Probability of Pressure Deficit in On-Demand Branched Networks and Incorporation into Design Decisions

This technical paper presents analytical expressions to estimate the probability function of head losses in any path of an on-demand branched irrigation network. They are developed for estimating the probability of pressure deficit of a given magnitude at any hydrant. They are also useful for examining the probability of a power deficit at a pumping station designed to guarantee service to a hydrant, as well as the head characteristic curve of the distribution system linked to a definite probability. All this quantified information is useful for decision making on network design and performance. The probabilities calculated with the developed expressions can be taken as complementary or alternative concepts to Clément’s classical design flow method, which is taken here as a benchmark for comparisons. Illustrative examples of network designs are presented to validate the proposed expressions. The least cost design solutions using Clément’s design flows are compared with design solutions here obtained to get the same probability of pressure deficit at the most unfavorable hydrants. The new solutions are less expensive because the flow constraint can be avoided.     

Joint First-Passage Probability and Reliability of Systems under Stochastic Excitation

The first-passage probability, describing the probability that a scalar process exceeds a prescribed threshold during an interval of time, is of great engineering interest. This probability is essential for estimating the reliability of a structural component whose response is a stochastic process. When considering the reliability of an engineering system composed of several interdependent components, the probability that two or more response processes exceed their respective safe thresholds during the operation time of the system is an equally essential quantity. This paper proposes simple and accurate formulas for approximating this joint first-passage probability of a vector process. The nth order joint first-passage probability is obtained from a recursive formula involving lower order joint first-passage probabilities and the out-crossing probability of the vector process over a safe domain. Interdependence between the crossings is approximately accounted for by considering the clumping of these events. The accuracy of the proposed formulas is examined by comparing analytical estimates with those obtained from Monte Carlo simulations for stationary Gaussian processes. As an example application, the reliability of a system of interconnected equipment items subjected to a stochastic earthquake excitation is estimated by linear programming bounds employing marginal and joint component fragilities obtained by the proposed formulas.     

Simulation of Highly Skewed Non-Gaussian Stochastic Processes

In this paper, a simulation methodology is proposed to generate sample functions of a stationary, non-Gaussian stochastic process with prescribed spectral density function and prescribed marginal probability distribution. The proposed methodology is a modified version of the Yamazaki and Shinozuka iterative algorithm that has certain difficulties matching the prescribed marginal probability distribution. Although these difficulties are usually sufficiently small when simulating non-Gaussian stochastic processes with slightly skewed marginal probability distributions, they become more pronounced for highly skewed probability distributions (especially at the tails of such distributions). Two major modifications are introduced in the original Yamazaki and Shinozuka iterative algorithm to ensure a practically perfect match of the prescribed marginal probability distribution regardless of the skewness of the distribution considered. First, since the underlying “Gaussian” stochastic process from which the desired non-Gaussian process is obtained as a translation process becomes non-Gaussian after the first iteration, the empirical (non-Gaussian) marginal probability distribution of the underlying stochastic process is calculated at each iteration. This empirical non-Gaussian distribution is then used instead of the Gaussian to perform the nonlinear mapping of the underlying stochastic process to the desired non-Gaussian process. This modification ensures that at the end of the iterative scheme every generated non-Gaussian sample function will have the exact prescribed non-Gaussian marginal probability distribution. Second, before the start of the iterative scheme, a procedure named “spectral preconditioning” is carried out to check the compatibility between the prescribed spectral density function and prescribed marginal probability distribution. If these two quantities are found to be incompatible, then the spectral density function can be slightly modified to make it compatible with the prescribed marginal probability distribution. Finally, numerical examples (including a stochastic process with a highly skewed marginal probability distribution) are provided to demonstrate the capabilities of the proposed algorithm.     

Impact of Phase Shifters on Locational Prices

With the introduction of restructuring in the electric power industry, the price of electricity has become the focus of power market activities. Phase shifters in a power system can mitigate or reduce transmission congestion by redirecting line flows, reduce the cost of power dispatch by adjusting locational marginal prices (LMPs), and enhance market competition by reducing the chance of market power occurrences due to limited transmission flows. This paper analyzes the role of phase shifters in restructured power systems by simulating electricity market prices. The paper further provides a comparison among various alternatives such as transmission expansion for mitigating congestion. The simulation results are analyzed for a three-bus and presented for the Institute of Electrical and Electronics Engineers (IEEE) 118-bus power system.     

