# Browsing by Subject "Uncertainty"

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Item A Preliminary Study to Assess Model Uncertainties in Fluid Flows(2011-08-08) Delchini, Marc OlivierShow more In this study, the impact of various flow models is assessed under free and forced convection: compressible versus incompressible models for a Pressurized Water Reactor, and Darcy's law vs full momentum equation for High Temperature Gas Reactor. Euler equations with friction forces and a momentum and energy source/sink are used. The geometric model consists of a one-dimensional rectangular loop system. The fluid is heated up and cooled down along the vertical legs. A pressurizer and a pump are included along the horizontal legs. The compressible model is assumed to be the most accurate model in this study. Simulations show that under forced convection compressible and incompressible models yield the same transient and steady-state. As free convection is studied, compressible and incompressible models have different transient but the same final steady-state. As Darcy's law is used, pressure and velocity steady-state profiles yield some differences compared to the compressible model both under free and forced convections. It is also noted some differences in the transient.Show more Item Addressing uncertainty and modeling error in the design and control of process systems : methods and applications(2016-08) Wang, Siyun, Ph.D.; Baldea, Michael; Edgar, Thomas F.; Rochelle, Gary T.; Truskett, Thomas M.; Biros, GeorgeShow more A process system faces the challenge of uncertainty throughout its lifetime. At the design stage, uncertainty originates from inaccurate knowledge of design parameters and unmeasured or unmeasurable ambient disturbances. Oftentimes, designers choose to increase system size to account for uncertainty and fluctuations; however, this approach has an economic limit, past which the capital expenditure outweighs the potential operational benefits. In the operational stage, uncertainty is manifest, amongst others, in fluctuations in operating conditions, market demand and raw material availability. Another type of uncertainty in (modern) process operations is related to the quality of process models that are used for making control and operational decisions. Of particular importance is the quality of the dynamic models that are used in real-time optimal control computations. The chemical industry has been the pioneer (and is currently the leader) of model predictive control (MPC) implementations, whereby the control moves are computed, over a receding time horizon, by solving an optimal control problem at each time step. While uniquely able to deal with large-scale, non-square constrained systems, MPC is vitally dependent on the predictive abilities of the built-in model. Changes in plant conditions are a a source of uncertainty in this case as-well, leading to a discrepancy (mismatch) between the model predictions and the true plant behavior. In this dissertation, I address the problems of design under uncertainty and plant-model mismatch. For the former, identification-based optimization (IBO) framework is proposed as a new, computationally efficient framework for optimizing the design of dynamic systems under uncertainty problem. The framework uses properly designed pseudo-random multilevel signals (PRMS) to represent time-varying uncertain variables. This allows us to formulate the design under uncertainty problem as a dynamic optimization problem. A solution algorithm is proposed using a sequential approach. Several application examples are discussed, demonstrating the superior computational performance of the IBO approach. Furthermore, an extension of the method that explicitly considers the tradeoff between conservativeness and dynamic performance is introduced. The latter, plant-model mismatch problem, is addressed using a novel autocovariance-based approach. Under appropriate assumptions, an explicit relation is established between the autocovariance of the process output and the plant-model mismatch terms, represented either in a step response model or a transfer function model. It is demonstrated that an asymptotically correct set of estimates of the values of plant-model mismatch for each model parameters is the global minimizer of the discrepancy between the autocovariance predicted using the relation and the autocovariance calculated from a data set collected from closed-loop operating data. Extensions of this approach handle cases where the active set of the MPC is changing over time and there are setpoint change and measurable disturbances occur in the control loop.Show more Item An investigation about relationship maintenance strategies after the discovery of deception about infidelity(2013-08) Xia, Shuang; Punyanunt-Carter, Narissa M.; Scholl, Juliann C.; Heuman, Amy N.Show more Both deception and infidelity are hurtful events to romantic relationships, and relationships might become worse when these hurtful events happen at the same time. It is hard to maintain a relationship after the discovery of deception about infidelity. This study seeks to uncover the individual’s response to