Professional English for Building Environment& Equipment

1. Lecturer: Hongqiangli Email:lihongqiang2009@yahoo.com.cn Professional English for Building Environment& Equipment

2. Unit Thirteen Measurement Errors and Accuracy

3. Basic Concepts and Terms A measurable quantity is a property of phenomena, bodies, or substances that can be defined qualitatively and expressed quantitatively. Measurable quantities are also called physical quantities. Measurement is the process of determinating the value of a physical quantity experimentally with the help of special technical means called measuring instruments. The value of a physical quantity is the product of a number and a unit adapted for these quantities. The true value of a measurand is the value of the measured physical quantity, which, being known, would ideally reflect, both qualitatively and quantitatively, the corresponding property of the object. We shall use the term uncertainty to characterize the inaccuracy of a measurement result, whereas the term error is used to characterize the components of the uncertainty.

4. Basic Concepts and Terms The measurement error is the deviation of the result of measurement from the true value of the measurable quantity, expressed in absolute or relative form. If A is the true value of the measurable quantity and ˜A is the result of measurement, then the absolute error of measurement is ζ = ˜A − A. The absolute error is usually identified by the fact that it is expressed in the same units as the measurable quantity. Absolute error is a physical quantity, and its value may be positive, negative, or even given by an interval that contains that value. One should not confuse the absolute error with the absolute value of that error. For example, the absolute error −0.3 mm has the absolute value 0.3. The relative error is the error expressed as a fraction of the true value of the measurable quantity ε = (˜A − A)/A. Relative errors are normally given as percent and sometimes per thousand (denoted by ‰).

5. Measurement Error 测量误差 Measurement error may be defined as the difference between the true value and the measured value of the quantity. Systematic errors 系统误差Random errors 随机误差

6. What Causes Measurement Errors? Now that we know the types of measurement errors that can occur, what factors lead to errors when we take measurements? We can separate this category into 2 basic categories: instrument and operator errors. instrument errors 仪器误差 operator errors 操作误差

7. Instrument Errors Some basic information that usually comes with an instrument is: accuracy range response time sensitivity accuracy - this is simply a measurement of how accurate is a measurement likely to be when making that measurement within the range of the instrument. For instance a mercury thermometer that is only marked off in 10th's of a degree can really only be measured to that degree of accuracy.

8. Instrument Errors Some basic information that usually comes with an instrument is: accuracy range response time sensitivity range - instruments are generally designed to measure values only within a certain range. This is usually a result of the physical properties of the instruments, such as instrument mass or the material used to make the instrument. For instance a cup anemometer that measures wind speed has a minimum rate that is can spin and thus puts a limit on the minimum wind speed it can measure.

9. Instrument Errors Some basic information that usually comes with an instrument is: accuracy range response time sensitivity response time - if an instrument is making measurements in changing conditions every instrument will take time to detect that change. This again is often associated with the physical properties of the instrument. For instance a mercury thermometer taken from room temperature and put into boiling water will take some time before it gets to 100 oC. Reading the thermometer too early will give an inaccurate observation of the temperature of boiling water.

10. Instrument Errors Some basic information that usually comes with an instrument is: accuracy range response time sensitivity sensitivity - many instruments are have a limited sensitivity when detecting changes in the parameter being measured. For instance some cup anemometers, because of their mass cannot detect small wind speeds. The problem gets the worse as the anemometer gets heavier.

11. Operator Errors These errors generally lead to systematic errors and sometimes cannot be traced and often can create quite large errors. Example－－Measurement Location Errors Data often has errors because the instrument making the measurements was not placed in an optimal location for making this measurement. A good example of this, is again associated with measurements of temperature. Any temperature measurement will be inaccurate if it is directly exposed to the sun or is not properly ventilated. In addition, a temperature device place too close to a building will also be erroneous because it receivesheat from the building through radiation.

12. Quality Indicator: Precision of measurement Precision is the degree of repeatability (or closeness) that repeated measurements of the same quantity display, and is therefore a means of describing the quality of the data with respect to random errors.

