基于非等间距GM(1,1)的校准周期预测方法研究

为科学合理地确定计量器具的校准周期,提出了基于非等间距GM(1,1)的计量器具校准周期预测方法.该方法以灰色系统理论为依据,首先将已知的非等间距序列进行累加生成处理,对生成序列建立白化微分方程,通过最小二乘法求待辩识参数,进而得出非等间距GM(1,1);并通过Matlab7.5.5实现了非等间距GM(1,1)模型的快速...     

模糊序列的GM(1,1)建模

本文在不改变GM(1,1)模型建模机理的前提条件下,运用模糊回归理论对GM(1,1)模型进行优化,通过定义三角模糊数的左、中、右距离,将模糊序列的GM(1,1)模型的求解转化为线性规划模型的求解,并通过实例加以论证。研究表明模糊序列的GM(1,1)模型保留了GM(1,1)模型所需建模数据少和具有预测功能的特点,且能为决策者提供一个决策区间。     

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。     

基于灰色GM(1,1)和自适应神经模糊推理的数据预测模型

综合利用灰色理论与自适应神经模糊推理系统( ANFIS)建立预测模型的思路,给出了利用自适应神经模糊推理系统对GM(1,1)模型残差进行修正,重构灰色GM(1,1)模型预测值的综合预测方法.选用我国某地区冬季最大电力负荷作为原始数据,用GM(1,1)模型对历年的电力负荷进行建模,并利用自适应神经模糊推理系统对其残差进行...     

汨罗市城市路基沉降的GM(2,1)模型预测

针对汨罗地裂缝沉降观测资料,运用灰色理论建立地面沉降的GM(2,1)模型,其中非等时距位移序列采用拉格朗日插值函数转变为等时距序列。为了减少对外界因素干扰的敏感性,方便求解,采用非等时距GM(2,1)和GM(1,1)模型对西安市地面沉降观测点进行安全预测。预测结果和实际吻合较好。本文提出的GM(2,1)地面沉降变形预测模型,计算简单,与原始数据的升降凹凸性保持一致。非等时距GM(2,1)模型预测地面沉降精度总体较GM(1,1)模型高,较好的反映了地面沉降的变形趋势,具有很好的实用价值。     

基于改进灰色预测模型的中长期电力负荷预测

介绍了等维灰度递补GM(1,1)的建模原理,采用山东省2000-2007年的用电需求负荷建立等维灰度递补GM(1,1)预测模型,预测山东省2008年和2009年的用电负荷,与实际用电负荷进行对比,验证了灰色马尔科夫模型在对电力负荷进行长期预测时具有较高的精度。     

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.     

缓冲算子修正的单桩极限承载力的灰色预测

如何利用未达到破坏的试桩资料确定单桩极限承载力是一个重要的工程问题。根据单桩初始加载阶段的实测数据,建立以灰色系统理论为基础的GM(1,1)模型,预估单桩极限承载力,已在工程实际中取得一定的效果,但其精度有待提高。该文系统地论述了缓冲算子的概念和公理系统,探求了缓冲算子的使用规律,介绍了几种典型的缓冲算子及其特性,并采用缓冲算子修正了GM(1,1)模型以预测单桩的极限承载力。工程实例表明:该文的模型提高了预测精度,可在工程实际和理论研究中推广应用。     

蜗轮副磨损量的灰色预测法

在灰色理论的基础上,建立了无偏的GM(1,1)模型,扩展了GM(1,1)模型预测使用的范围.并将无偏GM(1,1)用于对蜗轮副磨损数据的预测,获得了满意效果.     

一类改进的GOM(1,1)模型及其应用

本文考虑非负递减序列的建模预测问题.考虑到灰作用量会随着时间和空间的变化而发展变化,将灰作用量近似看作为时间的线性函数从而构建了灰作用量优化的GOM(1,1)模型.结合灰色预测模型数据序列的非齐次指数特性,利用积分推导出GOM(1,1)模型的最优化背景值.以原始序列和模拟序列的平均相对误差平方和最小为原则,确定最优的时...     