discovering deception about infidelity. It focuses on people who are deceived by their partners (deceivees) and assesses which strategy is the most effective for them to repair the relationship. At the same time, this study compares the deceived partners’ preference of relationship maintenance strategies and the strategy they perceive the deceivers have been using. In addition, the current research examines how people’s attachment style affects their preference of maintenance strategy. Furthermore, this study concentrates on the relationship between relational uncertainty and the deceived partner’s preference of relationship maintenance strategy. It is anticipated the results will assist couples suffering from hurtful events to repair their relationship.Show more Item Analyzing risk and uncertainty for improving water distribution system security from malevolent water supply contamination events(2009-05-15) Torres, Jacob ManuelShow more Previous efforts to apply risk analysis for water distribution systems (WDS) have not typically included explicit hydraulic simulations in their methodologies. A risk classification scheme is here employed for identifying vulnerable WDS components subject to an intentional water contamination event. A Monte Carlo simulation is conducted including uncertain stochastic diurnal demand patterns, seasonal demand, initial storage tank levels, time of day of contamination initiation, duration of contamination event, and contaminant quantity. An investigation is conducted on exposure sensitivities to the stochastic inputs and on mitigation measures for contaminant exposure reduction. Mitigation measures include topological modifications to the existing pipe network, valve installation, and an emergency purging system. Findings show that reasonable uncertainties in model inputs produce high variability in exposure levels. It is also shown that exposure level distributions experience noticeable sensitivities to population clusters within the contaminant spread area. The significant uncertainty in exposure patterns leads to greater resources needed for more effective mitigation.Show more Item Application of price uncertainty quantification models and their impacts on project evaluations(Texas A&M University, 2006-10-30) Fariyibi, Festus LekanShow more This study presents an analysis of several recently published methods for quantifying the uncertainty in economic evaluations due to uncertainty in future oil prices. Conventional price forecasting methods used in the industry typically underestimate the range of uncertainty in oil and gas price forecasts. These forecasts traditionally consider pessimistic, most-likely, and optimistic cases in an attempt to quantify economic uncertainty. The recently developed alternative methods have their unique strengths as well as weaknesses that may affect their applicability in particular situations. While stochastic methods can improve the assessment of price uncertainty they can also be tedious to implement. The inverted hockey stick method is found to be an easily applied alternative to the stochastic methods. However, the primary basis for validating this method has been found to be unreliable. In this study, a consistent and reliable validation of uncertainty estimates predicted by the inverted hockey stick method is presented. Verifying the reliability of this model will ensure reliable quantification of economic uncertainty. Although we cannot eliminate uncertainty from investment evaluations, we can better quantify the uncertainty by accurately predicting the volatility in future oil and gas prices. Reliably quantifying economic uncertainty will enable operators to make better decisions and allocate their capital with increased efficiency.Show more Item Archimedes, Gauss and Stochastic computation: A new (old) approach to Fast Algorithms for the evaluation of transcendental functions of generalized Polynomial Chaos Expansions(2011-05) Mckale, Kaleb D.; Long, Kevin; Howle, Victoria E.; Barnard, Roger W.; Monico, Christopher J.Show more In this paper, we extend the work of Debusschere et al. (2004) by introducing a new approach to evaluating transcendental functions of generalized polynomial chaos expansions. We derive the elementary algebraic operations for the generalized PC expansions and show how these operations can be extended to polynomial and rational functions of PC expansions. We introduce and implement the Borchardt-Gauss Algorithm, an Arithmetic-Geometric Mean (AGM)-type method to derive the arctangent for the Jacobi-Chaos expansion. We compare numerically the BG Algorithm versus the Line Integral Method of Debusschere et al. and the Non-intrusive Spectral Projection (NISP) Method. We present the future direction of our research, including incorporating more efficient AGM-type methods proposed by Carlson (1972) and Brent (1976) to calculate the arctangent and other transcendental functions.Show more Item Characterization and assessment of uncertainty in San Juan Reservoir Santa Rosa Field(Texas A&M University, 2005-02-17) Becerra, Ernesto JoseShow more This study proposes a new, easily applied method to quantify uncertainty in production forecasts