13. Quality Indicator: Accuracy of measurement Accuracy is the degree of closeness (or conformity) of a measurement to its true value.

14. Quality Indicator: Reliability of measurement reliability=precision+accuracy

16. mean percentage error (MPE) mean absolute percentage error (MAPE) mean bias error (MBE) mean absolute bias error (MABE) root mean square error (RMSE). where Him is the ith measured value, Hicis the ith calculated value and n is the total number of the observations.

17. Linear association Correlation can be used to summarize the amount of linear association between two continuous variables x and y If there is a strong linear association between the two variables, then the points lie nearly in a straight line, like this: A positive association between the x and y variables (i.e. an increase in x is accompanied by an increase in y) is shown by the scatterplot having a positive slope. Similarly, a strong negative association (i.e. an increase in x is accompanied by a decrease in y) is shown by points with a negative slope.

18. The strength of linear association, is summarized by the correlation coefficient, defined as: 标准差

19. Example - Calculation of R for students' heights and weights

20. R=0.72 R=0.28 R=0.89 R=0.99

21. How about this ?

22. Engineers are increasingly being asked to monitor or evaluate the efficiency of a process or the performance of a device. 1. Measurement Errors, Accuracy, and Precision three kinds of errors how to characterize measurements and instrumentation as being of high or low precision 2. Estimating Measurement Uncertainty multi-sample experiments single-sample experiments In this case we refer to an "uncertainty distribution" rather than a "frequency distribution".

23. Frequently used words and phrases: uncertainty 不确定性 measurement error 测量误差 true value 真值 measured value 测量值 recording errors 记录误差 systematic or fixed errors 系统误差 accidental or random errors 随机误差 measurement system 测量系统mean value 平均值 frequency distribution 频率分布 probability density function 概率密度函数 distribution function 分布函数 discrete probability distribution 离散型概率分布 continuous probability densities 连续型概率密度 conditional probability 条件概率 Law of Large Numbers 大数定律 Central Limit Theorem 中心极限定律

24. 1. Results are often derived from the combination of values determined from a number of individual measurements. • 2. Unfortunately, every measurement is subject to error, and the degree to which this error is minimized is a compromise between the (overall) accuracy desired and the expense required to reduce the error in the component measurements to an acceptable value. • 3. Good engineering practice dictates that an indication of the error or uncertainty should be reported along with the derived results. be derived from…: 从…中得到 be subject to…: 受…支配 compromise:妥协 折衷 dictate: 要求 规定 indication: 指标

25. 4.Implicit in this assumption is that the worst-case errors will occur simultaneously and in the most detrimental fashion. • 5. A more realistic estimate of error was presented by Kline and McClintock based on single-sample uncertainty analysis. • 6. The following discussion is meant to provide an insight into measurement uncertainty rather than a rigorous treatment of the theoretical basis. implicit:暗示 the worst-case error: 最大误差 detrimental: 有害的 single-sample uncertainty analysis: 单样本不确定性分析 insight into…:对…的洞察力或深入的理解 rigorous:严格的

26. 7. The errors that occur in an experiment are usually categorized as mistakes or recording errors, systematic or fixed errors, and accidental or random errors. 8. Systematic errors may result from incorrect instrumentcalibrations and relate to instrument accuracy (the ability of the instrument to indicate the true value). 9. Random errors cause readings to take random values on either side of some mean value. They may be due to the observer or the instrument and are revealed by repeated observations. be categorized as: 可分为 recording errors: 记录误差 systematic or fixed errors: 系统误差 accidental or random errors: 随机误差 instrument calibration: 仪表刻度 instrument accuracy: 仪表精度 indicate: 指示 显示 mean value: 平均值 reveal: 显现 显示

27. 10. In measurement systems, accuracy generally refers to the closeness of agreement of a measured value and the true value. 11. All measurements are subject to both systematic (bias) and random errors to differing degrees, and consequently the true value can only be estimated. 12. To illustrate the above concepts, consider the case shown in Fig. 13-1, where measurements of a fixed value are taken over a period of time. accuracy: 准确性 refer to: 指的是 differing degree: 不同程度 true value: 真值 illustrate: 举例说明 case: 例子 案例

