模糊神经网络在山区自然坡失稳预报中的应用

将模糊理论和神经网络相结合, 建立基于模糊神经系统的自然坡失稳预测模型--模糊神经网络(FANN)方法, 并针对我国湖北宜昌鄂西磷矿开采引起上部自然坡失稳的可能性进行了具体计算分析.     

高陡山区岩体移动分析的Fuzzy数学模型

本文利用 Fuzzy数学理论 ,针对高陡山区地下房柱法采矿所引起的岩体移动变形问题 ,建立了具体的数学模型和预测分析方法 .通过对工程实例的计算分析 ,表明本文所建立的数学模型和分析方法适用于工程实际     

Fuzzy概率理论用于研究采矿引起的岩体移动

本文运用 Fuzzy 概率理论,对矿山岩体力学中的岩体移动问题,建立了相应的Fuzzy 数学模型,并利用该模型对地下采矿导致的岩体垂直移动、水平移动、水平变形、岩体倾斜和曲率变化等指标进行了定量计算.对于山区开采导致的岩体移动问题也进行了初步探讨.最后还对几个矿山工程实例进行了计算分析,结果表明,本文提出的新方法可用于分析采矿导致的岩体移动问题.     

模糊测度模型用于爆破震动影响下山区露天矿山边坡变形分析

根据生产爆破震动对山区山坡露天矿高陡边坡稳定性影响的工程实际,本文采用非确定性方法,将爆破震动引起露天矿边坡岩体移动变形这一现象视为一模糊事件,建立了生产爆破震动影响下山区山坡露天矿边坡岩体移动变形分析的Fuzzy测度理论模型.并利用该模型对我国某露天矿边坡岩体移动变形及其稳定性进行了具体的分析预测,所获理论结果符合工程实际.     

模糊测度在山区开挖岩体移动分析中的应用

将山区地下开挖所引起的上覆岩土体的移动视为一模糊事件,应用模糊数学中的模糊测度理论,推导了相应的地表下沉及水平移动的理论计算公式,对煤矿开采所引起的地表移动进行了计算分析。通过工程实例计算分析表明,理论计算结果与工程实测资料吻合的很好。     

基于Schwarz-Christoffel变换的圆形隧道围岩应力分布特征研究

隧道围岩应力还原到实际区域的变换方法被越来越多地应用到工程实践中,对复杂形状围岩体内的隧道围岩应力计算方法和隧道围岩稳定性的研究具有重要的实践指导意义.该文建立了不规则岩体中开挖圆形隧道的力学模型,运用复变函数理论,通过映射函数Schwarz-Christoffel变换,得到复平面单位圆到隧道所处多边形岩体的映射函数,在复变函数数域内分析了多边形岩体应力的求解步骤,运用弹性力学理论等推导了不规则岩体中圆形隧道的复变应力函数Φ(ξ)和φ(ξ)的表达式,并得出围岩体任一点应力分量σρ和σθ的解析通式.通过具体算例分析可知,岩体形状对圆形隧道的稳定性有较大的影响,隧道所处4种形状下的围岩体最大应力值分布规律为:顶底板的最大应力值从六边形、五边形、四边形、圆形围岩体依次减小,帮部的最大应力值从圆形、四边形、五边形、六边形围岩体依次减小.     

考虑地震力方向的倾倒式危岩可靠度分析

侧向卸荷作用导致高陡边坡发育大量危岩体,危岩体在降雨、地震作用下易发生失稳破坏,判断其失稳的概率对危岩防治具有重要意义.该文以倾倒式危岩体为例,建立了考虑地震力作用方向下最危险方向的物理力学模型,利用函数极值理论建立了最危险地震力作用方向的表达式,结合可靠度理论建立了倾倒式危岩体可靠度指标、失稳概率表达式及判断标准.通过对重庆南川金佛山危岩体案例的分析表明:工况1的最危险地震力作用方向与水平方向的偏转角θ在5°范围内,工况2的最危险地震力作用方向与水平方向的偏转角θ在10°左右;危岩体最危险作用方向不是一个固定角,其值与危岩体形态、裂隙水作用力大小、岩腔深度等有关.当主控结构面裂隙长度较小时,最危险地震力作用方向与水平夹角很小,随主控结构面裂隙长度增大,最危险地震力作用方向与水平夹角显著增大;危岩体失稳概率随主控结构面裂隙长度增加而增大,工况2较工况1增大幅度更明显.该研究成果对危岩的防灾减灾具有重要意义.     

