测绘专业英语教案(9).pdf

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1、-精品文档-仅供参考学习第 1 页 教 案 2008 2009 学年第 一 学期 主 讲 教 师 周 保 兴 课 程 名 称 测 绘 专 业 英 语 课 程 类 别 专 业 选 修 课 学时及学分 45 学时 3 个学分 授 课 班 级 测绘 061062 使 用 教 材 测 绘 工 程 专 业 英 语 系(院、部)土木工程系 教研室(实验室)测绘工程教研室-精品文档-仅供参考学习第 2 页 课 时 授 课 计 划 次序号：9 一、课 题：Unit9 Basic Statistical Analysis of Random Errors 二、课 型：讲 授 三、目的要求：(1)Understa

2、nd the empirical rules that random errors follow.(2)Understand the definition of mean.(3)Understand the definition of Standard deviation.(4)Understand the definition of Propagation of errors.四、重点、难点：(1)the empirical rules that random errors follow.(2)the definition of mean.(3)the definition of Stand

3、ard deviation.(4)the definition of Propagation of errors.五、教学方法及手段：本次课程的教学内容为高程测量方法的英文表-精品文档-仅供参考学习第 3 页 达方式，在理解测绘专业知识的基础上，着重学习测绘专业知识的英文表达方式和写作方式，根据以上教学内容和教学目的本次课采用讲授的教学方式。同时为了提高学生的学习积极性，达到预定的教学效果，拟采用课堂讲授和课堂提问相结合的教学方式。六、参考资料：(1)测绘工程专业英语 尹 晖等 武汉大学出版社 七、作业：(1)预习 Unit10 Accuracy and Precision 八、授课记录：九、

4、授课效果分析：通过学习 Basic Statistical Analysis of Random Errors 的内容，加深了学生对文章中涉 及到的重点的测绘专业词语、词组、表达方式和测绘专业英语的翻译方式的理解，掌 握了误差统计的方法和英文的表达方式。十、教学进程（教学内容、教学环节及时间分配等）1、导入课题：精度和准确度是测量数据质量的评定指标，本次课主要是研究有关精度和准确度的英文表达方式。授课日期 2008.11.17 班 次 测绘 061、062 -精品文档-仅供参考学习第 4 页 2、教学内容：本次课的内容为 Basic Statistical Analysis of Random

5、 Errors，包括偶然误差应当遵循的原则，平均值、标准差、误差传播的定义公式和计算过程。(1)预习一下 Words and Expressions、Terms Highlights 了解有关全站仪和智能机 器人的词汇和专业的表达方式。(2)预习课程中正文的内容,让学生熟悉一下课程内容。(3)结合测绘工程专业知识，对课文的内容进行讲解，在讲解的过程中结合课堂提问，以便使学生能主动的结合所学的专业知识和英语理解能力，对测绘专业英语有深刻的理解。Unit 9 Basic Statistical Analysis of Random Errors（随机误差的统计学基本分析）Random errors

6、 are those variables that remain after mistakes are detected and eliminated and all systematic errors have been removed or corrected from the measured values.（随机误差是在错误被察觉【detect】和消除【eliminate】后，并且所有系统误差被从测量值中移除或修正后，保留下的那些变量【variable 变量、变化 n.】）They are beyond the control of the observer.（它们是观测者无法控制的）

7、So the random errors are errors the occurrence of which does not follow a deterministic pattern.-精品文档-仅供参考学习第 5 页（因 此 随 机 误 差 是 不 遵 循 某 个 确 定 性【deterministic 确定性的】模式【pattern】而发生的误差）In mathematical statistics,they are considered as stochastic variables,and despite their irregular behavior,the study o

8、f random errors in any well-conducted measuring process or experiment has indicated that random errors follow the following empirical rules:（在数理统计【mathematical statistics】中，它们被当成随机变量【stochastic variable】，尽管它们的行为无规律，在任一正确的【well-conducted 原意为品行端正的，这里指测量实验和活动是无误的】测量活动和实验中，对的随机误差的研究显示【indicate】随 机 误 差 遵

9、 循 以 下 经 验 法 则【empirical rule】：）A random error will not exceed a certain amount.（随即误差不会超过一个确定的值）Positive and negative random errors may occur at the same frequency.（正负误差出现的频率相同）Errors that are small in magnitude are more-精品文档-仅供参考学习第 6 页 likely to occur than those that are larger in magnitude.（误差数值【

10、magnitude 量值、大小】小的比数值大的误差出现可能性大【be likely to 可能】）The mean of random errors tends to zero as the sample size tends to infinite.（当【as】样本大小【sample size】趋近于无穷【infinite】时，随机误差的平均值趋近于 0）In mathematical statistics,random errors follow statistical behavioral laws such as the laws of probability.（在数理统计中，随机误差

