数学代写|概率论代写Probability theory代考|MATHS 7103

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概率论是与概率有关的数学分支。虽然有几种不同的概率解释,但概率论以严格的数学方式处理这一概念,通过一套公理来表达它。

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我们提供的概率论Probability theory及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
数学代写|概率论代写Probability theory代考|MATHS 7103

数学代写|概率论代写Probability theory代考|Shear Behavior of Granular Soils

The shear properties of soil refer to the contraction/dilatancy and yield strength properties or friction properties during shearing. The conventional testing method includes (1) shear tests for uneven deformation of soil samples, such as direct shear tests and simple shear tests, and (2) triaxial shear tests that lead to relatively uniform deformation of soil samples. According to different design requirements, methods such as slow shearing or fast shearing and drained or undrained test conditions are usually adopted, and different deformation and strength indexes are obtained. Triaxial shear tests are widely used due to the advantage of sample uniformity during shearing.
Based on the consolidation history, the current void ratio and the stress state, clay can be divided into normally consolidated and overconsolidated clay, while sandy soil is divided into loose and dense sand. The results of a large number of triaxial shear tests are shown in (Fig. 1.6):
(a) Normally consolidated and slightly overconsolidated clays and loose sand exhibit volumetric contraction during shearing; the void ratio decreases under drained conditions, and the mean effective stress decreases under undrained conditions.
(b) Highly overconsolidated clay and dense sand exhibit volumetric expansion during shearing, that is, dilative characteristics (the void ratio becomes larger under drained conditions, and the mean effective stress becomes larger under undrained conditions), along with the peak stress ratio above the critical stress ratio.

数学代写|概率论代写Probability theory代考|Critical State Line of Granular Soils

Several formulae for expressing the critical state concept have been proposed. The most typical formula is the linear formula in the $e$-log $p^{\prime}$ plane. The relationship has traditionally been written as follows:

$$
e_{c}=e_{r e f}-\lambda \ln \left(\frac{p^{\prime}}{p_{r e f}}\right)
$$
where $e_{\text {ref }}$ is a reference void ratio corresponding to a reference mean effective stress $p_{\text {ref }}$; and $\lambda$ is the slope of the critical state line (CSL) in the $e$-log $p^{\prime}$ plane. Therefore, two parameters ( $e_{\text {ref }}$ and $\lambda$ ) are required for the definition of the CSL. The advantage of this formula is the simplicity of its form. However, experimental results have shown that the CSL is not always linear in the $e-\log p^{\prime}$ plane, and mathematically, the critical void ratio $e_{c}$ could become negative for high stress levels, which is meaningless. Note that a very high stress level still exists in geotechnical structures, such as at the pile tip during its installation.

More recently, another formula was proposed by Li and Wang [169], who assumed a nonlinear critical state line in the $e$-log $p^{\prime}$ plane, representing an extension of the linear formula with one additional parameter $\xi$ :
$$
e_{c}=e_{c 0}-\lambda\left(\frac{p^{\prime}}{p_{a t}}\right)^{\xi}
$$
where the additional parameter $\xi$ controls the nonlinearity of the critical state line, giving a more flexible and accurate description according to experimental data, especially for very low to moderate stress levels. However, for high stress levels, the positiveness of the critical void ratio $e_{c}$ could not be guaranteed, which could possibly cause numerical problems in some local elements in finite element modeling. To overcome this difficulty, Gudehus [170] suggested a third formula for the CSL, which is also a nonlinear formula but with an ” $\mathrm{s}$ ” form by considering an ultimate critical void ratio at very high stress levels. This formula can be expressed as follows:
$$
e_{c}=e_{c u}+\left(e_{c 0}-e_{c u}\right) \exp \left(-\left(\frac{p^{\prime}}{p_{a t} \cdot \lambda}\right)^{\xi}\right)
$$
where $e_{\text {cu }}$ is the critical void ratio when $p^{\prime} \rightarrow \infty$. This expression eliminates the possibility of a negative value of the critical void ratio at high stress levels. However, two more parameters have to be determined.

数学代写|概率论代写Probability theory代考|Summary

This chapter reviewed the uncertainty in geotechnical engineering, and mainly discussed the uncertainties involved in the estimation of soil properties and geotechnical models. The influencing factors on the uncertainties and relevant studies were summarized. It was pointed out that the uncertainty of soil parameters should be considered and analyzed in estimating a certain soil property. Bayesian probabilistic approach as a useful tool was outlined from two application aspects, that is, parametric identification and model class selection. In view of the complex updated PDF, the chapter reviewed several available numerical simulation methods.

The chapter then reviewed previous studies on two problems of geotechnical engineering, that is, soil water retention property of unsaturated soil and creep behavior of soft soil. In the sections of soil water retention of unsaturated soil, the soil suction as an important factor for the development of the unsaturated soil mechanics was explained first, and its contribution on the soil shear strength, permeability and compressibility was discussed by reviewing the existing studies. The soil-water characteristic curve was then explained, and its influencing factors were summarized. The four commonly used methods for estimating SWCC were finally presented. The objective in the study of SWCC was mentioned, and a new model, which can consider the effect of initial void ratio on the SWCC of same textured soil sample, was required to be constructed and the relevant uncertainty analysis should also be conducted.

In the sections of creep behavior of soft soil, the mechanism of soil creep deformation was presented briefly, and the existing studies on the time-dependent models for describing the creep behavior were reviewed. As the basis of this study, the conceptual time line model proposed by Bjerrum [114] was illustrated, and the 1-D elastic viscoplastic model developed by Yin and Graham [122, 123, 149] based on the Bjerrum’s model and the development of EVP models were reviewed. Several methods for determining the parameters of EVP model were summarized, and the objectives in the study of creep behavior were proposed, that is, to analyze the model parameters by using the Bayesian probabilistic method and to select the suitable model for the predictions of creep behavior of soft soil.

