Probability Distribution of Ratio of China Aviation Network Edge Vertices Degree and Its Evolutionary Trace Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of ratio of China aviation network edge vertices degree were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the ratio of edge vertices degree in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the ratio of edge vertices degree had linear probability distribution and the two parameters of the probability distribution had linear evolution trace.

Flow pattern analysis of linear gradient flow distribution

This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An Lx-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.

Gravity effect calculation of threedimensional linear density distribution andits application

An algorithm for calculating gravity effect of three-dimensional (3D) linear density distribution is presented in this paper. The linear continuous density distribution is represented with 3D grid model, which has a resemblance to the velocity model used in some seismic tomography codes. The consensus in representation method of density model and velocity model facilitates the seismic-gravity-integrated interpretation or simultaneous inversion. The numerical test of synthetic data shows that although the analytical gravity formula for linear density distribution is more complex than that for piecewise constant density distribution, it takes less time to calculate the gravity effect with linear density model than that with piecewise constant density model. In addition, this method is used in the integrated interpretation of 3D seismological tomography and gravity data in Dabie Mountain area.

Balancing four-state continuous-variable quantum key distribution with linear optics cloning machine

We show that the secret key generation rate can be balanced with the maximum secure distance of four-state continuous-variable quantum key distribution（CV-QKD） by using the linear optics cloning machine（LOCM）. Benefiting from the LOCM operation, the LOCM-tuned noise can be employed by the reference partner of reconciliation to achieve higher secret key generation rates over a long distance. Simulation results show that the LOCM operation can flexibly regulate the secret key generation rate and the maximum secure distance and improve the performance of four-state CV-QKD protocol by dynamically tuning parameters in an appropriate range.

A Modification to Vertical Distribution of Tidal Flow Reynolds Stress in Shallow Sea

Tidal flow is a periodic movement of unsteady and non-uniform, which has acceleration and deceleration process obviously, especially in coastal shallow waters. Many researches show that vertical distribution of tidal flow Reynolds stress deviated from linear distribution. The parabolic distribution of the tidal flow Reynolds stress was proposed by Song et al. （2009）. Although the model fills better with field observations and indoor experimental data, it has the lower truncated series expansion of tidal flow Reynolds stress, and the description of the distribution is not very comprehensive By introducing the motion equation of tidal flow and improving the parabolic distribution established by Song et al. （2009）, the cubic distribution of the tidal flow Reynolds stress is proposed. The cubic distribution is verified well by field data （Bowden and Fairbairn, 1952; Bowden et al., 1959; Rippeth et al., 2002） and experimental data （Anwar and Atkins, 1980）, is consistent with the numerical model results of Kuo et al. （1996）, and is compared with the parabolic distribution of the tidal flow Reynolds stress. It is shown that this cubic distribution is not only better than the parabolic distribution, but also can better reflect the basic features of Reynolds stress deviating from linear distribution downward with the tidal flow acceleration and upward with the tidal flow deceleration, for the foundation of further study on the velocity profile of tidal flow.

Vertical Distribution of Tidal Flow Reynolds Stress in Shallow Sea

Based on the results of the tidal flow Reynolds stresses of the field observations, indoor experiments, and numerical models, the parabolic distribution of the tidal flow Reynolds stress is proposed and its coefficients are determined theoretically in this paper. Having been well verified with the field data and experimental data, the proposed distribution of Reynolds stress is also compared with numerical model results, and a good agreement is obtained, showing that this distribution can well reflect the basic features of Reynolds stress deviating from the linear distribution that is downward when the tidal flow is of acceleration, upward when the tidal flow is of deceleration. Its dynamics cause is also discussed preliminarily and the influence of the water depth is pointed out from the definition of Reynolds stress, turbulent generation, transmission, and so on. The established expression for the vertical distribution of the tidal flow Reynolds stress is not only simple and explicit, but can also well reflect the features of the tidal flow acceleration and deceleration for further study on the velocity profile of tidal flow.

