A probabilistic procedure was applied to the evaluation of predictions from the GLEAMS nonpoint source pollution model. Assessment of both the procedure and model was made by comparing absolute and relative predictions made with both probabilistic and deterministic procedures. Field data used came from a study of pesticide fate and transport in both no-till and conventional tillage plots in a Coastal plain soil. Variables examined were: runoff, sediment yield, surface losses, mass in the root zone, and depth of center of mass for two pesticides and a tracer. Random inputs were characterized with probability distributions. Values for inputs were sampled from these distributions for 5000 model executions to create output distributions in the probabilistic procedure. Central tendency values from the probabilistic input distributions were used as inputs for the deterministic runs. Model predictions generally followed expected trends and were within observed variability. Two exceptions were systematic under-predictions of runoff and pesticide losses and under-predictions of the depth of bromide in the root zone later in the observed period. These exceptions may indicate errors in the runoff and plant uptake components of the model. Neither procedure made relative predictions correctly all the time, however subjective assessment of the model results led to consistent decisions between the two procedures. The probabilistic procedure reduced parameter uncertainty by eliminating arbitrary parameter selection from available data by utilizing the complete range of data, however, it did not eliminate uncertainty in the data itself. / Master of Science

In data-poor regions around the world, particularly in less-privileged countries, hydrologists cannot always take advantage of available hydrological models to simulate a hydrological system due to the lack of reliable measurements of hydrological variables, in particular rainfall and streamflows, needed to implement and evaluate these models. Rainfall estimates obtained with remotely deployed sensors constitute an excellent source of precipitation for these basins, however they are prone to errors that can potentially affect hydrologic simulations. Concurrently, limited access to streamflow measurements does not allow a detailed representation of the system's structure through parameter estimation techniques. This dissertation presents multiple studies that evaluate the usefulness of remotely sensed products for different hydrological applications and the sensitivity of simulated streamflow to parameter uncertainty across basins with different hydroclimatic characteristics with the ultimate goal of increasing the applicability of land surface models in ungauged basins, particularly in South America. Paper 1 presents a sensitivity analysis of daily simulated streamflows to changes in model parameters along a hydroclimatic gradient. Parameters controlling the generation of surface and subsurface flow were targeted for the study. Results indicate that the sensitivity is strongly controlled by climate and that a more parsimonious version of the model could be implemented. Paper 2 explores how errors in satellite-estimated precipitation, due to infrequent satellite measurements, propagate through the simulation of a basin's hydrological cycle and impact the characteristics of peak streamflows within the basin. Findings indicate that nonlinearities in the hydrological cycle can introduce bias in simulated streamflows with error-corrupted precipitation. They also show that some characteristics of peak discharges are not conditioned by errors in satellite-estimated precipitation at a daily time step. Paper 3 evaluates the dominant sources of error in three satellite products when representing convective storms and how shifts in the location of the storm affect simulated peak streamflows in the basin. Results indicate that satellite products show some deficiencies retrieving convective processes and that a ground bias correction can mitigate these deficiencies but without sacrificing the potential for real-time hydrological applications. Finally, spatially shifted precipitation fields affect the magnitude of the peaks, however, its impact on the timing of the peaks is dampened out by the system's response at a daily time scale.

Natural attenuation refers to the observed reduction in contaminant concentration via natural processes as contaminants migrate from the source into environmental media. Assessment of the dimensions of contaminant plumes and prediction of their fate requires predictions of the rate of dissolution of contaminants from residual non-aqueous-phase liquids (NAPLs) into the aquifer and the rate of contaminant removal through biodegradation. The available techniques to estimate these parameters do not characterize their confidence intervals by accounting for their relationships to uncertainty in source geometry and hydraulic conductivity distribution. The central idea in this thesis is to develop a flexible modeling approach for characterization of uncertainty in residual NAPL dissolution rate and first-order biodegradation rate by tailoring the estimation of these parameters to distributions of uncertainty in source size and hydraulic conductivity field. The first development in this thesis is related to a distance function approach that characterizes the uncertainty in the areal limits of the source zones. Implementation of the approach for a given monitoring well arrangement results in a unique uncertainty band that meets the requirements of unbiasedness and fairness of the calibrated probabilities. The second development in this thesis is related to a probabilistic model for characterization of uncertainty in the 3D localized distribution of residual NAPL in a real site. A categorical variable is defined based on the available CPT-UVIF data, while secondary data based on soil texture and groundwater table elevation are also incorporated into the model. A cross-validation study shows the importance of incorporation of secondary data in improving the prediction of contaminated and uncontaminated locations. The third development in this thesis is related to the implementation of a Monte Carlo type inverse modeling to develop a screening model used to characterize the confidence intervals in the NAPL dissolution rate and first-order biodegradation rate. The development of the model is based on sequential self-calibration approach, distance-function approach and a gradient-based optimization. It is shown that tailoring the estimation of the transport parameters to joint realizations of source geometry and transmissivity field can effectively reduce the uncertainties in the predicted state variables.

