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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Spread of Values of a Cantor-Type Fractal Continuous Nonmonotone Function

By using the Q{sub 5}{sup ∗}-representation of numbers[0,1]∋x=β{sub α{sub 1(x)1}}+∑{sub k=2}{sup ∞}(β{sub α{sub k(x)k}}∏{sub j=1}{sup k−1}q{sub α{sub j(x)j}})=Δ{sub α{sub 1(x)α{sub 2(x)…α{sub k(x)…}{sup Q{sub 5}{sup ∗}}}}} determined by the quinary alphabet A{sub 5} ≡ {0, 1, 2, 3, 4} and an infinite stochastic matrix ‖q{sub ik}‖, i ∈ A{sub 5}, k ∈ N, with positive elements (q{sub 0k} + q{sub 1k} + q{sub 2k} + q{sub 3k} + q{sub 4k} = 1) such that ∏{sub k=1}{sup ∞}max{sub i}{q_i_k}=0 and β{sub 0k} = 0, β{sub i + 1, k} = β{sub ik} + q{sub ik}, i= (0,4)-bar , we define a continuous Cantor-type function by the equalityf(Δ{sub α{sub 1…α{sub k…}{sup Q{sub 5}{sup ∗}}}})=δ{sub α{sub 1(x)1}}+∑{sub k=2}{sup ∞}(δ{sub α{sub k(x)k}}∑{sub j=1}{sup k−1}g{sub α{sub j(x)j}})≡Δ{sub α{sub 1(x)…α{sub k(x)…}{sup G}}}, where δ{sub 0n} = 0, δ{sub 1n}=((2+ε{sub n})/4), δ{sub 2n}=(2/4)=δ{sub 3n}, and δ{sub 4n}=((2−ε{sub n})/4), i.e., δ{sub i + 1, n} = δ{sub in} + g{sub in}, n ∈ N, and (ε{sub n}) is a given sequence of real numbers such that 0 ≤ ε{sub n} ≤ 1. We prove that this function is well defined and continuous. Moreover, it does not have intervals of monotonicity, except the intervals where it is constant. A criterion of bounded variation of the function is also established. We are especially interested in the problem of level sets of the function and in the topological and metric properties of the images of Cantor-type sets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Stochastic Perturbations of Stable Dynamical Systems: Trajectory-Wise Approach

We study stochastic perturbations of a dynamical system with a locally stable fixed point. The perturbed system has the form of Ito stochastic differential equations. We assume that perturbations do not vanish at the equilibrium of the deterministic system. Using the approach based on consideration of trajectories to the analysis of stochastic differential equations, we find restrictions for perturbations under which the stability of the equilibrium is preserved with probability 1.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2010

Development of an Improved Methodology to Assess Potential Unconventional Gas Resources

Considering the important role played today by unconventional gas resources in North America and their enormous potential for the future around the world, it is vital to both policy makers and industry that the volumes of these resources and the impact of technology on these resources be assessed. To provide for optimal decision making regarding energy policy, research funding, and resource development, it is necessary to reliably quantify the uncertainty in these resource assessments. Since the 1970s, studies to assess potential unconventional gas resources have been conducted by various private and governmental agencies, the most rigorous of which was by the United States Geological Survey (USGS). The USGS employed a cell-based, probabilistic methodology which used analytical equations to calculate distributions of the resources assessed. USGS assessments have generally produced distributions for potential unconventional gas resources that, in our judgment, are unrealistically narrow for what are essentially undiscovered, untested resources. In this article, we present an improved methodology to assess potential unconventional gas resources. Our methodology is a stochastic approach that includes Monte Carlo simulation and correlation between input variables. Application of the improved methodology to the Uinta-Piceance province of Utah and Colorado with USGS data validates the means and standard deviations of resource distributions produced by the USGS methodology, but reveals that these distributions are not right skewed, as expected for a natural resource. Our investigation indicates that the unrealistic shape and width of the gas resource distributions are caused by the use of narrow triangular input parameter distributions. The stochastic methodology proposed here is more versatile and robust than the USGS analytic methodology. Adoption of the methodology, along with a careful examination and revision of input distributions, should allow a more realistic assessment of the uncertainty surrounding potential unconventional gas resources.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2013