Type I error rate of the chi-square test in independence in R?×?C tables that have small expected frequencies.

Sampling experiments are reported that show that the uncorrected chi-square test of independence is exceptionally robust with respect to small expected frequencies in R?×?C contingency tables. In general, error rates that exceed .06 occurred only when both marginal probability distributions were extremely skewed and sample size was small. Nevertheless, the quality of the approximation of chi-square probabilities for exact multinomial probabilities was sometimes poor, although excessive errors in approximation by W. G. Cochran's (1952) criteria usually resulted from actual error rates being smaller, not larger, than the nominal level. A distinction is made between accuracy of approximation and control of the Type I error rate as considerations dictating the advisability of using an approximate test. (38 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Modeling multivariate discrete failure time data

A bivariate discrete survival distribution that allows flexible modeling of the marginal distributions and yields a constant odds ratio at any grid point is proposed. The distribution can be extended to a multivariate distribution and is readily generalized to accommodate covariates in the marginal distributions and pairwise odds ratios. In addition, a pseudo-likelihood estimation procedure for estimating the regression coefficients in the marginal models and the association parameters in the pairwise odds ratios is presented. We evaluate the performance of the proposed estimation procedure through simulations. For bivariate data, pseudo-likelihood estimation of the association parameter has high efficiency. Loss of efficiency in the marginal regression coefficient estimates is small when the association is not strong. For both the marginal regression coefficients and the association parameter, coverage probabilities are close to the 95% nominal level. For multivariate data, the simulation results show that the parameter estimates are consistent. Coverage probability for the regression coefficient in the marginal model is close to the 95% nominal level but is slightly less than the nominal level for the association parameter. We illustrate the proposed methods using a subset of the Framingham Heart Study data where a significant positive association was found between the failure times of siblings.     

Rolling and Lifting Probabilities for Sediment Entrainment

This study addresses the rolling and lifting probabilities for sediment entrainment by incorporating the probabilistic features of the turbulent fluctuation and bed grain geometry. The lognormally distributed instantaneous velocity and uniformly distributed initial grain position, along with a relation between lift coefficient and particle Reynolds number, are used to extend the theoretical formulation of the entrainment probabilities in smooth-bed flows. The two threshold conditions identified herein enable us to precisely define the probabilities of entrainment in the rolling and lifting modes. The results obtained in this study coincide well with the published data. The lifting probability increases monotonously with the dimensionless shear stress θ, which is consistent with the earlier results yet displays improved agreement with the experimental data. The maximum value of rolling probability, with a magnitude of 0.25, occurs at θ ≈ 0.15. For θ<0.05 (or θ>0.6), the rolling (or lifting) probability makes up more than 90% of the total entrainment probability and thus can be used as an approximation to the total probability of entrainment. The proposed rolling and lifting probabilities are further linked to the two separate criteria for incipient motion to explore the critical entrainment probabilities. The results reveal that a consistent probability corresponding to the critical state of sediment entrainment cannot be found.     

Optimal Capacity Expansion in Electric Power Subtransmission Networks

A procedure is proposed to determine where and when to increase the capacity of lines and transformers in a power subtransmission network. The expansion plan must minimize cost while supplying the demand for energy over a time horizon, keeping the quality and reliability standards of the network and minimizing the impact over the environment. The procedure is iterative and takes into account AC flows, reliability analysis, different scenarios, demand uncertainty, discrete investment costs, voltage constraints, capacity, and power factor. A significant contribution of this procedure is that, along with the expansion plan, it considers the optimization of the operation, specifically the movement of transformer taps and the location and sizing of reactive banks. This allows significantly reducing or delaying the investment, thus reducing its present value. The approach ensures convergence when computing the power flows and allows making an analysis of the effects of distributed generation and, if necessary, load curtailment. The model is tested on the power subtransmission network of the most important electric power distribution company in Chile, serving a city of 6 million people.     

