含时滞参数的灰色GM(1,1,τ)模型及其应用

针对GM(1,1)模型未能反映系统时滞效应的问题,根据实际应用的需要,利用灰色建模思想构建了含时滞参数7的灰色GM(1,1,Υ)模型,并研究了该模型的建模机理、建模过程,给出参数估计方法.并根据模型的基本形式,构建出以原始值和背景值的一阶累减生成序列的灰色相对关联度最大化为目标的灰色关联分析法来探索时滞参数Υ的确定方法,并获得模型的离散解.最后利用该模型对美国制造业库存总量进行了模拟预测,获得较高的精度,验证了模型的有效性.     

面向混频数据的时滞GM(1,N)模型

采样频率不同、间距不等的混频数据背景下,考虑时滞是系统要素间因果作用的常见现象,提出含时滞参数的混频GM(1,N)建模方法。根据时滞特征不同,将模型划分为两类:同步推移型时滞GM(1,N)模型和累积型时滞GM(1,N)模型。同步推移型用于表征时滞长度固定但起始时间不确定、具有管道延迟性质的时滞关系。累积型用于表征时滞长度不确定、因果效应逐步叠加的时滞关系。将指数Almon函数作为时滞分布函数,该函数可完全由数据驱动生成递增、递减、S型、U型、钟型等多种形态,有助于挖掘混频数据中的时滞信息。数值分析的结果验证了模型的有效性。模型对于存在低频小样本数据的混频时滞系统具有很强的适用性。     

基于区间灰数序列的多变量灰色预测模型

针对传统的多变量灰色预测模型仅适用于实数序列的问题,对多变量在区间灰数序列的情形下进行建模.以核和灰度两个维度为基础,分别建立核序列和灰度序列的MGM(1,m)模型,通过核和灰度的模拟预测值还原计算得到多变量中各个变量对应的灰数序列的上界和下界,从而构建基于区间灰数序列的MGM(1,m)模型.最后,将提出的灰色多变量模型应用于雾霾的判别因素能见度和相对湿度,建立基于区间灰数序列的MGM(1,2)模型,对区间灰数序列的模拟预测取得了较好的效果,结果表明提出的基于核和灰度的灰色多变量预测模型具有可行性和实用性.     

组合预测模型时间要素研究

为了分析时间因素对组合预测模型预测精度的影响,基于对长期内各预测方法预测精度稳定性的考虑,借鉴一维AR(p)模型建模思路,提出了基于时间因素的组合预测模型建模方法。实例验证表明:相对于单个预测方法,考虑时间因素的组合预测方法的预测精度更高,且样本时间跨度越长,预测精度也越高。     

基于BSA-ELM模型的建筑工程施工成本预测研究

针对建筑工程施工成本管理中成本难以预测的问题,提出用鸟群算法(BSA)优化极限学习机(ELM)模型的参数.首先,利用BSA对ELM模型的输入权值和偏置值进行优化;其次,构建出BSA-ELM建筑工程施工成本预测模型;最后,将BSA-ELM模型与实际工程施工成本数据相结合进行验证.结果表明:模型在成本预测中的精度比ELM模型、CSO-ELM模型、PSO-ELM模型和BP神经网络模型预测精度高,也为类似预测问题提供了一种新的预测方法.     

基于初始值和背景值改进的GM(1, 1)模型优化与应用

针对在现实生活中, 经典GM(1,1)模型预测精度不稳定, 且以往的优化方法大部分具有片面性的缺点, 文章对经典GM(1,1)模型背景值与初始值进行改进, 提出了一种组合优化方法:根据动态寻优原则, 将背景值设为变量, 其参数以及时间响应式由MRE取最小值时确定;同时, 采用差分方程取代以x⁽¹⁾(1)为固定点的静态方程。将初始值和背景值看作变量, 以系统地减少模型误差。结合国内石油年消费量数据, 分别应用经典和改进后的GM(1,1)模型进行计算和误差对比, 验证了改进后的模型精度要显著优于经典模型。     

优化MGM(1,n)模型及其应用研究

从最小二乘估计的适用条件出发,在建立MGM(1,n)模型前,先采用BoxCox变换对原始数据进行变换,以解决或缓解误差项的正态性偏离问题.首先,以模型拟合平均误差最小化为目标,建立非线性优化模型,在参数的置信区间内,应用PSO(Particle Swarm Optimization)算法求最优解.然后,应用求解得到的参数,建立优化MGM(1,n)模型.在实例分析中,将优化MGM(1,n)模型应用于深基坑围护结构变形预测,实验结果表明通过对原始数据做合适的Box-Cox变换,能够有效提高模型的拟合及预测精度,拓广多变量灰色预测模型的适用范围.     