数学代写|概率论代写Probability theory代考|MATHS 7103

概率论代考

数学代写|概率论代写Probability theory代考|Shear Behavior of Granular Soils

土的剪切特性是指在剪切过程中的收缩/膨胀和屈服强度特性或摩擦特性。常规的试验方法包括(1)土样不均匀变形的剪切试验,如直剪试验和简单剪切试验;(2)使土样变形相对均匀的三轴剪切试验。根据不同的设计要求,通常采用慢剪或快剪等方法和排水或不排水试验条件,得到不同的变形和强度指标。由于在剪切过程中样品均匀性的优势,三轴剪切试验被广泛使用。
根据固结历史、当前孔隙比和受力状态,黏土可分为正常固结和超固结黏土,而砂土分为松散和致密砂。大量三轴剪切试验结果如图(图 1.6)所示
:排水条件下空隙率降低,不排水条件下平均有效应力降低。
(b) 高超固结黏土和致密砂在剪切过程中表现出体积膨胀,即膨胀特征(排水条件下孔隙比变大,不排水条件下平均有效应力变大),峰值应力比高于临界应力比。

数学代写|概率论代写Probability theory代考|Critical State Line of Granular Soils

已经提出了几种表达临界状态概念的公式。最典型的公式是线性公式和-日志p′飞机。传统上,这种关系被写成如下:

和C=和r和F−λln⁡(p′pr和F)
在哪里和参考 是对应于参考平均有效应力的参考空隙率p参考 ; 和λ是临界状态线 (CSL) 的斜率和-日志p′飞机。因此,两个参数(和参考 和λ) 是定义 CSL 所必需的。这个公式的优点是它的形式简单。然而,实验结果表明,CSL 并不总是线性的和−日志⁡p′平面,在数学上,临界空隙率和C对于高压力水平可能会变成负数,这是没有意义的。请注意,岩土结构中仍然存在非常高的应力水平,例如在安装过程中的桩尖。

最近,Li 和 Wang [169] 提出了另一个公式,他们假设在和-日志p′平面,表示带有一个附加参数的线性公式的扩展X :

和C=和C0−λ(p′p一个吨)X
其中附加参数X控制临界状态线的非线性,根据实验数据给出更灵活和准确的描述,特别是对于非常低到中等的应力水平。然而,对于高应力水平,临界空隙率的正值和C不能保证,这可能会导致有限元建模中某些局部单元出现数值问题。为了克服这个困难,Gudehus [170] 提出了 CSL 的第三个公式,它也是一个非线性公式,但具有“s”通过考虑在非常高的应力水平下的最终临界空隙率来形成。这个公式可以表示如下:

和C=和C在+(和C0−和C在)经验⁡(−(p′p一个吨⋅λ)X)
在哪里和和 是临界空隙率,当p′→∞. 该表达式消除了在高应力水平下临界空隙率出现负值的可能性。然而,必须确定另外两个参数。

数学代写|概率论代写Probability theory代考|Summary

本章回顾了岩土工程中的不确定性,主要讨论了土壤性质和岩土模型估计中涉及的不确定性。总结了不确定性的影响因素及相关研究。指出在估算某一土壤性质时应考虑和分析土壤参数的不确定性。贝叶斯概率方法作为一种有用的工具从两个应用方面进行了概述,即参数识别和模型类别选择。鉴于复杂的更新 PDF,本章回顾了几种可用的数值模拟方法。

本章接着回顾了前人对岩土工程两个问题的研究,即非饱和土的土壤保水性和软土的蠕变行为。在非饱和土的土壤保水剖面中,首先阐述了土壤吸力作为非饱和土力学发展的重要因素,并通过回顾现有研究讨论了其对土壤抗剪强度、渗透性和压缩性的贡献。然后解释了土壤-水特征曲线,并总结了其影响因素。最后给出了估算 SWCC 的四种常用方法。提出了研究 SWCC 的目标,并提出了一种新模型,该模型可以考虑初始孔隙比对相同质地土样 SWCC 的影响,

在软土的蠕变行为部分,简要介绍了土体蠕变变形的机理,并回顾了现有关于描述蠕变行为的时变模型的研究。作为本研究的基础,说明了 Bjerrum [114] 提出的概念时间线模型,以及 Yin 和 Graham [122, 123, 149] 基于 Bjerrum 模型和开发的一维弹性粘塑性模型。审查了 EVP 模型。总结了几种确定EVP模型参数的方法,提出了蠕变行为研究的目标,即利用贝叶斯概率方法分析模型参数,选择合适的模型进行蠕变行为预测。的软土。

数学代写|概率论代写Probability theory代考 请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题,以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法,其中不假设数据来自于由少数参数决定的规定模型;这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型(GLM)归属统计学领域,是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。

有限元方法代写

有限元方法(FEM)是一种流行的方法,用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

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随机分析代写


随机微积分是数学的一个分支,对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。

回归分析代写

多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中,其中问题和解决方案以熟悉的数学符号表示。典型用途包括:数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发,包括图形用户界面构建MATLAB 是一个交互式系统,其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题,尤其是那些具有矩阵和向量公式的问题,而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问,这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展,得到了许多用户的投入。在大学环境中,它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域,MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要,工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数(M 文件)的综合集合,可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

R语言代写问卷设计与分析代写
PYTHON代写回归分析与线性模型代写
MATLAB代写方差分析与试验设计代写
STATA代写机器学习/统计学习代写
SPSS代写计量经济学代写
EVIEWS代写时间序列分析代写
EXCEL代写深度学习代写
SQL代写各种数据建模与可视化代写

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