Uncertainty Quantification Procedure Research Articles

Application of Bound-to-Bound Data Collaboration approach for development and uncertainty quantification of a reduced char combustion model

The development of efficient industrial oxy-coal boilers can be significantly aided by Computational Fluid Dynamics (CFD) tools, as far as fidelity in modeling coal combustion is also complemented by feasible computational costs. Reduced and predictive models are the most suitable for this application scale. Reduced models feature predictivity when they are validated against a broad range of experiments and targeted by Uncertainty Quantification (UQ) procedures. This work proposes a numerical procedure that uses Bound-to-Bound Data Collaboration (B2B-DC) to derive a reduced char combustion model describing transport phenomena and reactions between char carbon and O2, CO2 and H2O, in both conventional and oxy-conditions. The approach determines the consistency between a numerical model and an experimental dataset. The latter is made up of the experiments carried out in an optically accessible laminar entrained flow reactor, operated by Sandia National Laboratories. The procedure follows five steps towards predictive modeling capability, namely: quantification of the uncertainty in the experiments, via instrument verification and modeling; development of a physics model and continuous improvement of its fidelity, via model-form uncertainty; identification of the uncertain and most sensitive parameters and of their prior bounds; sampling of the initial uncertain parameter space and training of a surrogate model; validation of the physics model via inference from the data. The last step, also known as inverse problem, is performed by applying the Bound-to-Bound Data Collaboration approach. A char combustion model is found consistent with the experimental data and its validity stands for conventional and oxy-combustion conditions. It accounts for heterogeneous reactions at the particle surface, mass transport of species in the particle boundary layer, pore diffusion and surface area changes. The consistent reduced model overcomes the differences in mass transport and kinetics observed in the experimental campaign. A reduction of the initial degree of uncertainty in both model and experiments is achieved.

Thermodynamic modeling and uncertainty quantification of CO2-loaded aqueous MEA solutions

The accurate characterization of the thermodynamic models of a reactive solvent-based CO2 capture system is essential for adequately capturing system behavior in a process model. Moreover, uncertainty in these models can significantly affect simulation results, although it is often neglected. With this incentive, a model of thermodynamic properties, including vapor-liquid equilibrium (VLE), enthalpy, and solution chemistry, has been developed using a rigorous methodology for the aqueous monoethanolamine (MEA) system as a baseline. The final thermodynamic framework consists of both a deterministic and stochastic model. The deterministic model is developed by regressing parameters of the e-NRTL activity coefficient model in Aspen Plus® to VLE, heat capacity, and heat of absorption data while downselecting the model’s large parameter space through use of information-theoretic criteria. The stochastic model is developed through an uncertainty quantification (UQ) procedure, using the results of the deterministic regression to determine a prior parameter distribution. This prior distribution and the experimental VLE data are used to derive a posterior distribution through Bayesian inference, which is used to represent the final stochastic model. A reaction model in which the kinetics are written in terms of the reaction equilibrium constants, to ensure consistency with the thermodynamics model, is developed. These new thermodynamic and reaction models are incorporated into an existing MEA system process model from the open literature, and the prior and posterior parameter distributions are propagated through the models. This provides valuable insight into the extent to which uncertainty in thermodynamic models affects key process variables, including CO2 capture efficiency and energy requirement for solvent regeneration.

Evaluating Mixture Rules for Multi-Component Pressure Dependence: H + O2 (+M) = HO2 (+M)

A substantial fraction of the reactions that take place in combustion are complex-forming (i.e. pressure-dependent) reactions, which depend on the collisional energy transfer characteristics of the surrounding mixture (“bath gas”). In contrast to the single-component bath gases used in nearly all fundamental investigations of these reactions, significant fractions of multiple species of disparate collisional energy transfer characteristics are usually present in combustion environments. Calculations of the rate constant for multi-component mixtures thereafter inevitably relies on a “mixture rule” based on rate constants for the individual single-component bath gases. Failure to implement a mixture rule, which is actually quite common in many implementations of kinetic models within combustion codes, can yield errors up to a factor equal to the number of separate expressions for each component. Even still, as demonstrated herein, rate constants evaluated through various proposed mixture rules can differ by over 60% for exactly the mixture compositions of interest to combustion modeling. Therefore, evaluating the suitability of various mixture rules for accurately representing multi-component pressure dependence for combustion modeling purposes appears particularly worthwhile, given that these differences now exceed achievable accuracies for single-component bath gases and, additionally, given that inverse uncertainty quantification procedures almost always rely on starting with an accurate model structure, including mixture rules. The present study evaluates various existing and new mixture rules for representations of multi-component pressure dependence for H+O2(+M)=HO2(+M) through comparison with master equation calculations. The results indicate that mixture rules based on the reduced pressure provide a considerably more accurate description than those based on pressure (reaching accuracies of 2% compared to ∼60%). Recommendations are made for incorporation of these new mixture rules within combustion codes. Until then, potential errors in the full condition-dependence for H+O2(+M)=HO2(+M) of up to ∼90% are essentially unavoidable merely due to available representation options within combustion codes.