Large-sample analysis for a stochastic epidemic model and its parameter estimators

This paper considers the simplest stochastic model for the spread of an epidemic in a closed, homogeneously mixing population. Approximate methods are presented for calculating the probability distribution of the epidemic size (i.e. number of infected individuals). In fact, a functional central limit theorem and a large deviation principle for the epidemic size when the population increases are shown. These results enable us to both obtain a global approximation for the epidemic size and study asymptotic properties of other random variables depending on the complete history of the epidemic. As an application of our results, we derive two sequences of estimators for the contact rate and analyze their asymptotic behaviour.     

零部件质量不确定对其再制造加工的影响

针对零部件再加工路线与再加工时间的不确定性问题,建立了零部件再加工系统的开环排队网络模型.该模型考虑了再加工机器故障和有限缓冲能力,并假定机器故障率、维修率和再加工时间服从指数分布.基于分解原理和扩展方法,给出了求解模型的近似分析算法以求解零部件的平均再加工时间、再加工效率等系统参数.提出了零部件质量的标定方法,并以此为基础探讨了零部件质量不确定性对其再加工时间的影响.算例分析表明,零部件的再加工时间与其质量呈负相关关系,且随着零部件质量的不断降低其边际再加工时间逐渐减少.     

Temperature-dependent variability in lifetime prediction of thermally activated systems

The lifetime of high-temperature systems is often controlled by thermally activated mechanisms such as diffusion. The variability in the lifetime of such systems is analyzed when the operating temperature varies according to a normal (Gaussian) distribution. Linear approximation analysis is employed to obtain simple closed form results for the probability density function (pdf) for the lifetime. The Gaussian variation in temperature is shown to transform to a log-normal distribution for the lifetime. The standard deviation of the log-normal distribution can be predicted from the activation energy, the peak temperature, and the standard deviation of the temperature distribution. Higher activation energy and lower operating temperature increase the variability of the lifetime. This approximate result is compared with the exact transformation. Lifetime experiments with incandescent tungsten lamps are compared to the theoretical prediction.     

Accurate confidence limits for quantiles under random censoring

In survival analysis, estimates of median survival times in homogeneous samples are often based on the Kaplan-Meier estimator of the survivor function. Confidence intervals for quantiles, such as median survival, are typically constructed via large sample theory or the bootstrap. The former has suspect accuracy for small sample sizes under moderate censoring and the latter is computationally intensive. In this paper, improvements on so-called test-based intervals and reflected intervals (cf., Slud, Byar, and Green, 1984, Biometrics 40, 587-600) are sought. Using the Edgeworth expansion for the distribution of the studentized Nelson-Aalen estimator derived in Strawderman and Wells (1997, Journal of the American Statistical Association 92), we propose a method for producing more accurate confidence intervals for quantiles with randomly censored data. The intervals are very simple to compute, and numerical results using simulated data show that our new test-based interval outperforms commonly used methods for computing confidence intervals for small sample sizes and/or heavy censoring, especially with regard to maintaining specified coverage.     

Computing Travel Time Reliability in Transportation Networks with Multistates and Dependent Link Failures

The measurement of transportation network travel time reliability is imperative to provide drivers with accurate route guidance information and to generate the shortest path (or alternative paths) connecting origins and destinations, especially under conditions of varying demands and limited capacities. Previous studies assumed that link failures in a road network are statistically independent and that reliability probabilities are perfectly determinable. In real life, these assumptions are dubious, because the failure of a link in one particular area does not necessarily result in the complete failure of the neighboring link, but may lead to deterioration of its performance. This paper presents a new methodology to study the multistate system reliability analysis of transportation networks for which one cannot formulate an “all or nothing” type of failure criterion and in which dependent link failures are considered. The methodology is presented, using a numerical example, for computing the probability that travel time between an origin and a destination may exceed a threshold.     