for a volumetric gas reservoir based on a material balance model (p/z vs. Gp). The new method uses only observed data and mismatches between regression values and observed values to identify the most probable value of gas reserves. The method also provides the range of probability of values of reserves from the minimum to the maximum likely value. The method is applicable even when only limited information is available from a field. Previous methods suggested in the literature require more information than our new method. Quantifying uncertainty in reserves estimation is becoming increasingly important in the petroleum industry. Many current investment opportunities in reservoir development require large investments, many in harsh exploration environments, with intensive technology requirements and possibly marginal investment indicators. Our method of quantifying uncertainty uses a priori information, which could come from different sources, typically from geological data, used to build a static or prior reservoir model. Additionally, we propose a method to determine the uncertainty in our reserves estimate at any stage in the life of the reservoir for which pressure-production data are available. We applied our method to San Juan reservoir at Santa Rosa Field, Venezuela. This field was ideal for this study because it is a volumetric reservoir for which the material balance method, the p/z vs. Gp plot, appears to be appropriate.Show more Item A column generation approach for stochastic optimization problems(2006) Wang, Yong Min; Bard, Jonathan F.; Morton, David P.Show more Item Determination of uncertainty in reserves estimate from analysis of production decline data(Texas A&M University, 2007-09-17) Wang, YuhongShow more Analysts increasingly have used probabilistic approaches to evaluate the uncertainty in reserves estimates based on a decline curve analysis. This is because the results represent statistical analysis of historical data that usually possess significant amounts of noise. Probabilistic approaches usually provide a distribution of reserves estimates with three confidence levels (P10, P50 and P90) and a corresponding 80% confidence interval. The question arises: how reliable is this 80% confidence interval? In other words, in a large set of analyses, is the true value of reserves contained within this interval 80% of the time? Our investigation indicates that it is common in practice for true values of reserves to lie outside the 80% confidence interval much more than 20% of the time using traditional statistical analyses. This indicates that uncertainty is being underestimated, often significantly. Thus, the challenge in probabilistic reserves estimation using a decline curve analysis is not only how to appropriately characterize probabilistic properties of complex production data sets, but also how to determine and then improve the reliability of the uncertainty quantifications. This thesis presents an improved methodology for probabilistic quantification of reserves estimates using a decline curve analysis and practical application of the methodology to actual individual well decline curves. The application of our proposed new method to 100 oil and gas wells demonstrates that it provides much wider 80% confidence intervals, which contain the true values approximately 80% of the time. In addition, the method yields more accurate P50 values than previously published methods. Thus, the new methodology provides more reliable probabilistic reserves estimation, which has important impacts on economic risk analysis and reservoir management.Show more Item Differences in dating relationships : an examination of attachment, disclosure, and relational uncertainty(2013-05) Pett, Rudolph Clarence; Dailey, René M.Show more This study assessed the associations between adult attachment, disclosure, and relational uncertainty in both cyclical and non-cyclical dating relationships using a sample of 114 participants. The analysis revealed significant relationships between relational disclosure and relational uncertainty, attachment avoidance and relational disclosure, attachment anxiety and relational uncertainty, as well as attachment avoidance and relational uncertainty. Relational status (i.e., cyclical/non-cyclical) was neither related to relational disclosure or self-disclosure, nor served as a significant moderator between relational disclosure and relational uncertainty or self-disclosure and relational uncertainty. The results are considered in terms of how individual characteristics shaped by interpersonal interaction (i.e., attachment, relational uncertainty) are associated with specific communication patterns (i.e., disclosure) in dating relationships.Show more Item Economic investigation of discount factors for agricultural greenhouse gas emission offsets(Texas A&M University, 2005-08-29) Kim, Man-KeunShow more This dissertation analyzes the basis for and magnitudes of discount factors based on the characteristics of greenhouse gas emission (GHGE) offsets that are applied to the GHGE reduction projects, concentrating on agricultural projects. Theoretical approaches to discount factors, estimation and