測繪專業(yè)英語教案 Microsoft W

1、 教 案2008 2009 學(xué)年第 一 學(xué)期主 講 教 師周 保 興課 程 名 稱測 繪 專 業(yè) 英 語 課程類別專 業(yè) 選 修 課學(xué)時及學(xué)分45學(xué)時 3個學(xué)分授 課 班 級測繪061062使 用 教 材測 繪 工 程 專 業(yè) 英 語系(院、部)土木工程系教研室(實(shí)驗(yàn)室)測繪工程教研室課時授課計(jì)劃課次序號： 9 一、課題：Unit9 Basic Statistical Analysis of Random Errors二、課型： 講 授三、目的要求：(1) Understand the empirical rules that random errors follow .(2) Underst

2、and the definition of mean.(3) Understand the definition of Standard deviation.(4) Understand the definition of Propagation of errors.四、重點(diǎn)、難點(diǎn)：(1) the empirical rules that random errors follow .(2) the definition of mean.(3) the definition of Standard deviation.(4) the definition of Propagation of er

3、rors.五、教學(xué)方法及手段：本次課程的教學(xué)內(nèi)容為高程測量方法的英文表達(dá)方式，在理解測繪專業(yè)知識的基礎(chǔ)上，著重學(xué)習(xí)測繪專業(yè)知識的英文表達(dá)方式和寫作方式，根據(jù)以上教學(xué)內(nèi)容和教學(xué)目的本次課采用講授的教學(xué)方式。同時為了提高學(xué)生的學(xué)習(xí)積極性，達(dá)到預(yù)定的教學(xué)效果，擬采用課堂講授和課堂提問相結(jié)合的教學(xué)方式。六、參考資料：(1)測繪工程專業(yè)英語 尹 暉等 武漢大學(xué)出版社七、作業(yè)：(1) 預(yù)習(xí) Unit10 Accuracy and Precision八、授課記錄：授課日期2008.11.17班次測繪061、062九、授課效果分析： 通過學(xué)習(xí)Basic Statistical Analysis of Rand

4、om Errors的內(nèi)容，加深了學(xué)生對文章中涉及到的重點(diǎn)的測繪專業(yè)詞語、詞組、表達(dá)方式和測繪專業(yè)英語的翻譯方式的理解，掌握了誤差統(tǒng)計(jì)的方法和英文的表達(dá)方式。十、教學(xué)進(jìn)程（教學(xué)內(nèi)容、教學(xué)環(huán)節(jié)及時間分配等）1、導(dǎo)入課題：精度和準(zhǔn)確度是測量數(shù)據(jù)質(zhì)量的評定指標(biāo)，本次課主要是研究有關(guān)精度和準(zhǔn)確度的英文表達(dá)方式。2、教學(xué)內(nèi)容：本次課的內(nèi)容為Basic Statistical Analysis of Random Errors，包括偶然誤差應(yīng)當(dāng)遵循的原則，平均值、標(biāo)準(zhǔn)差、誤差傳播的定義公式和計(jì)算過程。(1) 預(yù)習(xí)一下Words and Expressions、Terms Highlights了解有關(guān)全站儀和

5、智能機(jī)器人的詞匯和專業(yè)的表達(dá)方式。(2) 預(yù)習(xí)課程中正文的內(nèi)容,讓學(xué)生熟悉一下課程內(nèi)容。(3) 結(jié)合測繪工程專業(yè)知識，對課文的內(nèi)容進(jìn)行講解，在講解的過程中結(jié)合課堂提問，以便使學(xué)生能主動的結(jié)合所學(xué)的專業(yè)知識和英語理解能力，對測繪專業(yè)英語有深刻的理解。Unit 9 Basic Statistical Analysis of Random Errors （隨機(jī)誤差的統(tǒng)計(jì)學(xué)基本分析）Random errors are those variables that remain after mistakes are detected and eliminated and all systematic err

6、ors have been removed or corrected from the measured values.（隨機(jī)誤差是在錯誤被察覺【detect】和消除【eliminate】后，并且所有系統(tǒng)誤差被從測量值中移除或修正后，保留下的那些變量【variable變量、變化n.】）They are beyond the control of the observer.（它們是觀測者無法控制的）So the random errors are errors the occurrence of which does not follow a deterministic pattern.（因此隨

7、機(jī)誤差是不遵循某個確定性【deterministic確定性的】模式【pattern】而發(fā)生的誤差）In mathematical statistics, they are considered as stochastic variables, and despite their irregular behavior, the study of random errors in any well-conducted measuring process or experiment has indicated that random errors follow the following empir

