Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

基于GIS城市洪水淹没模拟分析

城市洪水淹没范围动态模拟分析是城市防洪规划与防治决策的一个重要基础工作。本文主要研究洪水从翻堤口出发在地理空间蔓延、扩散、动态行进及确定淹没范围的数字模拟方法。为此,根据数学形态学及测地圆概念,研究设计了洪水扩散范围的“膨胀”模拟算法和淹没范围搜索算法,用于查询淹没通块中从翻堤处到任一点之间的淹没路径和ｔ时刻洪水扩散范围。     

哀牢山-红河剪切带的热年代学研究——多重扩散域模式的应用实例

洛弗拉等人(1989)把Dodson(1973)建立的单一扩散域模式扩展成矿物扩散域不连续分布的模式,即多重扩散域模式,与之对应具有某一封闭温度范围,因此利用单个K-长石矿物样品可以揭示更长时间段上的冷却过程。对云南哀牢山-红河剪切带的K-长石样品(FA-2-1)进行40Ar/39Ar同位素分析,利用多重扩散域模式,揭示在距今约20～19Ma问该带存在一快速冷却过程,这与西藏南部曲水地区快速抬升的时间是一致的     

A combined study of macroseismic data and focal mechanisms applied to the West-Bohemian earthquake,Czechoslovakia

The main shock of the West-Bohemian earthquake swarm, Czechoslovakia, (magnitudem=4.5, depthh=10 km) exhibits an irregular areal distribution of macroseismic intensities 6° to 7° MSK-64. Four lobes of the 6° isoseismal are found and the maximum observed intensity is located at a distance of 8 km from the instrumentally determined epicentre. This distribution can be explained by the energy flux of the directS wave generated by a circular source, the hypocentral location and focal mechanism of which are taken from independent instrumental studies. The theoretical intensity, which is assumed to be logarithmically proportional to the integrated squared ground-motion velocity (i.e.,I=const+log v ² (t)dt), fits the observed intensity with an overall root-mean-square error less than 0.5°. It is important that the present intensity data can also be equally well explained by the isotropic source. The fit was attained by means of a horizontally layered model though large fault zones and an extended sedimentary basin suggest a significant lateral heterogeneity of the epicentral region. The results encourage a broader application of the simple modelling technique used.     

福建省第三产业发展的区域比较分析

运用可拓工程方法和主成分分析方法建立了福建省第三产业发展水平的综合评判物元模型。模型的输出结果表明：福建省各地区第三产业发展水平差距悬殊；综合关联度将第三产业发展水平划分成4个等级，单指标关联度则揭示了各地区第三产业发展的优、劣势。     

预测陕西关中地区需水量的改进GM(1,1)模型

需水量评价与预测是水资源规划与管理一项重要的研究内容。本文采用定额法计算需水量。通过对陕西关中地区需水量要素组成的分析,认为需水量要素属平稳时间序列,且一阶累加生成数据系列满足指数规律,符合灰色预测条件。为了提高GM(1,1)模型的精度,采用一种改变背景值的新方法,即:中心逼近方法。通过精度检验,中心逼近式GM(1,1)模型平均误差百分比、误差平方和分别比传统的GM(1,1)模型提高了0.147和1.579。用中心逼近式GM(1,1)模型预测需水量各要素近期和中长期值,经检验,其中非农业人口、农业人口、耕地面积、工业总产值预测模型满足一级模型,等级为良好。牲畜头数预测模型为不合格模型,分析其原因,主要是因为时间序列数据不完全符合指数规律。通过定额法计算,预计75%保证率时2005年和2010年关中地区工农业需水量分别占总需水量的92.21%和89.75%,生活需水量分别占7%和9.04%。     

Large eddy simulation of hydrocyclone—prediction of air-core diameter and shape

Hydrocyclones are widely used in the mining and chemical industries. An attempt has been made in this study, to develop a CFD (computational fluid dynamics) model, which is capable of predicting the flow patterns inside the hydrocyclone, including accurate prediction of flow split as well as the size of the air-core. The flow velocities and air-core diameters are predicted by DRSM (differential Reynolds stress model) and LES (large eddy simulations) models were compared to experimental results. The predicted water splits and air-core diameter with LES and RSM turbulence models along with VOF (volume of fluid) model for the air phase, through the outlets for various inlet pressures were also analyzed. The LES turbulence model led to an improved turbulence field prediction and thereby to more accurate prediction of pressure and velocity fields. This improvement was distinctive for the axial profile of pressure, indicating that air-core development is principally a transport effect rather than a pressure effect.     