A framework for assessing the uncertainty in wave energy delivery to targeted subsurface formations

Stress wave stimulation of geological formations has potential applications in petroleum engineering, hydro-geology, and environmental engineering. The stimulation can be applied using wave sources whose spatio-temporal characteristics are designed to focus the emitted wave energy into the target region. Typically, the design process involves numerical simulations of the underlying wave physics, and assumes a perfect knowledge of the material properties and the overall geometry of the geostructure. In practice, however, precise knowledge of the properties of the geological formations is elusive, and quantification of the reliability of a deterministic approach is crucial for evaluating the technical and economical feasibility of the design. In this article, we discuss a methodology that could be used to quantify the uncertainty in the wave energy delivery. We formulate the wave propagation problem for a two-dimensional, layered, isotropic, elastic solid truncated using hybrid perfectly-matched-layers (PMLs), and containing a target elastic or poroelastic inclusion. We define a wave motion metric to quantify the amount of the delivered wave energy. We, then, treat the material properties of the layers as random variables, and perform a first-order uncertainty analysis of the formation to compute the probabilities of failure to achieve threshold values of the motion metric. We illustrate the uncertainty quantification procedure using synthetic data.

Using the bootstrap for statistical inference on random graphs

AbstractIn this paper we propose a new nonparametric approach to network inference that may be viewed as a fusion of block sampling procedures for temporally and spatially dependent processes with the classical network methodology. We develop estimation and uncertainty quantification procedures for network mean degree using a “patchwork” sample and nonparametric bootstrap, under the assumption of unknown degree distribution. We provide a heuristic justification of asymptotic properties of the proposed “patchwork” sampling and present cross‐validation methodology for selecting an optimal “patch” size. We validate the new “patchwork” bootstrap on simulated networks with short‐ and long‐tailed mean degree distributions, and revisit the Erdös collaboration data to illustrate the proposed methodology. The Canadian Journal of Statistics 44: 3–24; 2016 © 2015 Statistical Society of Canada

Probabilistic Physics of Failure-based framework for fatigue life prediction of aircraft gas turbine discs under uncertainty

A probabilistic Physics of Failure-based framework for fatigue life prediction of aircraft gas turbine discs operating under uncertainty is developed. The framework incorporates the overall uncertainties appearing in a structural integrity assessment. A comprehensive uncertainty quantification (UQ) procedure is presented to quantify multiple types of uncertainty using multiplicative and additive UQ methods. In addition, the factors that contribute the most to the resulting output uncertainty are investigated and identified for uncertainty reduction in decision-making. A high prediction accuracy of the proposed framework is validated through a comparison of model predictions to the experimental results of GH4133 superalloy and full-scale tests of aero engine high-pressure turbine discs.

Development of V2UP (V&V plus uncertainty quantification and prediction) procedure for high cycle thermal fatigue in fast reactor—Framework for V&V and numerical prediction

High cycle thermal fatigue on a structure caused by thermal striping phenomena is one of the most important issues in the design of fast breeder reactors (FBRs). In development of numerical simulation codes and in plant design and estimation by using the numerical estimation code, implementation of verification and validation (V&V) is indispensable process and also scaling issue from the subscale experiments to the full scale reactor should be considered. Therefore, a procedure called as V2UP (verification and validation plus uncertainty quantification and prediction) was made by referring to the existing guidelines on V&V (ASME V&V-10 and 20) and the methodologies of the safety assessment (CSAU, ISTIR, EMDAP). The V2UP consisted of five components as follows: (1) phenomena analysis with the Phenomena Identification and Ranking Table (PIRT) method, (2) implementation of the V&V, (3) design and rearrangement of experiments for the V&V, (4) uncertainty quantification in each problem and integration of uncertainties and (5) numerical prediction (estimation) for the target issue. Although the complete application of the procedure has not been performed at this moment, a flow chart of the V2UP procedure was described in this paper with recent results of the examinations.

