Uncertain Input Parameters Research Articles

Variability Impact of Many Design Parameters: The Case of a Realistic Electronic Link

In this paper, we adopt the so-called sparse polynomial chaos metamodel for the uncertainty quantification in the framework of high-dimensional problems. This metamodel is used to model a realistic electronic bus structure with a large number of uncertain input parameters such as those related to microstrip line geometries. It aims at estimating quantities of interest, such as statistical moments, probability density functions, and provides sensitivity analysis of a response. It drastically reduces the model computational cost with regard to brute force Monte Carlo (MC) simulation. The method presents a good performance and is validated in comparison with MC simulation.

Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

We consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explor...

Development of fuzzy differential quadrature numerical method and its application for uncertainty quantification of solute transport model

Uncertainty analysis of solute transport model is an essential component for decision-making problem in the regulatory framework for safe discharge of liquid effluent in environment. Performance assessment of any industry is based on the violation of discharge limit stipulated on yearly basis by any regulatory body. Very often, regulatory bodies provide deterministic (point) solution of the solute concentration as limit of discharge which is derived using the closed-form solution. However, uncertainty of the model parameters of the governing advection dispersion equation with specific initial and field boundary conditions restricts user to obtain deterministic or closed-form solution of the solute transport model. This necessitates the numerical solution of the solute-transport model to fulfill the task of uncertainty quantification. The present paper proposes an innovative numerical method of solving solute-transport model in the presence of imprecise uncertain input parameters such as dispersivity and velocity of flow. Dispersivity and velocity of flow, both being measurable field parameters, generally posses an epistemic behavior, that is, imprecise. Therefore, uncertainty of these parameters is taken into account as triangular fuzzy number for its simplicity. Solute transport equation with these fuzzy (uncertain) parameters is numerically solved using differential quadrature method and fuzzy vertex method. Therefore, the present version of uncertainty modeling is named as fuzzy differential quadrature scheme of uncertainty modeling. The paper discusses the details of the differential quadrature method and fuzzy vertex method. The stability of the newly developed methodology of uncertainty modeling is assessed by comparing the numerical solution with possible analytical solution.

Critical uncertainty parameters influencing seismic performance of bridges using Lasso regression

SummaryRecent efforts of regional risk assessment of structures often pose a challenge in dealing with the potentially variable uncertain input parameters. The source of uncertainties can be either epistemic or aleatoric. This article identifies uncertain variables exhibiting strongest influences on the seismic demand of bridge components through various regression techniques such as linear, stepwise, Ridge, Lasso, and elastic net regressions. The statistical results indicate that Lasso regression is the most effective one in predicting the demand model as it has the lowest mean square error and absolute error. As the sensitivity study identifies more than 1 significant variable, a multiparameter fragility model using Lasso regression is suggested in this paper. The proposed fragility methodology is able to identify the relative impact of each uncertain input variable and level of treatment needed for these variables in the estimation of seismic demand models and fragility curves. Thus, the proposed approach helps bridge owners to spend their resources judiciously (e.g., data collection, field investigations, and censoring) in the generation of a more reliable database for regional risk assessment. This proposed approach can be applicable to other structures.

Uncertainty quantification and sensitivity analysis of thermoacoustic stability with non-intrusive polynomial chaos expansion

In this paper, non-intrusive polynomial chaos expansion (NIPCE) is used for forward uncertainty quantification and sensitivity analysis of thermoacoustic stability of two premixed flame configurations. The first configuration is a turbulent swirl combustor, modeled by the Helmholtz equation with an n−τ flame model. Uncertain input parameters are the gain and the time delay of the flame, as well as the magnitude and the phase of the outlet reflection coefficient. NIPCE is successfully validated against Monte Carlo simulation. It is observed that the first order expansion suffices to yield accurate results. The second configuration under investigation is a low order network model of a laminar slit burner, with the flame transfer function identified from weakly compressible CFD simulations of laminar reacting flow. Firstly the uncertainty and sensitivity of the growth rate due to three uncertain input parameters of the CFD model – i.e., flow velocity, burner plate temperature and equivalence ratio – are analyzed. A Monte Carlo simulation is no longer possible due to the computational cost of the CFD simulations. Secondly, two additional uncertain parameters are taken into account, i.e., the respective magnitudes of inlet and outlet reflection coefficients. This extension of the analysis does not entail a considerable increase in computational cost, since the additional parameters are included only in the low order network model. In both cases, the second order expansion is sufficient to model the uncertainties in growth rate.

