随机优化磨光算法对卫生陶瓷进出口的分析模型

结合磨光法和最优化理论提出一种随机优化磨光算法(SOS算法),算法通过原始值的参数化和调整幅度的修改,利用优化理论优化控制点.实例表明,随机优化磨光算法比样条修正磨光法和灰色马尔可夫链预测模型精度要高得多;而且所得到的误差变化更稳定.     

控制点优化磨光算法在长江径流量预测中的应用

盈亏修正磨光法所得到的逼近效果仍然很差,通过控制点的参数优化和目标函数的最小,提出一种控制点优化磨光算法,利用这个算法得到参数后代入模型,使预测的精度得到提高.通过实例,该算法简单易行,并通过相对误差进行了分析,控制点优化磨光算法所得到的预测值好于神经网络模型、PPAR和小波网络模型的预测值,这为研究磨光法提供了较好的分析方法.     

基于灰色马尔可夫模型的节能设备故障预测研究

精准预测节能设备故障可以有效节约节能服务公司运营成本,直接关系到节能服务公司的节能项目管理.根据灰色系统理论,将灰色均值GM(1,1)模型与马尔可夫模型融合,通过灰色马尔可夫模型预测节能设备的故障状况.具体而言,首先通过灰色均值GM(1,1)模型预测节能设备的未来故障情况,然后通过马尔可夫状态转移矩阵确定未来节能设备故障的可能状态,最后基于预测值与实际值的比值关系修正预测结果,以实现对节能设备故障次数的精准预测.结果表明灰色马尔可夫模型提高了预测精度,为精准预测节能设备故障提供了一种新思路.     

部分状态可见的隐马尔可夫模型的Viterbi算法

本文研究了隐马尔可夫模型的Viterbi算法,在已知隐马尔可夫模型的部分状态、初始概率分布、状态转移概率矩阵和观测概率矩阵的条件下,由此Viterbi算法给出最优状态序列的估计.相对于已有的算法,本文的算法考虑了部分可见状态对初始条件和递推公式的影响,并且本文的算法能保证预测的状态序列是整体最优的.最后,我们将本文的算法应用于故障识别,从而验证所设计算法的可行性.     

马尔可夫过程在医学干预措施成本效用分析中的应用

马尔可夫过程(Markov Process)是由一种状态转移至另一种状态的随机过程。本文探讨了医学干预措施成本效用分析中马尔可夫状态转移模型构建和模型参数的确定方法,并以全髋关节置换术为例,将具有吸收状态的离散马尔可夫过程应用于医学干预措施成本效用分析。结果表明,利用模型得出的预测结果与目前的医学认识和临床实际相符,提示应用离散马尔可夫过程预测医学干预措施成本效用是可行的。     

基于灰色-加权马尔可夫的机械钻速动态预测北大核心CSCD

在钻井工程中,科学准确地预测机械钻速(Rate of Penetration,ROP)对高效钻井以及钻井智能化发展具有重要意义.针对ROP的预测实效性以及波动性大的问题,在灰色系统理论的基础上,结合马尔可夫理论,建立灰色-加权马尔可夫机械钻速动态预测模型.其方法是利用灰色预测模型对ROP进行模拟预测,根据预测值的误差范围划分几个误差分布的状态空间,以不同转移步长间的状态转移信息构建状态转移概率矩阵,再利用该矩阵和不同井段的状态信息,对下一井段的ROP值进行状态空间判断并修正,同时通过不断更新模型中的数据,实现动态实时预测.以南海莺歌海盆地M井进行实例分析.结果表明:经灰色预测模型与加权马尔可夫的有效结合,ROP预测值拟合曲线不仅更加贴近实测值,而且降低了误差的离散性,具有更高的预测可信度,进而有效验证了该模型的有效性.     

基于灰色马尔可夫模型的物流配送需求量预测研究

研究可以较准确地预测物流配送需求量的数学模型,以服务于政府及企业的物流规划及其决策.将灰色理论和离散状态的马尔可夫链相结合,用灰色马尔可夫链对物流配送需求量进行实证研究.针对灰色数据系列首先用GM模型进行趋势预测,然后利用马尔可夫状态转移概率矩阵预报方法对其预测值进行二次拟合,预测精度明显高于GM模型预测.     

基于改进的灰色马尔可夫链模型的交通事故预测

交通事故预测是交通安全评价、规划和决策的基础.灰色预测适合于数据量少和波动小的系统对象,而马尔可夫链理论适用于预测随机波动大的动态过程.为克服一般灰色马尔可夫链模型运用的转移概率矩阵固定不变而影响预测精度的问题,本文建立了改进的灰色马尔可夫链模型.采用滑动转移概率矩阵方法,去掉最老数据并补充最新数据,从而建立新的一步转移概率矩阵.借助改进的灰色马尔可夫链模型,对全国2002-2004年交通事故10万人口死亡率进行了预测分析.结果表明,改进的灰色马尔可夫链模型比一般灰色马尔可夫链模型的预测范围更准确,预测精度更高.     

