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Unit 1 Definition of Measurement and Measurement Theory 定义的测量方法和测量理论 1 Definition of Measurement 测量的定义 A possible operational description of the term measurement which agrees with our intuition is the following measurement is the acquisition of information the aspect of gathering information is one of the most essential aspects of measurement measurement are conducted to learn about the object of measurement the measurand This means that a measurement must be descriptive with regard to that state or that phenomenon in the world around us which we are measuring 一个可能的操 作描述这个术语的同意 我们凭直觉测量是下列的 测量信息获取 采集信息 的方面是最重要的方面进行测量 计量了解测量的对象 进行测量 这意味着一个 测量必须描述对于这种状态或这一现象在我们周围的世界我们衡量 There must be a relationship between this state or phenomenon and the measurement result Although the aspect of acquiring information is elementary it is merely a necessary and not a sufficient aspect of measurement when one reads a textbook one gathers information but one does not perform a measurement 必须有一个关系状态或现象和测量结果信息获取的角度 即使是 基础 那只是一个必要的和非充分方面的测量 当一个人阅读教科书 一个收集信 息 但是一个人不能进行测量 A second aspect of measurement is that it must be selective It may only provide information about what we wish to measure the measurand and not about any other of the many states or phenomena around us 测量的第二个方面 它必须被选择 只能提供有关我们所希望的那样 进行测量测量 而不是对任何其他的许多州或现象在我们身边 This aspect too is a necessary but not sufficient aspect of measurement Admiring a painting inside an otherwise empty room will provide information about only the painting but does not constitute a measurement 这相位也是必 须的 但并非任何足够的测量方面 Admiring 一幅画在一个否则空房间会提供信 息 只有这幅画作 但不构成测量 A third and necessary aspect of measurement is that it must be objective The outcome of the measurement must be independent of an arbitrary observer Each observer must extract the same information from the measurement and must come to the same conclusion This however is almost impossible for an observer who uses only his her senses Observations made with our senses are highly subjective Our sense of temperature for example depends strongly on any sensation of hot or cold preceding the measurement 第三个和必要的 方面 它必须被测量 结果客观测量必须独立于任意观测器提取每观察者必须之 测相同的信息 必须得出了相同的结论 这 然而 几乎不可能一个观察人士只使 用他 她的感官感觉是我们 Observations 我们高度主观的感觉 例如 取决于温 度有任何感觉热或冷的 measuremen 前 This is demonstrated by trying to determine the temperature of a jug of water by hand If the hand is first dipped in cold water the water in the jug will feel relatively warm whereas if the hand is first dipped in warm water the water in the jug will feel relatively cold Besides the subjectivity of our observation we human observers are also handicapped by the fact that there are many states or phenomena in the real world around us which we cannot observe at all e g magnetic fields or only poorly e g extremely low temperatures or high speed movement In order to guarantee objectivity of a measurement we must therefore use artefacts tools or instruments 这是证明了在调查里面的水的温度用手 如果手先用冷水浸泡到 瓶子里的水会感到相对的温暖 而若手第一蘸温水 水到瓶子里会感觉比较冷 除了我们观察的主体性 我们人类的观察家们也不识字而事实有许多州或者现象 在现实世界中 我们不能遵守我们周围磁场 如只 poorl 支 The task of these instruments is to convert the state or phenomenon under observation into a different state or phenomenon that cannot be misinterpreted by an observer In other words the instrument converts the initial observation into a representation that all observers can observe and will agree on 这些仪器的任务是把国家或现象观察进入一种不同的国家或现象 不能被误解被 观察者 换句话说 仪器将最初的观察到任何观测者都表示会同意能封锁 For the measurement instrument s output therefore objectively observable output such as numbers on an alpha numerical display should be used rather than subjective assessment of such things as colour etc Designing such instruments which are referred to as measurement systems is the field of measurement instrumentation 用来测量仪器的输出 因此 客观观察的输 出如数字显示 alpha numerical 应使用而不是主观评价诸如色彩 等 设计这样 的仪器都被称为量测系统 域 计量仪表 In the following we will define measurement as the acquisition of information in the form of measurement results concerning characteristics states or phenomena the measurand of the world that surrounds us observed with the aid of measurement systems instruments The measurement system in this context must guarantee the required descriptiveness the selectivity and the objectivity of the measurement 在下面 我们将定义测量信息获取的测量结 果不确定度的形式 对特征 国家或现象 世界上进行测量在我们周遭 观察与援 助的测量系统 仪器测量系统 在此背景下 必须保证所需的 descriptiveness 选择性和客观性的测量 We can distinguish two types of information information on the state structure or nature of a certain characteristic so called structural information