8、ical rules:（在數(shù)理統(tǒng)計(jì)【mathematical statistics】中，它們被當(dāng)成隨機(jī)變量【stochastic variable】，盡管它們的行為無規(guī)律，在任一正確的【well-conducted原意為品行端正的，這里指測量實(shí)驗(yàn)和活動是無誤的】測量活動和實(shí)驗(yàn)中，對的隨機(jī)誤差的研究顯示【indicate】隨機(jī)誤差遵循以下經(jīng)驗(yàn)法則【empirical rule】：）A random error will not exceed a certain amount.（隨即誤差不會超過一個確定的值）Positive and negative random errors may occur

9、 at the same frequency.（正負(fù)誤差出現(xiàn)的頻率相同）Errors that are small in magnitude are more likely to occur than those that are larger in magnitude.（誤差數(shù)值【magnitude量值、大小】小的比數(shù)值大的誤差出現(xiàn)可能性大【be likely to 可能】）The mean of random errors tends to zero as the sample size tends to infinite.（當(dāng)【as】樣本大小【sample size】趨近于無窮【infi

10、nite】時，隨機(jī)誤差的平均值趨近于0）In mathematical statistics, random errors follow statistical behavioral laws such as the laws of probability.（在數(shù)理統(tǒng)計(jì)中，隨機(jī)誤差遵循統(tǒng)計(jì)學(xué)的【statistical】行為【behavioral行為的】規(guī)律，如概率法則）A characteristic theoretical pattern of error distribution occurs upon analysis of a large number of repeated meas

11、urements of a quantity, which conform to normal or Gaussian distribution.（發(fā)生在一個量的大量重復(fù)觀測分析【analysisn.】中的誤差分布的一個特征理論模式，遵照【conform to遵照】正態(tài)或高斯分布）【在對一個量進(jìn)行大量重復(fù)觀測分析后，得到一個誤差分布的理論特征正態(tài)或高斯分布】The plot of error sizes versus probabilities would approach a smooth curve of the characteristic bell-shape.（誤差大小與【versu

12、s與、與的關(guān)系、與相對】概率的關(guān)系圖，接近一條光滑的特有的【characteristic特有的】鐘形曲線。）This curve is known as the normal error distribution curve.（這條曲線被稱為正態(tài)分布曲線）It is also called the probability density function of a normal random variable.（也叫做正態(tài)隨機(jī)變量【normal random variable】的概率密度【probability density】函數(shù)）It is important to notice that

13、 the total area of the vertical bars for each plot equals 1.（需特別注意的是，每個圖的條形圖總面積為1。）This is true no matter the value of n (the number of single combined measurements), and thus the area under the smooth normal error distribution curve is equal to 1.（無論【no matter】n（單一的聯(lián)合的測量數(shù)目【獨(dú)立觀測數(shù)】）是多少，在光滑的誤差正態(tài)分布曲線下的

14、面積都是1。）If an event has a probability of 1, it is certain to occur, and therefore the area under the curve represents the sum of all the probabilities of the occurrence of errors.（如果一件事的概率為1，它一定會發(fā)生，因此曲線下方的面積代表了所有誤差發(fā)生的概率。）A number of properties that relate a random variable and its probability density

15、 function are useful in our understanding of its behavior.（有許多工具【property】與隨機(jī)變量和它的概率密度函數(shù)有關(guān)，有助于我們理解它的行為）Mean and standard deviation are two most popular statistical properties of a random variable.（平均值和標(biāo)準(zhǔn)偏差就是兩個最常用的隨機(jī)變量的統(tǒng)計(jì)工具【property】）Generally, a random variable which is normally distributed with a m

16、ean and standard deviation can be written in symbol form as N(,2).（一般地，一個通常由平均值和標(biāo)準(zhǔn)偏差描述的隨機(jī)變量可以用符號【symbol】表示為N(,2)。They can be explained as follows.（【它們可以】解釋如下） Mean: The most commonly used measure of central tendency is the mean of a set of data (a sample).（平均值：最普遍應(yīng)用的中心趨向的估計(jì)【measure】就是一系列數(shù)據(jù)（一個樣本）的平均值

17、）The concept of mean refers to the most probable value of the random variable.（平均值的概念【concept】涉及到隨機(jī)變量的最或是值）It is also called by any of the several termsexpectation, expected value, mean or average. （還可以由其它幾個術(shù)語來稱呼它期望、預(yù)期值、平均值或平均值）The mean is defined as （平均值定義為）Where xi are the observations, n is the s

18、ample size, or total number of observations in the sample, and x is the mean which is also called most probable value (MPV).（xi是觀測值，n是樣本大小，或者叫樣本內(nèi)觀測值的總數(shù)，x是平均值，經(jīng)常被稱為最或是值（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【approximati

19、on】，可以很容易由一系列數(shù)據(jù)得到。）It can be shown that the arithmetic mean of a set of independent observations is an unbiased estimate of the meanof the population.（可以看出【It can be shown that】一系列獨(dú)立【independent】觀測值的算數(shù)平均值【arithmetic mean】是一個樣本【population】的期望值的無偏估計(jì)【unbiased estimate】。）Standard deviation is a numerica

