Numerical Uncertainty Research Articles

Train-induced vibration attenuation measurements and prediction from ground soil to building column.

The investigation of the influence of soil-structure coupling on the vibration propagation pattern is the key to ensuring the reliability of the prediction of train-induced building vibration. This study selects different metro depots with over-track buildings as the research objects based on the existing engineering examples. It analyzes the general laws of vibration propagation from the ground soil to the building columns. The study provides valuable references for predicting vibration and designing vibration isolation measures for over-track buildings. Additionally, this study proposes a vibration prediction method for over-track buildings above metro depots based on the back propagation (BP) neural network model in machine learning. This model considers the soil-structure coupling loss in a data-driven manner based on the rich data samples, which avoids the problems of complex numerical simulation calculations and parameter uncertainties to some extent. This prediction method has a good balance of efficiency and convenience and also meets the accuracy requirements. It was judged to be a promising prediction method for the preliminary design stage of the over-track buildings above metro depots.

Verification and validation of open water test of B4-65 B-series propeller model

Verification and validation (V&V) are essential processes in computational simulations that aim to evaluate the accuracy and reliability of the results compared to experimental data. The quantification of error and uncertainty estimates is crucial in V&V. In this particular study, the open water test of a four-bladed B-series propeller model at 1/6.98 scale was conducted for three advanced coefficients (J = 0.50, J = 0.60, and J = 0.70) at the Indonesian Hydrodynamic Laboratory (IHL). The simulation was conducted under experimental conditions using FINE/Marine 7.2. Verification was performed to estimate the error 𝛿*REG and the numerical uncertainty USN according to the ITTC convergence ratio R and order of accuracy 𝑃𝐺. The average uncertainty estimated for the thrust and torque coefficient was found to be between 1.72% to 4.81%, with a 95% confidence level. Reducing errors and uncertainties associated with verification and validation in open-water experiments can increase the reliability of numerical simulations.

Effect of cavitation evolution on power characteristics of tidal current turbine

With the development of large-scale tidal current turbines and the increase in tidal current velocity, the possibility of cavitation increases. Furthermore, unsteady cavitation is a complicated multiphase flow that causes power degradation of tidal current turbine blade. There has been no comprehensive investigation of it so far. In this study, the blade captured power is obtained at different cavitation numbers using the Schnerr–Sauer cavitation model. The numerical uncertainty for the mesh and the time step is calculated by the grid convergence index method. It has been shown that, when the cavitation number is 5 and 2, cavitation has no effect on the blade power. With the decrease in the cavitation number, the rise in cavitation intensity occurs when the vapor distribution area stretches from the blade tip to the blade root and from the leading edge to the trailing edge, respectively. With a fall in cavitation number to 1.3, the vapor volume fraction rises, and the viscosity of the mixed phase reduces, resulting in a reduction in viscous power. When the cavitation number is 0.8, there exists a larger region in which an absolute value of minimum pressure coefficient is less than the cavitation number, a smaller blade load is present, and the pressure difference power is substantially decreased. Because of the huge inverse pressure gradient created by cavitation, the negative pressure difference power is generated, resulting in a decline of the blade power coefficient to 14%, when the cavitation number is 0.5.

Study on Pure Roll Test of a Ship Using CFD Simulation

Roll moment usually is ignored when analyzing the maneuverability of surface ships. However, it is well known that the influence of roll moment on maneuverability is significant for ships with small metacentric height such as container ships, passenger ships, etc. In this study, a pure roll test is performed to determine the hydrodynamic derivatives with respect to roll motion as added mass and damping. The target ship is an autonomous surface ship designed to carry containers with a small drift and large freeboard. The commercial code of STAR CCM+ software is applied as a specialized tool in naval hydrodynamic based on RANS equation for simulating the pure roll of the ship. The numerical uncertainty analysis is conducted to verify the numerical accuracy. By distinguishing the in-phase and out-of-phase from hydrodynamic forces and moments due to roll motion, added mass derivatives and damping derivatives relative to roll angular velocity are obtained.

