unit 8测量中的误差
Unit 8 Errors in Measurement
(测量工作中的误差)
Measurements are defined as observations made to determine unknown quantities.
(测量被定义为确定未知量【quantity 】的观测)
They may be classified as either direct or indirect.
(它们可以被分为直接观测和间接观测)
A direct measurement is one where the reading observed represents the quantity measured, without a need to add, take averages or use geometric formulas to compute the value desired.
(直接观测就是观测读数即代表了【represent 代表、描述】测量量,不需要另外加、取平均或利用几何【geometric 几何的】公式【formulas 】来计算出所需【desired 想得到的】值。)
Determining the distance between two points by making a direct measurement using a graduated tape is an example of direct measurement.
(用一把刻度尺直接确定两点之间的距离,就是一个直接观测的例子)
An indirect measurement requires calculation and can be determined from its mathematical relationship to direct measurements when it is not possible or practical to make direct measurements.
(间接观测需要计算,当直接观测是不可能或不实际【practical 实际的】时 ,可以利用它与直接观测量之间的数学关系来确定。)
For example, station coordinates can be mathematically computed by measuring angles and lengths of lines between points directly.
(例如,测点【station 测点】坐标可以由直接测得的点之间直线的角度和长度来计算)
Therefore the indirect measurements (computed station coordinates) contain errors that were present in the original direct observations and propagated (distributed) by the computational process.
(因此,这个间接测量值(计算出的测点坐标)包含了初始【original 】直接观测出现【present 】的和由计算过程传播【propagate 】(散播的)的误差。)【that 后面全都是修饰errors 的】
This distribution of errors is known as error propagation.
(这种误差的散播被认为【be known as被称为】误差传播)
Also, it is the indirect nature of measurements that forces the need to often apply some rather sophisticated mathematical procedures to analysis of errors and thus determine a “best value” to represent the size of the quantity. (同样,间接测量的特性需要【forces the need to使„„成为需要】经常应用一些更复杂的数学方法【procedure 】来分析误差并从而确定“最佳值”来代替【represent 代替、代表、扮演、表现】测量值的大小)
It can be stated unconditionally that all measurements, no matter how carefully executed, will contain error, and so the true value of a measurement is never known, and the exact sizes of the errors present are always unknown.
可以绝对地【unconditionally 无条件地】说【state 声明】,所有测量工作,无论多么仔细的实行【execute 】,也会包含误差,因此测量的真值是永远不知道的,出现【present 出现】的确切的【exact 】误差大小也永远不知道 Even with the most sophisticated equipment, a measurement is only an estimate of the true size of a quantity. (即使使用最复杂精密的装置,测量值也仅仅是一个量的真值的估计【estimate 】)
This is because the instruments, as well as the people using them are imperfect, because the environment in which the instruments and people operate influences the process, and because the behavior of people, instruments, and the environment cannot be fully predicted.
(这是因为同使用它们的人一样,仪器是不完美的【imperfect 】,仪器和人的操作环境影响会观测过程,并且人的行为,仪器,和环境不能完全预知【predicte 】)
However, measurements can approach their true values more closely as better equipment is developed, environmental conditions improve and observer ability increases, but they can never be exact.
(然而,当【as 】仪器的改进,环境条件改善和观测者技术【ability 】的进步时,测量可以非常接近它们的真值,但是它们永远不能达到真值)
By definition, an error is the difference between a measured value for any quantity and its true value.
(根据【By 】定义,误差是某一量的测量值和它的真值之间的差值。)
The sources of errors fall into three broad categories which are described as follows:
(误差来源分成【fall into分成、属于、落入】三个主要的【broad 】类型【category 】,描述如下:)
Instrumental Errors.(仪器误差)These errors are caused by imperfections in instrument construction or adjustment. (这种误差由仪器的结构和调节装置不完整性引起)
For example, the divisions on a theodolite or total station instrument may not be spaced uniformly.
(例如,经纬仪或全站仪中的刻度【divisions ,division 原意指分离、分开,这里指刻度】没有被均匀地【uniformly 】分划【即刻度分划不均】)
These error sources are present whether the equipment is read manually or digitally.
(不论是人工【manually 人工地】读取还是数字式读取,这种误差源均会出现)
Natural Errors.(自然【环境】误差)These errors are caused by variation in the surrounding environment conditions, such as atmospheric pressure, temperatures wind, gravitational fields, and magnetic fields, etc.