incorporation of discount factors procedures are developed. Discount factors would be imposed by credit purchasers due to noncompliance with regulatory program of the credits with GHG program including consideration of shortfall penalties and limited durations. Discount factors are proposed for (i) additionality, (ii) leakage, (iii) permanence, and (iv) uncertainty. Additionality arise when the region where an AO project is being proposed would have substantial adoption of the AO practice in the absence of GHG programs (business as usual GHGE offset). Leakage arises when the effect of a program is offset by an induced increase in economic activity and accompanying emissions elsewhere. The leakage effect depends on demand and supply elasticities. Permanence reflects the saturation and volatility characteristics of carbon sequestration. Carbon is stored in a volatile form and can be released quickly to the atmosphere when an AO practice is discontinued. The permanence discount depends on the project design including practice continuation after the program and the dynamic rate of offset. Also, consideration of multiple offsets is important. Uncertainty arises due to the stochastic nature of project quantity. The uncertainty discount tends to be smaller the larger the size of the offset contract due to aggregation over space and time. The magnitude of these discounts is investigated in Southeast Texas rice discontinuation study. The additionality and the leakage discounts are found to play an important role in case of rice lands conversion to other crops but less so for pasture conversions and yet less for forest conversions. The permanence discount is important when converting to other crops and short rotation forestry. When all discounts are considered, rice lands conversion to forest yields claimable credits amounting to 52.8% ~ 77.5% of the total offset. When converting rice lands to pasture, the claimable credits 45.1% ~ 64.2%, while a conversion of rice lands to other crops yields claimable credits 38.9% ~ 40.4%.Show more Item Effect of modeled pre-industrial Greenland ice sheet surface mass balance bias on uncertainty in sea level rise projections in 2100(2013-08) Gutowski, Gail Ruth; Blankenship, Donald D.; Jackson, Charles S., doctor of geophysical scienceShow more Changes to ice sheet surface mass balance (SMB) are going to play a significant role in future sea level rise (SLR), particularly for the Greenland ice sheet. The Coupled Model Intercomparison Project Phase 5 (CMIP5) found that Greenland ice sheet (GIS) response to changes in SMB is expected to contribute 9 ± 4 cm to sea level by 2100 (Fettweis et al 2013), though other estimates suggest the possibility of an even larger response. Modern ice sheet geometry and surface velocities are common metrics for determining a model’s predictability of future climate. However, care must be taken to robustly quantify prediction uncertainty because errors in boundary conditions such as SMB can be compensated by (and therefore practically inseparable from) errors in other aspects of the model, complicating calculations of total uncertainty. We find that SMB calculated using the Community Earth System Model (CESM) differs from established standards due to errors in the CESM SMB boundary condition. During the long ice sheet initialization process, small SMB errors such as these have an opportunity to amplify into larger uncertainties in GIS sensitivity to climate change. These uncertainties manifest themselves in ice sheet surface geometry changes, ice mass loss, and subsequent SLR. While any bias in SMB is not desirable, it is not yet clear how sensitive SLR projections are to boundary condition forcing errors. We explore several levels of SMB forcing bias in order to analyze their influence on future SLR. We evaluate ensembles of ice sheets forced by 4 different levels of SMB forcing error, covering a range of errors similar to SMB biases between CESM and RACMO SMB. We find that GIS SMB biases on the order of 1 m/yr result in 7.8 ± 3.4 cm SLR between 1850 and 2100, corresponding to 100% uncertainty at the 2σ level. However, we find unexpected feedbacks between SMB and surface geometry in the northern GIS. We propose that the use of elevation classes may be incorrectly altering the feedback mechanisms in that part of the ice sheet.Show more Item Error analysis for randomized uniaxial stretch test on high strain materials and tissues(Texas A&M University, 2006-08-16) Jhun, Choon-SikShow more Many people have readily suggested different types of hyperelastic models for high strain materials and biotissues since the 1940??s without validating them. But, there is no agreement for those models and no model is better than the other because of the ambiguity. The existence of ambiguity is because the error analysis has not been done yet (Criscione, 2003). The error analysis is motivated by the fact that no physical quantity can be measured without having some degree of uncertainties. Inelastic behavior is inevitable for the high strain materials and biotissues, and validity of the model should be justified by understanding the uncertainty due to it. We applied the fundamental