基于马尔可夫模型的我国东、中、西部的产业结构预测

应用马尔可夫预测方法对我国东、中、西部产业结构预测问题进行研究,并给出了其马尔可夫的状态转移概率矩阵的估算模型,经计算结果表明此方法具有较高的预测精度,并应用此方法预测了我国2009年和2010年的东、中、西部的产业结构.     

基于凝聚函数的拟牛顿算法求解绝对值方程

绝对值方程Ax-|x|=b是一个不可微的NP-hard问题.在假设矩阵A的奇异值大于1(这里矩阵A的奇异值定义为矩阵ATA特征值的非负平方根)时,给出了求解绝对值方程一个新的光滑化算法.通过引入一种凝聚函数对绝对值方程进行光滑化处理,得到一个非线性方程组;再引入适当的目标函数,进而把绝对值方程化为无约束优化问题,然后利用拟牛顿算法对其进行求解.数值实验结果表明了该方法的正确性和有效性.     

Infinite Penalization for Optimal Control Problems: An infinite-dimensional optimization method for constrained optimization problems

We present results on a method for infinite dimensional constrained optimization problems. In particular, we are interested in state constrained optimal control problems and discuss an algorithm based on penalization and smoothing. The algorithm contains update rules for the penalty and the smoothing parameter that depend on the constraint violation. Theoretical as well as numerical results are given. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Realization of multi-input/multi-output switched linear systems from Markov parameters

This paper presents a four-stage algorithm for the realization of multi-input/multi-output (MIMO) switched linear systems (SLSs) from Markov parameters. In the first stage, a linear time-varying (LTV) realization that is topologically equivalent to the true SLS is derived from the Markov parameters assuming that the discrete states have a common MacMillan degree and a mild condition on their dwell times holds. In the second stage, stationary point set of a Hankel matrix with fixed dimensions built from the Markov parameters is examined. Splitting of this set into disjoint intervals and complements reveals linear time-invariant dynamics prevailing on these intervals. Clustering over a feature space permits recovery of the discrete states up to similarity transformations which is complete if a unimodality assumption holds and the discrete states satisfy a residence requirement. In the third stage, the switching sequence is estimated by three schemes. The first scheme is non-iterative in time. The second scheme is based on matching the estimated and the true Markov parameters of the SLS system over segments. The third scheme works also on the same principle, but it is a discrete optimization/hypothesis testing algorithm. The three schemes operate on different dwell time and model structure requirements, but the dwell time requirements are weaker than that needed to recover the discrete states. In the fourth stage, the discrete state estimates are brought to a common basis by a novel basis transformation which is necessary for predicting outputs to prescribed inputs. Robustness of the four-stage algorithm to amplitude bounded noise is studied and it is shown that small perturbations may only produce small deviations in the estimates vanishing as noise amplitude diminishes. Time complexities of the stages are also studied. A numerical example illustrates the derived results.     

低阶精确罚函数的一种光滑化逼近

本文对不等式约束优化问题给出了低阶精确罚函数的一种光滑化逼近.提出了通过搜索光滑化后的罚问题的全局解而得到原优化问题的近似全局解的算法.给出了几个数值例子以说明所提出的光滑化方法的有效性.     

Second-Order Smoothing Objective Penalty Function for Constrained Optimization Problems

In this article, a novel objective penalty function as well as its second-order smoothing is introduced for constrained optimization problems (COP). It is shown that an optimal solution to the second-order smoothing objective penalty optimization problem is an optimal solution to the original optimization problem under some mild conditions. Based on the second-order smoothing objective penalty function, an algorithm that has better convergence is introduced. Numerical examples illustrate that this algorithm is efficient in solving COP.     

Finite termination of a Newton-type algorithm for a class of affine variational inequality problems

Many optimization problems can be reformulated as a system of equations. One may use the generalized Newton method or the smoothing Newton method to solve the reformulated equations so that a solution of the original problem can be found. Such methods have been powerful tools to solve many optimization problems in the literature. In this paper, we propose a Newton-type algorithm for solving a class of monotone affine variational inequality problems (AVIPs for short). In the proposed algorithm, the techniques based on both the generalized Newton method and the smoothing Newton method are used. In particular, we show that the algorithm can find an exact solution of the AVIP in a finite number of iterations under an assumption that the solution set of the AVIP is nonempty. Preliminary numerical results are reported.     

Distributionally robust Optimal Control and MDP modeling

In this paper we discuss Optimal Control and Markov Decision Process (MDP) formulations of multistage optimization problems when the involved probability distributions are not known exactly, but rather are assumed to belong to specified ambiguity families. The aim of this paper is to clarify a connection between such distributionally robust approaches to multistage stochastic optimization.     

A smoothing Newton method for second-order cone optimization based on a new smoothing function

A new smoothing function is given in this paper by smoothing the symmetric perturbed Fischer-Burmeister function. Based on this new smoothing function, we present a smoothing Newton method for solving the second-order cone optimization (SOCO). The method solves only one linear system of equations and performs only one line search at each iteration. Without requiring strict complementarity assumption at the SOCO solution, the proposed algorithm is shown to be globally and locally quadratically convergent. Numerical results demonstrate that our algorithm is promising and comparable to interior-point methods.