三维海洋水动力计算σ坐标转换存在的问题及改进方法

三维水动力模型在准确模拟海洋物理特性中起着重要的作用,传统的σ坐标转换由于当时计算机能力所限,舍去了复杂的高阶项,在实际复杂地形（或水深变化）环境下,会带来一定的误差或计算失真等问题.由此,为了适应高精度计算结果的需求,对原有σ坐标三维水动力模型进行了重新修正.在改进后的模型中,综合考虑了经σ坐标变换引入的与流速、水位、地形相关的复杂高阶项,选用特定的插值函数,利用有限元和差分相结合的方法,进行求解σ坐标下的完整三维浅水模式方程.相比原模型,改进的模型对底坡、水深、潮汐振幅等变化适用范围更为广泛,能更好地模拟出复杂水深变化下的垂向流动分布特征,计算结果具有更高的精确度;改进的模型针对一些极端水位条件（潮汐振幅与水深比大于0.15）,其计算误差同样可保持在一个较低的范围内;同时,改进的模型只需更短的时间就可运行至稳定状态.     

基于地形优化的无人机路径规划模型及其应用

有危害的地震往往发生在山区,震后的灾区有许多工作需要完成:人员搜救、灾情的巡视、次生灾害的监控、通讯网络的建立等等.由于山区的地形较为复杂,可以考虑使用无人机来完成灾后各项工作.针对一个特定的复杂区域,使用无人机来完成灾害后的一系列任务,通过地形优化等手段对无人机群进行合理的路径规划,使其效率达到最优,具有很强的实际应用价值.     

模糊遗传规划方法在预测深部开采岩体移动中的应用

运用模糊(Fuzzy)系统理论,给出了地下深部开采岩体移动变形预测分析的Fuzzy模型,对岩体移动参数采用遗传规划(GP)方法进行确定,进而形成了模糊遗传规划方法.用工程实测数据对遗传规划网络进行了训练,并用测试样本对GP模型进行了测试,证明了模型的预测性能是令人满意的.通过工程实例计算分析表明,采用本文提出的模糊遗传规划方法所获结果符合工程实际.     

The use of QP-free algorithm in the limit analysis of slope stability

In many mountainous areas, landslides and slope instabilities frequently occur after heavy rainfall and earthquake, and result in enormous casualties and huge economic losses. In order to mitigate the landslides hazard efficiently, a method is required for a better understanding of stability analysis. Fortunately, upper bound theorem of limit analysis provides a practical and effective upper bound approach to evaluate the stability of slopes. And in this approach, the search for the minimum factor of safety can be formulated as a nonlinear constrained optimization. In general, the SQP-type algorithms are used to solve this optimization problem. However, it is quite time consuming and difficult to search the optimum from an arbitrary starting point based on the SQP-type algorithms. Fortunately, a QP-free algorithm based on penalty function and active-set strategy can be globally convergent toward the KKT points with arbitrary starting point, and the rate of convergence is local superlinear or even quadratic. Two classical problems of slope stability are solved by this QP-free algorithm. The results show that the QP-free algorithm would be the better choice than SQP-type algorithms for solving the nonlinear constrained optimization problem which is derived from the upper bound limit analysis of slope stability.     

Dispersion models for extremes

We propose extreme value analogues of natural exponential families and exponential dispersion models, and introduce the slope function as an analogue of the variance function. A class of extreme generalized linear regression models for analysis of extremes and lifetime data is introduced. The set of quadratic and power slope functions characterize well-known families such as the Rayleigh, Gumbel, power, Pareto, logistic, negative exponential, Weibull and Fréchet. We show a convergence theorem for slope functions, by which we may express the classical extreme value convergence results in terms of asymptotics for extreme dispersion models. The key idea is to explore the parallels between location families and natural exponential families, and between the convolution and minimum operations.     

A new model of Saint Venant and Savage–Hutter type for gravity driven shallow water flows

We introduce a new model for shallow water flows with non-flat bottom. A prototype is the Saint Venant equation for rivers and coastal areas, which is valid for small slopes. An improved model, due to Savage–Hutter, is valid for small slope variations. We introduce a new model which relaxes all restrictions on the topography. Moreover it satisfies the properties (i) to provide an energy dissipation inequality, (ii) to be an exact hydrostatic solution of Euler equations. The difficulty we overcome here is the normal dependence of the velocity field, that we are able to establish exactly. Applications we have in mind concern, in particular, computational aspects of flows of granular material (for example in debris avalanches) where such models are especially relevant. To cite this article: F. Bouchut et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Geometric demonstration of the fundamental theorems of the calculus

After the monumental discovery of the fundamental theorems of the calculus nearly 350 years ago, it became possible to answer extremely complex questions regarding the natural world. Here, a straightforward yet profound demonstration, employing geometrically symmetric functions, describes the validity of the general power rules for integration and differentiation. Differentiation and integration are readily seen to be reverse operations that compute slopes and under-areas of curves, without requiring tedious infinitesimal limits or infinite summation algebraic procedures. The areas under any two symmetric curves within a square combine to equal its square measure. Corresponding evaluated integrals of any symmetric pair were also found to add to that same area. The general power rules and the fundamental theorems are confirmed for an infinite number of functions containing exponents from the entire real number line, rational or irrational. Any particular equation represents the slope of its own under-area formula, as first discovered by Isaac Newton, where the rate that area accumulates at a point under a curve, traced at constant horizontal velocity, is the value of the curve at that point. Applications of the calculus in mathematics, physics and chemistry elucidated the orbital structure of the atom, vast scientific formula and secrets of the nature of light and gravity.     