Based on the Lypunov stability theorem, a design methodology of adaptive backstepping control is proposed in this thesis for a class of multi-input systems with matched and mismatched perturbations to solve regulation problems. The systems to be controlled contain blocks¡¦ dynamic equations, hence virtual input controllers are firstly designed so that the state variables of first blocks are asymptotically stable if each virtual control input is equal to the state variable of next block. The control input is designed in the last block to ensure asymptotic stability for each state even if the perturbations exist. In addition, adaptive mechanisms are embedded in each virtual input function and control input, so that the upper bound of perturbations is not required to be known beforehand. Finally, a numerical example and a practical application are given for demonstrating the feasibility of the proposed control scheme. ­^¤åºK­n(keyword)¡Gadaptive block backstepping controller, mismatched parameter uncertainty, virtual input controller, Lyapunov stability .

No description available.

Pharmacometric model-based analysis using nonlinear mixed-effects models (NLMEM) has to date mainly been applied to learning activities in drug development. However, such analyses can also serve as the primary analysis in confirmatory studies, which is expected to bring higher power than traditional analysis methods, among other advantages. Because of the high expertise in designing and interpreting confirmatory studies with other types of analyses and because of a number of unresolved uncertainties regarding the magnitude of potential gains and risks, pharmacometric analyses are traditionally not used as primary analysis in confirmatory trials. The aim of this thesis was to address current hurdles hampering the use of pharmacometric model-based analysis in confirmatory settings by developing strategies to increase model compliance to distributional assumptions regarding the residual error, to improve the quantification of parameter uncertainty and to enable model prespecification. A dynamic transform-both-sides approach capable of handling skewed and/or heteroscedastic residuals and a t-distribution approach allowing for symmetric heavy tails were developed and proved relevant tools to increase model compliance to distributional assumptions regarding the residual error. A diagnostic capable of assessing the appropriateness of parameter uncertainty distributions was developed, showing that currently used uncertainty methods such as bootstrap have limitations for NLMEM. A method based on sampling importance resampling (SIR) was thus proposed, which could provide parameter uncertainty in many situations where other methods fail such as with small datasets, highly nonlinear models or meta-analysis. SIR was successfully applied to predict the uncertainty in human plasma concentrations for the antibiotic colistin and its prodrug colistin methanesulfonate based on an interspecies whole-body physiologically based pharmacokinetic model. Lastly, strategies based on model-averaging were proposed to enable full model prespecification and proved to be valid alternatives to standard methodologies for studies assessing the QT prolongation potential of a drug and for phase III trials in rheumatoid arthritis. In conclusion, improved methods for handling residual error, parameter uncertainty and model uncertainty in NLMEM were successfully developed. As confirmatory trials are among the most demanding in terms of patient-participation, cost and time in drug development, allowing (some of) these trials to be analyzed with pharmacometric model-based methods will help improve the safety and efficiency of drug development.

