Uncertainty Estimation Procedure Research Articles

Physically constrained eigenspace perturbation for turbulence model uncertainty estimation

Aerospace design is increasingly incorporating design under uncertainty-based approaches to lead to more robust and reliable optimal designs. These approaches require dependable estimates of uncertainty in simulations for their success. The key contributor of predictive uncertainty in computational fluid dynamics (CFD) simulations of turbulent flows are the structural limitations of Reynolds-averaged Navier–Stokes models, termed model-form uncertainty. Currently, the common procedure to estimate turbulence model-form uncertainty is the eigenspace perturbation framework (EPF), involving perturbations to the modeled Reynolds stress tensor within physical limits. The EPF has been applied with success in design and analysis tasks in numerous prior works from the industry and academia. Owing to its rapid success and adoption in several commercial and open-source CFD solvers, in-depth verification and validation of the EPF is critical. In this work, we show that under certain conditions, the perturbations in the EPF can lead to Reynolds stress dynamics that are not physically realizable. This analysis enables us to propose a set of necessary physics-based constraints, leading to a realizable EPF. We apply this constrained procedure to the illustrative test case of a converging-diverging channel, and we demonstrate that these constraints limit physically implausible dynamics of the Reynolds stress tensor, while enhancing the accuracy and stability of the uncertainty estimation procedure.

Evaluating the uncertainty of a virtual power quality disturbance generator and its use in power quality classifier evaluation

This paper presents the metrological evaluation of a proposed virtual power quality (PQ) disturbance generator. It explains in detail the calibration and measurement uncertainty estimation procedures for the RMS voltage and frequency of the generator, presents the results, and discusses their implications. The results indicate that the measurement uncertainty of the generator is satisfactory for all reference points, making it suitable for generation of PQ signals for research purposes, particularly in the development, testing, and improvement of PQ event classifiers. Additionally, the paper introduces a virtual power quality disturbance classifier for real-time classification of PQ events and verifies its accuracy through testing using the proposed PQ disturbance generator.

Temperature rise of power transformers: comments and proposals to IEC 60076-2:2011

Two years ago, a new, third edition of IEC 60076-2 standard was published [1]. Over a period of two years, we have had the opportunity to evaluate this new standard in practice. In the paper, it is shown that the criterion for stagnation 1K/ h + 3h is not entirely satisfying. Better criterion is 1K/3h, or extrapolation to stagnation - as given in second edition of the standard. A formula for hot-spot determination is not complete and it is suggested how to improve it. In the new standard, three formulas for winding average temperature determination are given. Based on experiments, we conclude that the best formula is the simplest one, and two additional formulas are without any benefit. According to [1], paragraph 7.11, measurement uncertainty estimates of results should be given in test reports - but only as information. No procedure for measurement uncertainty estimation is given, and measurement uncertainty is not used in decision-making. Therefore, the third edition of the standard is uncompleted and not motivating in terms of efforts to increase the quality of the measurement results. In the paper, the procedure for measurement uncertainty estimation is proposed and suggestion is given for appropriate decision making.

Influencing factors in insulation model testing

The aim of this paper is to examine different factors that influence the quality of insulation models high voltage testing results. These factors are related to model geometry and model testing procedures. Model geometry is visually checked, several influencing factors are detected and their influence on el. field calculation results is evaluated using finite element method (FEM) and cumulative method for oilbarrier insulation design. The procedure for model geometry uncertainty estimation is performed using first-order Taylor series approximation. Also, the influence of previous voltage exposure history of a specimen, so-called “memo effect”, is estimated with a cumulative exposure method.

