数学代写|随机过程统计代写Stochastic process statistics代考|MATH3801

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随机过程 用于表示在时间上发展的统计现象以及在处理这些现象时出现的理论模型,由于这些现象在许多领域都会遇到,因此这篇文章具有广泛的实际意义。

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我们提供的随机过程统计Stochastic process statistics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|随机过程统计代写Stochastic process statistics代考|MATH3801

数学代写|随机过程统计代写Stochastic process statistics代考|Importance of Software for Process Analysis

In process engineering, the simulation, design, and optimization of a chemical process plant, which comprises several processing units interconnected by process streams, are the core activities. These tasks require material and energy balancing, equipment sizing, and costing calculation. A computer package that can accomplish these duties is known as a computer-aided process design package or simply a process simulator (also known as process flowsheeting package, flowsheet simulator, or flowsheeting software). The capabilities of a process simulator include an accurate description of physical properties of pure components and complex mixtures, rigorous models for unit operations, as well as numerical techniques for solving large systems of algebraic and differential equations. By a process simulator, it is possible to obtain a comprehensive computer image of a running process, which is a valuable tool in understanding the operation of a complex chemical plant and on this basis can serve for continuously improving the process or for developing new processes.

The purpose of simulation is to model and predict the performance of a process. It involves decomposition of the process into its constituent units for individual study of performance. The process characteristics (e.g., flow rates, compositions, temperatures, pressures, properties, and equipment sizes) are predicted using analysis techniques, which include mathematical models, empirical correlations, and computer-aided process simulation tools (e.g., Aspen Plus). In addition, process analysis may involve the use of experimental methods to predict and validate performance. Therefore, in process simulation, the process inputs and the flowsheet are given, and we are required to predict process outputs (Figure 4.1). This book focuses on Aspen Plus. It is a computer-aided software that uses the underlying physical relationships (e.g., material and energy balances, thermodynamic equilibrium, and rate equations) to predict process performance (e.g., stream properties, operating conditions, and equipment sizes).
There are several advantages of computer-aided simulation:

  1. It allows the designer to quickly test the performance of synthesized process flowsheets and provide feedback to the process synthesis activities.
  2. It can be coordinated with process synthesis to develop optimum integrated designs.
  3. It minimizes experimental and scale-up efforts.
  4. It explores process flexibility and sensitivity by answering “what-if” questions.
  5. It quantitatively models the process and sheds insights on process performance.
  6. Following are the important issues to remember before venturing into the exciting world of computer-aided simulation:
  7. Do not implicitly trust the results of any simulation tool.
  8. Calculated results are only as good as the input you give the simulator.
  9. Always convince yourself that the obtained results make physical sense, otherwise you will never be able to convince someone else of the merits of your work.

数学代写|随机过程统计代写Stochastic process statistics代考|Characteristics of the Process Simulator Aspen Plus

The process simulation market underwent severe transformations in the 1985-1995 decade. Relatively few systems have survived; they are CHEMCAD, Aspen Plus, Aspen HYSYS, PRO/II, ProSimPlus, SuperPro Designer, and gPROMS. Nowadays, most of the current process simulators are developed following an object-oriented approach using languages such as $\mathrm{C}_{+}+$or Java. This shift in paradigm, from procedural to object-oriented, has no doubt benefited and will continue to benefit the process engineering community immensely.

Aspen Plus is designed for the simulation of steady-state processes; especially those that are computationally laborious to analyze by hand calculations, such as processes involving recycle streams, nonideal phase or chemical

equilibria, and adiabatic operations. It is ideally suited to provide answers on “what-if” type of questions on process design and optimization.

Fundamental to improving performance of the plant is an accurate representation of the basic processes. Companies require a solution that enables them to model their processes to develop insights to improve designs and optimize performance. Aspen Plus provides the solution to meet this requirement, solving the critical engineering and operating problems that arise throughout the life cycle of a chemical process.

