scholarly journals On the Role of Discretization Errors in the Quantification of Parameter Uncertainties

2020 ◽  
Author(s):  
Luís Eça ◽  
Filipe S. Pereira ◽  
Guilherme Vaz ◽  
Rui Lopes ◽  
Serge Toxopeus
Keyword(s):  
Finite Differences ◽  
Input Parameter ◽  
Parameter Uncertainties ◽  
Sensitivity Coefficients ◽  
Finite Difference Approximations ◽  
Monotonic Convergence ◽  
Power Series Expansions ◽  
Discretization Errors ◽  
Uncertain Input ◽  
Quantities Of Interest

Abstract The independence of numerical and parameter uncertainties is investigated for the flow around the KVLCC2 tanker at Re = 4.6 × 106 using the time-averaged RANS equations supplemented by the k–ω two-equation SST model. The uncertain input parameter is the inlet velocity that varies ±0.25% and ±0.50% for the determination of sensitivity coefficients using finite-difference approximations. The quantities of interest are the friction and pressure coefficients of the ship and the Cartesian velocity components and turbulence kinetic energy at the propeller plane. A grid refinement study is performed for the nominal conditions to allow the estimation of the discretization error with power series expansions. However, for grids between 6 × 106 and 47.6 × 106 cells, not all the selected quantities of interest exhibit monotonic convergence. Therefore, the estimates of the sensitivity coefficients of the selected quantities of interest using the local sensitivity method and finite-differences performed for refinement levels that correspond to 0.764 × 106, 6 × 106 and 47.6 × 106 cells lead to significantly different values. Nonetheless, for a given grid, negligible differences are obtained for the sensitivity coefficients obtained with two different intervals in the finite-differences approximation. Discrepancies between sensitivity coefficients are compared with the estimated numerical uncertainties. Results obtained in the study suggest that uncertainty quantification performed in coarse grids may be significantly affected by discretization errors.

Model assessment in scientific computing

2017 ◽  
Vol 34 (5) ◽  
pp. 1700-1723 ◽  
Author(s):  
Saurabh Prabhu ◽  
Sez Atamturktur ◽  
Scott Cogan
Keyword(s):  
Resource Allocation ◽  
Input Parameter ◽  
Error Tolerance ◽  
Model Parameters ◽  
Model Assessment ◽  
Parameter Uncertainties ◽  
Yield Model ◽  
Trade Off ◽  
Content Type ◽  
Uncertain Input

Purpose This paper aims to focus on the assessment of the ability of computer models with imperfect functional forms and uncertain input parameters to represent reality. Design/methodology/approach In this assessment, both the agreement between a model’s predictions and available experiments and the robustness of this agreement to uncertainty have been evaluated. The concept of satisfying boundaries to represent input parameter sets that yield model predictions with acceptable fidelity to observed experiments has been introduced. Findings Satisfying boundaries provide several useful indicators for model assessment, and when calculated for varying fidelity thresholds and input parameter uncertainties, reveal the trade-off between the robustness to uncertainty in model parameters, the threshold for satisfactory fidelity and the probability of satisfying the given fidelity threshold. Using a controlled case-study example, important modeling decisions such as acceptable level of uncertainty, fidelity requirements and resource allocation for additional experiments are shown. Originality/value Traditional methods of model assessment are solely based on fidelity to experiments, leading to a single parameter set that is considered fidelity-optimal, which essentially represents the values which yield the optimal compensation between various sources of errors and uncertainties. Rather than maximizing fidelity, this study advocates for basing model assessment on the model’s ability to satisfy a required fidelity (or error tolerance). Evaluating the trade-off between error tolerance, parameter uncertainty and probability of satisfying this predefined error threshold provides us with a powerful tool for model assessment and resource allocation.

scholarly journals Propagation of input parameter uncertainties in transport models

2018 ◽  
Vol 25 (10) ◽  
pp. 102309
Author(s):  
P. Vaezi ◽  
C. Holland ◽  
B. A. Grierson ◽  
G. M. Staebler ◽  
S. P. Smith ◽  
...  
Keyword(s):  
Input Parameter ◽  
Parameter Uncertainties ◽  
Transport Models

An Introduction to Finite Differencing

1998 ◽  
Author(s):  
T. N. Krishnamurti ◽  
H. S. Bedi ◽  
V. M. Hardiker
Keyword(s):  
Finite Difference ◽  
Finite Differences ◽  
Single Point ◽  
Finite Differencing ◽  
Finite Difference Approximations ◽  
Difference Approximations ◽  
Student Reading ◽  
Higher Derivatives ◽  
Derivatives Of

This chapter on finite differencing appears oddly placed in the early part of a text on spectral modeling. Finite differences are still traditionally used for vertical differencing and for time differencing. Therefore, we feel that an introduction to finite-differencing methods is quite useful. Furthermore, the student reading this chapter has the opportunity to compare these methods with the spectral method which will be developed in later chapters. One may use Taylor’s expansion of a given function about a single point to approximate the derivative(s) at that point. Derivatives in the equation involving a function are replaced by finite difference approximations. The values of the function are known at discrete points in both space and time. The resulting equation is then solved algebraically with appropriate restrictions. Suppose u is a function of x possessing derivatives of all orders in the interval (x — n∆x, x + n∆x). Then we can obtain the values of u at points x ± n∆ x, where n is any integer, in terms of the value of the function and its derivatives at point x, that is, u(x) and its higher derivatives.

