On-line estimation of nonlinear physical systems

Recursive algorithms for estimating states of nonlinear physical systems are presented. Orthogonality properties are rediscovered and the associated polynomials are used to linearize state and observation models of the underlying random processes. This requires some key hypotheses regarding the structure of these processes, which may then take account of a wide range of applications. The latter include streamflow forecasting, flood estimation, environmental protection, earthquake engineering, and mine planning. The proposed estimation algorithm may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. Moreover, the method has several advantages over nonrecursive estimators like disjunctive kriging. To link theory with practice, some numerical results for a simulated system are presented, in which responses from the proposed and extended Kalman algorithms are compared.     

Allocycles and Autocycles in the Upper Part of the Limestone Coal Group (Pendleian E1) in the Glasgow–Stirling Region of the Midland Valley of Scotland

The upper part of the Limestone Coal Group (Pendleian E₁), between the major marine transgressions of the Black Metals and the Index Limestone, represents an early example of ‘coal measures’ facies. It comprises a distal and a proximal facies association. The distal facies association, which was subject to relatively strong marine influences and included both deltaic and fluvial elements, is characterized by a regular ‘layer-cake’ succession with laterally-persistent lithological members. By contrast, the proximal association, which was more subject to fluvial influences and is typified by the variable Bannockburn Main Complex, is characterized by abrupt lateral changes in lithofacies. The distal facies association is dominant in the west of the Kilsyth Trough, but proximal facies intercalations increase eastwards, so that they constitute a fairly high proportion of the succession in the Kincardine Basin, particularly in areas of locally-increased tectonic subsidence that were frequently occupied by major channel belts. Some of the sheet sandstones within the distal association have a lower, upward-coarsening portion succeeded by a coarser-grained, erosive-based, upward-fining portion. The resulting ‘two-storey’ profile may reflect deltaic sand bodies having been suceeded by fluvial sand bodies, following a general fall in base level. Linear regression lines showing the relationship between the number of horizons colonized by vegetation and net subsidence, suggest that local autocyclic, tectonosedimentary processes, such as delta switching, channel migration, and avulsion, were superimposed upon a widespread allocyclic, probably glacial-eustatic, process. The former processes were most effective within the proximal facies association and in the Kincardine Basin and the latter in the distal association and the Kilsyth Trough.     

场地土的随机地震反应分析

研究了剪切模量随深度呈线性变化时场地土的随机地震反应分析方法, 分别建立了基岩输入地震动加速度功率谱函数为白噪声和过滤白噪声时场地土的随机地震反应分析理论。     

随机-模糊处理方法在岩石力学指标统计及岩组划分中的应用

探讨了随机 模糊处理方法在岩石力学指标统计和岩组定量划分中的应用。文中对计算中的隶属函数取值及迭代方式进行了深入讨论。通过计算结果的比较分析, 认为随机 模糊处理方法更符合实际, 并优于其他方法。最后作者提出了岩组定性划分 岩石样本参数的随机 模糊统计分析 岩组定量划分及参数重新统计的分析程序。     

Predictive geochemical mapping using environmental correlation

The distribution of chemical elements at and near the Earth's surface, the so-called critical zone, is complex and reflects the geochemistry and mineralogy of the original substrate modified by environmental factors that include physical, chemical and biological processes over time.Geochemical data typically is illustrated in the form of plan view maps or vertical cross-sections, where the composition of regolith, soil, bedrock or any other material is represented. These are primarily point observations that frequently are interpolated to produce rasters of element distributions. Here we propose the application of environmental or covariate regression modelling to predict and better understand the controls on major and trace element geochemistry within the regolith. Available environmental covariate datasets (raster or vector) representing factors influencing regolith or soil composition are intersected with the geochemical point data in a spatial statistical correlation model to develop a system of multiple linear correlations. The spatial resolution of the environmental covariates, which typically is much finer (e.g. ∼90 m pixel) than that of geochemical surveys (e.g. 1 sample per 10-10,000 km²), carries over to the predictions. Therefore the derived predictive models of element concentrations take the form of continuous geochemical landscape representations that are potentially much more informative than geostatistical interpolations.Environmental correlation is applied to the Sir Samuel 1:250,000 scale map sheet in Western Australia to produce distribution models of individual elements describing the geochemical composition of the regolith and exposed bedrock. As an example we model the distribution of two elements – chromium and sodium. We show that the environmental correlation approach generates high resolution predictive maps that are statistically more accurate and effective than ordinary kriging and inverse distance weighting interpolation methods. Furthermore, insights can be gained into the landscape processes controlling element concentration, distribution and mobility from analysis of the covariates used in the model. This modelling approach can be extended to groups of elements (indices), element ratios, isotopes or mineralogy over a range of scales and in a variety of environments.     