20、l value indicating the amount of variation about a central value.（標(biāo)準(zhǔn)偏差是一個數(shù)值【numerical value】，指示【indicate】相對于中值的偏離）In order to appreciate the concept upon which indices【index的復(fù)數(shù)】 of precision devolve one must consider a measure that takes into account all the values in a set of data.（考慮一系列數(shù)據(jù)的所有值精度指標(biāo)

21、必需顧及一個量，這個量考慮到【takes into account考慮】一組【a set of】數(shù)據(jù)的所有值）Such a measure 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 be used, and this is called the variance2,（這個量是每個觀測值xi相對于平均值x 的離差【deviation】，也就是，(xi- x)，離差的平方的平均值被采用，稱之為方差

22、2） Where is the mean (expectation) of the population.（這里是對象總體【樣本】的平均值（期望值）。）The square root of the variance is called standard deviation . （方差的平方根被稱為標(biāo)準(zhǔn)差）Theoretically the standard deviation, which is the value on the X axis of the probability curve that occurs at the points of inflecxion【估計(jì)應(yīng)為inflexi

23、ons拐點(diǎn)】 of the curve, is obtained from an infinite number of variables known as the population.（理論上標(biāo)準(zhǔn)差，是概率曲線拐點(diǎn)的X軸坐標(biāo)，由無窮多的變量（被稱為樣本）得到）In practice, however, only a sample of variables is available and S is used as an unbiased estimator.（然而，實(shí)際上，只有變量的樣本是可以利用的，S被稱為無偏【unbiased】估計(jì)【estimator估計(jì)、估計(jì)者】。）Account

24、is taken of the small number of variables in the sample by using (n-1) as the divisor, which is referred to in statistics as the Bessel correction; hence, variance is（樣本中有限的【small小的】變量的計(jì)算，用n-1作為除數(shù)【divisor除數(shù)、約數(shù)】，在統(tǒng)計(jì)學(xué)中稱之為白塞爾修正；因此，變化【variance變化、不一致n.】如下：）To obtain an index of precision in the same unit

25、s as the original data, therefore the square root of the variance is used, and this also called the standard deviation S. （為了獲得與源數(shù)據(jù)一樣單位的精度指標(biāo)，方差的平方根被采用，又叫做標(biāo)準(zhǔn)差S）The standard deviation is the measure of the dispersion or spread of the random variable.（標(biāo)準(zhǔn)差是隨機(jī)變量的離差或離散的量度標(biāo)準(zhǔn)。）A survey measurement, such as

26、a distance or angle, after mistakes are eliminated and systematic errors corrected, is a random variable.（一個測量值，例如距離或角度，在錯誤被去除、系統(tǒng)誤差被修正后，就是一個隨機(jī)變量。）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 kn

27、own.（如果一段距離被測了20次，每次的測量值與永遠(yuǎn)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】隨機(jī)可變性，誤差被定義為隨機(jī)變量、測量值和常量之間的差值，也就是，誤差測量值【常量，這里估計(jì)是掉了

28、】。）And a correction (residual), 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，習(xí)慣上【in practice】是誤差的負(fù)值，定義為MPV和測量值之間的修正值，也就是改正值MPV測量值）When the so-called true values are available to compare with calcu

29、lated values, the mean square error (MSE) is given by （當(dāng)所謂的真值可以與計(jì)算值相比較時，誤差均方差（MSE）為：）In which xi is the measured value, x is the true value and n is the number of measurements.（其中xi是測量值，x是真值，n是觀測數(shù)）Propagation of errors (or error propagation): Much data in surveying is obtained indirectly from variou

30、s combinations of observations.（誤差傳播：測量的許多數(shù)據(jù)是間接由各種測量值綜合得到的【combination是名詞，這里翻譯時用到了詞性轉(zhuǎn)換】）For instance the coordinates of a line are a function of its length and bearing.（例如，一條直線的坐標(biāo)就是其長度和方位的函數(shù)）As each measurement contains an error, it is necessary to consider the combined effect of these errors on the

31、 derived quantity.（由于每項(xiàng)測量值都包含誤差，必需考慮這些源數(shù)據(jù)的誤差的聯(lián)合影響）Error propagation is one of the many aspects of analyzing errors.（誤差傳播是誤差分析的許多方面的其中一個）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 estimat

32、ed random errors in one or more identified variables that influence the precision of the quantity.（它是一個數(shù)學(xué)方法【process或者譯為 過程】，用來估計(jì)【estimate】在一個計(jì)算出的或間接測量的參量【quantity】中的期望隨機(jī)誤差【或偶然誤差】，該參量是在一個或多個確定的【identified】變量中由一個或多個限定或確定的偶然誤差引起的，影響該量的精度。）The general procedure is to differentiate with respect to each of the observed quantities in turn and sum them to obtain their tota