Uncertainty quantification of the finite element model of existing bridges for dynamic analysis

With increasing number of aging civil structures including bridges, the finite element (FE) analysis assumes key roles in the use of the maintenance and repair design, and structural health monitoring. Despite the changes in dynamic characteristics of the aging structures from the nominal condition due to deteriorations or possible damages, limited attention has generally been paid to the verification and validation (V&V) of the numerical models used in the dynamic analysis. In this paper, we describe some practical considerations on the systematic V&V especially for the modeling of existing and aging bridges by applying a series of V&V procedure to the bridge FE model. The applied V&V procedure includes: (1) experimental data acquisition by impact tests, (2) model verification using grid convergence index, (3) sensitivity analysis to extract influential parameters to the comparative feature, namely the modal parameters, and (4) uncertainty quantification based on Bayesian inference. Posterior probability distributions of uncertain parameters in the FE model, especially material properties of the girders and slab, were then successfully derived in the uncertainty quantification procedure. The study also discusses some important considerations to improve implementation of V&V for the modeling of existing structures in terms of the verification procedure for complex FE models, the choice of comparative features, and the appropriate experimental data acquisition.

A Compressed Sensing Approach for Partial Differential Equations with Random Input Data

AbstractIn this paper, a novel approach for quantifying the parametric uncertainty associated with a stochastic problem output is presented. As with Monte-Carlo and stochastic collocation methods, only point-wise evaluations of the stochastic output response surface are required allowing the use of legacy deterministic codes and precluding the need for any dedicated stochastic code to solve the uncertain problem of interest. The new approach differs from these standard methods in that it is based on ideas directly linked to the recently developed compressed sensing theory. The technique allows the retrieval of the modes that contribute most significantly to the approximation of the solution using a minimal amount of information. The generation of this information,viamany solver calls, is almost always the bottle-neck of an uncertainty quantification procedure. If the stochastic model output has a reasonably compressible representation in the retained approximation basis, the proposed method makes the best use of the available information and retrieves the dominant modes. Uncertainty quantification of the solution of both a 2-D and 8-D stochastic Shallow Water problem is used to demonstrate the significant performance improvement of the new method, requiring up to several orders of magnitude fewer solver calls than the usual sparse grid-based Polynomial Chaos (Smolyak scheme) to achieve comparable approximation accuracy.

Experimental Validation and Uncertainty Quantification of a Single-Mode Optical Fiber Transmission Model

The radial intensity distribution of a transmission from a single-mode optical fiber is often approximated using Gaussian-shaped spatial field distributions. While such approximations are useful for some applications, they do not accurately describe optical transmission intensity off of the axis of propagation. A recent paper was presented that more accurately describes the intensity distribution, and this paper presents a simple experimental setup that verifies the model's accuracy through formal uncertainty quantification procedures. Agreement between the model and the experiment is established both on and off of the axis of propagation. These results are then discussed in the context of displacement sensor designs based on the optical lever architecture. Transmission behavior off of the axis of propagation controls the sensor performance when large lateral offsets (25-1500 μ m) exist between transmitting and receiving fibers. The practical implications of modeling accuracy over this lateral offset region are discussed as they relate to the development of high-performance, intensity-modulated optical displacement sensors. Specifically, the sensitivity, linearity, resolution, and displacement range of a sensor are functions of the relative positioning of the sensor's transmitting and receiving fibers. It is concluded that the predictive capability of the model presented in this paper could enable an improved methodology for high-performance sensor design.

Uncertainty quantification and robust design of aircraft components under thermal loads

In this work an uncertainty quantification procedure and a robust design method are applied to the thermal design of a skin panel and a wing box section. The uncertainty quantification method selected is based on Monte Carlo simulations and a set of common design parameters have been considered and formulated with random values. Numerical results show that the most significant randomness comes from thermal loads and also that the amount of uncertainty decreases from input to output. On the other hand, the Taguchi's method of robust design has been applied to obtain the most appropriate values of a set of control factors in several design situations. In this case, the results show an improvement in the response of the components, maintaining a low dependence on input value variations and producing designs that increase the quality level.