Assessment of uncertainty in the CFD simulation of the wave-induced loads on a vertical cylinder

The paper addresses different uncertainty analysis methods commonly used for uncertainty quantification in Computational Fluid Dynamics (CFD) studies and compares a constant Courant–Friedrichs–Lewy (CFL) number based approach for uncertainty estimation to the ITTC recommended grid and time-independent procedures. Four different uncertainty estimation procedures are presented and discussed. To compare their performance and better understand CFD related uncertainty quantification in wave load simulations on offshore structures, the methods are applied to a case study of the wave loads on a fixed vertical cylinder. The numerical or CFD wave tank is generated using the open-source CFD toolkit OpenFOAM. Uncertainty is assessed for the case study using four different uncertainty estimation procedures for verification and later, validation is attempted by comparing the CFD results with experiments. The study concludes that a constant CFL number based uncertainty study provides more stable results and is better suited for uncertainty estimation in CFD than the ITTC recommended individual grid and time step uncertainty study.

Uncertainty analysis of the HORTSYST model applied to fertigated tomatoes cultivated in a hydroponic greenhouse system

Aim of study: The objective was to perform an uncertainty analysis (UA) of the dynamic HORTSYST model applied to greenhouse grown hydroponic tomato crop. A frequentist method based on Monte Carlo simulation and the Generalized Likelihood Uncertainty Estimation (GLUE) procedure were used.Area of study: Two tomato cultivation experiments were carried out, during autumn-winter and spring-summer crop seasons, in a research greenhouse located at University of Chapingo, Chapingo, Mexico.Material and methods: The uncertainties of the HORTSYST model predictions PTI, LAI, DMP, ETc, Nup, Pup, Kup, Caup, and Mgup uptake, were calculated, by specifying the uncertainty of model parameters 10% and 20% around their nominal values. Uniform PDFs were specified for all model parameters and LHS sampling was applied. The Monte Carlo and the GLUE methods used 10,000 and 2,000 simulations, respectively. The frequentist method included the statistical measures: minimum, maximum, average values, CV, skewness, and kurtosis whilst GLUE used CI, RMSE, and scatter plots.Main results: As parameters were changed 10%, the CV, for all outputs, were lower than 15%. The smallest values were for LAI (10.75%) and DMP (11.14%) and the largest was for ETc (14.47%). For Caup (12.15%) and Pup (12.27%), the CV was lower than the one for Nup and Kup. Kurtosis and skewness values were close as expected for a normal distribution. According to GLUE, crop density was found to be the most relevant parameter given that it yielded the lowest RMSE value between the simulated and measured values.Research highlights: Acceptable fitting of HORTSYST was achieved since its predictions were inside 95% CI with the GLUE procedure.

Evaluating stream CO<sub>2</sub> outgassing via drifting and anchored flux chambers in a controlled flume experiment

Abstract. Carbon dioxide (CO2) emissions from running waters represent a key component of the global carbon cycle. However, quantifying CO2 fluxes across air–water boundaries remains challenging due to practical difficulties in the estimation of reach-scale standardized gas exchange velocities (k600) and water equilibrium concentrations. Whereas craft-made floating chambers supplied by internal CO2 sensors represent a promising technique to estimate CO2 fluxes from rivers, the existing literature lacks rigorous comparisons among differently designed chambers and deployment techniques. Moreover, as of now the uncertainty of k600 estimates from chamber data has not been evaluated. Here, these issues were addressed by analysing the results of a flume experiment carried out in the Summer of 2019 in the Lunzer:::Rinnen – Experimental Facility (Austria). During the experiment, 100 runs were performed using two different chamber designs (namely, a standard chamber and a flexible foil chamber with an external floating system and a flexible sealing) and two different deployment modes (drifting and anchored). The runs were performed using various combinations of discharge and channel slope, leading to variable turbulent kinetic energy dissipation rates (1.5×10-3<ε<1×10-1 m2 s−3). Estimates of gas exchange velocities were in line with the existing literature (4<k600<32 m2 s−3), with a general increase in k600 for larger turbulent kinetic energy dissipation rates. The flexible foil chamber gave consistent k600 patterns in response to changes in the slope and/or the flow rate. Moreover, acoustic Doppler velocimeter measurements indicated a limited increase in the turbulence induced by the flexible foil chamber on the flow field (22 % increase in ε, leading to a theoretical 5 % increase in k600). The uncertainty in the estimate of gas exchange velocities was then estimated using a generalized likelihood uncertainty estimation (GLUE) procedure. Overall, uncertainty in k600 was moderate to high, with enhanced uncertainty in high-energy set-ups. For the anchored mode, the standard deviations of k600 were between 1.6 and 8.2 m d−1, whereas significantly higher values were obtained in drifting mode. Interestingly, for the standard chamber the uncertainty was larger (+ 20 %) as compared to the flexible foil chamber. Our study suggests that a flexible foil design and the anchored deployment might be useful techniques to enhance the robustness and the accuracy of CO2 measurements in low-order streams. Furthermore, the study demonstrates the value of analytical and numerical tools in the identification of accurate estimations for gas exchange velocities. These findings have important implications for improving estimates of greenhouse gas emissions and reaeration rates in running waters.

