饮酒驾车模型的数值分析

论文编号:XXLW031 论文字数:7689,页数:25

摘     要
 本文从生物学角度出发，通过对酒精进入人体后的生理代谢过程进行分析，利用药物动力学的房室模型，针对不同的饮酒方式，分别建立了在短时间内喝酒和长时间喝酒两种情况下，血液中酒精的浓度随时间变化的模型。结合给定的数据，根据Matlab的最小二乘法，用非线性曲线拟合的方法确定参数，准确地模拟出酒精浓度变化趋势的曲线，拟合结果与原始数据吻合程度较高。继而，对不同喝酒方式下，血液中酒精浓度进行分析，对一些实际问题给出了合理的分析。为司机安排饮酒与开车的关系提供了借鉴。最后，结合以上模型的分析及所得结果，对Matlab语言在微分方程的应用做了客观的评价，同时也指出本文中的优缺点。
 
关键词： 房室模型；微分方程；拟合；Matlab
 

Abstract

 This article from the biological point of view, set up in a short period of time to drink alcohol and a long time both cases, the model about the ralation of alcohol in body and time, using the compartment model pharmacokinetics for different ways of drinking, after the analysis process of that alcohol enters the body through metabolism. Using the given data, the least squares method based on Matlab, and non-linear curve fitting method to determine the parameters, we accurately simulate changes in the trend of alcohol concentration curve, fitting results with a higher degree of raw data. Then, on different modes of alcohol, by the analysis of blood alcohol concentration, some practical problems are given a reasonable analysis. It provide the benchmark for the drivers to deal with the relationship between drinking and driving. Finally, combining the analysis and the outcome of the above model, we give an objective evaluation of the Matlab language in the application of differential equations, but also point out the advantages and disadvantages of this article.
 
Keywords: compartment model; differential equation; fitting; Matlab

目  录
中文摘要 I
英文摘要 II
目录 III
前言 1
第一章    研究背景 2
1.1  现状 2
1.2  已有研究方法 2
1.3  本文研究方法 2
第二章    MATLAB软件 3
2.1  MATLAB的简介 3
2.2  MATLAB函数lsqcurvefit 3
2.2.1基本函数原理 3
2.2.2有关函数介绍 3
第三章    饮酒的模型 6
3.1  饮酒的基本原理 6
3.2  房室模型（compartment model） 6
3.3  饮酒模型 7
3.3.1模型假设 7
3.3.2符号说明 7
3.3.3模型建立 8
3.3.4参数估计 10
第四章 酒后驾车数值分析 11
4.1  模型例证 11
4.2  模型方法 11
4.3  模型参数估计 11
4.3  模型分析与检验 15
第五章    结果分析 17
致  谢 18
参考文献 19