Uncertainty quantification of creep in concrete by Taylor expansion

If deterministic creep prediction models are compared with actual measurement data, often significant differences can be observed. These inconsistencies are associated with different causes, i.e. model uncertainty, uncertain input parameters, measurement errors and wrongfully applying creep prediction models outside their limitations. First, the physical mechanism causing creep of concrete is not yet fully understood. Therefore, it is very likely that certain influences on creep of concrete are not considered in these prediction models, resulting in systematic model errors. The model errors can be quantified by comparing prediction results with experimental data. Secondly, the stochastic character of the input parameters form an additional source of uncertainty which can be quantified by the variance of the model response. The coefficient of variation in function of time-duration, i.e. the time since the application of the load, is a useful measure to quantify the level of uncertainty. In the literature, statistical analysis by means of numerical simulations are often used for this matter. However, even for specialized sampling techniques, a large amount of samples is necessary to cover the relevant ranges of various input parameters. The aim of the present study is to provide an approximate uncertainty quantification of the creep prediction models given uncertain input parameters. This approximation is based on a Taylor series approach. This approach has the advantage that is does not require numerical simulations nor does it require the knowledge of the probability density function of the input parameters. This method is evaluated and compared with the statistical analysis for several creep prediction models available in literature and design codes.

Comparison of polynomial chaos and Gaussian process surrogates for uncertainty quantification and correlation estimation of spatially distributed open-channel steady flows

Data assimilation is widely used to improve flood forecasting capability, especially through parameter inference requiring statistical information on the uncertain input parameters (upstream discharge, friction coefficient) as well as on the variability of the water level and its sensitivity with respect to the inputs. For particle filter or ensemble Kalman filter, stochastically estimating probability density function and covariance matrices from a Monte Carlo random sampling requires a large ensemble of model evaluations, limiting their use in real-time application. To tackle this issue, fast surrogate models based on Polynomial Chaos and Gaussian Process can be used to represent the spatially distributed water level in place of solving the shallow water equations. This study investigates the use of these surrogates to estimate probability density functions and covariance matrices at a reduced computational cost and without the loss of accuracy, in the perspective of ensemble-based data assimilation. This study focuses on 1-D steady state flow simulated with MASCARET over the Garonne River (South-West France). Results show that both surrogates feature similar performance to the Monte-Carlo random sampling, but for a much smaller computational budget; a few MASCARET simulations (on the order of 10-100) are sufficient to accurately retrieve covariance matrices and probability density functions all along the river, even where the flow dynamic is more complex due to heterogeneous bathymetry. This paves the way for the design of surrogate strategies suitable for representing unsteady open-channel flows in data assimilation.

Kriging-based inverse uncertainty quantification of nuclear fuel performance code BISON fission gas release model using time series measurement data

In nuclear reactor fuel performance simulation, fission gas release (FGR) and swelling involve treatment of several complicated and interrelated physical processes, which inevitably depend on uncertain input parameters. However, the uncertainties associated with these input parameters are only known by “expert judgment”. In this paper, inverse Uncertainty Quantification (UQ) under the Bayesian framework is applied to BISON code FGR model based on Risø-AN3 time series experimental data. Inverse UQ seeks statistical descriptions of the uncertain input parameters that are consistent with the available measurement data. It always captures the uncertainties in its estimates rather than merely determining the best-fit values. Kriging metamodel is applied to greatly reduce the computational cost during Markov Chain Monte Carlo sampling.We performed a dimension reduction for the FGR time series data using Principal Component Analysis. We also projected the original FGR time series measurement data onto the PC subspace as “transformed experiment data”. A forward uncertainty propagation based on the posterior distributions shows that the agreement between BISON simulation and Risø-AN3 time series measurement data is greatly improved. The posterior distributions for the uncertain input factors can be used to replace the expert specifications for future uncertainty/sensitivity analysis.

Use of the Principles of Maximum Entropy and Maximum Relative Entropy for the Determination of Uncertain Parameter Distributions in Engineering Applications

The determination of the probability distribution function (PDF) of uncertain input and model parameters in engineering application codes is an issue of importance for uncertainty quantification methods. One of the approaches that can be used for the PDF determination of input and model parameters is the application of methods based on the maximum entropy principle (MEP) and the maximum relative entropy (MREP). These methods determine the PDF that maximizes the information entropy when only partial information about the parameter distribution is known, such as some moments of the distribution and its support. In addition, this paper shows the application of the MREP to update the PDF when the parameter must fulfill some technical specifications (TS) imposed by the regulations. Three computer programs have been developed: GEDIPA, which provides the parameter PDF using empirical distribution function (EDF) methods; UNTHERCO, which performs the Monte Carlo sampling on the parameter distribution; and DCP, which updates the PDF considering the TS and the MREP. Finally, the paper displays several applications and examples for the determination of the PDF applying the MEP and the MREP, and the influence of several factors on the PDF.