and information on the magnitude amplitude or intensity of a certain characteristic so called metric information The acquisition of structural information is called a qualitative measurement the acquisition of metric information is called a quantitative measurement If the nature of the characteristic to be measured is not yet known it must be determined first by means of a qualitative measurement This can then be followed by a quantitative measurement of the magnitude of the respective characteristic 我们能 区分出两种类型的信息 信息对国家 结构或自然的一个特定的特点 所谓的结构 信息 信息在大小 振幅或强度一定的特点 所谓的度量信息 获得结构信息被称 为定性测量 获取信息度量称为定量测量 如果性质测量特点 还不知道的 它必 须实现 2 Measurement Theory In the previous section we have seen that measurements from the essential link between the empirical world and our theoretical abstract image of the world This concept forms the basis of a theory of measurement In this theory a measurement result is considered to be a representation of the actual empirical quantity Measurement theory treats measurements as a mapping of elements of a source set belonging to the empirical domain space see Fig 1 1 onto the elements of an image or outcome set which is part of the abstract range or image space 在上一节中我们 已经看到 测量来自必要的联系 我们的经验世界理论 抽象形象的世界 这观的 基础上测量理论 理论 讨论了测量结果被认为是代表了实际经验数 量 Measurement 理论对测量数据元素的地图源设置属于实证域空间 见图 1 1 的元素上一幅图像 whi 或结果 The quantity to be measured the measurand is an element of the source set For instance in the electrical domain we measure electrical current source set but only within a certain range of magnitude elements The result of the measurement process is abstract it forms an element of the image set in the abstract range space 测量的量进行测量 是一种元素的源设置情况 因为在电领域受到我们测量电流 但只有在一定范围内的大小 原理 测量过程的结果是抽象的 它形成了一个元 素的抽象的图像范围空间 For example the magnitude of the electrical current to be measured in the above example is by measurement assigned a certain number element out of the set of real numbers image set 例如 电流的大小来衡量在上面的例子中 通过测量 分配一定数量 元素 从套真 实数字 图像 In other words the elements of the source set are empirical characteristics of States and phenomena of the world around us the elements of the image set are symbols of the abstract image set of symbols The symbols can be numbers quantitative measurements but can also be for example names quantitative measurements 换句话说 元素的来 源是实证特点设置状态和我们周围的世界的现象 要素的图像的抽象符号图像集 象徵 符号可以是数字 定量测量 还可以为例 定量测量 名字 Restricting the definition of measurement further measurement theory states that measurement is the mapping of elements from an empirical source set onto elements of an abstract image set according to a particular transformation function The transformation function consists of the assignment algorithms results or procedures that define the representation of empirical quantities by abstract symbols 限制测量的 定义进一步 测量理论认为测量测绘的要素 从实证源固定在抽象的图像元素根 据特定的转换功能 转换函数由任务的算法 结果或程序确定表示的实证数量由 抽象符号 In practice the assignment algorithm rule or procedure is implemented by the employed measurement system The measurement system therefore determines the representation As stated earlier this representation must be done in a description objective and selective way Thus the image set must consist of elements measurement outcomes which are abstract symbols with a unique meaning about which by definition all observers agree 在实践中 分派算法 规则 程序是由受雇测量系统实施 测量系统因此决定表示 如前所述 这些表示都被做以描述 客观 有选择的 因此 对图像集必须包含的元素 测量结果 有抽象符号具有独特的意义 被定义 所有的观察家们也一致 A measurement must be descriptive In measurement theory this is described in terms of set theory the relations that exist between the elements of the source set must be maintained under the transformation in the image set for example larger than equal to and smaller than 一个测量必须描述了在测量理论从集理论存在的 关系成分之间的源设置下必须保持对图像集的转型中 例如 比 等于 和 小于 The set of relations between the elements of the source set is referred to as the relational system of the source set 之间的关系的 来源的元素将被称为关联系统 的源套 This empirical relational system determines the structure of the source set Likewise an abstract relational system determines the structure of the image set for instance the set of relational that apply to the set of integer numbers A measurement representation is now called descriptive if the relational system or structure of the empirical source set is invariant under the transformation measurement 本实证关系系统确定源的结构 同样地 抽象的关系系统确定图像的结构 例如 关系 适用于整数的数字 测量 表示 现在称为描述性如果关系系统或结构变化设置经验主义来源转换 下测 量 The measurement only represents that which is measured if the two relational systems are identical otherwise information is lost in the mapping An example is measuring with a very low resolution