不确定需求下铁路集装箱班列开行方案与定价联合优化

铁路集装箱班列开行方案与运价是影响铁路集装箱运输企业盈利的两个关键因素,且这二者相互联系、相互影响,对其进行联合优化可以提升铁路集装箱运输的市场竞争力。以最大化铁路集装箱运输预期利润为目标,构建联合优化班列开行方案与定价的随机混合整数非线性规划(SMINP)模型。此模型以二项Logit模型描述托运人在铁路集装箱运输与公路集装箱运输之间的运输方式选择行为,在集装箱总运输需求概率分布形式、一阶矩与二阶矩均不确定的情形下,基于分布鲁棒优化方法将此SMINP模型转化为其确定性等价类,根据转化后模型特点进一步利用增量分段线性化以及McCormick包络法对模型线性化,使其可通过调用Gurobi求解器高效求解。以大朗至大红门铁路集装箱运输线路进行算例分析,在线路通过能力与运价可变动范围等信息已知的前提下,求得最优集装箱班列开行方案与运价。算例结果表明本文所提方法能够提升铁路集装箱运输效率与收益。

Rapid Optimization of Tension Distribution for Cable-Driven Parallel Manipulators with Redundant Cables

The solution of tension distributions is infinite for cable-driven parallel manipulators（CDPMs） with redundant cables. A rapid optimization method for determining the optimal tension distribution is presented. The new optimization method is primarily based on the geometry properties of a polyhedron and convex analysis. The computational efficiency of the optimization method is improved by the designed projection algorithm, and a fast algorithm is proposed to determine which two of the lines are intersected at the optimal point. Moreover, a method for avoiding the operating point on the lower tension limit is developed. Simulation experiments are implemented on a six degree-of-freedom（6-DOF） CDPM with eight cables, and the results indicate that the new method is one order of magnitude faster than the standard simplex method. The optimal distribution of tension distribution is thus rapidly established on real-time by the proposed method.

基于分布鲁棒优化的灵活爬坡备用调度方法

可再生能源大规模接入电网对电力系统的爬坡能力提出很大挑战,工业界得到应用的灵活爬坡产品的调度模型为含确定性爬坡需求约束的模型,该模型无法保证得到的爬坡容量决策解在不确定性实现下的可行性。该文研究灵活爬坡备用的分布鲁棒调度方法,提出考虑灵活爬坡备用可调度性的两阶段分布鲁棒调度模型,并考虑安全约束违反的风险,基于Wasserstein距离构建不确定性模糊集。所提方法能自动确定系统所需的灵活爬坡需求,并能保证得到的爬坡容量具有可调度性。所建两阶段模型可等效为混合整数线性规划问题直接进行求解。通过IEEE 14节点系统和IEEE 118节点系统的算例分析,验证所提方法的有效性。对比所提方法相对于含确定性爬坡需求调度模型和考虑不确定性的随机调度模型的优势,并进行灵敏度分析。

CONSISTENT NONPARAMETRIC ESTIMATION OF ERROR DISTRIBUTIONS IN LINEAR MODEL'

For the linear model y_i=x_iθ+e_i, i=1, 2,…, let the error sequence {e_i}_i=1 be iidr.v.’s, with unknown density f(x). In this paper,a nonparametric estimation method based onthe residuals is proposed for estimating f(x) and the consistency of the estimators is obtained.

A New Generalized Linear Exponential Distribution and Its Applications

A new generalized linear exponential distribution （NCLED） is considered in this paper which can be deemed as a new and more flexible extension of linear exponential distribution. Some statistical properties for the NGLED such as the hazard rate function, moments, quantiles are given. The maximum likelihood estimations （MLE） of unknown parameters are also discussed. A simulation study and two real data analyzes are carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.