Heat Transfer Modeling of Spent Nuclear Fuel Using Uncertainty Quantification and Polynomial Chaos Expansion

A novel method that incorporates uncertainty quantification (UQ) into numerical simulations of heat transfer for a 9 × 9 square array of spent nuclear fuel (SNF) assemblies in a boiling water reactor (BWR) is presented in this paper. The results predict the maximum mean temperature at the center of the 9 × 9 BWR fuel assembly to be 462 K using a range of fuel burn-up power. Current related modeling techniques used to predict the heat transfer and the maximum temperature inside SNF assemblies rely on commercial codes and address the uncertainty in the input parameters by running separate simulations for different input parameters. The utility of leveraging polynomial chaos expansion (PCE) to develop a surrogate model that permits the efficient evaluation of the distribution of temperature and heat transfer while accounting for all uncertain input parameters to the model is explored and validated for a complex case of heat transfer that could be substituted with other problems of intricacy. UQ computational methods generated results that are encompassing continuous ranges of variable parameters that also served to conduct sensitivity analysis on heat transfer simulations of SNF assemblies with respect to physically relevant parameters. A two-dimensional (2D) model is used to describe the physical processes within the fuel assembly, and a second-order PCE is used to characterize the dependence of center temperature on ten input parameters.

Effect of Truncated Input Parameter Distribution on the Integrity of Safety Instrumented Systems Under Epistemic Uncertainty

Safety instrumented system (SIS) is widely applied to reduce or prevent risk in industry. Practical SIS commonly meets with epistemic uncertainty arising from incompleteness of knowledge on various input parameters due to lack of data. Epistemic uncertainty can be reduced by collecting more knowledge or data. Epistemic uncertainty in input parameters can lead to variation in probability of failure to perform its intended functions on demand (PFD) for an SIS. This paper employs the complementary cumulative distribution function of PFD to define exceedance probability (EP) that the PFD exceeds a prescribed value. Sensitivity analysis is further investigated, analyzing the effect of an epistemically uncertain input parameter with truncated distribution on EP of an SIS. We have derived the analytic expression for evaluating the effect, and only an evaluation is needed to estimate the effects of all the parameters. Two examples are employed to demonstrate the applicability of the proposed method. We further compare the effects for the truncated and nontruncated parameter situations. Their results converge to the same ones as the truncated region of an input parameter decreases to zero. When the truncated region of an input parameter is less than 10–3 , the corresponding results can be approximated by the ones of the nontruncated case with lower computational cost.

The impact of personalized probabilistic wall thickness models on peak wall stress in abdominal aortic aneurysms.

If computational models are ever to be used in high-stakes decision making in clinical practice, the use of personalized models and predictive simulation techniques is a must. This entails rigorous quantification of uncertainties as well as harnessing available patient-specific data to the greatest extent possible. Although researchers are beginning to realize that taking uncertainty in model input parameters into account is a necessity, the predominantly used probabilistic description for these uncertain parameters is based on elementary random variable models. In this work, we set out for a comparison of different probabilistic models for uncertain input parameters using the example of an uncertain wall thickness in finite element models of abdominal aortic aneurysms. We provide the first comparison between a random variable and a random field model for the aortic wall and investigate the impact on the probability distribution of the computed peak wall stress. Moreover, we show that the uncertainty about the prevailing peak wall stress can be reduced if noninvasively available, patient-specific data are harnessed for the construction of the probabilistic wall thickness model.