Aspen Plus predicts process behavior using engineering relationships, such as mass and energy balances, phase and chemical equilibria, and reaction kinetics. With reliable physical properties, thermodynamic data, realistic operating conditions, and rigorous equipment models, engineers are able to simulate actual plant behaviors. Applications include the following:

  • Improving engineering productivity and reducing costs
  • Reducing energy consumption and greenhouse gas emissions
  • Enhancing product yields and quality
  • Minimizing capital and operating costs
  • Optimizing designs for large-scale integrated chemical plants
  • Optimizing plant operations

数学代写|随机过程统计代写Stochastic process statistics代考|Sequential Modular Simulation

The sequential modular approach is based on the concept of modularity, which extends the chemical engineering concept of unit operation to a “unit calculation” of the computer code (i.e., subroutine) responsible for the calculations of an equipment. This method is similar in principle to the traditional method of hand calculation of unit operations. The equations for each equipment unit are grouped together in a subroutine or module. Thus, each module calculates the output streams for the given input streams and parameters for that equipment, irrespective of the source of input information or the sink of output information. In the equation-oriented type, the complete model of the plant is expressed in the form of one large sparse system of nonlinear algebraic equations that is simultaneously solved for all the unknowns. This approach combines the modularizing of the equations related to specific equipment with the efficient solution algorithms for the simultaneous equation-solving technique. For each unit, an additional module is written, which approximately relates each output value by a linear combination of all input values. Accordingly, rigorous models are used at units’ level, which are solved sequentially, whereas linear models are used at flowsheet level, solved globally. The linear models are updated based on results obtained with rigorous models (Martin-Martin, 2015).
Following are the basic components of a simulation package:

  1. Component data bank
  2. Thermodynamic property prediction methods
  3. Flowsheet builder (graphical user interface)
  4. Unit module library
  5. Numerical routines
  6. Data output generator
  7. Executive program (flowsheet solver)
    Modular process simulators are very robust solving each unit operation with numerical methods tailored to the specific characteristics to each one of these units. These include from specific inside-out algorithms to “flash” a material stream going through detailed methods for reactors and heat exchangers until complex methods for distillation. However, one drawback of the approach is that some unit operations introduce numerical noise (this is also simulator and unit dependent). In other words, if we solve the same problem starting from different initial points, we will obtain, for some variables, slightly different values. The difference can be in the second or third decimal point, which is not significant from a simulation point of view but is a really large error if we try to estimate a derivative (derivative information is not provided by the simulator, although some unit operations internally use it to solve the module). This problem is magnified by information loops that could act as “error accumulators.”
数学代写|随机过程统计代写Stochastic process statistics代考|MATH3801


数学代写|随机过程统计代写Stochastic process statistics代考|Importance of Software for Process Analysis

模拟的目的是对过程的性能进行建模和预测。它涉及将过程分解为其组成单元,以进行单独的绩效研究。使用包括数学模型、经验相关性和计算机辅助过程模拟工具(例如 Aspen Plus)在内的分析技术预测过程特性(例如,流速、成分、温度、压力、性质和设备尺寸)。此外,过程分析可能涉及使用实验方法来预测和验证性能。因此,在过程模拟中,给出了过程输入和流程图,我们需要预测过程输出(图 4.1)。本书重点介绍 Aspen Plus。它是一种计算机辅助软件,它使用底层的物理关系(例如,

数学代写|随机过程统计代写Stochastic process statistics代考|Characteristics of the Process Simulator Aspen Plus
过程模拟市场在 1985-1995 十年期间经历了剧烈的转变。幸存下来的系统相对较少;它们是 CHEMCAD、Aspen Plus、Aspen HYSYS、PRO/II、ProSimPlus、SuperPro Designer 和 gPROMS。如今,大多数当前的过程模拟器都是按照面向对象的方法开发的,使用诸如或Java。这种范式的转变,从面向过程到面向对象,无疑已经并将继续极大地造福于过程工程社区。

Aspen Plus 专为模拟稳态过程而设计;尤其是那些通过手工计算难以计算的分析,例如涉及循环流、非理想相或化学的过程


提高工厂绩效的基础是基本流程的准确表示。公司需要一种解决方案,使他们能够对其流程进行建模,以开发洞察力以改进设计和优化性能。Aspen Plus 提供了满足这一要求的解决方案,解决了整个化学过程生命周期中出现的关键工程和操作问题。

Aspen Plus 使用工程关系预测过程行为,例如质量和能量平衡、相和化学平衡以及反应动力学。凭借可靠的物理特性、热力学数据、真实的运行条件和严格的设备模型,工程师能够模拟实际的工厂行为。应用包括以下内容:

数学代写|随机过程统计代写Stochastic process statistics代考|Sequential Modular Simulation


数学代写|随机过程统计代写Stochastic process statistics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。







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。





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。


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 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。