非等距时间序列的GM（1,N）模型及其在地下工程中的应用

文献（１）给出了等距时间序列的灰色预测ＧＭ（１，Ｎ）模型，本文把它推广到非等距时间序列，得到了相应模型，并应用于地下工程的几个实例。     

非等距时间序列的GM（1，N）模型及其在地下工程中的应用

文献〔１〕给出了等距时间序列的灰色预测ＧＭ（１，Ｎ）模型，本文把它推广到非等距时间序列，得到了相应模型，并应用于地下工程的几个实例     

基于灰色模型的混合建模预测方法及其应用

针对陀螺仪寿命预测的特点,提出了一种基于灰色模型的混合建模预测方法。为了提高一阶灰色模型GM（1,1）的建模能力,此模型引入了小波变换。首先小波变换对实测的动力调谐陀螺（DTG）漂移数据进行预处理以减少干扰噪声,接着处理后的数据被用来建立灰色模型。来自于长期测量的DTG的漂移数据的实验结果证明了文中所提混合策略的有效性。并且为了进行比较,对神经网络建模方法进行了相应的研究,结果表明当小波变换被引入到混合模型中,此基于灰色模型的混合建模预测方法具有令人满意的性能,为陀螺仪的寿命预测提供了借鉴和参考。     

某飞行器惯性器件贮存可靠性评估和预测方法研究

本文对某飞行器的惯性器件贮存可靠性研究时，采用了三种可靠性指标：贮存性能可靠性、贮存功能可靠性和贮存后工作可靠性。其中还考虑到１：１贮备可维修系统的具体情况和环境因子。并对大量的测试数据进行了可靠性计算和分析。最后列出了速率陀螺仪的可靠性计算结果，并用ＧＭ（１，１）模型对其进行了可靠性灰色预测。     

摩擦过程中真实接触面积的灰色分析

灰色系统理论是近几年以随机过程为研究对象而形成和发展起来的，在农业和自动控制等方面的研究与应用发展较快．为了使这种理论应用于摩擦学研究领域，从光全反射测量和计算机数值计算两方面，考察了粗糙表面接触时真实接触面积的随机特性，指出摩擦过程中的真实接触面积是一种含有随机成分的变化量，研究目标应当侧重于真实接触面积的变化趋势和范围，而不是它的精确解．在此基础上，首次利用灰色系统理论，分别对静态和动态接触条件下真实接触面积的变化规律进行了灰色分析，建立了精度比较高的预测真实接触面积的灰色模型ＣＭ（１，１）．这种模型对动、静接触面积的计算值与实测值具有良好的一致性，可以用于动态跟踪描述摩擦过程中真实接触面积的变化规律     

软岩巷道开巷初期围岩变形灰色模型预测的研究

应用灰色系统理论对软岩巷道开巷初期围岩变形进行了预测，通过实例说明用GM（1，1）模型和双向差分模型预测巷道的围岩变形都是简单可行的。对GM（1，1）模型进行了改进，建立了具有较小原点误差的改进的GM（1，1）的模型，并且给出了双向差分模型，GM（1，1）模型与其改进模型对软巷道围岩变形预测结果的比较，为灰色系统理论用于软岩巷道开巷初始围岩及支扩变形预测的实践进行了新的探讨，它将在软岩工程未来行为的预测方面起着重要的参考作用。     

软土地区工程性地面沉降预测的非等时距GM(1,1)模型

大规模城市建设诱发的工程性地面沉降已成为上海软土地区地面沉降新的制约因素。本文针对上海地区工程性地面沉降特点,运用灰色理论建立了非等时距GM(1,1)预测模型,并用工程实测数据进行检验,得到令人满意的预测结果。研究结果对预测和控制软土地区由建筑物群引起的地面沉降具有重要意义。     

加权函数组合预测边坡变形模型的研究

边坡变形监测是边坡监测的主要内容之一,其变形预测问题是边坡工程中主要技术难题之一。考虑边坡位移变形预测模型的局限性,如神经网络预测方法需要大量的实测数据作为学习样本,灰色系统模型要求原始数据序列必须满足指数规律,且数据序列变化速度不能太快等。建立了边坡变形反向传播神经网络预测模型,同时给出了灰色GM(1,1)边坡预测模型。提出边坡的神经网络与灰色系统加权函数组合预测模型,采用动态规划解法,将原模型转化为多阶段决策问题,使组合预测误差的平方和最小,得到组合权重,这样得到的变形预测结果的精度将大大提高,弥补了单一方法的局限性,满足工程预测的需要。通过边坡实例加以验证,加权函数组合预测模型的预测结果精度有一定提高,能够与实际监测数据相吻合,达到准确预测的目的。     