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.     

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。     

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

1　ＩｎｔｒｏｄｕｃｔｉｏｎＯｉｌｓｕｐｅｒｖｉｓｉｏｎｔｅｃｈｎｏｌｏｇｙ ,ｗｈｉｃｈｗａｓｄｉｒｅｃｔｅｄｉｎｔｈｅｓｙｓｔｅｍｉｃｃｏｎｃｅｐｔｏｆｔｒｉｂｏｌｏｇｙａｎｄｗｈｏｓｅｍａｉｎｍｅａｎｓｗａｓｔｏｃｈｅｃｋｏｉｌｐｒｏｐｅｒｔｙａｎｄａｎａｌｙｚｅａｂｒａｓｉｏｎｇｒａｉｎｓ ,ｗａｓｅｘｔｅｎｓｉｖｅｌｙａｐｐｌｉｅｄｉｎｗｏｒｋｉｎｇｓｕｐｅｒｖｉｓｉｏｎａｎｄｆａｕｌｔａｎａｌｙｓｉｓｏｆｔｈｅｅｑｕｉｐｍｅｎｔｏｐｅｒａｔｅｄｉｎｗｏｒｋｉｎｇｖａｒｉａｔｉｏｎ ,ｌｏｗ…     

Modeling imperfectly repaired system data via grey differential equations with unequal-gapped times

In this paper, we argue that grey differential equation models are useful in repairable system modeling. The arguments starts with the review on GM(1,1) model with equal- and unequal-spaced stopping time sequence. In terms of two-stage GM(1,1) filtering, system stopping time can be partitioned into system intrinsic function and repair effect. Furthermore, we propose an approach to use grey differential equation to specify a semi-statistical membership function for system intrinsic function times. Also, we engage an effort to use GM(1,N) model to model system stopping times and the associated operating covariates and propose an unequal-gapped GM(1,N) model for such analysis. Finally, we investigate the GM(1,1)-embed systematic grey equation system modeling of imperfectly repaired system operating data. Practical examples are given in step-by-step manner to illustrate the grey differential equation modeling of repairable system data.     

Improved Grey predictor rolling models for wind power prediction

A new technique for one step ahead average hourly wind speed forecasting and wind turbines' output power prediction based on using the Grey predictor models is presented. The required mathematical formulation for developing the Grey predictor models is also presented. The obtained results from the proposed models are compared with the corresponding results obtained when using the persistent model. Utilising the traditional Grey model, GM(1,1) was first investigated and showed good improvement over the persistent model. However, the generated results demonstrate the presence of intervals with overshoots in the predicted values. To reduce such overshoots, a modified version for the Grey predictor model referred to as the adaptive alpha GM(1,1) model is investigated and two new models are proposed, hereafter, referred to as the improved Grey model and the averaged Grey model. The presented results demonstrate the effectiveness, the accuracy and the superiority of the proposed averaged Grey model for wind speed and wind power prediction.     

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。     

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.     

Small sample reliability growth modeling using a grey systems model

ABSTRACT

When performing system-level developmental testing, time and expenses generally warrant a small sample size for failure data. Upon failure discovery, redesigns and/or corrective actions can be implemented to improve system reliability. Current methods for estimating reliability growth, namely the Crow (AMSAA) growth model, stipulate that parameter estimates have a great level of uncertainty when dealing with small sample sizes. For purposes of handling limited failure data, we propose the use of a modified GM(1,1) model to predict system reliability growth parameters and investigate how parameter estimates are affected by systems whose failures follow a poly-Weibull distribution. Monte-Carlo simulation is used to map the response surface of system reliability, and results are used to compare the accuracy of the modified GM(1,1) model to that of the AMSAA growth model. It is shown that with small sample sizes and multiple failure modes, the modified GM(1,1) model is more accurate than the AMSAA model for prediction of growth model parameters.     

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。