statistical theory to the data obtained by randomized uniaxial stretch-controlled tests. The goodness-of-fit test (2R) and test of significance (t-test) were also employed. We initially presumed the factors that give rise to the inelastic deviation are time spent testing, stretch-rate, and stretch history. We found that these factors characterize the inelastic deviation in a systematic way. A huge amount of inelastic deviation was found at the stretch ratio of 1.1 for both specimens. The significance of this fact is that the inelastic uncertainties in the low stretch ranges of the rubber-like materials and biotissues are primarily related to the entropy. This is why the strain energy can hardly be determined by the experimentation at low strain ranges and there has been a deficiency in the understanding of the exclusive nature of the strain energy function at low strain ranges of the rubber-like materials and biotissues (Criscione, 2003). We also found the answers for the significance, effectiveness, and differences of the presumed factors above. Lastly, we checked the predictive capability by comparing the unused deviation data to the predicted deviation. To check if we have missed any variables for the prediction, we newly defined the prediction deviation which is the difference between the observed deviation and the point forecasting deviation. We found that the prediction deviation is off in a random way and what we have missed is random which means we didn??t miss any factors to predict the degree of inelastic deviation in our fitting.Show more Item Essays on real options and strategic interactions(2012-08) Dehghani Firouzabadi, Mohammad Hossein; Boyarchenko, Svetlana I.; Almazan, Andres; Stinchcombe, Maxwell B.; Tompaidis, Stathis; Wiseman, ThomasShow more Chapter 2 considers technology adoption under both technological and subsidy uncertainties. Uncertainty in subsidies for green technologies is considered as an example. Technological progress is exogenous and modeled as a jump process with a drift. The analytical solution is presented for cases when there is no subsidy uncertainty and when the subsidy changes once. The case when the subsidy follows a time invariant Markov process is analyzed numerically. The results show that improving the innovation process raises the investment thresholds. When technological jumps are small or rare, this improvement reduces the expected time before technology adoption. However, when technological jumps are large or abundant, this improvement may raise this expected time. Chapter 3 studies technology adoption in a duopoly where the unbiased technological change improves production efficiency. Technological progress is exogenous and modeled as a jump process with a drift. There is always a Markov perfect equilibrium in which the firm with more efficient technology never preempts its rival. Also, a class of equilibria may exist that lead to a smaller industry surplus. In these equilibria either of the firms may preempt its rival in a set of technology efficiency values. The first investment does not necessarily happen at the boundary of this set due to the discrete nature of the technology progress. The set shrinks and eventually disappears when the difference between firms’ efficiencies increases. Chapter 4 studies the behavior of two firms after a new investment opportunity arises. Firms either invest immediately or wait until market uncertainty is resolved. Two types of separating equilibrium are possible when sunk costs are private information. In the first type the firm with lower cost invests first. In the second type the firm with higher cost invests first leading to a smaller industry surplus. The results indicate that the second type is possible only for strictly negatively correlated sunk costs. Numerical analysis illustrates that when first mover advantage is large, the firm that delays the investment should be almost certain about its rival’s sunk cost. When market risk increases, the equilibria can exist when the firm is less certain.Show more Item Facility planning and value of information using a tank reservoir model : a case study in reserve uncertainty(2010-05) Singh, Ashutosh; Jablonowski, Christopher J.; Groat, Charles G.Show more This thesis presents a methodology to incorporate reservoir uncertainties and estimate the loss in project value when facility planning decisions are based on erroneous estimates of input variables. We propose a tank model along with integrated asset development model to simulate the concept selection process. The model endogenizes drilling decisions and includes an option to expand. Key decision variables included in the model are number of pre-drill wells, initial facility capacity and number of well slots. Comparison is made between project value derived under erroneous estimates for reserve size and under an alternate hypothesis. The results suggest loss in project value of up to 40% when reservoir estimates are erroneous. Moreover, both optimistic and pessimistic reserve estimates results in a loss in project value. However, loss in project value is bigger when reserve size is underestimated than when it is overestimated.Show