工程环境效应引起上海地面沉降预测

地面沉降是目前常见的地质灾害之一,其长期的积累给城市带来巨大的经济损失,成为制约城市发展的主要因素。进入20世纪90年代以来,工程环境效应诱发的沉降已经成为上海地面沉降的新趋势,对于外荷载引起的地面沉降过程而言,影响因素较多,既无法用明确的数学关系式表达,又非“黑箱”那样内部结构、参数和特征一无所知,因此可将灰色预测理论应用于地面沉降的预测。针对监测和观测时间的非等时性,本文应用非等时距灰色理论模型对上海陆家嘴地区某高层建筑的沉降进行预测,并和实际监测沉降量进行了比较;对室内模型试验进行沉降预测,并和实验观测数据以及自适应神经网络系统(ANFIS)预测结果进行了比较。研究发现,对于工程环境效应引起的地面沉降,应用非等时距灰色理论模型进行沉降预测是可行、精确的。     

异常天气条件下潮位过程神经网络补遗预测方法的研究

以异常天气条件下的实测潮位过程为研究对象,根据其为非平稳时间序列的特点,以人工神经网络BP算法作为预测工具,对潮位时间序列中缺失的数据进行补遗建立:差分方法人工神经网络模型;同一海域邻近潮汐测站潮位过程对应预测的去平均值法人工神经网络模型;对增减水现象潮汐过程预测的气象资料数据库人工神经网络模型。以实测资料验证上述方法的可行性,并取得了很好的预测结果。     

滑坡预报模型的质量检验研究

 
滑坡预报模型主要用来预报滑坡发生的时间,但是如何检验效果是滑坡预报者和决策者面临的一个重要课题。本文通过提出滑坡拟合效果指标（包括后验差指标、模型拟合效率指数和均方根误差）和试预报效果指标（包括试报效果指标和相关系数指标）,初步建立了滑坡的预报质量检验模型。依据建立的检验模型,针对链子崖危岩体监测资料分别采用灰色GM（1, 1）数学模型、三次指数平滑模型和时间序列模型进行预报。预报结果表明：三种模型中,综合指标GM（1, 1）数值最高,建议该滑坡采用GM（1, 1）进行预报。通过模型的综合分析评判,不仅分析了模拟效果,而且直接比较了模型间的拟合效果,并为建立模拟效果好的模型提供了充分的依据,从而表明滑坡预报质量检验模型是一种有效、实用的方法。


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Dynamical randomicity and predictive analysis in cubic chaotic system

The dynamical randomicity and grey prediction in cubic chaotic system will be studied in this paper. These stochastic symbolic sequences bear three features. The distribution of frequency, inter-occurrence times, the first passage time, the rth passage time and the ordinal passage time are discussed separately. By using transfer probability of Markov chain (MC), one obtains analytic expressions of generating functions in three-probabilities stochastic wander model, which can be applied to all three symbolic systems. The visitation density function of cubic map will also be resolved. Especially, after introducing grey system theory, one is mainly using GM(1,1) model to forecast data sequences, and the usual forecast precision is approximately 90%. In the symbolic prediction of cubic chaotic dynamical system, the precision of grey prediction certainly will decrease as the length of symbolic sequence is increasing. But in this place we have found a generating rule that may realize chaotic synchronization at least in short and medium terms, and we can analyze and forecast in this way.     

回采工作面周期来压步距的灰色预测

利用灰色系统理论, 将回采工作面周期来压视为灾变, 仿线性GM(1, 1)预测模型建模机理, 本文建立了包括线性模型在内的统一非线性GM(1, 1)预报模型。利用非线性模型特例Verhulst模型和线性模型分别对两个不同矿山条件老顶周期来压步距进行预测, 结果表明, 不同的地质条件将适合不同的预测模型, 不能简单一概用线性模型进行预测。对于地质条件发生灾变的情形可建立激励预测模型对周期来压步距进行预测。     

Dynamical analysis of the infection status in diverse communities due to COVID-19 using a modified SIR model

In this article, we model and study the spread of COVID-19 in Germany, Japan, India and highly impacted states in India, i.e., in Delhi, Maharashtra, West Bengal, Kerala and Karnataka. We consider recorded data published in Worldometers and COVID-19 India websites from April 2020 to July 2021, including periods of interest where these countries and states were hit severely by the pandemic. Our methodology is based on the classic susceptible–infected–removed (SIR) model and can track the evolution of infections in communities, i.e., in countries, states or groups of individuals, where we (a) allow for the susceptible and infected populations to be reset at times where surges, outbreaks or secondary waves appear in the recorded data sets, (b) consider the parameters in the SIR model that represent the effective transmission and recovery rates to be functions of time and (c) estimate the number of deaths by combining the model solutions with the recorded data sets to approximate them between consecutive surges, outbreaks or secondary waves, providing a more accurate estimate. We report on the status of the current infections in these countries and states, and the infections and deaths in India and Japan. Our model can adapt to the recorded data and can be used to explain them and importantly, to forecast the number of infected, recovered, removed and dead individuals, as well as it can estimate the effective infection and recovery rates as functions of time, assuming an outbreak occurs at a given time. The latter information can be used to forecast the future basic reproduction number and together with the forecast on the number of infected and dead individuals, our approach can further be used to suggest the implementation of intervention strategies and mitigation policies to keep at bay the number of infected and dead individuals. This, in conjunction with the implementation of vaccination programs worldwide, can help reduce significantly the impact of the spread around the world and improve the wellbeing of people.