Reducing hydrological modelling uncertainty by using MODIS snow cover data and a topography-based distribution function snowmelt model

This work introduces a general multi-objective parameter estimation framework to exploit MODIS-based snow cover maps to reduce predictive streamflow uncertainty in snow-dominated catchments. The well-known GLUE methodology is applied with a multi-objective approach, combining streamflow observations recorded at the outlet section and satellite-derived snow cover maps, aggregated to fractional values of the catchment area. The hydrological model used in this study includes a snowpack routine which exploits a statistical representation of the distribution of clear sky potential solar radiation - a significant advantage when parameter sensitivity and uncertainty estimation procedures are carried out. The study provides an assessment of this approach based on operational quality data from two medium-size mountainous basins (a nested one included in a larger parent basin) located in the eastern Italian Alps. The nested basin is considered as ungauged, thus allowing a spatial assessment of the multi-objective approach. Results show a positive feedback between streamflow and snow cover area likelihoods, highlighted by means of the Pareto plot. Moreover, a better identifiability of the parameters driving snowmelt rate is found and consequently a shrink of the predictive streamflow uncertainty is observed. A containing ratio of 0.54 and a mean sharpness of 0.11 are found at the outlet of the parent basin, while a containing ratio equal to 0.65 and a mean sharpness equal to 0.17 are estimated at the nested basin, used as a validation test. These results confirm the potential of MODIS snow cover maps as additional data to inform hydrological models leading to more reliable and sharper streamflow simulations. This approach might be also appealing when streamflow simulations are required for ungauged basins.

Uncertainty Quantification of Ultrasound Image Velocimetry for Liquid Metal Flow Mapping

Ultrasound image velocimetry (UIV) allows noninvasive flow imaging of opaque media with high spatial and temporal resolution, which is especially relevant for experimental research in magnetohydrodynamics (MHD). To extract quantitative flow data from lab-scale experiments in low melting alloys and interpret the results, the measurement uncertainty of a specific experiment has to be determined. In this article, we describe a novel, generic method for estimating the uncertainty of a specific experimental setup according to the guide to the expression of uncertainty in measurement (GUM). It is based on an uncertainty model of the UIV processing, which is calibrated using a flow reference in liquid metal. The proposed model uses a priori knowledge of an expected velocity gradient, a static calibration of the focus distortion, and the peak ratio of the correlation from the measurement data itself to yield the optimal parameterization of UIV and the velocity uncertainty for a specific experiment. This enables the use of the UIV method for quantitative flow imaging with an explicit uncertainty estimate in experiments where no reference flow is available. Building on this, we derive generic guidelines for an optimal parameterization of UIV to a specific experiment. The approach is demonstrated on a magnetically driven flow of gallium-indium-tin (GaInSn) alloy in a cuboid container. In conclusion, this work is a blueprint to obtain quantified planar vector flow maps with UIV in diverse MHD experiments; practical guidelines are derived and an uncertainty estimation procedure is elaborated.