Representative Points Based on Power Exponential Kernel Discrepancy

Representative points (rep-points) are a set of points that are optimally chosen for representing a big original data set or a target distribution in terms of a statistical criterion, such as mean square error and discrepancy. Most of the existing criteria can only assure the representing properties in the whole variable space. In this paper, a new kernel discrepancy, named power exponential kernel discrepancy (PEKD), is proposed to measure the representativeness of the point set with respect to the general multivariate distribution. Different from the commonly used criteria, PEKD can improve the projection properties of the point set, which is important in high-dimensional circumstances. Some theoretical results are presented for understanding the new discrepancy better and guiding the hyperparameter setting. An efficient algorithm for searching rep-points under the PEKD criterion is presented and its convergence has also been proven. Examples are given to illustrate its potential applications in the numerical integration, uncertainty propagation, and reduction of Markov Chain Monte Carlo chains.

Verification, validation, and parameter study of a computational model for corrosion pit growth adopting the level-set method. Part I: Corrosion

Corrosion is a phenomenon observed in structural components in corrosive environments such as pipelines, bridges, aircrafts, turbines, etc. The computational model of corrosion should enjoy two features: a) accurately considering the electrochemistry of corrosion and b) properly dealing with the moving interface between solid and electrolyte. There are several approaches to model corrosion such as using FEM with mesh refinement algorithms, combining FEM and level-set method, employing finite volume methods, adopting peridynamic formulation, and utilizing phase field models. Because of its accuracy, lower computational cost, and robust dealing with multiple pit merging, the model which combines FEM with level-set method is selected to be more extensively assessed in this paper. Part I focuses on demonstrating the model’s capabilities of simulating pitting corrosion through a set of numerical examples which include numerical solution verification, experimental validation, and uncertainty quantification of model parameters and properties.

Induced Electric Field in Learning-Based Head Models With Smooth Conductivity for Exposure to Uniform Low-Frequency Magnetic Fields

Computational human models generated from medical images have been widely used to assess induced electric field for exposure to electromagnetic field. Traditional methods to develop human models include tissue segmentation, which involves huge effort in identifying tissues from medical images. When such models are applied to low-frequency electromagnetic dosimetry, computational artifacts result in substantial error. Deep learning techniques have been utilized to map medical images directly to tissue electrical conductivity, generating human models with smooth transitions in tissue conductivity across tissue boundaries and even within the same tissue. In this study, eight head models with smoothed conductivities were generated using the deep learning network. The induced electric fields in the models were assessed for exposure to a uniform low-frequency magnetic field and were compared with traditional segmented models. Computational results showed that the induced electric field distributions in learning-based and segmented models were consistent, and the former was smoother. The differences in the 99th to 99.99th percentile values between nonuniform and segmented models were within 8% and 13% for gray and white matter, respectively. The staircasing errors were suppressed in the learning-based models because of the smooth transition of the conductivity values, especially at the tissue interface. The intersubject variation of the maximum electric fields was smaller for the nonuniform models than for the segmented models, with a relative standard deviation within 12% for nonuniform models and 22% for segmented models. This difference is much smaller than the reduction factor of 3 associated with the numerical uncertainty set in the International Commission on Non-Ionizing Radiation Protection 2010 guidelines. Our findings could be helpful in deriving appropriate reduction factor in international guidelines, which is used for setting the limit from the threshold of adverse health effects.

High-fidelity CFD simulations for the wake characteristics of the NTNU BT1 wind turbine

In this work, we present the results of the wake characteristics of a model-scale horizontal-axis wind turbine (HAWT) obtained from high-fidelity CFD simulations. A thorough verification and validation (V&V) study is performed to quantify the numerical uncertainties in the CFD results. The RANS equations with the k−ω SST turbulence model are adopted in the present study. The geometry of the HAWT is fully resolved including the blades, hub, nacelle, and tower. The Moving-Grid-Formulation (MVG) approach with a sliding interface technique is leveraged to handle the relative motion between the rotating hub and turbine blades and the stationary tower and nacelle. First, to evaluate the spatial and temporal discretization uncertainties in the predicted wake characteristics, a simulation matrix consisting of three systematically refined grids coupled with three different time increments is established. In all the simulations, a tip speed ratio (TSR) of 6 and an inlet velocity of 10 m/s are specified. The numerical uncertainties for the predicted velocity and turbulent kinetic energy at different downstream locations are then obtained by applying a systematic verification procedure to the CFD results. Second, a validation study is carried out by comparing the CFD results against the experimental data. It is shown that the CFD predictions are in good agreement with the measurements. In addition, the details of the wind turbine wake are visualized and discussed. It is found that the tower wake is skewed by the rotating turbine blades. As the result, the wake profiles at downstream locations are asymmetric. Further, the tower wake is carried upwards by the rotating blade wakes, and thus the location of the asymmetry peak at different downstream distances is changing. We therefore confirm that the asymmetry of the wake profile is physical and it is not a measurement error in the experiment as suspected by other researchers in the previous studies. Finally, the interaction between the rotor wake and the tower wake is visualized and discussed. It is observed that due to the presence of the tower, the wake below the hub height is highly unsteady compared to the wake above the hub height. The results show that the methodologies adopted in this study are capable of accurately capturing the wake characteristics of the NTNU BT1 wind turbine.