     

中心逼近式灰色GM(1,1)模型在滑坡变形预测中的应用

黄龙西村滑坡位于甘肃天水,属黄土高势能滑坡,滑体体积3.9×10⁵m³,基底为花岗闪长岩。为了提高滑坡灰色GM(1,1)模型的预测精度,采用一种改变背景值的方法--中心逼近式灰色GM(1,1)模型。通过黄龙西村滑坡实例验证分析,结果表明中心逼近式灰色GM(1,1)模型的预测值与该滑坡实际监测值十分接近,且其残差平方和及平均误差百分比明显比传统灰色GM(1,1)模型的残差平方和及平均误差百分比小,具有较高的预测精度。同时,可通过调整模型中参数m的取值,使中心逼近式灰色GM(1,1)模型具有更高的预测精度。经计算,当m=6时,中心逼近式灰色GM(1,1)模型的预测精度比传统灰色GM(1,1)模型提高了5.34%。     

Study on application of random walk method to calculate water exchange in large-scale bay

The water exchange matrix is an efficient tool to study the water exchange among the sub-areas in large-scale bays. The application of the random walk method to calculate the water exchange matrix is studied. Compared with the advection-diffusion model, the random walk model is more flexible to calculate the water exchange matrix. The forecast matrix suggested by Thompson et al. is used to evaluate the water exchange characteristics among the sub-areas fast. According to the theoretic analysis, it is found that the precision of the predicted results is mainly affected by three factors, namely, the particle number, the generated time of the forecast matrix, and the number of the sub-areas. The impact of the above factors is analyzed based on the results of a series of numerical tests. The results show that the precision of the forecast matrix increases with the increase of the generated time of the forecast matrix and the number of the particles. If there are enough particles in each sub-area, the precision of the forecast matrix will increase with the number of the sub-areas. Moreover, if the particles in each sub-area are not enough, the excessive number of the sub-areas can result in the decrease of the precision of the forecast matrix.     

基于超声波反射系数相移的油膜厚度测量方法研究

超声波液相厚度测量技术已经在柴油机气缸油膜测量领域中得以验证,并得到了一定的应用. 然而,当油膜厚度变化尺度较大时,常规谐振模型与弹簧模型之间存在较大的测量盲区,使超声波测量技术的应用受到较大程度的限制. 基于超声波反射系数相移的油膜厚度测量方法可突破两种模型在大尺度油膜厚度测量方面的局限性,拓展超声波油膜厚度测量范围. 通过开展超声波反射系数相移机理研究,首次建立油膜两侧介质声阻抗相同时的直接求解方法;搭建油膜厚度超声波反射系数相移测量系统,利用单一中心频率对10~90 μm的油膜厚度展开测量,测量厚度与设置厚度具有很好的一致性,从理论和实验角度证明基于超声波反射系数相移的油膜厚度测量方法在大尺度油膜厚度测量方面的适用性.      

Rotational-oscillational motions of the nonrigid Earth about the center of mass

We use the model of a nearly axisymmetric viscoelastic rigid body to study perturbed rotational-oscillational motions of the Earth’s pole. We point out that the Chandler component of oscillations is of celestial-mechanics nature and is caused by the gravitational-tidal actions of the Sun and the Moon. We analyze the pole oscillation excitation mechanism at a frequency close to the Chandler frequency and show that the undamped pole oscillations are caused by the resonance harmonic of the external perturbation at a frequency close to the free nutation frequency. We discuss whether it is possible to solve the problem of constructing a short-term forecast of the pole motion on the basis of a polynomial filter obtained by the least-squares method without taking into account small-scale oscillations caused by wide-band random factors of arbitrary physical nature. In the present paper, we perform numerical simulation of tidal inhomogeneities in the Earth’s axial rotation. Attention is mainly paid to the analysis of day length variations on short time intervals with periods less than or equal to one year (interannual oscillations) and to their forecast.     

基于交通流实测数据的加速度研究

采用6 个不同密度下的交通流样本, 从视频中提取大量跟驰车对的车头间距、车速、加速度和速度差数据. 统计分析发现, 加速度值域关于0 点具有对称性; 不同密度下加速度分布具有不同特征; 车头间距、车速和速度差对加速度的影响程度随密度不同而不同. 利用实测数据对GM 模型和Bando 模型进行参数优化, 据此提出一种GM 模型的简化形式和一种改进的Bando 模型, 两者拟合该文实测数据的平均误差都在6% 以下.