Uncertainty estimation of low voltage LI measurements with recurrent surge generator and oscilloscope

Low voltage LI measurement with recurrent surge generator and oscilloscope is a method used for investigatingLI distribution in transformer windings or in model prototypes for various conditions. In the paper, the procedure for measurement uncertainty estimation of characteristic voltage and time quantities is given. The procedure is similar to the procedure given in the IEC 60076-2 standard for high voltage testing, but it is fully adapted to low voltage measurement with recurrent generator and oscilloscope. For the purpose of reducing the measurement uncertainties and the measurement time, a new procedure is proposed.

Development of measurement quantity determination procedure for estimation of uncertainty of influence of conditions during calibration of thermal engineering measurement instruments

Calculation of uncertainty and identification of influencing factors is one of the current problems of measuring instruments (MI) operation, because testing programs of MI including only typical influence and don’t take into account specific measuring instruments. Calibration of measuring instruments during their operation and calculation of uncertainty of measurement results will allow to establish in the long term the actual values of measurement results traced to the national primary standard. One of the tasks in assessing the uncertainty of measurements is to assess the impact of calibration conditions, which is evaluated based on parallel measurements at each calibration point. The aim of the study is to develop a method for determining the number of parallel measurements when calibrating thermal measuring instruments on the basis of statistical information based on the results of verification of measuring instruments. In that research, was determined and experimentally tested method for determining the number of parallel measurements during calibration of thermal measuring instruments. The method was tested on the calculator of a quantity of heat VKT-7. Was identify strengths and weaknesses parts of the technique, as well as its field of application, have been revealed.

TOPMELT 1.0: a topography-based distribution function approach to snowmelt simulation for hydrological modelling at basin scale

Abstract. Enhanced temperature-index distributed models for snowpack simulation, incorporating air temperature and a term for clear sky potential solar radiation, are increasingly used to simulate the spatial variability of the snow water equivalent. This paper presents a new snowpack model (termed TOPMELT) which integrates an enhanced temperature-index model into the ICHYMOD semi-distributed basin-scale hydrological model by exploiting a statistical representation of the distribution of clear sky potential solar radiation. This is obtained by discretizing the full spatial distribution of clear sky potential solar radiation into a number of radiation classes. The computation required to generate a spatially distributed water equivalent reduces to a single calculation for each radiation class. This turns into a potentially significant advantage when parameter sensitivity and uncertainty estimation procedures are carried out. The radiation index may be also averaged in time over given time periods. Thus, the model resembles a classical temperature-index model when only one radiation class for each elevation band and a temporal aggregation of 1 year is used, whereas it approximates a fully distributed model by increasing the number of the radiation classes and decreasing the temporal aggregation. TOPMELT is integrated within the semi-distributed ICHYMOD model and is applied at an hourly time step over the Aurino Basin (also known as the Ahr River) at San Giorgio (San Giorgio Aurino), a 614 km2 catchment in the Upper Adige River basin (eastern Alps, Italy) to examine the sensitivity of the snowpack and runoff model results to the spatial and temporal aggregation of the radiation fluxes. It is shown that the spatial simulation of the snow water equivalent is strongly affected by the aggregation scales. However, limited degradation of the snow simulations is achieved when using 10 radiation classes and 4 weeks as spatial and temporal aggregation scales respectively. Results highlight that the effects of space–time aggregation of the solar radiation patterns on the runoff response are scale dependent. They are minimal at the scale of the whole Aurino Basin, while considerable impact is seen at a basin scale of 5 km2.

Development of uncertainty estimation procedure for measurement of nonlinear distortions

The article is devoted to the question of expediency of development of uncertainty estimation procedure for measurement of nonlinear distortions. The article deals with the sequence of uncertainty estimation in the measurement of nonlinear distortions. Using the reference calibration tool, the installation of the measuring sample K2C-57, calibration was carried out and the results of experimental studies were obtained, in assessing the uncertainty of measuring the harmonic distortion.

