灰色模型GM(1, 1)优化

分析了GM(1, 1)模型产生模拟误差的原因，经大量的数据模拟和GM(1, 1)模型比较，发现背景值的优化使GM(1, 1)模型在短期、中期及长期预测中扩大了适用范围，并且模拟及预测精度显著提高。     

一类改进的非等间距灰色模型及应用

现实中存在着大量近似非齐次指数增长规律的数据序列.根据非等间距灰色模型建模机理,本文构造了一个用非齐次指数序列来拟合原始数据序列的非等间距灰色模型,以原始数据序列的观测值与模拟值的相对误差平方和最小为目标,推导出新模型参数的最小二乘解及其时间响应函数的表达式.最后通过两个实例,将改进模型与经典模型对比,取得了良好的效果,进而验证了所提出模型的有效性和实用性.     

非等间距GM(1,1)幂模型及其工程应用

针对工程中大量存在的非等间距序列的建模问题,提出了非等间距GM(1,1)幂模型。以平均相对误差绝对值最小化为目标,以模型参数之间的关系为约束,构建了一个非线性优化模型实现非等间距GM(1,1)幂模型的参数估计。结果表明,非等间距GM(1,1)幂模型的形式较为灵活,非等间距GM(1,1)模型和灰色Verhulst模型均是非等间距GM(1,1)幂模型的特殊情形,幂指数的优化有利于提高建模精度。最后通过一个工程实例验证了非等间距GM(1,1)幂模型的有效性与实用性。     

Grey GM(1,1) Model with Function-Transfer Method for Wear Trend Prediction and its Application

1　ＩｎｔｒｏｄｕｃｔｉｏｎＯｉｌｓｕｐｅｒｖｉｓｉｏｎｔｅｃｈｎｏｌｏｇｙ ,ｗｈｉｃｈｗａｓｄｉｒｅｃｔｅｄｉｎｔｈｅｓｙｓｔｅｍｉｃｃｏｎｃｅｐｔｏｆｔｒｉｂｏｌｏｇｙａｎｄｗｈｏｓｅｍａｉｎｍｅａｎｓｗａｓｔｏｃｈｅｃｋｏｉｌｐｒｏｐｅｒｔｙａｎｄａｎａｌｙｚｅａｂｒａｓｉｏｎｇｒａｉｎｓ ,ｗａｓｅｘｔｅｎｓｉｖｅｌｙａｐｐｌｉｅｄｉｎｗｏｒｋｉｎｇｓｕｐｅｒｖｉｓｉｏｎａｎｄｆａｕｌｔａｎａｌｙｓｉｓｏｆｔｈｅｅｑｕｉｐｍｅｎｔｏｐｅｒａｔｅｄｉｎｗｏｒｋｉｎｇｖａｒｉａｔｉｏｎ ,ｌｏｗ…     

基于GM(1,1)模型的东辛采油厂产量预测研究

本文介绍了GM(1,1)模型的建模过程,考虑油田产量数据较少的现状,将其视为灰色系统,并利用灰色系统GM(1,1)模型对油田石油产量进行了预测。经实证,模型的精度符合要求,预测结果可以为采油厂提供决策依据。     

灰色预测模型GM（１，１）的适用性分析及在火灾风险预测中的应用

通过对灰色预测模型———GM（１,１）的理论分析,证明了该模型的预测值及其变化趋势均具有单调 性,进而提出了GM（１,１）模型的适用性判据,并给出了该判据在火灾风险灰色预测中的应用实例。     

灰色序列模型在物流园区货运量预测中的应用

运用灰色系统理论建立了货运量的灰色预测模型-GM（1,1）模型,并通过实例对货运量进行了预测,结果表明,该方法具有所需原始数据少、预测精度高等优点．     

A Grey Prediction Model on Vibration Severity Development of a Pump

The method to enhance the precision of a grey model GM (1,1) for predicting the development of vibration severity of a pump is inwestigated. The rectifying procedures involve the structure and the parameters regarding GM(1,1).A new model based on GM(1,1),which is GM(E,1,1), is proposed. In GM(E,1,1),the distribution of relative errors ratios between the original series and predicting series obtained by the mean of GM(1,1)are considered in special points to set up the threshold and adjusting coefficients to control the modified action and the rectified amount based on distribution of the original series. The case shows that GM(E,1,1) is good at predicting the vibration severity development of the pump.     