对背景值优化的新GM(1,1)模型

为了提高灰色GM(1,1)模型的模拟及预测精度,考虑对模型的初始条件x(1)(n)增加扰动因素β,把x(1)(n)+β作为模型的新初始条件,并对模型的背景值进行优化,从而得到了一种改进的GM(1,1)模型.还通过实例验证了新建模型比原有模型提高了拟合的效果及预测的精度.     

ABC-PSO算法优化混合核SVM参数及应用

针对混合核支持向量机(SVM)中的可调参数一般是根据经验或人工随机调试得到,不能确保参数最优的局限性,提出用粒子群和人工蜂群的并行混合优化(ABC-PSO)算法来优化混合核SVM参数,找出满足条件的最优参数组合.将该SVM模型应用到语音识别中,通过对三个不同语种的语音数据库的实验仿真,验证了混合算法优化SVM参数所得的优化SVM模型比PSO算法优化SVM所得的模型,具有良好的泛化能力和语音识别能力.     

具有时滞和周期特征的短时交通流灰建模及其应用

针对短时交通流的延迟性、随机性和周期性特征,采用灰关联分析和分数阶累加生成方法建立了带时滞和周期特征的分数阶累加灰色新模型.针对短时交通流的延迟性,将短时交通流数据拆分成参考时间序列和对应的比较时间序列,进行关联度分析,得到计算时滞值的方法.针对短时交通流的随机性和周期性,利用分数阶累加生成方法,并引入tan(kp)为发展系数,sin(kp)为输入变量,建立了短时交通流的分数阶GM(1,1|tan(kp),sin(kp))模型,给出了模型参数的最小二乘估计和周期性参数与分数阶阶数的优化求解算法.最后将模型应用于长沙市芙蓉区某交叉路口的交通流建模及预测中,并与常规的五种模型进行了对比分析,结果表明,模型能较为准确地反映交通流的实际情况,且有较高的预测精度和较为稳定的结果.     

向量灰色模型的建立及应用

针对传统多变量灰色预测模型(MGM(1,m))有时存在的建模数据失真问题,以系统中关联变量具有趋同性为基础,提出了一种新的模型——向量灰色模型(VGM(1,m))。与MGM(1,m)模型相比,VGM(1,m)结构更简单,模型参数更少,从而有利于参数的估计。将VGM(1,m)、MGM(1,m)、GM(1,1)模型应用于四个实例的分析,结果表明VGM(1,m)消除了MGM(1,m)的建模失真现象,模型的稳定性得到了增强。进一步,与GM(1,1)建模结果相比,VGM(1,m)模型的预测精度更高,即新模型有更好的泛化性。     

灰色GM(1,1,k,k2)模型背景值及时间响应函数优化

本文提出了一种新的带有时间幂次项的灰色GM(1,1,k,k²)模型,给出了其灰微分方程和白化微分方程基本形式。基于最小二乘法获得了该模型参数估计值,并推导了该模型时间响应函数。鉴于GM(1,1,k,k²)模型灰微分方程与白化微分方程之间存在跳跃关系,首先对灰微分方程的背景值进行了优化,并推导了优化后的背景值计算公式。为了克服初始值的影响,根据误差平方和最小,进一步优化了GM(1,1,k,k²)模型时间响应函数。最后,该优化后的GM(1,1,k,k²)模型被应用于软土地基沉降预测,获得了较好的模拟预测效果,说明模型是可行的。     

Normal Sylow subgroups and monomial Brauer characters

Let G be a finite group, p be a prime divisor of |G|, and P be a Sylow p-subgroup of G. We prove that P is normal in a solvable group G if |G : ker φ|p' = φ(1)p' for every nonlinear irreducible monomial p-Brauer character φ of G, where ker φ is the kernel of φ and φ(1)p' is the p'-part of φ(1).     

非线性随机分数阶延迟积分微分方程Euler-Maruyama方法的强收敛性

本文研究了一类新的模型问题:非线性随机分数阶延迟积分微分方程.当方程中的漂移项和扩散项满足全局Lipschitz条件和线性增长条件时,基于压缩映射原理给出了该方程解存在唯一的充分条件.由于理论求解的困难,构造了一种数值方法(Euler-Maruyama方法),并证得强收敛阶为α-1/2,α∈(1/2,1].最后通过数值试验,验证了这一理论结果.     