Among other sources of uncertainties in hydrologic modeling, spatial rainfall variability, channel hydraulic variability, and model parameter uncertainty were evaluated. The Monte Carlo and Harr methods were used to assess 90% certainty bounds on simulated flows. The lumped watershed model, Hydrologic Simulation Program FORTRAN ? HSPF, was used to simulate streamflow at the outlet of the Luxapallila Creek watershed in Mississippi and Alabama. 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. Spatial rainfall variability propagation on simulated flows was studied using six random grid point sets of Next Generation Weather Radar (NEXRAD) rainfall data (i.e., 109, 86, 58, 29, 6, and 2 grid points) from the baseline scenario (115 NEXRAD grid points). Uncertainty in channel hydraulic properties was assessed comparing the baseline scenario (USGS FTABLE) versus the EPA RF1 FTABLE scenario. The difference between the baseline scenario and the remaining scenarios in this study was evaluated using two criteria: the percentage of observed flows within the HSPF 90% certainty bounds (Reliability) and the width of the HSPF 90% certainty bounds (Sharpness). Daily observed streamflow data were clustered into three groups to assess the model performance by each class: below normal, normal, and above normal flows. The parameter uncertainty propagation results revealed that the higher the model Sharpness the lower the model Reliability. The model Sharpness and Reliability results using 2 NEXRAD grid points were markedly different from those results using the remaining NEXRAD data sets. The hydraulic property variability of the main channel affected storm event paths at the watershed outlet, especially the time to peak flow and recessing limbs of storm events. The comparison showed that Harr?s method could be an appropriate initial indicator of parameter uncertainty propagation on streamflow simulations, in particular for hydrology models with several parameters. Parameter uncertainty was still more important than those sources of uncertainty accomplished in this study because all of the median relative errors of model Reliability and Sharpness were lower than +/- 100%.

Approved for public release; distribution is unlimited / To ensure sufficient capacity to handle unexpected demands for electric power, decision makers often over-estimate expeditionary power requirements. Therefore, we often use limited resources inefficiently by purchasing more generators and investing in more renewable energy sources than needed to run power systems on the battlefield. Improvement of the efficiency of expeditionary power units requires better managing of load requirements on the power grids and, where possible, shifting those loads to a more economical time of day. We analyze the performance of a previously developed optimization model for scheduling time-shiftable electrical loads in an expeditionary power grids model in two experiments. One experiment uses model data similar to the original baseline data, in which expected demand and expected renewable production remain constant throughout the day. The second experiment introduces unscheduled demand and realistic fluctuations in the power production and the demand distributions data that more closely reflect actual data. Our major findings show energy grid power production composition affects which uncertain factor(s) influence fuel con-sumption, and uncertainty in the energy grid system does not always increase fuel consumption by a large amount. We also discover that the generators running the most do not always have the best load factor on the grid, even when optimally scheduled. / Lieutenant Commander, United States Navy