How do machine learning techniques help in increasing accuracy of landslide susceptibility maps?

Landslides are abundant in mountainous regions.They are responsible for substantial damages and losses in those areas.The A1 Highway,which is an important road in Algeria,was sometimes constructed in mountainous and/or semi-mountainous areas.Previous studies of landslide susceptibility mapping conducted near this road using statistical and expert methods have yielded ordinary results.In this research,we are interested in how do machine learning techniques help in increasing accuracy of landslide susceptibility maps in the vicinity of the A1 Highway corridor.To do this,an important section at Ain Bouziane(NE,Algeria) is chosen as a case study to evaluate the landslide susceptibility using three different machine learning methods,namely,random forest(RF),support vector machine(SVM),and boosted regression tree(BRT).First,an inventory map and nine input factors were prepared for landslide susceptibility mapping(LSM) analyses.The three models were constructed to find the most susceptible areas to this phenomenon.The results were assessed by calculating the receiver operating characteristic(ROC) curve,the standard error(Std.error),and the confidence interval(CI) at 95%.The RF model reached the highest predictive accuracy(AUC=97.2%) comparatively to the other models.The outcomes of this research proved that the obtained machine learning models had the ability to predict future landslide locations in this important road section.In addition,their application gives an improvement of the accuracy of LSMs near the road corridor.The machine learning models may become an important prediction tool that will identify landslide alleviation actions.     

Modèles géostatistiques de concentrations ou de débits le long des cours d'eau

Estimating concentrations or flow rates along a stream network requires specific models. Two classes of models, recently proposed in the literature, are generalized, to the intrinsic case in particular. We present a global construction by ‘streams’, i.e. on the whole set of paths between sources and outlet. Combining stationary or intrinsic one-dimensional random functions leads to stationary or intrinsic models on segments, with discontinuities at the forks. A construction from outlet to sources, leads to stationary or intrinsic models on each stream, without any discontinuity at the forks. The linear variogram is found as a particular case. The extension to the linear model of coregionalization is immediate, allowing a multivariate modelling of concentrations. To cite this article: C. de Fouquet, C. Bernard-Michel, C. R. Geoscience 338 (2006).     

The critical scale of fluctuation for active lateral forces in spatially variable undrained clays

This study addresses the phenomenon of the critical scale of fluctuation (SOF) for active lateral force (P_a) in undrained clay when there is a spatial variability in the clay. The phenomenon is significant under shear strength (τ_f) random fields but is insignificant under unit weight (γ) random fields. It is found that the phenomenon of the critical SOF is connected to the nature of the spatial averaging, which is “line averaging” under τ_f random fields and is “area averaging” under γ random fields. The former averaging effect (line) is significantly weaker than the latter (area), so the tendency for the critical slip plane to seek for a favorable location is stronger for the τ_f random field than for the γ random field. Hence, the phenomenon of the critical SOF is more pronounced under τ_f random fields than under γ random fields. The underlying mechanisms for the phenomenon of the critical SOF will be explored in this paper.     

研究气温变化趋势的新方法——三组耐抗线

针对气象资料难以满足高斯分布的情况,引进了具有耐抗性的三组耐抗线方法,分析了满足不同信度情况下最小二乘回归和三组耐抗线的差异,并用西藏近30 a气温资料进行了检验。结果表明三组耐抗线方法比最小二乘法研究气候变化趋势有明显优势;采用最小二乘法得到的西藏气候变暖估计偏高。     

转移概率预报方法在霜冻预报中的应用

本文在简介转移概率预报方法及最大概率预报原理的基础上,分析了吕梁市1957年～2000年霜冻初、终日期各随机时间序列状态之间的转换规律,结合各序列的初始分布,建立预报模型,并对1995年～2004年的初、终霜日期进行了预报效果检验。结果表明,该方法预报效果好,使用性强,具有良好的应用前景。