Stochastic resonance with different periodic forces in overdamped two coupled anharmonic oscillators

We study the stochastic resonance phenomenon in the overdamped two coupled anharmonic oscillators with Gaussian noise and driven by different external periodic forces. We consider (i) sine, (ii) square, (iii) symmetric saw-tooth, (iv) asymmetric saw-tooth, (v) modulus of sine and (vi) rectified sinusoidal forces. The external periodic forces and Gaussian noise term are added to one of the two state variables of the system. The effect of each force is studied separately. In the absence of noise term, when the amplitude f of the applied periodic force is varied cross-well motion is realized above a critical value (f_c) of f. This is found for all the forces except the modulus of sine and rectified sinusoidal forces. For fixed values of angular frequency ω of the periodic forces, f_c is minimum for square wave and maximum for asymmetric saw-tooth wave. f_c is found to scale as Ae^0.75ω + B where A and B are constants. Stochastic resonance is observed in the presence of noise and periodic forces. The effect of different forces is compared. The stochastic resonance behaviour is quantized using power spectrum, signal-to-noise ratio, mean residence time and distribution of normalized residence times. The logarithmic plot of mean residence time τ_MR against 1/(D − D_c) where D is the intensity of the noise and D_c is the value of D at which cross-well motion is initiated shows a sharp knee-like structure for all the forces. Signal-to-noise ratio is found to be maximum at the noise intensity D = D_max at which mean residence time is half of the period of the driving force for the forces such as sine, square, symmetric saw-tooth and asymmetric saw-tooth waves. With modulus of sine wave and rectified sine wave, the SNR peaks at a value of D for which sum of τ_MR in two wells of the potential of the system is half of the period of the driving force. For the chosen values of f and ω, signal-to-noise ratio is found to be maximum for square wave while it is minimum for modulus of sine and rectified sinusoidal waves. The values of D_c at which cross-well behaviour is initiated and D_max are found to depend on the shape of the periodic forces.     

Analytic modelling of solar radiation: driven temperature variations of outdoor surfaces

An analytic model is described for the variation of surface temperature T₀(t) ofa freely evaporating or totally dry surface exposed to complicated, non-analytic variations of meteorological conditions expressed in (N + 1)-point time series form. Its basis is a parameterized, analytic representation of T₀, inserted in linearized equations describing the surface energy balance and the concurrent underlying heat conduction. Applied to diurnal variations (with N = 24) over bare soil, the model reproduces observed temperatures with a typical standard deviation less than 1K, and the daily mean within 0.1 K.

The method should find general application in modelling of storage systems subject to complicated, discretely-sampled boundary conditions, where a linear analytic equation links the latter to the storage term.     

Law of iterated logarithm and model selection consistency for generalized linear models with independent and dependent responses

We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent (\rho-mixing) responses under mild conditions. The LIL is useful to derive the asymptotic bounds for the discrepancy between the empirical process of the log-likelihood function and the true log-likelihood. The strong consistency of some penalized likelihood-based model selection criteria can be shown as an application of the LIL. Under some regularity conditions, the model selection criterion will be helpful to select the simplest correct model almost surely when the penalty term increases with the model dimension, and the penalty term has an order higher than O(log log n) but lower than O(n): Simulation studies are implemented to verify the selection consistency of Bayesian information criterion.     

Stability and bifurcation in a harvested one-predator–two-prey model with delays

It is known that one-predator–two-prey system with constant rate harvesting can exhibit very rich dynamics. If such a system contains time delayed component, it can have more interesting behavior. In this paper we study the effects of the time delay on the dynamics of the harvested one-predator–two-prey model. It is shown that time delay can cause a stable equilibrium to become unstable. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhães. An example is given and numerical simulations are finally performed for justifying the theoretical results.     

Complexity analysis of an interior point algorithm for the semidefinite optimization based on a kernel function with a double barrier term

In this paper, we establish the polynomial complexity of a primal-dual path-following interior point algorithm for solving semidefinite optimization(SDO) problems. The proposed algorithm is based on a new kernel function which differs from the existing kernel functions in which it has a double barrier term. With this function we define a new search direction and also a new proximity function for analyzing its complexity. We show that if q1 q2 1, the algorithm has O((q1 + 1) nq1+1/2(q1-q2)logn/ε)and O((q1 + 1)3q1-2q2+1/2(q1-q2)n~1/2 logn/ε) complexity results for large- and small-update methods, respectively.