Ductile deformation of garnet in mylonitic gneisses from the Münchberg Massif (Germany)

Mylonitic gneisses from the Münchberg Massif contain single grains (type I) and polycrystalline aggregates (type II) of garnet displaying a distinct elongation parallel to a macroscopic lineation which is interpreted as the result of ductile deformation. Lattice-preferred orientations of quartz (textures) symmetrical to the macroscopic foliation and lineation and the lack of rotational microfabrics indicate that the bulk deformation was pure shear at least during the latest strain increments. Garnet textures measured by EBSD together with microprobe analyses demonstrate that these two structural types of garnet can be related to two different processes of ductile deformation: (1) For the single grains stretching can be attributed to diffusion creep along grain boundary zones (Coble creep). The related mass transfer is indicated by the fact that primary growth zones are cut off at the long faces of the grains while the related strain shadow domains do not show comparable chemical zoning. Pressure solution and precipitation suitable to produce similar structures can be largely ruled out because retrogressive reactions pointing to the presence of free hydrous fluids are missing. (2) For the polycrystalline garnet aggregates consisting of cores grading into fine-grained mantles, dislocation creep and associated rotation recrystallization can be assumed. Continuous lattice rotation from the core to the outer polycrystalline rim allow a determination of the related dominant slip systems which are {100}<010> and equivalent systems according to the cubic lattice symmetry. The same holds for garnets which appear to be completely recrystallized. For this type of fine-grained aggregates an alternative nucleation model is discussed. Due to penetrative dislocation glide in connection with short range diffusion and the resulting lattice rotation, primary growth zones are strongly disturbed.Since for the considered rock unit of the Münchberg Massif peak metamorphic temperatures between 630 and 670 °C can be assumed, this study clearly demonstrates that the inferred processes of ductile garnet deformation can occur not only in HT regimes as often suggested in the literature even if embedded within a matrix of “low-strength” minerals like quartz, feldspars and micas.     

A laboratory experiment to monitor the contact state of a fault by transmission waves

We performed a series of laboratory experiments in which elastic waves were transmitted across a simulated fault. Two types of experiments were carried out: (1) Normal Stress Holding Test (NSHT): normal stress was kept constant for about 3 h without shear stress and transmission waves were observed. (2) Shear Stress Increasing Test (SSIT): shear stress was gradually increased until a stick-slip event occurred. Transmission waves were continuously observed throughout the process of stress accumulation. We focused on the change in transmission waves during the application of shear stress and especially during precursory slips.It was found in NSHT that the amplitude of transmission waves linearly increased with the logarithm of stationary contact time. The increase amounted to a few percent after about 3 h. Creep at asperity contacts is responsible for this phenomenon. From a theoretical consideration, it was concluded that the real contact area increased with the logarithm of stationary contact time.We observed in SSIT a significant increase in wave amplitude with shear stress application. This phenomenon cannot be attributed to the time effect observed in NSHT. Instead, it can be explained by the mechanism of “junction growth” proposed by Tabor. Junction growth yields an increase in real contact area. It is required for junction growth to occur that the material in contact is already plastic under a purely normal loading condition. A computer simulation confirmed that this requirement was satisfied in our experiments. We also found that the rate at which the amplitude increased was slightly reduced prior to a stick-slip event. The onset time of the reduction well coincides with the onset of precursory slip. The cause of the reduction is attributed to the reset of stationary contact time due to displacement. This interpretation is supported by the result of NSHT. Taking the time of stationary contact in SSIT into account, we may expect the change in wave amplitude to be, at most, only a few percent. The observed slight reduction in increasing rate is, in this sense, reasonable. The static stiffness of the fault also decreases with precursory slip. It was also found that low frequency waves are a better indicator of precursory slip than high frequency waves. This might suggest that low frequency waves with longer wavelength are a better indicator of average behavior of faults. The problem, however, merits a further investigation. The shifts in phase were also found to be a good indicator of the change in contact state of the fault. The changes in both amplitude and phase of transmission waves are unifyingly understood through the theory of transmission coefficient presented by Pyrak-Nolte et al. Rough surfaces have a tendency to give larger stick-slips than smooth surfaces. The amount of precursory slip is larger for rough surfaces than for smooth surfaces. Although it was confirmed by a computer simulation that rough surfaces have larger contact diameters than smooth surfaces, the rigorous relationship between the surface roughness (contact diameter) and the amount of precursory slips was not established.