Vibrational instabilities in multilayer graphene and graphite: Effects of strain and number of layers

We study the rippling instabilities of multilayer graphene and graphite as a function of strain and number of layers using density-functional theory and density-functional perturbation theory calculations. We find that, for multilayer graphene, a small but finite compressive strain is needed to induce a rippling instability, signaled by the onset of imaginary frequencies near the center of the Brillouin zone. For monolayer graphene, this critical strain is zero within numerical uncertainty. Using insights from continuum elasticity theory, we fit the phonon dispersion of the ZA mode near the zone center to a function ${\ensuremath{\omega}}^{2}(q)={C}_{2}{q}^{2}+{C}_{4}{q}^{4}$ and determine the ${C}_{2}$ and ${C}_{4}$ coefficients as a function of strain and number of layers. In particular, the ${C}_{2}$ coefficient is positive for multilayers in the absence of strain and shows a linear dependence with strain. It assumes negative values for compressive strains beyond a critical value and it is responsible for the appearance of imaginary frequencies in the ZA mode. We discuss these results in light of both continuum and atomistic approaches. Critical parameters vary smoothly with the number of layers from monolayer graphene (two-dimensional) to graphite (three-dimensional).

Social cost of carbon: A revisit from a systems analysis perspective

The social cost of carbon (SCC) is estimated by integrated assessment models (IAMs) and is widely used by government agencies to value climate policy impacts. Although there is an ongoing debate about obtained numerical estimates and related uncertainties, little attention has been paid so far to the SCC calculation method itself. This work attempts to fill the gap by providing the theoretical background and economic interpretation of the SCC calculation approach implemented in the DICE (Dynamic Integrated Climate-Economy) IAM. Our analysis indicates that the present calculation method is unable to reflect the linkages between two key IAM components—complex interconnected systems—climate and economy, both influenced by emission abatement policies. Within the modeling framework of DICE, the presently estimated SCC valuates emissions, which are beyond policy control, against consumption of products, which cannot be produced by the economy. This makes the SCC irrelevant for application in climate-economic policies and, therefore, calls for a replacement by a more appropriate indicator. An apparent SCC alternative, which can be considered for policy formulation, is the direct output of the DICE model, the socially optimal marginal abatement cost (SMAC), which corresponds to technological possibilities at the optimal level of carbon emissions abatement. In policymaking, because of the revealed SCC deficiency, great attention needs to be paid to the use of estimates obtained earlier.

Communicating Uncertainty Information in a Dynamic Decision Environment

Abstract The likelihood of threatening events is often simplified for members of the public and presented as risk categories such as the “watches” and “warnings” currently issued by National Weather Service in the United States. However, research (e.g., Joslyn and LeClerc) suggests that explicit numeric uncertainty information—for example, 30%—improves people’s understanding as well as their decisions. Whether this benefit extends to dynamic situations in which users must process multiple forecast updates is as yet unknown. It may be that other likelihood expressions, such as color coding, are required under those circumstances. The experimental study reported here compared the effect of the categorical expressions “watches” and “warnings” with both color-coded and numeric percent chance expressions of the likelihood of a tornado in a situation with multiple updates. Participants decided whether and when to take shelter to protect themselves from a tornado on each of 40 trials, each with seven updated tornado forecasts. Understanding, decision quality, and trust were highest in conditions that provided percent chance information. Color-coded likelihood information inspired the least trust and led to the greatest overestimation of likelihood and confusion with severity information of all expressions.