Parameter Estimation Based on Censored Data under Partially Accelerated Life Testing for Hybrid Systems due to Unknown Failure Causes

In general,simple subsystems like series or parallel are integrated to produce a complex hybrid system.The reliability of a system is determined by the reliability of its constituent components.It is often extremely difficult or impossible to get specific information about the component that caused the system to fail.Unknown failure causes are instances in which the actual cause of systemfailure is unknown.On the other side,thanks to current advanced technology based on computers,automation,and simulation,products have become incredibly dependable and trustworthy,and as a result,obtaining failure data for testing such exceptionally reliable items have become a very costly and time-consuming procedure.Therefore,because of its capacity to produce rapid and adequate failure data in a short period of time,accelerated life testing(ALT)is the most utilized approach in the field of product reliability and life testing.Based on progressively hybrid censored(PrHC)data froma three-component parallel series hybrid system that failed to owe to unknown causes,this paper investigates a challenging problem of parameter estimation and reliability assessment under a step stress partially accelerated life-test(SSPALT).Failures of components are considered to follow a power linear hazard rate(PLHR),which can be used when the failure rate displays linear,decreasing,increasing or bathtub failure patterns.The Tempered random variable(TRV)model is considered to reflect the effect of the high stress level used to induce early failure data.The maximum likelihood estimation(MLE)approach is used to estimate the parameters of the PLHR distribution and the acceleration factor.A variance covariance matrix(VCM)is then obtained to construct the approximate confidence intervals(ACIs).In addition,studentized bootstrap confidence intervals(ST-B CIs)are also constructed and compared with ACIs in terms of their respective interval lengths(ILs).Moreover,a simulation study is conducted to demonstrate the performance of the estimation procedures and the methodology discussed in this paper.Finally,real failure data from the air conditioning systems of an airplane is used to illustrate further the performance of the suggested estimation technique.

带矩约束的二阶段分布式鲁棒优化

针对带有矩约束的两阶段分布式鲁棒优化问题,当随机变量的支撑集是多面体时,利用线性规划对偶、无穷维规划对偶、二次规划的Wolfe对偶等理论研究两阶段分布式鲁棒优化问题的等价可求解模型.在分布式鲁棒优化的决策变量服从线性决策和第二阶段中的右端项为随机变量两种不同的情形下,给出对应的两阶段分布式鲁棒优化均能等价转化为可用已有算法求解的二阶锥优化问题.

A Complex Algorithm for Solving a Kind of Stochastic Programming

Considering that the probability distribution of random variables in stochastic programming usually has incomplete information due to a perfect sample data in many real applications, this paper discusses a class of two-stage stochastic programming problems modeling with maximum minimum expectation compensation criterion (MaxEMin) under the probability distribution having linear partial information (LPI). In view of the nondifferentiability of this kind of stochastic programming modeling, an improved complex algorithm is designed and analyzed. This algorithm can effectively solve the nondifferentiable stochastic programming problem under LPI through the variable polyhedron iteration. The calculation and discussion of numerical examples show the effectiveness of the proposed algorithm.

基于分布鲁棒优化的社区型能源系统低碳经济调度

随着可再生能源渗透率的提高以及能源转型进程的推进,能源系统在保证调度策略鲁棒性的同时,也要考虑系统的绿色性和低碳性.针对含碳捕集机组的社区型能源系统中各社区在风电功率不确定性下的最优决策问题,提出一种非合作博弈模式下的分布鲁棒优化方法.首先,以运行成本最低为目标,构建各社区的两阶段调度模型.其次,将风电功率的分布信息纳入到两阶段模型中,考虑各社区之间的非合作博弈关系,构建分布鲁棒博弈模型.最后,利用线性决策理论及对偶原理求解模型.仿真结果表明,所提分布鲁棒博弈方法可以保证博弈策略的鲁棒性,同时也克服了鲁棒优化强保守性的问题.