Incomplete statistical information limits the utility of high-order polynomial chaos expansions

Polynomial chaos expansion (PCE) is a well-established massive stochastic model reduction technique that approximates the dependence of model output on uncertain input parameters. In many practical situations, only incomplete and inaccurate statistical knowledge on uncertain input parameters are available. Fortunately, to construct a finite-order expansion, only some partial information on the probability measure is required that can be simply represented by a finite number of statistical moments. Such situations, however, trigger the question to what degree higher-order statistical moments of input data are increasingly uncertain. On the one hand, increasing uncertainty in higher moments will lead to increasing inaccuracy in the corresponding chaos expansion and its result. On the other hand, the degree of expansion should adequately reflect the non-linearity of the analyzed model to minimize the approximation error of the expansion. Observation of the PCE convergence when statistical input information is incomplete demonstrates that higher-order PCE expansions without adequate data support are useless. Moreover, it makes apparent that PCE of a certain order is adequate just for a corresponding amount of available input data. The key idea of the current work is to align the order of expansion with a compromise between the degree of non-linearity of the model and the reliability of statistical information on the input parameters. To assure an optimal choice of the expansion order, we offer a simple relation that helps to align available input statistical data with an adequate expansion order. As fundamental steps into this direction, we propose overall error estimates for the statistical type of error that results from inaccurate statistical information plus the error that results from truncating the expansion of a non-linear model. Our key message is that any order of expansion is only justified if accompanied by reliable statistical information on input moments of a certain higher order.

Fuzzy finite element model updating of the DLR AIRMOD test structure

This article presents the application of finite-element fuzzy model updating to the DLR AIRMOD structure. The proposed approach is initially demonstrated on a simulated mass-spring system with three degrees of freedom. Considering the effect of the assembly process on variability measurements, modal tests were carried out for the repeatedly disassembled and reassembled DLR AIRMOD structure. The histograms of the measured data attributed to the uncertainty of the structural components in terms of mass and stiffness are utilised to obtain the membership functions of the chosen fuzzy outputs and to determine the updated membership functions of the uncertain input parameters represented by fuzzy variables. In this regard, a fuzzy parameter is introduced to represent a set of interval parameters through the membership function, and a meta model (kriging, in this work) is used to speed up the updating. The use of non-probabilistic models, i.e. interval and fuzzy models, for updating models with uncertainties is often more practical when the large quantities of test data that are necessary for probabilistic model updating are unavailable.

Multifidelity Sparse-Grid-Based Uncertainty Quantification for the Hokkaido Nansei-oki Tsunami

With uncertainty quantification, we aim to efficiently propagate the uncertainties in the input parameters of a computer simulation, in order to obtain a probability distribution of its output. In this work, we use multi-fidelity sparse grid interpolation to propagate the uncertainty in the shape of the incoming wave for the Okushiri test-case, which is a wave tank model of a part of the 1993 Hokkaido Nansei-oki tsunami. An important issue with many uncertainty quantification approaches is the ‘curse of dimensionality’: the overall computational cost of the uncertainty propagation increases rapidly when we increase the number of uncertain input parameters. We aim to mitigate the curse of dimensionality by using a multifidelity approach. In the multifidelity approach, we combine results from a small number of accurate and expensive high-fidelity simulations with a large number of less accurate but also less expensive low-fidelity simulations. For the Okushiri test-case, we find an improved scaling when we increase the number of uncertain input parameters. This results in a significant reduction of the overall computational cost. For example, for four uncertain input parameters, accurate uncertainty quantification based on only high-fidelity simulations comes at a normalised cost of 219 high-fidelity simulations; when we use a multifidelity approach, this is reduced to a normalised cost of only 10 high-fidelity simulations.

Model assessment in scientific computing

PurposeThis 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/approachIn 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.FindingsSatisfying 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/valueTraditional 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.

CALCULATION OF “NORMAL” CONSTRUCTION TIME FOR BUILDING CONSTRUCTION PROJECTS WHILST CONSIDERING UNCERTAINTIES

Construction time has a major influence both on the cost-efficient execution of construction works and on the overall project outcome achieved by the client. Clients would do themselves a disservice if they specified short or extremely short construction periods for their projects. The same applies to time made available for project preparation, particularly for the design and tender stages. Any project that is poorly planned, tendered, and executed under time pressure will adversely affect actual construction work but also the building’s use and possible reuse. Cost, time and quality targets are at risk due to the resulting disruptions to the construction process. Productivity is adversely affected not only by unduly short but also exceedingly long construction times. Short or very short construction times have a major influence on the efficient and effective utilization of production factors, including elementary (workforce, materials, equipment and machinery) and discretionary factors (project manager, site manager, technicians, etc.). This paper outlines the basic correlation between construction time, labor consumption rates and productivity as well as construction cost. Furthermore, it sets out to determine the influence of construction time on costing and, consequently, on the construction process. A practical example demonstrates how normal construction time can be calculated for reinforced concrete works based on uncertain input parameters. In addition, the benefits of specifying normal construction time for clients and contractors are outlined.