more Item Fast assessment of uncertainty in buoyant fluid displacement using a connectivity-based proxy(2016-05) Jeong, Hoonyoung; Sepehrnoori, Kamy, 1951-; Srinivasan, Sanjay; Wheeler, Mary; Delshad, Mojdeh; Sen, MrinalShow more It is crucial to estimate the uncertainty in flow characteristics of injected fluid. However, because a large suite of geological models is probable given sparse static data, it is impractical to conduct full physics flow simulations on the entire suite of models in order to quantify the uncertainty in fluid displacements. Thus a fast alternative to a full physics simulator is necessary to quickly predict the fluid displacements. Most of the proxies proposed thus far are inappropriate to approximate the buoyant flow of injected fluid for 3D heterogeneous rock during the injection period. In this dissertation, a new proxy will be proposed to quickly predict the buoyant flow of injected fluid during CO2 sequestration. The geological models are ranked based on the extent of the approximated CO2 plumes. By selecting a representative group of models among the ranked models, the uncertainty in the spatial and temporal characteristics of the CO2 plume migrations can be quickly quantified. About 90% of the computational cost of quantifying the uncertainty in the extent of CO2 plumes was saved using the proposed connectivity based proxy. In a geological carbon storage project, the spatial and temporal characteristics of CO2 plume migrations can be monitored by 4D seismic surveys. The images of CO2 plumes obtained from 4D seismic surveys are used as observed data to find subsurface models honoring the spatial and temporal characteristics of the observed CO2 plumes. However, because manually comparing an observed CO2 plume and prior CO2 plumes in a large suite of subsurface models is inefficient, an automatic measure to calculate the dissimilarity between the CO2 plumes is necessary. The most intuitive way to calculate the dissimilarity is the Euclidean distance between vectors representing CO2 plumes. However, this is inappropriate to measure the dissimilarity between CO2 plumes because it does not consider spatial relation between the elements of the vectors. The shape dissimilarity between the CO2 plumes that reflects the spatial relation can be calculated using the Hausdorff distance. The computational cost of calculating the shape dissimilarity between CO2 plumes is significantly reduced by calculating the Hausdorff distance between the representations of the CO2 plumes such as perimeter, surface, and skeleton instead of the original CO2 plumes. An appropriate representation should be chosen according to the spatial characteristics of CO2 plumes.Show more Item Greedy structure learning of Markov Random Fields(2011-08) Johnson, Christopher Carroll; Ravikumar, Pradeep; Dhillon, InderjitShow more Probabilistic graphical models are used in a variety of domains to capture and represent general dependencies in joint probability distributions. In this document we examine the problem of learning the structure of an undirected graphical model, also called a Markov Random Field (MRF), given a set of independent and identically distributed (i.i.d.) samples. Specifically, we introduce an adaptive forward-backward greedy algorithm for learning the structure of a discrete, pairwise MRF given a high dimensional set of i.i.d. samples. The algorithm works by greedily estimating the neighborhood of each node independently through a series of forward and backward steps. By imposing a restricted strong convexity condition on the structure of the learned graph we show that the structure can be fully learned with high probability given $n=\Omega(d\log (p))$ samples where $d$ is the dimension of the graph and $p$ is the number of nodes. This is a significant improvement over existing convex-optimization based algorithms that require a sample complexity of $n=\Omega(d^2\log(p))$ and a stronger irrepresentability condition. We further support these claims with an empirical comparison of the greedy algorithm to node-wise $\ell_1$-regularized logistic regression as well as provide a real data analysis of the greedy algorithm using the Audioscrobbler music listener dataset. The results of this document provide an additional representation of work submitted by A. Jalali, C. Johnson, and P. Ravikumar to NIPS 2011.Show more Item How does uncertainty influence spatial projections of Anopheles presence in Kenya?