Adaptive Uncertainty Propagation for Coupled Multidisciplinary Systems

This thesis discusses inverse problems in interpreting satellite observations. When we solve the inverse problem in atmospheric remote sensing, we make simplifications and assumptions about the atmosphere. In addition to the observation noise, this contributes to the uncertainty of the solution. We focus on statistical inverse problems which naturally take into account uncertainties in the solution. Uncertainty analysis is important both in utilizing satellite data and in developing algorithms. In this work, we solve the inverse problem based on the Bayesian method in looking for the best match between satellite observations and the state of the atmosphere related to aerosol load and vertical ozone profiles. One important goal was to achieve a more realistic uncertainty estimate by considering forward model uncertainty, i.e., model discrepancy. Another objective is to acknowledge uncertainty in aerosol model selection. In this thesis we developed a novel method to obtain aerosol optical depth (AOD) based on the Bayesian inference and where a concept of model evidence is used for model comparison. We applied the Bayesian model averaging technique for combining inference from several aerosol optical models. We utilized the residuals of the model fits and Gaussian processes for characterizing the model discrepancy. We applied the method for the observations of the OMI and TROPOMI instruments and compared the resulting AOD with the ground-based aerosol measurements. Acknowledging of the model discrepancy as well as difficulty in the model selection are reflected in the uncertainty of the AOD estimate. The Bayesian approach can give additional information about the sources of uncertainty, assists in the uncertainty analysis of the results, and may guide improving the retrieval algorithms. This thesis also assessed the quality of the operational satellite ozone profile product depending on season, latitude and altitude. The comparison of GOME-2/Metop-A ozone profiles in a global scale concerning the years 2008-2011 was done against the reference data of three satellites. Based on the results, we assessed the reliability of the satellite ozone profile data, also considering the ageing of the instrument and identified the potential points of improvement.

Water resources modelers face the challenge of dealing with numerous uncertainties due to the lack of knowledge of the natural systems, numerical approaches used in modeling (equations, parameters, structures, solutions), and field data collected to set up and evaluate models. Propagation of parameter uncertainty into model results is a relevant topic in environmental hydrology. Uncertainty analyses improve assessment of hydrological modeling. There is a need in modern hydrology of developing and testing uncertainty analysis methods that support hydrological model evaluation. In this research the propagation of model parameter uncertainty into streamflow model results is evaluated. The Hydrological Simulation Program – FORTRAN (HSPF) supported by the US Environmental Protection Agency was evaluated using hydroenvironmental data from the Luxapallila Creek watershed located in Mississippi and Alabama, USA. The uncertainty bounds of model outputs were computed using the Monte Carlo simulation and Harr’s point estimation methods. Analysis of parameter uncertainty propagation on streamflow simulations from 12 HSPF parameters was accomplished using 5,000 Monte Carlo random samples and 24 Harr selected points for each selected parameter. The comparison showed that Harr’s method could be an appropriate initial indicator of parameter uncertainty propagation on streamflow simulations, particularly for hydrology models with several parameters.

Aerodynamic response of structures with parametric uncertainties

In recent years, the demand to provide best-estimate predictions with confident bounds is increasing for the nuclear reactor performance and safety analysis. The Organisation for Economic Co-operation and Development Nuclear Energy Agency has been developing an international benchmark of the light water reactor (LWR) uncertainty analysis in modeling (UAM) for the examination of uncertainty quantification and propagation methodologies with various modeling and simulation code systems. The objective of the present work is to develop an uncertainty propagation mechanism based on the stochastic sampling method by taking into account the uncertainties of both basic nuclear data and fuel modeling parameters in the simulation of pressurized water reactors (PWRs) that can be incorporated in the conventional LWR simulation approach. More specifically, the Three Mile Island Unit 1–related exercises from the LWR-UAM benchmark have been modeled using the coupled TRACE/PARCS code system in the three-dimensional core representation. The input uncertainties of the neutronics simulation include few-group cross sections and kinetics parameters generated using the Sampler/Polaris sequence of SCALE 6.2.1. Several heat transfer–related variables for the fuel modeling were considered as sources of input uncertainty of the thermal-hydraulics simulations, including the thermal conductivity of fuel and cladding, fuel heat capacity, and the gap conductance. Dakota was used to sample input parameters of the coupled code system and to perform the uncertainty analysis. Two types of simulations were conducted: steady-state calculation at hot full-power condition and transient scenario initiated by the spatially asymmetric rod ejection accident. Quantities of interest for the steady-state calculation, including core multiplication factor and power peaking factors, were calculated with associated uncertainties. For transient calculations, best-estimate plus uncertainty results of the time evolution of core reactivity, core power, and peak fuel temperature were generated and analyzed. The Wilks’ formula was used to determine the necessary sample size to achieve a 95% confidence of the 95% limit of output quantities of interest. Although the uncertainty propagation and quantification method presented in this paper was developed for PWRs, it could be in general applicable to the multiphysics uncertainty quantification of other types of LWR cores.