CFD code comparison, verification and validation for decay tests of a FOWT semi-submersible floater

With the advancement of high-performance computation capabilities in recent years, high-fidelity modelling tools such as computational fluid dynamics are becoming increasingly popular in the offshore renewable sector. To justify the credibility of the numerical simulations, thorough verification and validation is essential. In this work, preparatory heave decay tests for a freely floating single cylinder are modelled. Subsequently, the surge and sway decays of a linearly moored floating offshore wind turbine model of the OC4 (Offshore Code Comparison Collaboration Continuation) phase II semi-submersible platform are simulated. Two different viscous-flow CFD codes are used: OpenFOAM (open-source), and ReFRESCO (community-based open-usage). Their results are compared against each other and with water tank experiments. For the single-cylinder decay simulations, it is found that the natural period is accurately modelled compared to the experimental results. Regarding the damping, both CFD codes are overly dissipative. Differences and their potential explanations become apparent in the analysis of the flow field data. Meanwhile, large numerical uncertainties especially in later oscillations make a distinct conclusion difficult. For the OC4 semi-submersible decay simulations, a better agreement in damping can be achieved, however discrepancies in results are observed when restricting the degrees of freedom of the platform. Flow field data again reveals differences between the CFD codes. Meanwhile, through the effort to use similar numerical settings and quantify the numerical uncertainties of the CFD simulations, this work represents a stepping stone towards fairer and more accurate comparison between CFD and experimental results.

STEP FORWARD FOR CFD UNCERTAINTY ANALYSIS OF SHIP RESISTANCE BENCHMARK MODEL LHI-007

Computational Fluid Dynamics (CFD) is a tool for solving the basic problems of equations for model flow motion. The CFD application can be used to predict the magnitude of the ship's resistance which is related to the engine power needed to move the ship. Benchmarking is the process of comparing different methods, procedures, and physical models to provide a common basis for the validation of numerical methods. This study simulates the resistance test on the LHI 007 benchmark ship model using FINE™/Marine with speed ranges 1.63 m/s – 2.47 m/s at a temperature of 27°C. The purpose of this research is to complete the simulation approach and numerical uncertainty for the previous study. By adding a time step component to the verification and validation of the uncertainty analysis, the error value gets smaller than the validation value for various speeds 1.63 m/s, 1.8 m/s, 1.91 m/s and 2.02 m/s. It shows that validation was achieved.

A study into the FSI modelling of flat plate water entry and related uncertainties

This paper presents systematic comparisons of experiments against fluid structure interaction (FSI) simulations for flat water plate entry. Special focus is attributed on hydroelasticity and air trapping effects, quantification of the experimental and numerical uncertainties and the validity of modelling assumptions for the prediction of bottom slamming induced loads. Consequently, the American society of Mechanical Engineers standard for Verification and Validation is used to estimate the errors. Numerical and experimental results agree favourably. It is shown that pressures and strains may be prone to spatial effects that lead to minor deviations between experiments and simulations. High frequency vibration modes and model boundary conditions may also influence the results.

Two Calculation Verification Metrics Used in the Medical Device Industry: Revisiting the Limitations of Fractional Change

Abstract Quantifying the fractional change in a predicted quantity of interest with successive mesh refinement is an attractive and widely used but limited approach to assessing numerical error and uncertainty in physics-based computational modeling. Herein, we introduce the concept of a scalar multiplier αGCI to clarify the connection between fractional change and a more rigorous and accepted estimate of numerical uncertainty, the grid convergence index (GCI). Specifically, we generate lookup tables for αGCI as a function of observed order of accuracy and mesh refinement factor. We then illustrate the limitations of relying on fractional change alone as an acceptance criterion for mesh refinement using a case study involving the radial compression of a Nitinol stent. Results illustrate that numerical uncertainty is often many times larger than the observed fractional change in a mesh pair, especially in the presence of small mesh refinement factors or low orders of accuracy. We strongly caution against relying on fractional change alone as an acceptance criterion for mesh refinement studies, particularly in any high-risk applications requiring absolute prediction of quantities of interest. When computational resources make the systematic refinement required for calculating GCI impractical, submodeling approaches as demonstrated herein can be used to rigorously quantify discretization error at a comparatively minimal computational cost. To facilitate future quantitative mesh refinement studies, αGCI lookup tables herein provide a useful tool for guiding the selection of mesh refinement factor and element order.

Communicating uncertainty in national security intelligence: Expert and nonexpert interpretations of and preferences for verbal and numeric formats.