11、遵循统计学的【statistical】行为【behavioral行为的】规律，如概率法则）A characteristic theoretical pattern of error distribution occurs upon analysis of a large number of repeated measurements of a quantity,which conform to normal or Gaussian distribution.（发生在一个量的大量重复观测分析【analysisn.】中的误差分布的一个特征理论模式，遵照【conform to 遵照】正态或高斯分布）

12、【在对一个量进行大量重复观测分析后，得到一个误差分布的理论特征正态或高斯分布】-精品文档-仅供参考学习第 7 页 The plot of error sizes versus probabilities would approach a smooth curve of the characteristic bell-shape.（误差大小与【versus与、与的关系、与相对】概率的关系图，接近一条光滑的特有的【characteristic 特有的】钟形曲线。）This curve is known as the normal error distribution curve.（这条曲线被称为正

13、态分布曲线）It is also called the probability density function of a normal random variable.（也叫做正态随机变量【normal random variable】的概率密度【probability density】函数）It is important to notice that the total area of the vertical bars for each plot equals 1.（需特别注意的是，每个图的条形图总面积为 1。）This is true no matter the value of n(

14、the number of single combined measurements),and thus the area under the smooth normal error distribution curve is equal to 1.（无论【no matter】n（单一的联合的测量数目【独立观测数】）是多少，在光滑的误差正态分布曲线下的面积都是 1。）-精品文档-仅供参考学习第 8 页 If an event has a probability of 1,it is certain to occur,and therefore the area under the curve

15、represents the sum of all the probabilities of the occurrence of errors.（如果一件事的概率为1，它一定会发生，因此曲线下方的面积代表了所有误差发生的概率。）A number of properties that relate a random variable and its probability density function are useful in our understanding of its behavior.（有许多工具【property】与随机变量和它的概率密度函数有关，有助于我们理解它的行为）Mea

16、n and standard deviation are two most popular statistical properties of a random variable.（平均值和标准偏差就是两个最常用的随机变量的统计工具【property】）Generally,a random variable which is normally distributed with a mean and standard deviation can be written in symbol form as N(,2).（一般地，一个通常由平均值和标准偏差描述的随机变量可以用符号【symbol】表示为

17、 N(,2)。They can be explained as follows.（【它们可以】解释如下）-精品文档-仅供参考学习第 9 页 Mean:The most commonly used measure of central tendency is the mean of a set of data(a sample).（平均值：最普遍应用的中心趋向的估计【measure】就是一系列数据（一个样本）的平均值）The concept of mean refers to the most probable value of the random variable.（平均值的概念【conce

18、pt】涉及到随机变量的最或是值）It is also called by any of the several termsexpectation,expected value,mean or average.（还可以由其它几个术语来称呼它期望、预期值、平均值或平均值）The mean is defined as（平均值定义为）Where xi are the observations,n is the sample size,or total number of observations in the sample,and x is the mean which is also called

19、most probable value(MPV).（xi 是观测值，n 是样本大小，或者叫样本内观测值的总数，x 是平均值，经常被称为最或是值（MPV）The MPV is the closest approximation to the true value that can be easily achieved from a set of data.（MPV是 最 接 近 真 值 的 近 似 值【approximation】，可以很容易由一系列数据得-精品文档-仅供参考学习第 10 页 到。）It can be shown that the arithmetic mean of a set

20、 of independent observations is an unbiased estimate of the meanof the population.（可以看出【It can be shown that】一系列独立【independent】观测值的算数平均值【arithmetic mean】是一个样本【population】的期望值的无偏估计【unbiased estimate】。）Standard deviation is a numerical value indicating the amount of variation about a central value.（标准

21、偏差是一个数值【numerical value】，指示【indicate】相对于中值的偏离）In order to appreciate the concept upon which indices【index 的复数】of precision devolve one must consider a measure that takes into account all the values in a set of data.（考虑一系列数据的所有值精度指标 必需顾及一个量，这个量考虑到【takes into account 考虑】一组【a set of】数据的所有值）Such a measu

22、re is the deviation from the mean x of each observed value xi i.e.(xi-x),and the mean of the squares of the deviations may-精品文档-仅供参考学习第 11 页 be used,and this is called the variance2,（这个量是每个观测值 xi 相对于平均值 x 的离差【deviation】，也就是，(xi-x)，离差的平方的平均值被采用，称之为方差2）Where is the mean(expectation)of the population.（

23、这里是对象总体【样本】的平均值（期望值）。）The square root of the variance is called standard deviation.（方差的平方根被称为标准差）Theoretically the standard deviation,which is the value on the X axis of the probability curve that occurs at the points of inflecxion【估计应为 inflexions 拐点】of the curve,is obtained from an infinite number

24、of variables known as the population.（理论上标准差，是概率曲线拐点的 X 轴坐标，由无穷多的变量（被称为样本）得到）In practice,however,only a sample of variables is available and S is used as an unbiased estimator.（然而，实际上，只有变量的样本是可以利用的，S 被称为无偏【unbiased】估计【estimator估计、估计者】。）-精品文档-仅供参考学习第 12 页 Account is taken of the small number of varia