two different current magnitudes are mapped onto the same outcome and are indistinguishable from each other 测量测量只代表了 如果两个关系系统都 是相同的 否则资料遗失在映射 一个例子是测量一个非常低分辨率 两个不同电 流大小映射到相同的结果 与对方 Unit2 Measurement of Physical Quantity 物理量测量 The physical quantities listed bellow are often used in test and measurement technology The first 2 are commonly called as electrical quantities and the other are commonly called as electrical parameters Usually the sensors receive the information of quantities under measurement QUM and convert it into variation of electrical parameters or electrical potential which will normally be conditioned and then converted into the electrical quantities specially the current and sent to the A D converters 如下所示的物理量的常被用于测试和测量技术 第 2 通常被称为电子数量和其他通常被称为电气参数 通常传感器接收信息清单 QUM 测量 下 把它转化成电气参数的变化或电气 潜力 通常会条件 然后转化为电气数量 特别是当前的众长老 就差人到 A D 耐 Electrical potential difference 电气电位差 The primary standard for electrical potential difference used to be provided by an electrochemical standard cell the Weston standard cell The voltage of a Weston cell is approximately 1 01860 V at 20 C with an inaccuracy of 3X10 6 under optimal conditions Optimal conditions means a variation of temperature less than 10 3 K no load no vibrations or jolting The cell must remain in an upright position A Weston standard cell has a very long thermal after effect After the cell has been heated to 30 C it can take 6 months before it is totally stable within 0 3u V of the original value at 20degrees Furthermore a Weston cell will age resulting in an increase in the internal resistance R1 500 1000 欧 and a small decrease of a few uV in the output voltage during the first years 电气的基本标准的用于电位差由电化学标准电池的 韦斯顿标准电池电压成 大约 1 01860 韦斯顿细胞是五世在 20 C 的精度 在优 化的分析条件下 3X10 最优性条件温度的变化是指小于 10 3 钾 空载 没有振动或震动 细胞必须保持在一个垂直位置 一个韦斯顿标准电池的有很长 的热 after effect 在细胞被加热到 3 Electrical current 电流 lectrical current is standardized by measurement with an instrument called a current balance This device measures the electromagnetic force between two current carrying coils one fixed one moving by balancing it with the force of gravity acting on a known mass The force between the coils is given by F I 2dM dx in which M is the known mutual induction of the coils and x is the known distance between them The differential quotient dM dx is determined by known geometry of the coils 通过测量规范激励激光器阻抗电流被称为 用铁器当期资产 这种装置措施电 磁力在两个电流负载线圈 一个固定的 一个运动 平衡与重力的作用下 行动在 一个已知的质量 线圈间的力进行女 我 2dM dx M 是已知的相互感应的线 圈与 x 是已知的间距 鉴别商 dM 远程接收由已知的几何学的线圈 Electrical resistance 电阻 Standards of electrical resistance are resistors wound of special alloy wire giving a minimal temperature effect An example of such an alloy is evanohm consisting of 74 nickel 20 chromium and 6 aluminium and iron This alloy is frequently used for high resistance standards 10kQ For low resistance values 1Q manganine 86 Cu 12 Mn 2 Ni or constantan 54 Cu 45 Ni 1 Mn is often used Higher order resistance standards are kept at very accurately stabilised temperature by thermostats 标 准是电阻的特殊合金线电阻伤口给一个最小的温度效应的代表 An evanohm 是一 种合金 由 74 镍 20 chromium 和 6 aluminium 与铁 这种合金是经常用于高阻 标准 10kQ 低阻值 第 manganine 86 Cu 12 Mn 2 Ni 或 constantan 54 Cu 45 Ni 1 Mn 常常被 Higher order 电阻标准保持非常准确 稳定温度温控器 Capacitance 电容 It is possible to construct a capacitor from four coaxial cylinders whose capacitance only depends on the length of the cylinders Such a capacitor is particularly suitable as a standard of capacitance since only the length has to be determined accurately With the aid of optical interferometry this can be done extremely accurately These so called Thompson Lampard cylinder capacitors can achieve an inaccuracy of less than 10 8 它可以构建电容器的从四个同轴钢瓶 电容仅凭长度的汽缸 这样 的电容器是特别适合标准的电容 因为只有长度必须提供准确的参数 与援助的 光学干涉技术能够依此作成 非常准确 这些所谓的 Thompson Lampard 缸电容可 以达到不小于 10 8 A disadvantage however is the fact that the capacitance is small approximately 1 9pF per metre For lower order standards other configurations of electrodes are used which provide larger capacitance values 10 1000pF but also come larger uncertainties 然而 一个不利条件的人来说 这一事实 1 9pF 电容小 大约每米 其它结构的标 准为查核使用电极 提供较大的电容值 10 1000pF 但也来了更大的不确定性 Inductance 电感 Accurate standards of inductance are difficult to realise This is caused by the many parameters that determine the relatively complex of a coil all of which influence the accuracy of the inductor Furthermore power losses occur due to wire resistance proximately effects and eddy currents which add to inaccuracy Currently a available standards of inductance have an inaccuracy of about 10 5 精确的标准的电感难以想象 这是由于很多参数 确定的较为复杂的线圈 