Organizations in several domains including national security intelligence communicate judgments under uncertainty using verbal probabilities (e.g., likely) instead of numeric probabilities (e.g., 75% chance), despite research indicating that the former have variable meanings across individuals. In the intelligence domain, uncertainty is also communicated using terms such as low, moderate, or high to describe the analyst's confidence level. However, little research has examined how intelligence professionals interpret these terms and whether they prefer them to numeric uncertainty quantifiers. In two experiments (N=481 and 624, respectively), uncertainty communication preferences of expert (n =41 intelligence analysts in Experiment 1) and nonexpert intelligence consumers were elicited. We examined which format participants judged to be more informative and simpler to process. We further tested whether participants treated verbal probability and confidence terms as independent constructs and whether participants provided coherent numeric probability translations of verbal probabilities. Results showed that although most nonexperts favored the numeric format, experts were about equally split, and most participants in both samples regarded the numeric format as more informative. Experts and nonexperts consistently conflated probability and confidence. For instance, confidence intervals inferred from verbal confidence terms had a greater effect on the location of the estimate than the width of the estimate, contrary to normative expectation. Approximately one-fourth of experts and over one-half of nonexperts provided incoherent numeric probability translations for the terms likely and unlikely when the elicitation of best estimates and lower and upper bounds were briefly spaced by intervening tasks.

CFD study of a Dual Chamber Floating Oscillating Water Column device

A comprehensive Computational Fluid Dynamics study of a Dual Chamber Floating Oscillating Water Column device fixed in space is presented. Firstly, the numerical wave flume model is calibrated and validated for a simple case of a floating box fixed in space. Spectral components of the vertical wave force on the box are evaluated and the Computational Fluid Dynamics numerical model uncertainty is assessed. Secondly, the numerical wave flume is used to study the hydrodynamics around the Dual Chamber Floating Oscillating Water Column. The wave forces acting on the device when fixed in space are calculated, also free surface elevations and air pressures inside the chambers are evaluated and the efficiency of the device is determined. The present numerical results show that the model can describe properly the two main components of the vertical force of a fixed floating box. Efficiency results of the device show that it is the same whether it is moving or not for the low wave height. For higher wave heights, the efficiency improves when the device is moving due to its resonance mechanisms.

Numerical Study of Scale Effects on Open Water Propeller Performance

The present study aims to investigate the scale effects of the open water propeller performance using computational fluid dynamics (CFD). The results are presented for the propeller which was previously 3D scanned and digitized. The results obtained using two turbulence models within the numerical simulations are compared. The verification study is conducted to assess the numerical uncertainty and thus obtain the optimal grid size for the numerical simulations. A transition model is used at the model scale to account for the partially laminar flow. The propeller is then scaled, and numerical simulations are performed to assess the scale effects on the open water performance of the considered propeller. The results demonstrate the significant scale effects on open water characteristics however, scale effects are considerably lower when the transition model is applied within the numerical simulations at the model scale.

Probabilistic solvers enable a straight-forward exploration of numerical uncertainty in neuroscience models

Understanding neural computation on the mechanistic level requires models of neurons and neuronal networks. To analyze such models one typically has to solve coupled ordinary differential equations (ODEs), which describe the dynamics of the underlying neural system. These ODEs are solved numerically with deterministic ODE solvers that yield single solutions with either no, or only a global scalar error indicator on precision. It can therefore be challenging to estimate the effect of numerical uncertainty on quantities of interest, such as spike-times and the number of spikes. To overcome this problem, we propose to use recently developed sampling-based probabilistic solvers, which are able to quantify such numerical uncertainties. They neither require detailed insights into the kinetics of the models, nor are they difficult to implement. We show that numerical uncertainty can affect the outcome of typical neuroscience simulations, e.g. jittering spikes by milliseconds or even adding or removing individual spikes from simulations altogether, and demonstrate that probabilistic solvers reveal these numerical uncertainties with only moderate computational overhead.

Towards efficient application-dependent dimensional measurements with computed tomography: optimized reduction of measurement duration using continuous scan mode: experimental investigations

Abstract. Due to the complex physical and technical relationships in dimensional X-ray computed tomography measurement technology, the precise influences on the measurement result are still not fully understood. A deeper understanding of these influences is essential in order to improve the measurement accuracy and economy of computed tomographic measurement systems. In addition, this enables better numerical determination of measurement uncertainties, which is also a topic of current research. Two factors that have a significant influence on the lead times are the scan mode and the number of projections per measurement. In this article, these factors are investigated experimentally using a calibrated workpiece, and the influence of the workpiece position on the measurement result is also examined. It can be shown that the workpiece position has a considerable influence on the quality of the measurement, especially in the case of a continuous scan. The results show a vast potential for application-dependent reduction of lead times.