Bounds on System Reliability by Linear Programming

Bounds on system probability in terms of marginal or joint component probabilities are of interest when exact solutions cannot be obtained. Currently, bounding formulas employing unicomponent probabilities are available for series and parallel systems, and formulas employing bi- and higher-order component probabilities are available for series systems. No theoretical formulas exist for general systems. It is shown in this paper that linear programming (LP) can be used to compute bounds for any system for any level of information available on the component probabilities. Unlike the theoretical bicomponent and higher-order bounds, the LP bounds are independent of the ordering of the components and are guaranteed to produce the narrowest possible bounds for the given information. Furthermore, the LP bounds can incorporate any type of information, including an incomplete set of component probabilities or inequality constraints on component probabilities. Numerical examples involving series, parallel and general structural systems are used to demonstrate the methodology.     

Stochastic Solution for Uncertainty Propagation in Nonlinear Shallow-Water Equations

This paper presents a stochastic approach to describe input uncertainties and their propagation through the nonlinear shallow-water equations. The formulation builds on a finite-volume model with a Godunov-type scheme for its shock capturing capabilities. Orthogonal polynomials from the Askey scheme provide expansion of the variables in terms of a finite number of modes from which the mean and higher-order moments of the distribution can be derived. The orthogonal property of the polynomials allows the use of a Galerkin projection to derive separate equations for the individual modes. Implementation of the polynomial chaos expansion and its nonintrusive counterpart determines the modal contributions from the resulting system of equations. Examples of long-wave transformation over a submerged hump illustrate the stochastic approach with uncertainties represented by Gaussian distribution. Additional results demonstrate the applicability of the approach with other distributions as well. The stochastic solution agrees well with the results from the Monte Carlo method, but at a small fraction of its computing cost.     

Determinants of microcomputer technology use: implications for education and training of health staff

Electrophysiological properties of spiking neurons receiving complex stimuli perturbed by noise are investigated. A semi-analytical estimate of firing probabilities and subthreshold behavior of the stochastic system can be made in terms of the solution of a purely deterministic system. The method comes from an approximation for the distribution function and moments of the underlying non linear multidimensional diffusion process. This so called moment method works for general conductance-based systems and an application is presented for the Hodgkin-Huxley neuronal model. Statistical properties obtained from the moment method are compared with direct numerical integration of the stochastic system. The firing probability due to external noise is derived as a closed formula. Results are given for different forms of the deterministic component of the stimulus. A generalization to neural networks of conductance-based systems with internal currents perturbed by noise can be obtained using the same approach. In the case of fully connected networks, a mean field population equation is derived which may be compared to Kuramoto's master equation for weakly coupled neural oscillators.     

A multivariate logistic model (MLM) for analyzing binary family data

We consider modeling the familial correlation between 2 related individuals using a multiple logistic regressive model. It is shown that there is a discrepancy in the marginal probability of the second individual. We investigate the conditions under which this discrepancy can be minimized and show how it can have a direct effect on handling missing values and ascertainment. We derive a functional relationship between the parameters in the model that eliminates this discrepancy, hence solving the problems that can arise in the handling of missing values and ascertainment. Because this methodology fails when there are more than 2 related individuals, we present a new model based on a multivariate logistic distribution. Residual familial correlations can be directly related to the parameters of this model. The likelihood for family data under this model is independent of the order in which the family members enter the calculation. The marginal probabilities can be easily computed.     

New Approximations for Reliability Integrals

A new asymptotic expansion is applied to approximate reliability integrals. The asymptotic approximation reduces the problem of evaluating a multidimensional probability integral to solving an unconstrained minimization problem. Approximations are developed in both the transformed (independently, normally distributed) variables and the original variables. In the transformed variables, the asymptotic approximation yields a very simple formula for approximating the value of the second-order reliability method integrals. In many cases, it may be computationally expensive to transform to normal variables, and an approximation using the probability distribution for the original variables can be used. Examples are presented illustrating the accuracy of the approximations, and results are compared with some existing approximations of reliability integrals.     

包钢高炉炼铁优化配矿平台的开发与应用

为了降低高炉炼铁系统原料成本,实现自铁矿石采购到高炉炼铁全过程协同优化,开发了一个高炉炼铁全系统、全流程优化配矿平台.全流程是指从铁矿石采购到高炉产出铁水的整个工艺流程,全系统是指钢铁企业所有高炉炼铁整体系统.优化配矿平台包括数据库系统、单座高炉优化配矿平台、全系统高炉优化配矿平台、生产数据采集与分析平台4部分.平台以...