影响电感的准确性发生 损增益 再 说 由于线电阻 迟延直接影响和涡流 增加到不准确 目前提供标准的电感有一 个不大约 10 5 Frequency 频率 The standard of frequency is based on quantum mechanical effect that electrons in an atom can only occupy one of a limited number of energy levels If an electron jumps to a higher or a lower energy level the difference in energy E of the photon that is absorbed or a emitted respectively is related to the frequency of the photon by the expression E h f0 When atoms are irradiated with electromagnetic energy of frequency f0 many electrons will pass to higher energy levels 标准的频率是基于 量子力学效应原子电子之一只能占据数量有限的能量水平 如果一个电子的价格 涨到一个更高的或较低的能量水平 不同的能源 E 被吸收的光 分别或发出有关 光子的频率的表情 E h f0 当原子电磁能量下的频率 f0 许多电子将通过更 高能量水平 2 easurement of non physical quantities 测量非物理性的数量 Non physical quantities found in non technical fields are very difficult or even impossible to measure mainly because they are part of very complex systems people organizations societies etc Cardinal measurements can therefore very rarely be made when dealing with the non physical characteristics states or phenomena in such systems 物质中发现数量非 技术方面非常困难 甚至是不可能了 主要是因为他们测量非常复杂的系统的一 部分 人们 组织 学会等 因此基本测量很少会处理的非物质的特点 国家或 现象在这种系统中 When measuring complex systems or objects the measurand often also depends on all kinds of other quantities Usually the nature and magnitude of these dependencies are unknown Furthermore these parasitic quantities which influence the measurement result are not constant during the measurement making it impossible to correct any errors in the measurement This means that the measurement is no longer selective other factors are also being measured 在测量复杂系统或者对象 进行测量也经常 取决于其他各种数量 Usually 性质及大小并不为人所知 再说 这些依赖这些寄 生虫数量 影响了测量结果 在测量过程不是固定不变 让人很难矫正错误的测 量 这意味着测量不再是选择性 其他的因素也被测量 Non physical quantities are usually a part of a living organism or an organization of living beings It is essential to the nature of an organism or an organization that they maintain social cultural political interactions with their environment 物质通常数量的一部分或生物的一个组 织 它是必要的生物有机体的性质或组织让他们保持 社会 文化 政治 相互作 用与环境 For this reason it is usually not possible to perform an isolated measurement in the same way we can with inanimate things putting in a thermostat hooking up to a fixed supply voltage etc 基于这个 原因 它通常不可能完成一个孤立的测量同样地我们可以和无生命的东西 放进 一个温控器 猎艳以一个固定的电源电压等 It is for example not very practicable to isolate a section of the population from the rest of the world for the sake of an economic measurement conducted to verify the relationship between the scarcity and the price of consumer goods The object of the measurement continues to interact with its surroundings to an extent and in a manner that remains unknown 例如 不太可行的隔离 人群的一部分从世界的其他地方 为了进行经济测量 验证的缺乏和之间的关系 的消费品的价格 测量对象继续相互作用 它周围的环境中 在某种程度上 而在 某种程度上 但仍是未知的 These interactions obscure and corrupt the measurement results to some unknown degree depending on the sensitivity to these interference 这些互动晦涩 腐败的测试结果 一些不为人知的程度 根据这些敏感的干扰 Also the repetition of experiment is often not possible when dealing with such complex measurement objects With physical measurements we often repeat a measurement to see how reproducible it is and to determine the magnitude of random errors With non physical measurements however the object often behaves differently the second time because it no longer motivated to co operate has become tired etc Think for example of taking the same examination twice 同时 重复实验通常是不可能在处理复杂的测量各种物理测量物体我们经常重复 测量重复性看到并决定随机误差的大小以非物理性的测量 但对象第二次常常表 现出不同 因为它不再有动力去合作 已成为累了 等 Think 例如建立相同的检 查两次 For ethical political or financial reasons it is also usually not possible to freely modify variables to determine how they influence the measurement object for example increasing the scarcity of food in an economic community to determine the influence on the consumer s spending behavior 为职业道德 政治或经济的原因也通常不可能自由修改变 量来确定他们怎样影响测量对象 例如 提高食物的缺乏经济社会确定影响消费 者的消费行为 As opposed to a physical measurement the object of a non physical measurement is often conscious of being measured The mere fact that we measure influences the subject The subject will behave differently in a laboratory than in daily life An example for an often used and abused test animal the rat A measurement can even cause irrevocable processes in the object 我们反对一种物理测量 非物质的对 象测量被测经常意识到 单单是我们测量的影响 这个问题行为不同学科将在一 个实验室比的日常生活中 一种常用的榜样 几乎被滥用 试验鼠动物 测量 甚 至导致不可撤销的过程中 Certain psychological experiments for example can cause catatonic states in certain patients resulting in disorders or even chronic schizophrenia The effects measureme

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