Probabilistic Risk Assessment of CO2 Trapping Mechanisms in a Sandstone CO2-EOR Field in Northern Texas, USA

This study employs a polynomial chaos expansion (PCE) technique to develop the reduced order models (ROMs) integrated with the Monte Carlo simulations to quantify uncertainties of CO2 storage associated with enhanced oil recovery (EOR) in a commercial-scale CO2-EOR field. The Morrow B sandstone at the Farnsworth Unit (FWU) EOR field in northern Texas was selected as a case study. A 3-D reservoir model, including simulation of a five-spot injection/production well pattern, was constructed based on the data from well logs and cores, and an updated seismic interpretation in the FWU. Porosity and permeability were considered as sources of uncertainty. The 1000-realization heterogeneous random fields of porosity and permeability were generated based on the variogram analysis on the core measurements of the FWU. Three model outputs of interest include the amount of CO2 trapped by three trapping mechanisms, i.e. hydrodynamic trapping, oil dissolution trapping, and aqueous dissolution trapping. The total of 25 runs were conducted with the simulations of a 20-year CO2-EOR period, and a 20-year monitoring period to develop the ROMs between uncertain model input parameters (i.e., porosity and permeability in this study) and model outputs at the end of simulation for each grid cell using PCE approach. The high coefficient of determination (R2) and small normalized root mean square error (NRMSE) between the simulated (using reservoir modeling) and predicted (using ROMs) CO2 storage indicate that the ROMs are acceptable and reliable to be used for the predictions. Given the 1000 Monte Carlo samplings of the model input parameters, cumulative distribution functions (CDFs) and uncertainty bounds (10th and 90th percentiles) of model outputs were estimated based on ROMs. At the end of simulation, the most injected CO2 at the FWU was stored by hydrodynamic trapping (between 121,400 and 166,860 tonnes), followed by oil dissolution trapping (between 55,303 and 76,816 tonnes), and aqueous dissolution trapping (between 1979 and 2751 tonnes).

Developing synthetic reservoir type curve model for use in evaluating surface facility and gathering pipe network designs

Surface facilities and unconventional gas gathering networks are typically designed to collect gas from a large number of wells to a central location. The unit operations that make up the surface network need to be installed before the wells are producing and thus need to be sized on predicted performance rather than actual performance which is not known until production data is available. This means each reservoir's production profile which is based on uncertain input parameters and imperfect reservoir models forms the sizing basis for the surface facilities.In this study a method is developed to generate synthetic reservoir flow type curves based on a set of input parameters that is independent of reservoir parameters. The main qualitative characteristics of an unconventional gas reservoir type curve are described such as gas ramp to peak, peak gas flow and production decline, along with the discontinuities and variations from expected performance seen in operating trends. The synthetic type curve proposed in this work can be parameterised to mimic these characteristics, along with a well deliverability mechanism and subsurface communication between wells.The method of being able to describe a type curve by means of input parameterisation allows an unconventional gas surface facility of gathering pipe network and in-field booster compressors to be designed against many sets of synthetic type curves rapidly generated by randomisation of those input parameters.

Assessment of the Pitting Corrosion Degradation Lifetime: A Case Study of Boiler Tubes

Abstract Corrosion degradation is a common problem for boiler tubes in power plants, resulting in an unscheduled plant shutdown. In this research, degradation of the corrosion is investigated for boiler tubes by estimating the corrosion lifetime. A special focus is made on the corrosion failures, important failure modes, and mechanisms for the metallic boiler tubes via failure modes and effect analysis (FMEA) method, thereby evaluating the pitting corrosion as the most common failure mode in the tubes. Majority of the available approaches estimates lifetime of the pitting corrosion by deterministic approaches, in which the results are valid only for limited conditions. In order to improve deficiencies of available models, a stochastic method is proposed here to study the corrosion life. The temporal behavior of the metal degradation is analyzed in different conditions through the developed approach, and a proper degradation model is selected. Uncertainty intervals/distributions are determined for some of the model parameters. The deterministic model is converted to a probabilistic model by taking into account the variability of the uncertain input parameters. The model is simulated using Monte Carlo method via simple sampling. The result of the life estimation is updated by the Bayesian framework using Monte Carlo Markov Chain. Finally, for the element that is subjected to the pitting corrosion degradation, the life distribution is obtained. The modeling results show that the pitting corrosion has stochastic behavior with lognormal distribution as proper fit for the pitting corrosion behavior. In order to validate the results, the estimations were compared with the power plant field failure data.