Uncertainty Quantification of Aeroacoustic Power Sources in Corrugated Pipes

2015 ◽  
Author(s):  
Maharudrayya Swamy ◽  
Pejman Shoeibi Omrani ◽  
Nestor Gonzalez Diez
Keyword(s):  
Uncertainty Quantification ◽  
Input Parameter ◽  
Distribution Functions ◽  
Geometrical Parameters ◽  
Acoustic Source ◽  
Parameter Uncertainties ◽  
Source Power ◽  
Power Sources ◽  
Edge Radius ◽  
Onset Velocity

Gas transport in corrugated pipes often exhibit whistling behavior, due to periodic flow-induced pulsations generated in the pipe cavities. These aero-acoustic sources are strongly dependent on the geometrical dimensions and features of the cavities. As a result, uncertainties in the exact shape and geometry play a significant role in determining the singing behavior of corrugated pipes. While predictive modelling for idealized periodic structures is well established, this paper focusses on the sensitivity analysis and uncertainty quantification (UQ) of uncertain geometrical parameters using probabilistic models. The two most influential geometrical parameters varied within this study are the cavity width and downstream edge radius. Computational Fluid Dynamics (CFD) analysis was used to characterize the acoustic source. Stochastic collocation method was used for propagation of input parameter uncertainties. The analysis was performed with both full tensor product grid and sparse grid based on level-2 Clenshaw-Curtis points. The results show that uncertainties in the width and downstream edge radius of the cavity have an effect on the acoustic source power, peak Strouhal number and consequently the whistling onset velocity. Based on the assumed input parameters distribution functions, the confidence levels for the prediction of onset velocity were calculated. Finally, the results show the importance of performing uncertainty analysis to get more insights in the source of errors and consequently leading to a more robust design or risk-management oriented decision.

Monte-Carlo Simulation of the Theoretical Site Response Variability at Turkey Flat, California, Given the Uncertainty in the Geotechnically Derived Input Parameters

1993 ◽  
Vol 9 (4) ◽  
pp. 669-701 ◽  
Author(s):  
Edward H. Field ◽  
Klaus H. Jacob
Keyword(s):  
Monte Carlo ◽  
Physical Model ◽  
Site Response ◽  
Input Parameter ◽  
Model Parameters ◽  
Spectral Ratios ◽  
Parameter Uncertainties ◽  
Theoretical Predictions ◽  
High Degree ◽  
Geotechnical Studies

In the weak-motion phase of the Turkey Flat blind-prediction effort, it was found that given a particular physical model of each sediment site, various theoretical techniques give similar estimates of the site response. However, it remained to be determined how uncertainties in the physical model parameters influence the theoretical predictions. We have studied this question by propagating the physical parameter uncertainties into the theoretical site-response predictions using monte-carlo simulations. The input-parameter uncertainties were estimated directly from the results of several independent geotechnical studies performed at Turkey Flat. While the computed results generally agree with empirical site-response estimates (average spectral ratios of earthquake recordings), we found that the uncertainties lead to a high degree of variability in the theoretical predictions. Most of this variability comes from poor constraints on the shear-wave velocity and thickness of a thin (∼2m) surface layer, and on the attenuation of the sediments. Our results suggest that in site-response studies which rely exclusively on geotechnically based theoretical predictions, it will be important that the variability resulting from input-parameter uncertainties is recognized and accounted for.

scholarly journals Fluxes from soil moisture measurements (FluSM v1.0): a data-driven water balance framework for permeable pavements

2021 ◽  
Vol 14 (4) ◽  
pp. 2127-2142
Author(s):  
Axel Schaffitel ◽  
Tobias Schuetz ◽  
Markus Weiler
Keyword(s):  
Soil Moisture ◽  
Water Balance ◽  
Input Parameter ◽  
Infiltration Rate ◽  
Data Driven ◽  
Minor Role ◽  
Water Fluxes ◽  
Parameter Uncertainties ◽  
Data Set ◽  
Permeable Pavements