Joint analysis of input and parametric uncertainties in watershed water quality modeling: A formal Bayesian approach

Predictive Modeling Methodology constitutes an innovative approach to perform uncertainty analysis (UA) that reduces the subjective and user-defined ways to manage experimental data and derive uncertainty of input parameters that characterize the Propagation of Input Uncertainties (PIU) and/or Propagation of Output Accuracies (POA) methods. The Code with the capability of Adjoint Sensitivity and Uncertainty AnaLysis by Internal Data ADjustment and assimilation (CASUALIDAD) method can be developed as a fully deterministic method based on advanced mathematical tools to internally perform in the thermal-hydraulic system code the sensitivity analysis (SA) and the UA. The method is based upon powerful mathematical tools to perform the SA and upon the Data Adjustment and Assimilation methodology by which experimental observations are combined with code predictions and their respective errors through the application of the Bayes theorem and of the Principle of Maximum Likelihood to provide an improved estimate of the system state and of the associated uncertainty considering all input parameters that affect any prediction. The methodology has been structured in two main steps. The first step generates the database of improved estimations (IEs) starting from the available set of experimental data and related qualified calculations. The second step deals with the use of the selected (from the obtained database) set of IEs for the uncertainty evaluation of the predicted nuclear power plant transient scenario. The proposed methodology clearly interrelates in a consistent and robust framework the code validation issue with the evaluation of the uncertainty of code responses passing through the quantification of input uncertainty parameters of code models, thus constituting a step forward with respect to the subjectivity of the current methods based on PIU and/or POA.

A RELAP5 input model was established for a scaled-up facility simulating China's Advanced Passive Water Reactor with passive safety features. The simulation was performed to reproduce a Main Steam Line Break (MSLB) scenario at steam line connected to one Steam Generator. The figure of merit selected in this accident scenario includes the maximum containment pressure, mass and energy release to containment. Driving factors of this response function include Passive Residue Heat Removal material thermal conductivity, Pressurizer temperature, and broken steam line temperature.To achieve an adequately justified safety margin using a Best Estimate Plus Uncertainty analysis, dominant phenomena were selected from a reference Phenomenon Identification and Ranking Table. The calculation results were compared with the available reference data of similar Generation III Passive Water Reactor to assess the code's capability to predict the MSLB phenomena. The DAKOTA toolkit is used to drive both parameter sensitivity analysis and uncertainty propagation. The 95/95 uncertainty bands of key output parameters were obtained using the Wilks’ statistical methods.Compared with the reference data, the simulation results partially confirmed the stability and repeatability of the code model for initial and boundary condition perturbations. The uncertainty bands of important output parameters were demonstrated. The results indicated that the maximum containment pressure value was below the safety limit, and the passive safety system can mitigate the consequence of the MSLB. The mass and energy released into the containment were assessed according to the containment design.The parameter sensitivity analysis was performed with 34 input parameters, and the results were evaluated by Spearman's Simple Rank Correlation Coefficients.

Statistical model calibration and design optimization under aleatory and epistemic uncertainty

Fuzzy uncertainty propagation in composites using Gram–Schmidt polynomial chaos expansion

The objective of the study described in this paper was to develop an efficient uncertainty quantification framework capable of analyzing uncertainty in integrated spacecraft system models. Specifically, this paper discusses the capabilities of the developed framework and the res ults when applied to the multidisciplinary analysis of a reusable launch veh icle (RLV). This particular framework is capable of efficiently propagating mixed (inherent and epistemic) uncertainties through complex simulation codes. The Second-Order Probability Theory utilizing a stochastic response surface obta ined with Point-Collocation NonIntrusive Polynomial Chaos was used for the propagation of the mixed uncertainties. This particular methodology was applied to the RLV analysis, and the uncertainty in the output parameters of interested was obtained in terms of intervals at various probability levels. This study has also demonstrated the feasibility of the developed uncertainty quantifica tion framework for efficient propagation of mixed uncertainties in the analysis of complex aerospace systems. I. Introduction ncertainties are generally ubiquitous in the analys is and design of highly complex engineering systems. Uncertainties can arise from the lack of k nowledge in physical modeling (epistemic uncertainty), inherent variations in the systems (a leatory uncertainty), and numerical errors in the computational procedures used for analysis. It is i mportant to account for all of these uncertainties in applications such as robust and reliable design of multi-disciplinary aerospace systems. A reusable la unch vehicle (RLV) is a highly complex aerospace system, which represents a cost viable option for access t o space missions due to its reusability aspect. Since an RLV system is composed of various subsystems which must work together to serve an over-arching p urpose or mission objective/constraint, a multidisciplinary approach for the analysis and des ign of RLV systems is required. Uncertainties are generally present in the models used in each discipline of an RLV multidisciplinary analysis framework. It is important to account for all of these uncertainties for accurate and reliabl e estimates of the RLV system performance. The primary purpose of this paper will be to demonstrate an efficient approach for uncertainty quantification in the multidiscipl inary analysis of a RLV, which has a mixture of aleatory (inherent) and epistemic input uncertainties. Uncertainty quantification will be performed on various output variables of interest f or an RLV system such as the weight and vehicle crossrange. For the propagation of mixed (aleatory-epist emic) uncertainty, Second-Order Probability Theory utilizing Point-Collocation Non-Intrusive Polynomia l Chaos (NIPC) 1 will be used. 2-3 In general, the NIPC methods, which are based on the spectral representa tion of uncertainty, are computationally more effic ient than traditional Monte Carlo methods for moderate number of uncertain variables and can give highly 1 Aerospace Engineer, 4020 Long Beach Blvd, Long Beach, CA, 90807, Member AIAA