Le fonctionnement de la pile à combustible (PAC) de type PEM (à membrane polymère) est encore soumis à de nombreuses incertitudes, aux natures différentes, qui affectent ses performances électriques, sa fiabilité et sa durée de vie. L'objectif général de cette thèse est de proposer une méthode d'aide à l'évaluation de la fiabilité des PAC par la simulation ; la fiabilité étant vue ici comme la garantie d’accéder à un niveau de performance électrique donné dans les différentes conditions d’usage envisagées pour la PAC. La démarche proposée s’appuie sur un couplage physico-fiabiliste où la complexité des phénomènes physiques présents dans la pile est prise en compte par une modélisation de connaissance, dynamique, symbolique et acausale, développée dans l’environnement Modelica - Dymola. La modélisation retenue, monodimensionnelle, non isotherme inclut une représentation diphasique des écoulements fluidiques pour mieux retranscrire la complexité des échanges d’eau dans le coeur de la pile PEM. La modélisation permet aussi d’intégrer des incertitudes sur certains de ses paramètres physiques et semi-empiriques (classés en trois catégories : opératoires, intrinsèques et semi-empiriques) puis d’entreprendre, par des tirages de Monte-Carlo, la modélisation probabiliste des conséquences des incertitudes injectées sur la performance d’une PAC. Il est ainsi possible, par la suite, d’estimer la fiabilité d’une PAC par le calcul de la probabilité que la performance électrique reste supérieure à un seuil minimal à définir en fonction de l’application. Une analyse physico-fiabiliste détaillée a été menée en introduisant à titre d’exemple une incertitude sur la valeur de la porosité de la couche de diffusion cathodique d’une PAC de type PEM (coefficients de variation retenus : 1%, 5% et 10%). L’étude des conséquences de cette incertitude sur la tension et l’impédance d’une PAC a été menée en réalisant un plan d’expériences numériques et en mettant en oeuvre différents outils d’analyse statistique : graphes des effets, analyses de la variance, graphes des coefficients de variation des distributions en entrée et sortie du modèle déterministe. Dans cet exemple d’analyse et dans les conditions d’usages considérées, le taux de fiabilité prévisionnel (probabilité pour que la cellule de pile fournisse un minimum de tension de 0.68V) a été estimé à 91% avec un coefficient de variation d’entrée à 10%. / The Proton Exchange Membrane Fuel Cell (PEMFC) operation is subject to inherent uncertainty in various material, design and control parameters, which leads to performance variability and impacts the cell reliability. Some inaccuracies in the building process of the fuel cell (in the realization of the cell components and also during the assembly of the complete fuel cell stack), some fluctuations in the controls of the operating parameters (e.g. cell and gas temperatures, gas pressures, flows and relative humidity rates) affect the electrical performance of the cell (i.e. cell voltage) as well as its reliability and durability. For a given application, the selections of the different materials used in the various components of the electrochemical cell, the choices in the cell design (geometrical characteristics / sizes of the cell components) correspond to tradeoffs between maximal electrical performances, minimal fuel consumption, high lifespan and reliability targets, and minimal costs.In this PhD thesis, a novel method is proposed to help evaluating the reliability of a PEMFC stack. The aim is to guarantee a target level of electrical performance that can be considered as sufficient to meet any application requirements. The approach is based on the close coupling between physical modeling and statistical analysis of reliability. The complexity of the physical phenomena involved in the fuel cell is taken into account through the development of a dynamical, symbolic, acausal modeling tool including physical and semi-empirical parameters as well. The proposed knowledge PEMFC model is one-dimensional, non-isothermal and it includes a two-phase fluidic flow representation (each reactant is considered as a mix of gases and liquid water) in order to better take into account the complexity of the water management in the cell. The modeling is implemented using the MODELICA language and the DYMOLA software; one of the advantages of this simulation tool is that it allows an effective connection between multi-physical modeling and statistical treatments. In this perspective, the modeling is done with the aim of having as much relevant physical parameters as possible (classified in our work as operating, intrinsic, and semi-empirical parameters). The different effects of these parameters on the PEMFC electrical behavior can be observed and the performance sensitivity can be determined by considering some statistical distributions of input parameters, which is a step towards reliability analysis.A detailed physical and reliability analysis is conducted by introducing (as an example) an uncertainty rate in the porosity value of the cathodic Gas Diffusion Layer (coefficients of variance equal to 1%, 5% and 10%). The study of the uncertainty consequences on the cell voltage and electrical impedance is done through a design of numerical experiments and with the use of various statistical analysis tools, namely: graphs of the average effects, statistical sensitivity analyses (ANOVAs), graphs displaying the coefficients of variances linked with the statistical distributions observed in the inputs and outputs of the deterministic model. In this example of analysis and in the considered cell operating conditions, the provisional reliability rate (probability that the cell voltage is higher than 0.68V) is estimated to 91% with an input coefficient of variance equal to 10%.

The hidden state Markov (HSM) model is introduced as a new conceptual framework for modelling long-term persistence in hydrological time series. Unlike the stochastic models currently used, the conceptual basis of the HSM model can be related to the physical processes that influence long-term hydrological time series in the Australian climatic regime. A Bayesian approach was used for model calibration. This enabled rigourous evaluation of parameter uncertainty, which proved crucial for the interpretation of the results. Applying the single site HSM model to rainfall data from selected Australian capital cities provided some revealing insights. In eastern Australia, where there is a significant influence from the tropical Pacific weather systems, the results showed a weak wet and medium dry state persistence was likely to exist. In southern Australia the results were inconclusive. However, they suggested a weak wet and strong dry persistence structure may exist, possibly due to the infrequent incursion of tropical weather systems in southern Australia. This led to the postulate that the tropical weather systems are the primary cause of two-state long-term persistence. The single and multi-site HSM model results for the Warragamba catchment rainfall data supported this hypothesis. A strong two-state persistence structure was likely to exist in the rainfall regime of this important water supply catchment. In contrast, the single and multi-site results for the Williams River catchment rainfall data were inconsistent. This illustrates further work is required to understand the application of the HSM model. Comparisons with the lag-one autoregressive [AR(1)] model showed that it was not able to reproduce the same long-term persistence as the HSM model. However, with record lengths typical of real data the difference between the two approaches was not statistically significant. Nevertheless, it was concluded that the HSM model provides a conceptually richer framework than the AR(1) model. / PhD Doctorate