密闭空间爆炸温度动态不确定度评估方法研究

融合了灰色模型GM(1,1)、Bootstrap方法以及不确定度评定理论,建立了密闭空间内爆炸温度动态测量不确定度的灰自助评估模型GBM(1,1),选取某次爆炸试验300s的温度数据作为分析数据,运用估计真值、估计区间和平均不确定度等参数表征其估计结果。实验结果表明,GBM(1,1)模型融合了灰色模型GM(1,1)和Bootstrap方法的优势,可以准确模拟动态测量数据的概率分布,并实时跟踪被测量瞬时值的变化趋势。相比于灰色模型GM(1,1)和Bootstrap方法,灰自助模型GBM(1,1)具有更高的真值估计准确度和区间估计可靠度,其估计误差分布区间为［-12.62, 13.58］,标准差为8.69℃,最大相对误差为1.2%,区间估计可靠度高于90%,估计区间能够较完整地包络被测量的动态波动范围。由此证明GBM(1,1)模型能够对密闭空间内爆炸温度的动态测量不确定度做出准确评估。     

基于改进GM(1,1)-Markov模型的国内生产安全事故预测研究

为准确预测我国生产安全事故发展趋势,本文在传统GM(1,1)模型和马尔科夫模型的基础上,结合二者优点提出改进灰色马尔科夫预测模型,并以2005—2018年全国生产安全事故起数为原始序列探讨了改进模型的实际应用。区别于传统灰色残差修正理论,选取灰色模型预测结果的相对误差作为修正指标,2次应用马尔科夫模型对相对误差状态和误差符号状态进行优化预测,并使用平均相对误差和小概率误差对模型进行精度检验。结果表明,改进GM(1,1)-Markov模型预测结果的相对误差为3.0%,较单一灰色预测模型预测误差减少19.5%,预测精度显著提高,同时预测得到2019年我国生产安全事故起数为479。     

基于新陈代谢GM(1,1)模型的校准间隔预测

针对测量仪器校准间隔的优化问题,根据校准数据非线性、小样本的特点,提出了一种基于新陈代谢GM(1,1)模型的校准间隔预测方法.通过分析历史校准数据的特征,建立了新陈代谢GM(1,1)预测模型,通过仿真实验对预测模型进行了对比验证.结果表明,相对于灰色GM(1,1)模型,新陈代谢GM(1,1)模型克服了随机扰动对系统的影响,更能反映系统的变化趋势,预测精度更高,适合用于测量仪器校准间隔的预测.     

区域物流规模的改进灰色马尔可夫预测

在分析灰色GM(1,1)方法、灰色马尔可夫方法的基础上,建立区域物流规模预测的改进灰色马尔可夫模型,以国家统计局公布的陕西省1997-2006年货物周转量的统计数据为依据,对其2007-2008年的物流规模进行预测.与灰色GM(1,1)方法、灰色马尔可夫方法的预测结果相比,改进灰色马尔可夫链模型对区域物流规模的预测更加有效.     

基于灰色预测GM(1,1)模型的网格孔洞填补算法

针对三角网格曲面中存在的孔洞提出了一种填补算法.在空洞曲面的投影平面上,每次寻找孔洞多边形最小内角所在顶点,用GM(1,1)模型在孔洞内部插入新点,构造三角形并生成新的孔洞边界多边形,直到所有的孔洞边界多边形全部处理完.最后将平面三角面片返回到三维空间并用基于径向基函数的平滑算法对其进行平滑处理.实例表明用本算法进行孔洞填补能避免出现错误和狭长的三角形,而且和原孔洞边界能光滑连接,对曲率变化较大的孔洞也能得到满意的填补结果.     

Application of the number-theoretic method to the study on chromatographic retention

The traditional modeling method for the grey model GM(1,1) was discussed in some detail. The number-theoretic method was applied to the grey model with the least sum of absolute deviations as objective function in order to make it robust. The proposed method was employed in the study of the relationship between the capacity factors of six polyaromatic hydrocarbons and the compositions of the mobile phase in liquid chromatography, and the relationship between the retention time of the six compounds and the column temperature in gas chromatography. Satisfactory results were obtained.     