(这种误差是由周围环境条件的变化【variation 】引起的,如大气压力,温度,风力,重力场,和磁场)
Personal Errors.(人为误差)These errors arise due to limitations in human senses, such as the ability to read a micrometer or to center a level bubble.
(这种误差的出现【arise 出现v. 】是由于【due to 由于adv. 】人类的感官局限性【limitation 局限性】,比如读取千分尺和对中水平气泡的能力)
The sizes of these errors are affected by personal ability to see and by manual dexterity.
(这种误差的大小受到人眼观察能力和手的灵活性【dexterity 灵活n. 】的影响)
These factors may be influenced further by temperature, insects, and other physical conditions that cause humans to behave in a less precise manner than they would under ideal conditions.
(这种因素受温度、蚊虫【insect 虫】和其它引起人不精确行为的自然条件的影响,使得操作者在这种环境中的行为精度较理想条件下更低)
From the discussion thus far it can be stated with absolute certainty that all measured values contain errors, whether due to lack of refinement in readings, instabilities in environmental conditions, instrumental imperfection or human limitations.
(从以上【thus far 迄今】我们的讨论中,可以绝对确定的【certainty 确定n. 】说【state 声明】,所有测量值都有误差,不论是归咎于【due to 归于】读数缺乏精确、环境条件的不稳定性【instability 】、仪器的不完整性
【imperfection 】还是人的局限性【limitation 】)
Some of these errors result from physical conditions that cause them to occur in a systematic way, whereas others occur with apparent randomness.
(这些误差中有些由物理条件产生【result from由„„产生】的,使它们以系统的方式发生【表现为系统性】,而【whereas 】其它的表现为显著的随机性【randomness 】)
Accordingly, errors are classified as either systematic or random.
(因此【Accordingly 】,误差分为系统误差和随机误差【偶然误差】)
But before defining systematic and random errors, it is helpful to define mistakes.
(但是在定义体统误差和随机误差前,先来定义下错误对我们很有帮助)
These three terms are defined as follows: (下面是这三个术语的定义)
1、Mistakes. (错误) Mistakes or blunders (gross errors) actually are not errors because they usually are so gross in magnitude compared to the other two types of errors.
(错误或粗差【blunder 大错误,gross 粗的】实际上不是误差,因为它们相对于其它两种误差在量级【magnitude 大小、量级】上通常太粗了)
Carelessness, inattention, improper training, bad habits, poor judgment, adverse measuring or observing conditions,
and various negative attitudes and emotions are the traces or the common reasons for mistakes.
(粗心、疏忽、不恰当的【improper 】训练、不好的习惯、错误的判断、不利的【adverse 不利的】观测条件,和各种消极态度和情绪是引起错误的普遍原因【trace 线索、轨迹】)
They are not classified as errors and must be removed from any set of observations.
(它们不能被分进误差里,必需从观测中从予以移除)
Typical examples of mistakes are omitting a whole tape length when measuring distance, sighting the wrong target in a round of angles, writing down 27.55 for 25.75 in recording.
(错误的典型的例子如测距时遗漏掉了一个尺段的长度,在测一系列【in a round of 】角时瞄错了目标,在记录时将27.55写成了25.75)
Therefore great care must be taken to obviate them.(因此必需非常仔细的消除它们)
Mistakes will never be completely eliminated from measurements, but surveyor ’s careful, attentive, conscientious attitude can reduce the mistakes in most cases.
(错误永远不能从测量中完全排除【eliminate 】,但是在大多数情况下【in most cases】测量者的细心、专心、负责的【conscientious 尽责的】态度能够减少错误。)
Through proper training and development of good work habits, development and maintenance of positive attitudes, and understanding the theory and practice involved with the variable being measured, mistakes can be controlled and practically eliminated.
(通过恰当的训练和改善好的工作习惯,保持和改进积极的态度,以及对所测变量【variable 】理论和实践上的理解,错误可以得到限制【control 】和大致【practically 大致、几乎】消除)
2. Systematic Errors.(系统误差)
Systematic Errors are defined as those errors whose magnitude and algebraic sign can be calculated and applied as a correction to the measured quantity, or these errors follow some physical law and thus can be predicted.