Nonlinear Distributed Model Predictive Control for Multiple Missiles Against Maneuvering Target with a Trajectory Predictor

This study aims to solve the problem of multi-missile simultaneous attacks on maneuvering target.The challenges include multimissile cooperative control and target's trajectory prediction.A controller based on nonlinear distributed model predictive control(NDMPC)is designed for multiple missiles against a maneuvering target,and a trajectory prediction inethod based on particle swarm optimization(PSO)algorithm is proposed.This study has mainly completed the following three aspects of work.Firstly,the cost function of the cont roller is constructed to optimize the accuracy and synchronization of the multi-missile system with consideration of collision avoidance.Secondly,the velocity control of the leading missile is designed by using the range-to-go in-formation in real time to ensure the attack fficiency and the control of the terminal velocity difference.Finally,a kinematic model of the target is cstimated by using short-term real-time data with the PSO algorithm.The established model is employed to predict the target trajectory in the interval between radar scans.Numerical simulation results of two different s enarios demonstrate the effectiveness of the proposed cooperative guidance approach.

Efficient Algorithms for Generating Truncated Multivariate Normal Distributions

Sampling from a truncated multivariate normal distribution （TMVND） constitutes the core computational module in fitting many statistical and econometric models. We propose two efficient methods, an iterative data augmentation （DA） algorithm and a non-iterative inverse Bayes formulae （IBF） sampler, to simulate TMVND and generalize them to multivariate normal distributions with linear inequality constraints. By creating a Bayesian incomplete-data structure, the posterior step of the DA Mgorithm directly generates random vector draws as opposed to single element draws, resulting obvious computational advantage and easy coding with common statistical software packages such as S-PLUS, MATLAB and GAUSS. Furthermore, the DA provides a ready structure for implementing a fast EM algorithm to identify the mode of TMVND, which has many potential applications in statistical inference of constrained parameter problems. In addition, utilizing this mode as an intermediate result, the IBF sampling provides a novel alternative to Gibbs sampling and elimi- nares problems with convergence and possible slow convergence due to the high correlation between components of a TMVND. The DA algorithm is applied to a linear regression model with constrained parameters and is illustrated with a published data set. Numerical comparisons show that the proposed DA algorithm and IBF sampler are more efficient than the Gibbs sampler and the accept-reject algorithm.

Distributionally robust optimization model of active distribution network considering uncertainties of source and load

To ensure the safety and reliability of the distribution network and adapt to the uncertain development of renewable energy sources and loads,a two-stage distributionally robust optimization model is proposed for the active distribution network(ADN)optimization problem considering the uncertainties of the source and load in this paper.By establishing an ambiguity set to capture the uncertainties of the photovoltaic(PV)power,wind power and load,the piecewise-linear function and auxiliary parameters are introduced to help characterize the probability distribution of uncertain variables.The optimization goal of the model is to minimize the total expected cost under the worst-case distribution in the ambiguity set.The first-stage expected cost is obtained based on the predicted value of the uncertainty variable.The second-stage expected cost is based on the actual value of the uncertainty variable to solve the first-stage decision.The generalized linear decision rule approximates the two-stage optimization model,and the affine function is introduced to provide a closer approximation to the second-stage optimization model.Finally,the improved IEEE 33-node and IEEE 118-node systems are simulated and analyzed with deterministic methods,stochastic programming,and robust optimization methods to verify the feasibility and superiority of the proposed model and algorithm.

需求不确定下的两阶段订货分布式鲁棒优化模型

在现代供应链管理中,订货决策在不确定需求下尤为关键。本研究针对这一问题,提出了一个两阶段分布式鲁棒优化模型以应对市场需求波动带来的风险,并采用线性决策规则和拓展的线性规则对其进行近似求解,最后通过数值实验验证模型的有效性。本研究的创新之处在于多产品库存管理模型的构建及其求解方法的优化,由此提供了在需求不确定条件下优化订货决策的新方法。

一类分布鲁棒线性决策随机优化研究

随机优化广泛应用于经济、管理、工程和国防等领域,分布鲁棒优化作为解决分布信息模糊下的随机优化问题近年来成为学术界的研究热点.本文基于φ-散度不确定集和线性决策方式研究一类分布鲁棒随机优化的建模与计算,构建了易于计算实现的分布鲁棒随机优化的上界和下界问题.数值算例验证了模型分析的有效性.