28. 13. If we further grouped the data into ranges of values, it would be possible to plot the frequency of occurrence in each range as a histogram. • 14. Figure 13.3 is often referred to as a plot of the probability density function, and the area under the curve represents the probability that a particular value of x (the measured quantity) will occur. • 15. The total area under the curve has a value of 1, and the probability that a particular measurement will fall within a specified range (e.g., between x1 and x2 ) is determined by the area under the curve bounded by these values. grouped into: 按…分类 frequency of occurrence : 出现频率 histogram: 柱状图 直方图 probability density function: 概率密度函数 area: 面积 fall within: 落入 bounded by: 受…限制 以…为界

29. histogram

30. 16. Figure 13-3 indicates that there is a likelihood of individual measurements being close to xm , and that the likelihood of obtaining a particular value decreases for values farther away from the mean value, xm. • 17. The frequency distribution shown in Fig. 13-3 corresponds to a Gaussian or normal distribution curve, the form generally assumed to represent random measurement uncertainty. • 18. There is no guarantee that this symmetrical distribution, indicating an equal probability of measurements falling above or below the mean value, xm , will occur, but experience has shown that the normal distribution is generally suitable for most measurement applications. likelihood: 可能性 frequency distribution: 频率分布 Gaussian or normal distribution: 高斯分布 正态分布 guarantee: 保证 证明 symmetrical distribution: 对成分布 unsymmetrical: 非对称的

32. 19. In analyzing these results we may apply standard statistical tools to express our confidence in the determined value based on the probability of obtaining a particular result. • 20. If experimental errors follow a normal distribution, then a widely reported value is the standard deviation, σ. There is a 68% (68.27%) probability that an observed value x will fall within ± σ of xm (Fig. 13-3). • 21. In reporting measurements, an indication of the probable error in the result is often stated based on an absolute error prediction [e.g., a temperature of 48.3±0.1℃ (based on a 95% probability)] or on a relative error basis [e.g., voltage of 9.0 V ±2% (based on a 95% probability)]. statistical tool: 统计工具 confidence: 信心 信任 standard deviation: 标准偏差 observed value: 观测值 测量值 indication: 指标 state: 表达 陈述 absolute error: 绝对误差 relative error: 相对误差

33. 22. Based on the previous discussions we may characterize measurements and instrumentation as being of high or low precision. • 23. The low-precision measurements have a wider distribution and are characterized by a greater standard deviation, ±σlp, compared with the high-precision measurements, ±σhp. • 24. Therefore, in the absence of bias or systematic error, the mean of a large sample of low-precision measurements theoretically indicates the true value. characterize as: 描述为… low-precision measurement: 低精度测量 high-precision measurement:高精度测量 in the absence of: 缺少 mean: 平均值 a large sample: 大量样本

34. 25. The previous discussion, illustrating the concept of random measurement error, has not addressed the effects of systematic or fixed (bias) errors. • 26. In reality, even though a high probability exists that an individual measurement will be close to the mean value, there is no guarantee that the value of the mean of the large sample of measurements will be the true value (Fig. 13-5). • 27. An example of a source of systematic error is a pressure gauge needle that is bent (i.e., not zeroed). address：指出 exist: 存在 pressure gauge needle: 压力表指针 bent: 弯曲的 偏离的 zero: 指零

36. 28. Multi-sample experiments are those in which, for a given set of the independent experimental variables, the readings are taken many times. 29. If we could repeat our tests many times, with many observers and a variety of instruments, we could apply statistics to determine the reliability of the results as in the previously discussed methods. 30. Single-sample experiments are those in which, for a given set of experimental conditions, the readings are taken only once. These are typical in engineering, where financial or time constraints limit the number of repetitions of a particular test. multi-sample experiment: 多样本实验 set: 系列 independent experimental variable: 独立测量变量 statistics: 统计学 single-sample experiment: 单样本实验

37. 31. The experimenter also expresses the degree of confidence in the stated uncertainty based on "odds," in a manner analogous to the standard deviation. odds: 几率 set: 系列 analogous to: 类似于