基于优化GM(1,1)模型的可视化沉降预测数据的精度研究

软土地基的最终沉降变形对于高速公路、铁路、机场及港口码头等建设工程的设计安全及正常使用影响重大,从用灰色理论进行沉降预测的结果看,模型的取值直接决定了预测结果的准确性．如何取值、按什么规律取值是灰色理论计算准确性的核心．为此,基于优化的GM(1,1)模型,开发了用VB语言编写的沉降预测灰色可视化软件,通过对不同时间间隔的取值进行精度分析,并将预测结果与实际监测数椐进行对比,表明该方法能够更为精准地预测软土地基沉降,具有工程实用价值．     

基于灰色马尔可夫模型的煤层气抽采量预测

煤层气抽采量的准确预测,对煤层气开发利用工作的科学决策和发展规划具有重要意义。通过灰色系统理论与马尔可夫理论的结合,建立灰色马尔可夫模型对煤层气抽采量进行预测分析。首先建立煤层气抽采量的GM(1,1)预测模型,确定其变动趋势和初始预测值,然后应用马尔可夫理论对初始预测结果进行修正,最后通过实例计算验证了灰色马尔可夫模型的适用性。结果表明,灰色马尔可夫模型的预测精度明显高于传统GM(1,1),更适用于随机波动性较大的序列预测问题,因此将灰色马尔可夫模型用于煤层气抽采量预测是合理和可行的。     

A stochastic regime switching model for the failure process of a repairable system

This paper presents a stochastic model and estimation procedure for analyzing the failure process of a repairable system. We consider repairable systems whose successive interfailure times reveal a significant dependence while showing an insignificant trend. Neither the renewal process nor the non-homogeneous Poisson process are adequate for modeling such failure processes. Especially when the interfailure times show a cyclic pattern, we may consider a switching of the regimes (states) governing the lifetime distribution of the system. We propose a Markov switching model describing the failure process for such a case. The model postulates that a finite number of states governs the distinct lifetime distributions, and the state makes transitions according to a discrete-time Markov chain. Each of the distinct lifetime distributions represents a failure type that may change after successive repairs. Our model generalizes the mixture model by allowing the mixture probabilities to change during the transient period of the system. The model can capture the transient behavior of the system. The interfailure times constitute a set of incomplete data because the states are not explicitly identified. For the incomplete data, we propose a procedure for finding the maximum likelihood estimates of the model parameters by adopting the expectation and maximization principle. We also suggest a statistical method to determine the number of significant states. A Monte Carlo study is performed with two-parameter Weibull lifetime distributions. The results show consistency and good properties of the estimates. Some sets of Proschan's air conditioning unit data [Technometrics, 1963, 5′ 375–383] are also analyzed and the results are discussed with respect to the number of significant states and the performance of the prediction.     

A geometric process repair model for a repairable cold standby system with priority in use and repair

In this paper, a deteriorating cold standby repairable system consisting of two dissimilar components and one repairman is studied. For each component, assume that the successive working times form a decreasing geometric process while the consecutive repair times constitute an increasing geometric process, and component 1 has priority in use and repair. Under these assumptions, we consider a replacement policy N based on the number of repairs of component 1 under which the system is replaced when the number of repairs of component 1 reaches N. Our problem is to determine an optimal policy N^* such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit equation of the average cost rate of the system is derived and the corresponding optimal replacement policy N^* can be determined analytically or numerically. Finally, a numerical example with Weibull distribution is given to illustrate some theoretical results in this paper.     

火灾预测的改进GM(1,1)模型

火灾的发生受很多因素的影响,有的因素已知、有的未知,符合灰色系统的特征,从而可以利用灰色理论进行预测.现从传统GM(1,1)预测模型构造原理出发分析其存在的理论缺陷,通过采用平均斜率法、等维替换和变换灰色预测公式的方法建立改进的GM(1,1)模型,以适应火灾频数序列的波动特性,从而达到精确预测的目的.我国1997—2006年火灾数据预测计算表明,新方法有满意的拟合和预测效果,从而为火灾预测精度提高提供了新的途径.     

The study of α in GM(1,1) model

Abstract

The purpose of this paper is to analyze a predicted error in using the GM(1, 1) model based on the parameter α. The transfer function for the predicted error with the parameter α in the GM(1, 1) model is presented. The algorithm of solving equations in calculus is used to analyze whether the α is adaptive or not. The criterion of α is applied to describe the adaptive criterion of α. Finally, an example of the cagenet amounts of fish in the Peng‐hu area is used to demonstrate the small prediction error due to the optimal α value. The result shows that the criterion for α is applicable for minimizing the predicted error easily.