A New Stochastic Modeling of 3-D Mud Drapes Inside Point Bar Sands in Meandering River Deposits

The environment of major sediments of eastern China oilfields is a meandering river where mud drapes inside point bar sand occur and are recognized as important factors for underground fluid flow and distribution of the remaining oil. The present detailed architectural analysis, and the related mud drapes' modeling inside a point bar, is practical work to enhance oil recovery. This paper illustrates a new stochastic modeling of mud drapes inside point bars. The method is a hierarchical strategy and composed of three nested steps. Firstly, the model of meandering channel bodies is established using the Fluvsim method. Each channel centerline obtained from the Fluvsim is preserved for the next simulation. Secondly, the curvature ratios of each meandering river at various positions are calculated to determine the occurrence of each point bar. The abandoned channel is used to characterize the geometry of each defined point bar. Finally, mud drapes inside each point bar are predicted through random sampling of various parameters, such as number, horizontal intervals, dip angle, and extended distance of mud drapes. A dataset, collected from a reservoir in the Shengli oilfield of China, was used to illustrate the mud drapes' building procedure proposed in this paper. The results show that the inner architectural elements of the meandering river are depicted fairly well in the model. More importantly, the high prediction precision from the cross validation of five drilled wells shows the practical value and significance of the proposed method.

42 ENGINEERING↗
DOE OSTI2013

Reservoir Modeling by Data Integration via Intermediate Spaces and Artificial Intelligence Tools in MPS Simulation Frameworks

Conditioning stochastic simulations are very important in many geostatistical applications that call for the introduction of nonlinear and multiple-point data in reservoir modeling. Here, a new methodology is proposed for the incorporation of different data types into multiple-point statistics (MPS) simulation frameworks. Unlike the previous techniques that call for an approximate forward model (filter) for integration of secondary data into geologically constructed models, the proposed approach develops an intermediate space where all the primary and secondary data are easily mapped onto. Definition of the intermediate space, as may be achieved via application of artificial intelligence tools like neural networks and fuzzy inference systems, eliminates the need for using filters as in previous techniques. The applicability of the proposed approach in conditioning MPS simulations to static and geologic data is verified by modeling a real example of discrete fracture networks using conventional well-log data. The training patterns are well reproduced in the realizations, while the model is also consistent with the map of secondary data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Development Optimization and Uncertainty Analysis Methods for Oil and Gas Reservoirs

Uncertainty complicates the development optimization of oil and gas exploration and production projects, but methods have been devised to analyze uncertainty and its impact on optimal decision-making. This paper compares two methods for development optimization and uncertainty analysis: Monte Carlo (MC) simulation and stochastic programming. Two example problems for a gas field development and an oilfield development are solved and discussed to elaborate the advantages and disadvantages of each method. Development optimization involves decisions regarding the configuration of initial capital investment and subsequent operational decisions. Uncertainty analysis involves the quantification of the impact of uncertain parameters on the optimum design concept. The gas field development problem is designed to highlight the differences in the implementation of the two methods and to show that both methods yield the exact same optimum design. The results show that both MC optimization and stochastic programming provide unique benefits, and that the choice of method depends on the goal of the analysis. While the MC method generates more useful information, along with the optimum design configuration, the stochastic programming method is more computationally efficient in determining the optimal solution. Reservoirs comprise multiple compartments and layers with multiphase flow of oil, water, and gas. We present a workflow for development optimization under uncertainty for these reservoirs, and solve an example on the design optimization of a multicompartment, multilayer oilfield development.