A heterodyne interferometer constructed in an integrated optics and its metrological evaluation of a picometre-order periodic error

It is known that the periodic error of heterodyne interferometers limits the accuracy of measurement to nanometre order. It is mainly derived from frequency mixing in the interferometer optics and this can be resolved using the configuration with two spatially separated beams. However, there remains a periodic error associated with parasitic reflections. Recently, we have developed a differential single-path heterodyne interferometer with two spatially separated beams, which was constructed within a single small quasi-cubic optical unit to minimize the parasitic reflections. In this work, the residual periodic error of this interferometer was evaluated with two evaluation methods, ‘the amplitude method’ and ‘the subtraction method’, and their results were compared. By applying uncertainty estimation procedures to the results, these two methods were shown to be highly consistent, confirming the reliability of our evaluation results. The error in λ/2 period of this interferometer was 7.6 pm.

CALCULATION OF MEASUREMENTS UNCERTAINTY AT CARRYING OUT OF BALLISTIC RESEARCHES

Today one of the priority problems is receiving an accreditation certificate under the international standard ISO/IEC 17025:2006 by measurement laboratories of Expert service subdivision of the Ministry of Internal Affairs of Ukraine. One of the requirements which is shown to the accredited testing laboratories, is a presence of uncertainty estimation procedure and ability to apply it. As the ballistic researches are one of the important directions of researches which are carried out in the expert subdivisions, therefore the paper is devoted to the consideration ofa question of uncertainty calculation in such measurements. In the mathematical statistics two types of paramètres which characterize dispersion of not correlated random variables are known: a root-mean-square deviation and a confidential interval. As the characteristics of uncertainty they are applied under the title standard and expanded uncertainty. An elementary estimation of measurements result and its uncertainty is carried out in such an order: description of the measured quantity; revealing of uncertainty sources; quantitative description uncertainty constituents (there are estimated uncertainty constituents which can be received a posteriori or a priori); calculation of standard uncertainty of each source, total standard uncertainty and expanded uncertainty. A posterior estimation is possible only in the case of carrying out multiple observations of the measured quantity (standard uncertainty of type A). An a priori estimation is carried out when multiple observations are not performed. In this case it’s necessary to use the information received from the measurements performed before, from the passport data on the facilities ofmeasuring technics orfrom reference books (standard uncertainty of type B). Short consideration of uncertainty concept, elucidation of the basic stages measurements result estimation and its uncertainty gives the chance to transform the theoretical knowledge into practical application of uncertainty estimation on examples of measurements uncertainty calculation during carrying out ballistic ammunition researches by two different ways.

Two-phase CFD simulation of research reactor siphon breakers: A verification, validation and applicability study

During a nuclear reactors design phase many possible accidents are postulated. The main accident that could occur in an open pool reactor, such as the Brazilian Multipurpose Reactor (RMB) is the Loss-Of-Coolant Accident (LOCA). This type of accident occurs when the primary cooling piping breaks and the pressure gradient induces the refrigerant (water) to flow through this pipe by siphon effect, draining the pool. This accident can be avoided with a siphon breaking mechanism, which could consist of an orifice in the coolant pipe at a level above the minimum required water level in the pool. If the pipe breaks, air will enter through this orifice, interrupting the siphon flow. However, tests have shown that the mechanism in most cases does not stop the water flow immediately, causing a reduced water level. The siphon break phenomenon is a complex two-phase transient flow. Experimental studies of the siphon break are very expensive and time-consuming tasks. In this case, it would be appropriate to make a Computational Fluid Dynamics (CFD) analysis of this phenomenon, allowing a detailed evaluation of the flow characteristics in a simpler and cheaper way than an experiment. However, the complexity of this phenomenon imposes difficulties to its computer modeling and its accuracy must be assessed. In this study, a methodology is proposed for the simulation of orifice type siphon breaker for research reactors. In order to properly evaluate the numerical methodology, an experimental model available in the literature was simulated and a Verification and Validation (V&V) procedure was performed based on the Grid Convergence Index (GCI) method. Numerical uncertainties due to mesh were evaluated and estimated for other simulations with different siphon breaker orifice diameters to assess the applicability of the proposed methodology. Results showed good agreement with experimental results with reasonable uncertainty range. The proposed simple numerical uncertainty estimation procedure aims to encourage the discussion towards an uncertainty quantification culture in the CFD community.