(2016-05) Ames, Jillian Elizabeth; Miller, Jennifer A. (Jennifer Anne); Crews, Kelley A.; Busby, Joshua W.Show more Species distribution models (SDM) are becoming a widely used framework for studying distribution and risk of vector-borne diseases, particularly as a consequence of climate change (Gonzalez et al. 2010; Porretta et al. 2013; Rochlin et al. 2013). Malaria has been one of the most extensively studied vector-borne diseases (Minakawa et al. 2005; Ryan et al. 2006; Afrane et al. 2008; Mboera et al. 2010; Nath et al. 2012), and SDM output has been used by policy makers and various aid organizations to design and implement preventative malaria programs for areas that have been identified as current or future high risk (Gething et al. 2012; Hongoh et al. 2012; Cianci et al. 2015). However, these maps and models are often developed by epidemiologists or other medical researchers and therefore issues related to representing or exploring the uncertainty in the results have often been ignored (Lindsay et al. 1998; Levine et al. 2004). Many sources of uncertainty in model outputs have been identified in SDM research, ranging from data type or measurement level (e.g., presence-only vs. presence-absence, abundance), to statistical method, to subjective decisions related to mapping the results (e.g., threshold selected to discretize continuous output). This studies employs SDM to project the spatial distribution of four species of Anopheles (malaria-carrying mosquitoes) in Kenya, focusing on the representation of uncertainty and its propagation associated with aspects of the modeling methods and the data used.Show more Item Impact of budget uncertainty on network-level pavement condition : a robust optimization approach(2013-12) Al-Amin, Md; Zhang, Zhanmin, 1962-Show more Highway agencies usually face budget uncertainty for pavement maintenance and rehabilitation activities due to limitation in resources and changes in government policies. Highway agencies perform maintenance planning for the pavement network commonly based on the nominal available budget without taking the variability of budget into consideration. The maintenance program based on deterministic budget consideration results in suboptimal maintenance decisions that impact the overall network conditions, if the budget falls short in some future year in the planning horizon. As a result, it is important for highway agencies to adopt maintenance and rehabilitation policies that are protected against the uncertainty in maintenance and rehabilitation budget. In this study a multi-period linear integer programming model is proposed with its robust counterpart considering uncertain maintenance and rehabilitation budget. The proposed model is able to provide a maintenance and rehabilitation program for the pavement network that results in minimal impact of budget variability on the network conditions. A case study was carried out for a network of ten pavement sections. The solution of the robust optimization model was compared to those with deterministic model. The results show that the robust optimization model is an attractive method that can minimize the effect of budget uncertainty on pavement conditions at the network level.Show more Item Integration and quantification of uncertainty of volumetric and material balance analyses using a Bayesian framework(Texas A&M University, 2005-11-01) Ogele, ChileShow more Estimating original hydrocarbons in place (OHIP) in a reservoir is fundamentally important to estimating reserves and potential profitability. Quantifying the uncertainties in OHIP estimates can improve reservoir development and investment decision-making for individual reservoirs and can lead to improved portfolio performance. Two traditional methods for estimating OHIP are volumetric and material balance methods. Probabilistic estimates of OHIP are commonly generated prior to significant production from a reservoir by combining volumetric analysis with Monte Carlo methods. Material balance is routinely used to analyze reservoir performance and estimate OHIP. Although material balance has uncertainties due to errors in pressure and other parameters, probabilistic estimates are seldom done. In this thesis I use a Bayesian formulation to integrate volumetric and material balance analyses and to quantify uncertainty in the combined OHIP estimates. Specifically, I apply Bayes?? rule to the Havlena and Odeh material balance equation to estimate original oil in place, N, and relative gas-cap size, m, for a gas-cap drive oil reservoir. The paper considers uncertainty and correlation in the volumetric estimates of N and m (reflected in the prior probability distribution), as well as uncertainty in the pressure data (reflected in the likelihood distribution). Approximation of the covariance of the posterior distribution allows quantification of uncertainty in the estimates of N and m resulting from the combined volumetric and material balance analyses. Several example applications to illustrate the value of this integrated approach are presented. Material balance data reduce the uncertainty in the volumetric estimate, and the volumetric data reduce the considerable non-uniqueness of the material balance solution, resulting in more accurate OHIP estimates than from the separate analyses. One of the advantages over reservoir simulation is that, with the smaller number of parameters in this approach, we can easily sample the entire posterior distribution, resulting in more complete quantification of uncertainty. The approach can also detect underestimation of uncertainty in either volumetric data or material balance data, indicated by insufficient overlap of the prior and likelihood distributions. When this occurs, the volumetric and material balance analyses should be revisited and the uncertainties of each reevaluated.Show more

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