02 PETROLEUM↗
DOE OSTI2019

Bayesian and LASSO Regressions for Comparative Permeability Modeling of Sandstone Reservoirs

In this research, Bayesian model averaging (BMA) and least absolute shrinkage and selection operator regression (LASSO) algorithms were adopted for the core permeability modeling as a function of well log and core measurements. More specifically, the core permeability (dependent factor) was modeled given the well log and core data (independent variables) and then predicted in non-cored intervals of a well in a sandstone formation. The BMA is a stochastic linear modeling and a Bayesian parameter selection. Among 50 linear models generated as a function of the independent variables and depicted in Occam’s window, the best model of the highest posterior probability is determined. The best model has the optimal subset parameters that most influences the response factor. The core permeability modeling was again conducted using the LASSO algorithm, which adopts a completely different way of modeling and subset selection by using the penalized least-squared equation. Both BMA and LASSO resulted in a very accurate prediction of the core permeability by achieving perfect measured and calculated permeability matching. Matches for the two algorithms were quantified by computing the adjusted R-squared and root-mean-squared prediction error. In addition, results of the BMA and LASSO were compared to the conventional multiple linear regression (LM). The LASSO algorithm led to an accurate matching similar to LM, but slightly better than BMA. Therefore, both BMA and LASSO represent integrated procedures for accurate permeability estimation similar to conventional regression analysis.

58 GEOSCIENCES↗
DOE OSTI2019

Pilot Point Optimization of Mining Boundaries for Lateritic Metal Deposits: Finding the Trade-off Between Dilution and Ore Loss

Geological contacts in lateritic metal deposits (footwall topographies) often delineate the orebody boundaries. Spatial variations seen in such contacts are frequently higher than those for the metal grades of the deposit. Therefore, borehole spacing chosen based on the grade variations cannot adequately capture the geological contact variability. Consequently, models created using such boreholes cause high volumetric uncertainties in the actual and targeted ore extraction volumes, which, in turn, lead to high unplanned dilution and ore losses. In this paper, a method to design optimum ore/mining boundaries for lateritic metal deposits is presented. The proposed approach minimizes the dilution/ore losses and comprises two main steps. First, the uncertainty on the orebody boundary is represented using a set of stochastic realizations generated with a multiple-point statistics algorithm. Then, the optimal orebody boundary is determined using an optimization technique inspired by a model calibration method called Pilot Points. The pilot points represent synthetic elevation values, and they are used to construct smooth mining boundaries using the multilevel B-spline technique. The performance of a generated surface is evaluated using the expected sum of losses in each of the stochastic realizations. The simulated annealing algorithm is used to iteratively determine the pilot point values which minimize the expected losses. The results show a significant reduction in the dilution volume as compared to those obtained from the actual mining operation.

58 GEOSCIENCES↗
DOE OSTI2019

Capturing Hidden Geochemical Anomalies in Scarce Data by Fractal Analysis and Stochastic Modeling

Fractal/multifractal modeling is a widely used geomathematical approach to capturing different populations in geochemical mapping. The rationale of this methodology is based on empirical frequency density functions attained from global or local distributions. This approach is quite popular because of its simplicity and versatility; it accounts for the frequency and spatial distribution of geochemical data considering self-similarity across a range of scales. Using this technique for detection of geochemical anomalies in scarce data, however, is problematic and can lead to systematic bias in the characterization of the underlying populations. In this paper, an innovative technique is presented that provides good results without a priori assumptions. A simulation approach is adopted for fractal analysis by generating different possible distribution scenarios for the variable under study to reveal the underlying populations that are frequently hidden due to lack of data. The proposed technique is called the global simulated size–number method, and it is validated in a case study with two synthetic datasets and another case study with real dataset from the Ushtagan gold deposit in northeast Kazakhstan.