Uncertainty estimation of an indexed metrology platform for the verification of portable coordinate measuring instruments

This work presents the development of an uncertainty estimation procedure for an indexed metrology platform. The use of an indexed metrology platform in calibration and verification procedures for portable coordinate measuring instruments, enables the evaluation of different working volumes of the instrument that rotates with the platform in six rotating positions without moving the gauge from a fixed location, reducing in this way the testing time and test setups in comparison with the tests included in the applicable standards. The platform is able to express points in a global reference coordinate system located in the lower platform through its mathematical model. Due to the platform model complexity and according to the GUM supplement 1, the propagation of distributions using the Monte Carlo method was applied to estimate the platform measurement uncertainty. The different error sources affecting the platform uncertainty were first identified. An analysis of the dynamic behavior of the platform by means of a computational and experimental modal test was done in this work. The capacitive sensors assembled in the platform determine the position and orientation of the upper platform with respect to the lower platform and were selected as input variables of the model with their related errors. The n-homogeneous transformation matrices obtained in the simulation as output variables will allow the coordinate reference system change from the upper platform to the lower platform. In this way, it is possible to estimate the influence of the indexed metrology platform position and orientation uncertainty in the generation of points in a global reference system and as a consequence, its influence in a distance measurement.

Application of a Bayesian Watershed Model Linking Multivariate Statistical Analysis to Support Watershed-Scale Nitrogen Management in China

Excessive nitrogen loads and subsequent eutrophication risk have led to a series of critical water quality problems in Chinese watersheds. To address this issue, a modeling approach is useful for quantifying nitrogen sources, assessing source apportionment, and guiding management responses. In this study, we modeled the main hydrochemical processes of the Lian River watershed located in the south of China using the Regional Nutrient Management (ReNuMa) model, a model derived from the Generalized Watershed Loading Function (GWLF) model and incorporating Net Anthropogenic Nitrogen Inputs (NANI) to estimate runoff nitrogen concentrations. An informal Bayesian method, the Generalized Likelihood Uncertainty Estimation (GLUE) procedure, was applied for model calibration and uncertainty analysis. The resulting modeled monthly total nitrogen fluxes have high Nash-Sutcliff coefficients (>0.85) for the calibration (2005–2009) and verification (2003, 2004 and 2010) periods, representing an acceptable goodness-of-fit. The model outputs were further processed using multivariate statistical analysis to determine latent rules of nitrogen source apportionment under different circumstances, including different water regimes, seasonal patterns, and loading levels. The main nitrogen contributions in different natural and management-driven conditions have been identified, and appear to be significant for supporting decision-making priorities. We find that the ReNuMa model, with its Bayesian procedure and the linkage of subsequent multivariate statistical analysis, represents a useful approach with applicability within China and a great potential to be extended elsewhere.

A procedure for the estimation of the numerical uncertainty of CFD calculations based on grid refinement studies

This paper offers a procedure for the estimation of the numerical uncertainty of any integral or local flow quantity as a result of a fluid flow computation; the procedure requires solutions on sys...

A dedicated LIMS for routine gamma-ray spectrometry

We developed a Microsoft® Access-based LIMS (Laboratory Information and Management Systems), γ-LIMS, for the management of our gamma-spectrometry laboratory, in which thousands of routine, but high-quality analyses are performed each year. This paper explains the main features of the γ-LIMS and puts special attention on the interfacing methods and solutions for using the Genie™2000 spectrometry software in conjunction with the EFFTRAN package, which serves for efficiency transfer calculations, coincidence summing corrections and a procedure for uncertainty estimation.