Input uncertainty propagation methods and hazard mapping of geophysical mass flows

This paper presents several standard and new methods for characterizing the effect of input data uncertainty on model output for hazardous geophysical mass flows. Note that we do not attempt here to characterize the inherent randomness of such flow events. We focus here on the problem of characterizing uncertainty in model output due to lack of knowledge of such input for a particular event. Methods applied include classical Monte Carlo and Latin hypercube sampling and more recent stochastic collocation, polynomial chaos, spectral projection and a newly developed extension thereof named polynomial chaos quadrature. The simple and robust samplings based Monte Carlo type methods are usually computationally intractable for reasonable physical models, while the more sophisticated and computationally efficient polynomial chaos method often breaks down for complex models. The spectral projection and polynomial chaos quadrature methods discussed here produce results of quality comparable to the polynomial chaos type methods while preserving the simplicity and robustness of the Monte Carlo‐type sampling based approaches at much lower cost. The computational efficiency, however, degrades with increasing numbers of random variables. A procedure for converting the output uncertainty characterization into a map showing the probability of a hazard threshold being exceeded is also presented. The uncertainty quantification procedures are applied first in simple settings to illustrate the procedure and then subsequently applied to the 1991 block‐and‐ash flows at Colima Volcano, Mexico.

On the Uncertainties of Flash Flood Guidance: Toward Probabilistic Forecasting of Flash Floods

Abstract Quantifying uncertainty associated with flash flood warning or forecast systems is required to enable informed decision making by those responsible for operation and management of natural hazard protection systems. The current system used by the U.S. National Weather Service (NWS) to issue flash-flood warnings and watches over the Unites States is a purely deterministic system. The authors propose a simple approach to augment the Flash Flood Guidance System (FFGS) with uncertainty propagation components. The authors briefly discuss the main components of the system, propose changes to improve it, and allow accounting for several sources of uncertainty. They illustrate their discussion with examples of uncertainty quantification procedures for several small basins of the Illinois River basin in Oklahoma. As the current FFGS is tightly coupled with two technologies, that is, threshold-runoff mapping and the Sacramento Soil Moisture Accounting Hydrologic Model, the authors discuss both as sources of uncertainty. To quantify and propagate those sources of uncertainty throughout the system, they develop a simple version of the Sacramento model and use Monte Carlo simulation to study several uncertainty scenarios. The results point out the significance of the stream characteristics such as top width and the hydraulic depth on the overall uncertainty of the Flash Flood Guidance System. They also show that the overall flash flood guidance uncertainty is higher under drier initial soil moisture conditions. The results presented herein, although limited, are a necessary first step toward the development of probabilistic operational flash flood guidance forecast-response systems.

Evaluation of the uncertainty of element determination using the energy‐dispersive x‐ray fluorescence technique and the emission–transmission method

AbstractA detailed study of the uncertainty quantification procedure for the determination of element mass fractions in a soil matrix by using energy‐dispersive x‐ray fluorescence spectrometry and the emission–transmission method was carried out. The particular case of secondary target excitation with an Mo target and Mo anode x‐ray tube was addressed. The effects of simplification of the theoretical model on the determined mass fractions of elements were studied. The main contributions to the uncertainty were identified and the ways of reducing their magnitude were indicated. The approach was found to be helpful in designing an optimum analytical strategy. It can also be used as guidance for assessing the uncertainty in other modes of x‐ray fluorescence analysis. Copyright © 2003 John Wiley & Sons, Ltd.

Climate change. Uncertainty and climate change assessments.

Clear and quantitative discussion of uncertainties is critical for public policy making on climate change. The recently completed report of the Intergovernmental Panel on Climate Change assessed the uncertainty in its findings and forecasts. The uncertainty assessment process of the IPCC should be improved in the future by using a consistent approach to quantifying uncertainty, focusing the quantification on the few key results most important for policy making. The uncertainty quantification procedure should be fully documented, and if expert judgment is used, a specific list of the experts consulted should be included.