58 GEOSCIENCES↗
DOE OSTI2019

Optimal Allocation of Water Resources Using a Two-Stage Stochastic Programming Method with Interval and Fuzzy Parameters

Efficient water allocation is one of the most prominent issues in water resources management. In this research, a two-stage interval-parameter stochastic fuzzy programming with type 2 membership functions was used to allocate water resources optimally to different users under uncertainty. This method can handle uncertainties expressed as probability distributions, discrete intervals, and fuzzy sets. The model considers treated wastewater as an allocable water resource in a scenario, in addition to water that is extracted from wellheads, springs, and qanats. Moreover, the loss rate of water during distribution, surplus water in the reservoir in the previous and the next period, and treated wastewater parameters have been incorporated into the model. This model was applied to a case study of water resources allocation within a multi-user and multi-reservoir context in the Zarand region of Kerman, Iran. The results indicate that reasonable solutions have been generated, in the form of interval and fuzzy information under different scenarios that could help managers provide optimal water resources allocation plans. The results also demonstrate that establishing a wastewater treatment station increases the system net benefits, surplus water in wellheads for the next period, and system reliability (level of satisfying the fuzzy goal and constraints), and decreases encountering water shortages.

58 GEOSCIENCES↗
DOE OSTI2019

On the pull-in behavior of optical injection phase-lock loop

This paper presents a detailed study of the pull-in behavior of an optical injection phase-lock loop (OIPLL) neglecting the noise components of the loop. We provide formulas for pull-in voltage and pull-in range of OIPLL in terms of the loop propagation delay, line-width enhancement factor and other parameters of the loop. In addition, we give a compact expression for the frequency pulling time of OIPLL for low injection and high injection level in presence of loop-delay. The effects of loop-delay and optical injection on the pull-in performance of the OIPLL are studied for non-zero values of line-width enhancement factor. Analytical expression of the maximum allowable loop delay is presented to study the deterministic stability of the loop. From the stochastic stability of the loop, we provide formula for the maximum value of the laser line-width to achieve the desired tracking performance. The simulation results are given in partial support of the conclusions of the analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Fluid Flow, Thermal Stratification, and Inclusion Motion During Holding Period in Steel Ladles

In the current study, the fluid flow and thermal stratification during the holding period are numerically simulated. The standard k–ε two-equation turbulence model is adopted to describe the turbulence. The trajectories of inclusions are calculated by the discrete phase model (DPM) considering the stochastic effect of turbulence. Two different initial conditions for the flow field are compared: the quiescent state of flow and the fluid flow induced by gas stirring. Significant differences are observed between these cases. In practice, the holding period starts from the shut-off of the gas blowing. Thus, it is proposed that the flow field at the terminal of gas stirring should be considered for the simulation of the fluid flow, heat transfer, and inclusion motion during the holding period.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Dose–volume histogram evaluation scheme for beam orientations in intensity-modulated radiation therapy

Beam orientations in intensity-modulated radiation therapy (IMRT) is an important, but difficult NP-hard optimization problem. A considerable part of this difficulty is due to the essential prerequisite of defining, appropriately, counter-intuitive criteria for a mathematical plan evaluation that coincides with the clinical judgment of the considered plan. Moreover, the quality of beam directions depends heavily on their intensities. Usually a stochastic selector is utilized for optimizing beam orientations, and the intensities are thus calculated many thousands of times, each time for a different selection of beam directions, resulting in excessive time complexity. Therefore, selecting an appropriate set of beam directions in IMRT is still a time-consuming manual trial-and-error search procedure that depends on intuition and empirical knowledge. To overcome these difficulties, this work utilizes the concept of dose–volume histogram (DVH), which is one of the main recognized quantitative measurement tools used for plan judgment, and presents a DVH evaluation scheme that parallelizes plan evaluation with clinical plan judgment. This scheme is then utilized to optimize the intensities of each individual beam, enabling it to be represented by its DVHs, produced for the different irradiated volumes. Finally, an evolutionary algorithm is employed to search for the best combination of those DVHs reflecting the clinical optimal. The presented methods have been applied to three real clinical examples. In comparison to the standard equally spaced beam plans, improvements were reported in all three cases. In comparison with the greedy algorithm, improvements were reported in those examples requiring more than five beam directions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2018