This paper presents a framework for assessing the contribution of different sources of parametric uncertainty in sediment runoff simulations. The proposed uncertainty assessment is comprised in the three procedures. First, global parametric sensitivity and uncertainty analysis based on a Monte Carlo Simulation technique was applied to identify the dominant uncertainty sources. The analysis revealed a few parameters significantly affecting the model behaviours. Second, the propagation of parametric uncertainties through sediment runoff simulations was investigated, which identified that sediment simulations tend to involve more uncertainty than only streamflow simulations. Third, by conducting scenario simulations considering different uncertainty sources, it explores a strategy for reducing the parametric uncertainty considering its propagation effect. The proposed framework can provide useful information for improving sediment runoff modelling and its application to river basin management recognizing predictive uncertainty.

A novel procedure to analyse the uncertainty associated to the output of GIS-based models is presented. The procedure can handle models of any degree of complexity that accept any kind of input data. Two important aspects of spatial modelling are addressed: the propagation of uncertainty from model inputs and model parameters up to the model output (uncertainty analysis); and the assessment of the relative importance of the sources of uncertainty in the output uncertainty (sensitivity analysis). Two main applications are proposed. The procedure allows implementation of a GIS-based model whose output can reliably support the decision process with an optimized allocation of resources for spatial data acquisition. This is possible in low cost strategy, based on numerical simulations on a small prototype of the GIS-based model. Furthermore, the procedure provides an effective model building tool to choose, from a group of alternative models, the best one in terms of cost-benefit analysis. A comprehensive case study is described. It concerns the implementation of a new GIS-based hydrologic model, whose goal is providing near real-time flood forecasting.

On the use of uncertainty analyses to test hypotheses regarding deterministic model predictions of environmental processes

The results of transport modeling codes, e.g., GENE for the plasma core or SOLPS-ITER for the plasma edge, depend critically on reliable profile and equilibrium estimates. The propagation of uncertainties (UP) of input quantities to the results of modeling codes, e.g., power and particle exhaust and plasma stability, is frequently neglected because of the costs of running the codes as well as because of the missing uncertainty quantification of input quantities. The situation becomes even more cumbersome if profile gradients and their uncertainties are of major concern for transport analyses. Two different techniques are presented to estimate profiles, profile gradients, their uncertainties, and candidate profiles for UP in modeling codes. Markov Chain Monte Carlo sampling of the posterior probability density of an integrated data analysis approach is applied to estimate electron density and temperature profiles. Nonstationary Gaussian process regression is applied to estimate ion temperature and angular velocity profiles. Both methods provide in a natural way profile gradients, profile logarithmic gradients, and their uncertainties. Modeling codes benefit also from reliable equilibrium reconstructions and quantification of the uncertainty of various equilibrium parameters. For the analysis of diagnostics data, the position and uncertainty of flux surfaces as well as of the magnetic axis are important. For plasma transport and stability codes, the estimation of uncertainties of current and q-profiles is presented. For plasma edge codes the position of the separatrix contour and its uncertainty at various poloidal positions is of primary interest especially if steep profile gradients are present. Examples of uncertainties and their sources in magnetic scalar quantities, profiles, and separatrix contours are shown.

Ecosystem models are useful tools for understanding ecological processes and for sustainable management of resources. In biogeochemical field, numerical models have been widely used for investigating carbon dynamics under global changes from site to regional and global scales. However, it is still challenging to optimize parameters and estimate parameterization uncertainty for complex process‐based models such as the Erosion Deposition Carbon Model (EDCM), a modified version of CENTURY, that consider carbon, water, and nutrient cycles of ecosystems. This study was designed to conduct the parameter identifiability, optimization, sensitivity, and uncertainty analysis of EDCM using our developed EDCM‐Auto, which incorporated a comprehensive R package—Flexible Modeling Framework (FME) and the Shuffled Complex Evolution (SCE) algorithm. Using a forest flux tower site as a case study, we implemented a comprehensive modeling analysis involving nine parameters and four target variables (carbon and water fluxes) with their corresponding measurements based on the eddy covariance technique. The local sensitivity analysis shows that the plant production‐related parameters (e.g., PPDF1 and PRDX) are most sensitive to the model cost function. Both SCE and FME are comparable and performed well in deriving the optimal parameter set with satisfactory simulations of target variables. Global sensitivity and uncertainty analysis indicate that the parameter uncertainty and the resulting output uncertainty can be quantified, and that the magnitude of parameter‐uncertainty effects depends on variables and seasons. This study also demonstrates that using the cutting‐edge R functions such as FME can be feasible and attractive for conducting comprehensive parameter analysis for ecosystem modeling.