(系统误差定义为,大小【magnitude 】和符号【algebraic sign代数符号】均可以被计算,并当作修正值应用在观测量上,这些误差遵循某些物理法则【physical law】因而可以被预知【predicte 】)
Some systematic errors are removed by some correct measurement procedures (e.g. , balancing backsight and foresight distances in differential leveling to compensate for earth curvature and refraction).
(有些系统误差可以由某些恰当的测量程序来消除(举例来说,在微差水准测量中使前后视距相等来低偿
【compensate 】地球曲率和折光)
Others are removed by deriving corrections based on the physical conditions that were responsible for their creation (e.g., applying a computed correction for earth curvature and refraction on a trigonometric leveling observation).
(有些系统误差则是利用推出【derive 得来、得出、推出】改正值来消除,【based on后面是讲改正值怎么得到】改正值是基于它们产生的原因的物理条件推出(例如,对于三角高程测量,加以地球曲率和大气折光的计算改正)
Surveyors should know how to deal with systematic errors.
(测量者应该知道怎样处理体统误差)
The first requirement is to recognize and accept the possible existence of errors.
(第一个要求是认可并承认误差的存在可能性)
Next, identify the various sources that might be affecting a reading systematically, then, determine what the “system ” is. (接下来,辨别可能系统地影响到读数的不同的来源,然后确定这个“系统”是什么。)
Is it a constant, linear, or in proportion to the size of the quantity being measured? Or, does it follow some other mathematical relationship? Is there some physics involved?
(它是常量【constant 】?是线性的【linear 】?还是和被测量的大小成比例【in proportion to】?还是,它遵循其它一些数学关系?和物理过程有关吗?)
Once systematic errors discovered and quantified, the errors can be essentially compensated by certain processes of measuring or corrected to reduce their effect.
(一旦系统误差被发现和量化【quantify 】,误差就可以得到实质的【essentially 实质地】低偿,【by 后面是低偿
的方法】利用某一【certain 某一个】测量过程或者修正来减少它们的影响)
Careful calibration of all instruments is an essential part of controlling systematic errors.
(仪器的仔细的校准【calibration 校准n. 】,是控制系统误差的必要方面)
3. Random Errors.(随即误差)
Random (also known as accident) errors are introduced into each measurement mainly because of human and instrument imperfections as well as uncertainties in determining the effects of the environment on measurements. (随机(也叫偶然)误差存在于每个测量工作中,主要因为人和仪器的不完美,以及环境对测量工作的影响的不确定性)
After all mistakes and systematic errors have been removed from the measured values, the random errors remain. (在所有的错误和系统误差被移除出测量值后,剩下的误差就是随机误差)
In general, random errors are unavoidable and relatively small.
(通常【In general】,随即误差是不可避免的并且相对较小)
They usually do not follow any physical law, but follow random patterns, or the laws of “chance ”.
(它们通常并不遵循任何物理法则,但却遵循随机模式【pattern 模式、式样】,或概率法则)
They have unknown signs and are as likely to be negative or positive.
(它们符号不可知,可能是正或是负)
The magnitude of such an error is unknown, but it can be dealt with and estimated according to the mathematical laws of probability.
(这样的【such 】误差的大小【magnitude 】未知,但是可以依照【according to】数学的概率论【laws of probability概率论】来处理和估计【estimate 】)
Examples of random errors are (a) imperfect centering over a ground point during distance measurement with an EDM instrument, (b) bubble not centered at the instant a level rod is read, and (c) small errors in reading graduated scales.
(随机误差的例子如(a)在使用EDM 测距时没有完全【imperfect 有缺点的、未完成的】对中地面点,(b) 在水准尺上读数时【at the instant在„„时】气泡没有居中 (c)读刻度尺时的小误差)
Understanding the nature of random errors helps to understand why random errors are never really fully corrected, since the observation of the physical phenomena contains personal, random errors.
(对随机误差特性的理解有助于理解为什么随机误差永远不能真正【really 】完全的【fully 】修正,因为对物理现象的观测包含了人为误差和随机误差)
Thus, measurements have “uncertainties ” or random errors that remain unquantifiable.
因此,测量具有不确定性,或者随机误差难以量化
Random errors are dealt with by controlling or managing them.
处理随机误差的方法是限制【control 和manage 这里都是限制的意思】它们
It is a quality control process. They cannot be corrected or eliminated, only minimized and controlled.
(这是一个质量控制过程。它们不能被修正或消除,只能最小化和限制)