions and management were found to affect the ranking of parameter sensitivities more strongly than weather conditions for the selected outputs. Parameters related to drainage were strongly influential for simulations of soil water dynamics, yield and biomass of wheat, runoff, and leaching from soil during individual and consecutive growing years. Wheat yield and biomass simulations were sensitive to the ‘ammonium immobilised fraction’ parameter that related to soil mineralization and immobilisation. Simulations of CO2 release from the soil and soil nutrient pool changes were most sensitive to external nutrient inputs and the process of denitrification, mineralization, and decomposition. This study provides important evidence of which SPACSYS parameters require the most care in their specification. Moving forward, this evidence can help direct efficient sampling and lab analyses for increased accuracy of such parameters. Results provide a useful reference for model users on which parameters are most influential for different simulation goals, which in turn provides better informed decision making for farmers and government policy alike.

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Global Sensitivity Analysis of a Homogenized Constrained Mixture Model of Arterial Growth and Remodeling

Journal of Elasticity ◽

10.1007/s10659-021-09833-9 ◽

2021 ◽

Author(s):

Sebastian Brandstaeter ◽

Sebastian L. Fuchs ◽

Jonas Biehler ◽

Roland C. Aydin ◽

Wolfgang A. Wall ◽

...

Keyword(s):

Sensitivity Analysis ◽

Global Sensitivity Analysis ◽

Model Parameters ◽

Computational Studies ◽

Growth And Remodeling ◽

Global Sensitivity ◽

Output Variability ◽

Constrained Mixture ◽

The One ◽

Influential Parameters

AbstractGrowth and remodeling in arterial tissue have attracted considerable attention over the last decade. Mathematical models have been proposed, and computational studies with these have helped to understand the role of the different model parameters. So far it remains, however, poorly understood how much of the model output variability can be attributed to the individual input parameters and their interactions. To clarify this, we propose herein a global sensitivity analysis, based on Sobol indices, for a homogenized constrained mixture model of aortic growth and remodeling. In two representative examples, we found that 54–80% of the long term output variability resulted from only three model parameters. In our study, the two most influential parameters were the one characterizing the ability of the tissue to increase collagen production under increased stress and the one characterizing the collagen half-life time. The third most influential parameter was the one characterizing the strain-stiffening of collagen under large deformation. Our results suggest that in future computational studies it may - at least in scenarios similar to the ones studied herein - suffice to use population average values for the other parameters. Moreover, our results suggest that developing methods to measure the said three most influential parameters may be an important step towards reliable patient-specific predictions of the enlargement of abdominal aortic aneurysms in clinical practice.

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