25、bles in the sample by using(n-1)as the divisor,which is referred to in statistics as the Bessel correction;hence,variance is（样本中有限的【small 小的】变量的计算，用 n-1 作为除数【divisor 除数、约数】，在统计学中称之为白塞尔修正；因此，变化【variance 变化、不一致 n.】如下：）To obtain an index of precision in the same units as the original data,therefore the

26、 square root of the variance is used,and this also called the standard deviation S.（为了获得与源数据一样单位的精度指标，方差的平方根被采用，又叫做标准差 S）The standard deviation is the measure of the dispersion or spread of the random variable.（标准差是随机变量的离差或离散的量度标准。）A survey measurement,such as a distance or angle,after mistakes are

27、eliminated and systematic errors corrected,is a random variable.（一个测量值，例如距离或角度，在错误被去除、系统误差被修正后，就是一个随机变量。）-精品文档-仅供参考学习第 13 页 If a distance is measured 20 times,it is not unusual to get values for each of the measurements that differ slightly from its true value that is never known.（如果一段距离被测了 20 次，每次的

28、测量值与永远未知的真值有些微的差值是很正常的）So owing to random variability,an error was defined as the difference between a random variable,the measured value(observation)and the constant,the true value i.e.error=measured value.（因此，由于【owing to】随机可变性，误差被定义为随机变量、测量值和常量之间的差值，也就是，误差测量值【常量，这里估计是掉了】。）And a correction(residual

29、),which is the negative of the error in practice,was defined as correction between the MPV and measured value i.e.correction=MPV-measured value.（改正值，习惯上【in practice】是误差的负值，定义为 MPV和测量值之间的修正值，也就是改正值MPV测量值）When the so-called true values are available to-精品文档-仅供参考学习第 14 页 compare with calculated values,

30、the mean square error(MSE)is given by（当所谓的真值可以与计算值相比较时，误差均方差（MSE）为：）In which xi is the measured value,x is the true value and n is the number of measurements.（其中 xi 是测量值，x 是真值，n 是观测数）Propagation of errors(or error propagation):Much data in surveying is obtained indirectly from various combinations o

31、f observations.（误差传播：测量的许多数据是间接由各种测量值综合得到的【combination 是名词，这里翻译时用到了词性转换】）For instance the coordinates of a line are a function of its length and bearing.（例如，一条直线的坐标就是其长度和方位的函数）As each measurement contains an error,it is necessary to consider the combined effect of these errors on the derived quantit

32、y.（由于每项测量值都包含误差，必需考虑这些源数据的误差的联合影响）Error propagation is one of the many aspects of analyzing errors.（误差传播是误差分析的许多方-精品文档-仅供参考学习第 15 页 面的其中一个）It is the mathematical process used to estimate the expected random error in a computed or indirectly measured quantity caused by one or more identified and esti

33、mated random errors in one or more identified variables that influence the precision of the quantity.（它是一个数学方 法【process 或 者译为 过 程】，用 来估 计【estimate】在一个计算出的或间接测量的参量【quantity】中的期望随机误差【或偶然误差】，该参量是在一个或多个确定的【identified】变量中由一个或多个限定或确定的偶然误差引起的，影响该量的精度。）The general procedure is to differentiate with respect

34、to each of the observed quantities in turn and sum them to obtain their total effect.（一 般 的 程 序 是 取 每 个 观 测 量 的 微 分【differentiate 求微分】然后把它们加起来，来获得它们的总的影响）Thus if Z=f(x1,x2,xn),and each independent variable changes by a small amount(an error)x1,x 2,xn,then Z will change by a-精品文档-仅供参考学习第 16 页 small a

35、mount equal to Z,obtained from the following expression:（这样，如果Z=f(x1,x2,xn)，每个独立变量用一个小的量（误差）代换x1,x 2,xn，Z 由一个小的量Z代换，Z 由下面表达式得到：）in which is the partial derivative of Z with respect to x,etc.（其中 是 Z 对 x 的偏导数【partial derivative】，等等）is used to replace the partial symbol d.（用来替代偏导符号 d）As the observation

36、s are considered independent and uncorrelated,the variance2Z is therefore（假设观测值是独立和不相关的，方差2Z为：）which is the general equation for the variance of any function which is called the rationale of Error Propagation.（是 任 意 函 授 的 方 差【variance】计算的普适方程，被称为误差传播【Error Propagation】定律【rationale 基本原理】）This equation is very important and is used extensively in surveying for error analysis.（这个方程非常重要，在测量中广泛应用于误差分析）-精品文档-仅供参考学习第 17 页 3、课堂总结：对所学的 Basic Statistical Analysis of Random Errors 的内容进行总结，对 文章中涉及到的重点的测绘专业词语、词组、表达方式和测绘专业英语的翻译方式进 行总结。4、布置作业：(1)预 习 Unit10 Accuracy and Precision。