On polymorphism for discrete evolutionary dynamics driven either by selection or segregation distortion

We revisit some problems arising in the context of multiallelic discrete-time and deterministic evolutionary dynamics driven first by fitness differences and then by segregation distortion. In the model with fitness, we describe classes of fitness matrices exhibiting polymorphism. In the segregation case, still in search for conditions of polymorphism, we focus on a class of skew-symmetric matrices with a unique strictly positive kernel vector. Our main results reduce the study of these cases to the analysis of stochastic matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A new hybrid algorithm combining a new chaos optimization approach with gradient descent for high dimensional optimization problems

Chaos optimization algorithm (COA) is a recently developed method for global optimization based on chaos theory. It has the features of easy implementation, short execution time and robust mechanisms of escaping from local optima compared with the existing stochastic searching algorithm. By integrating the gradient descent method with a new COA approach using new strategies including symmetrization and levelling, a novel hybrid method, called SCGD, is proposed in this paper. The main idea is to combine the good ability of exploitation of the gradient descent with the high ability of exploration of COA. The purpose is to avoid being trapped into local optima and to improve convergence in large space and high-dimension optimization problems. The simulation results based on a set of 50 benchmark functions with diverse properties and different dimensions show the efficiency and the abilities of the proposed method in finding the global optima compared with the existing methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A state estimation approach based on stochastic expansions

This paper presents a new approach for state estimation problems. It is based on the representation of random variables using stochastic functions. Its main idea is to expand the state variables in terms of the noise variables of the system, and then estimate the unnoisy value of the state variables by taking the mean value of the stochastic expansion. Moreover, it was shown that in some situations, the proposed approach may be adapted to the determination of the probability distribution of the state noise. For the determination of the coefficients of the expansions, we present three approaches: moment matching (MM), collocation (COL) and variational (VAR). In the numerical analysis section, three examples are analyzed including a discrete linear system, the Influenza in a boarding school and the state estimation problem in the Hodgkin–Huxley’s model. In all these examples, the proposed approach was able to estimate the values of the state variables with precision, i.e., with very low RMS values.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Predictive drug dosage control through a Fokker–Planck observer

During the years, various techniques have been presented for optimal control of tumor growth for which its stochastic behavior has rarely been considered. This article uses the well-known Gompertz stochastic model, for describing tumor growth, and by receding horizon model predictive control (RH-MPC) scheme computes the drug dosage for minimizing the tumor-cell population. To do this, a predictive control problem is defined based on the difference between the probability density function of tumor-cell population and the desired probability density function. In the model, both the drug dosage limitation and the Fokker–Planck equation have been considered as constraints. By solving this problem, the drug dosage which is considered as an external input to tumor model, is computed. In this article, the Fokker–Planck equation is used (1) as a nonlinear observer of probability density function of tumor-cell population and (2) a mapping vehicle from stochastic to deterministic domain. The Fokker–Planck equation is written for the Gompertz stochastic model of tumor growth. The equation is then solved through the path integral method. In this way, the probability density function of tumor-cell population, which contains the entire stochastic characteristics of the tumor growth, is obtained for any instance of time. The simulation results have also been presented for the evaluation of the suggested approach. The results show that the tumor-cell population can be controlled within a number of time windows (15 time windows in our case study) if an appropriate desired PDF is selected.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On an asymptotic viscosity solution property of solutions of discrete Hamilton–Jacobi–Bellman equations

In this paper, we show that a proper limit of solutions of discrete Hamilton–Jacobi–Bellman (dHJB) equations in a random walk model becomes a viscosity solution of a Hamilton–Jacobi–Bellman (HJB) variational inequality in a continuous-time geometric Brownian model. HJB variational inequalities are used to analyze singular stochastic control problems in mathematical finance. By our result, with the help of dHJB equations, we can obtain viscosity solutions of HJB variational inequalities which are usually identified with the value functions of the singular stochastic control problems.

97 MATHEMATICS AND COMPUTING↗