Complex variable solutions for tunnel excavation at great depth in visco-elastic geomaterial considering the three-dimensional effects of tunnel advance

This paper proposes complex variable solutions for stress and displacement fields for tunnel excavation at great depth in a visco-elastic geomaterial, considering the equivalent three-dimensional effect, liner installation, supporting delay, and the interaction between liner and geomaterial. The geomaterial is simulated by three typical visco-elastic models: the three-parameter solid model, the Poyting–Thomson model and the Burgers model. The proposed solutions can simulate both tunnel excavation and liner installation stages, which are continuous in the time dimension. In the derivation, the variable substitution, the Laplace transform, and their inverse computations are applied. The proposed solutions are verified in detail by comparing to a numerical solution and a set of field data. Good agreements between the analytical solution and the numerical solution/field data are observed, indicating the validity of the proposed solutions. Subsequently, a parametric study is performed to investigate the influences of tunnel geometry (including tunnel size and liner thickness), material parameters of liner and geomaterial (including Poisson's ratio, shear modulus and viscosity of both elements), tunnel advance rate, and liner installation time moment (denoting supporting delay) on the stress and displacement fields in liner and geomaterial. The proposed solutions may serve as an alternative method for the conceptual and preliminary designs in tunnel engineering.     

近似Bayes计算前沿研究进展及应用

在大数据和人工智能时代,建立能够有效处理复杂数据的模型和算法,以从数据中获取有用的信息和知识是应用数学、统计学和计算机科学面临的共同难题.为复杂数据建立生成模型并依据这些模型进行分析和推断是解决上述难题的一种有效手段.从一种宏观的视角来看,无论是应用数学中常用的微分方程和动力系统,或是统计学中表现为概率分布的统计模型,还是机器学习领域兴起的生成对抗网络和变分自编码器,都可以看作是一种广义的生成模型.随着所处理的数据规模越来越大,结构越来越复杂,在实际问题中所需要的生成模型也变得也越来越复杂,对这些生成模型的数学结构进行精确地解析刻画变得越来越困难.如何对没有精确解析形式（或其解析形式的精确计算非常困难）的生成模型进行有效的分析和推断,逐渐成为一个十分重要的问题.起源于Bayes统计推断,近似Bayes计算是一种可以免于计算似然函数的统计推断技术,近年来在复杂统计模型和生成模型的分析和推断中发挥了重要作用.该文从经典的近似Bayes计算方法出发,对近似Bayes计算方法的前沿研究进展进行了系统的综述,并对近似Bayes计算方法在复杂数据处理中的应用前景及其和前沿人工智能方法的深刻联系进行了分析和讨论.     

Analytical prediction of tunneling-induced ground movements and liner deformation in saturated soils considering influences of shield air pressure

Complex underground constructions in urban areas require strict predictions for ground movements and liner deformation induced by shield-driven tunneling, in which the complex interaction mechanics between ground and liner play a substantial role. Previous studies, however, provided little information on the ground-liner interaction and less attention to the effects of groundwater and compressed air during the shield operation. This paper presents a closed-form analytical solution for predicting long- and short-term ground deformation and liner internal forces induced by tunneling in saturated soils in which shield excavation effects with and without air pressure are both considered. The oval-shaped convergence deformation pattern is incorporated as the boundary condition of displacements around the tunnel section. This paper also investigates the difference between uniform radial and oval-shaped convergence deformation patterns on the ground and tunnel responses. Generally, the predicted ground movements by the oval-shaped deformation pattern aligns well with measured data of actual tunnels with and without considering the shield air pressure. It is comparatively observed that the shield excavation under air pressure obtains larger ground deformation than the non-pressure condition, and the long-term ground settlements induced by tunneling in saturated soils are confidently larger than the short-term. Moreover, the effects of sensitive parameters, including the shield air pressure, the long- and short-term effects on the tunneling-induced ground movements are assessed based on the oval-shaped deformation pattern. Furthermore, parametric analyses are conducted to measure the influences of concerned tunneling coefficients on the liner displacements and internal forces, namely, soil Young's modulus, soil unit weight, coefficient of lateral soil pressure, tunnel radius, tunnel buried depth and gap parameter. In summary, the analytical approach proposed in this research provides an effective insight into the ground-liner interaction mechanics related with the shield air pressure, which can serve as an alternative approach in the preliminary design for conservatively estimating the excavation influences caused by tunneling in saturated soils.     

Non-Gaussian non-stationary models for natural hazard modeling

This paper addresses the construction of probabilistic models for time or space dependent natural hazards. The proposed method uses Karhunen-Loève expansion in order to construct an empirical model matching the non-stationarity and the randomness of natural phenomena such as earthquakes or other complex environmental processes. The terms of the Karhunen-Loève expansion are identified directly from measured data. The approach is illustrated and its performance assessed through two academic examples. It is then applied to seismic ground motion modeling using recorded data.