Abstract. Water fluxes at the soil–atmosphere interface are a key piece of information for studying the terrestrial water cycle. However, measuring and modeling water fluxes in the vadose zone poses great challenges. While direct measurements require costly lysimeters, common soil hydrologic models rely on a correct parametrization, a correct representation of the involved processes, and the selection of correct initial and boundary conditions. In contrast to lysimeter measurements, soil moisture measurements are relatively cheap and easy to perform. Using such measurements, data-driven approaches offer the possibility to derive water fluxes directly. Here we present FluSM (fluxes from soil moisture measurements), which is a simple, parsimonious and robust data-driven water balancing framework. FluSM requires only a single input parameter (the infiltration rate) and is especially valuable for cases where the application of Richards-based models is critical. Since permeable pavements (PPs) present such a case, we apply FluSM on a recently published soil moisture data set to obtain the water balance of 15 different PPs over a period of 2 years. Consistent with findings from previous studies, our results show that vertical drainage dominates the water balance of PPs, while surface runoff plays only a minor role. An additional uncertainty analysis demonstrates the ability of the FluSM-approach for water balance studies, since input and parameter uncertainties only have a small effect on the characteristics of the derived water balances. Due to the lack of data on the hydrologic behavior of PPs under field conditions, our results are of special interest for urban hydrology.

scholarly journals Fluxes from Soil Moisture Measurements (FluSM v1.0). A Data-driven Water Balance Framework for Permeable Pavements

2020 ◽  
Author(s):  
Axel Schaffitel ◽  
Tobias Schuetz ◽  
Markus Weiler
Keyword(s):  
Soil Moisture ◽  
Water Balance ◽  
Water Cycle ◽  
Input Parameter ◽  
Data Driven ◽  
Minor Role ◽  
Water Fluxes ◽  
Parameter Uncertainties ◽  
Infiltration Capacity ◽  
Permeable Pavements

Abstract. Water fluxes at the soil-atmosphere interface are a key information for studying the terrestrial water cycle. However, measuring and modelling water fluxes in the vadose zone poses great challenges. While direct measurements require costly lysimeters, common soil hydrologic models rely on a correct parametrization, a correct representation of the involved processes and on the selection of correct initial and boundary conditions. In contrast to lysimeter measurements, soil moisture measurements are relatively cheap and easy to perform. Using such measurements, data-driven approaches offer the possibility to derive water fluxes directly. Here we present FluSM (Fluxes from Soil Moisture measurements), which is a simple, parsimonious and robust data-driven water balancing framework. FluSM requires only one single input parameter (the infiltration capacity) and is especially valuable for cases where the application of Richards based models is critical. Since Permeable Pavements (PPs) present such a case, we apply FluSM on a recently published soil moisture dataset to obtain the water balance of 15 different PPs over a period of two years. Consistent with findings from previous studies, our results show that vertical drainage dominates the water balance of PPs, while surface runoff plays only a minor role. An additional uncertainty analysis demonstrates the ability of the FluSM-approach for water balance studies, since input and parameter uncertainties have only small effects on the characteristics of the derived water balances. Due to the lack of data on the hydrologic behavior of PPs under field conditions, our results are of special interest for urban hydrology.

Uncertainty propagation through an empirical model of cutting forces in end milling

2021 ◽  
pp. 1-14
Author(s):  
Abhijit Bhattacharyya ◽  
John Schueller ◽  
Brian Mann ◽  
Tony Schmitz ◽  
Michael Gomez
Keyword(s):  
Monte Carlo ◽  
Uncertainty Analysis ◽  
Cutting Forces ◽  
Prediction Models ◽  
End Milling ◽  
Input Parameter ◽  
Parameter Uncertainties ◽  
Machining Processes ◽  
Systematic Effects ◽  
The Impact

Abstract Empirical mathematical models of cutting forces in machining processes use experimentally determined input parameters to make predictions. A general method for propagation of input parameter uncertainties through such predictive models is developed. Sources of uncertainty are identified and classified. First, a classical uncertainty procedure is employed to estimate uncertainties associated with the data reduction equation using a first order Taylor series expansion. Small values of input parameter uncertainties justify this local linearization. Coverage factors required to estimate confidence intervals are computed based on appropriate underlying statistical distributions. A root sum of squares method yields the overall expanded uncertainty in force predictions. A popular model used for predicting cutting forces in end milling is selected to demonstrate the procedure, but the demonstrated approach is general. The analysis is applied to experimental data. Force predictions are quoted along with a confidence interval attached to them. An alternative analysis based on Monte Carlo simulations is also presented. This procedure yields different insights compared with the classical uncertainty analysis and complements it. Monte Carlo simulation provides combined uncertainties directly without sensitivity calculations. Classical uncertainty analysis reveals the impacts of random effects and systematic effects separately. This information can prompt the user to improve the experimental setup if the impact of systematic effects is observed to be comparatively large. The method of quoting an estimate of the uncertainty in force predictions presented in this paper will permit users to assess the suitability of given empirical force prediction models in specific applications.

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