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Basic dataStandard ID: DL/T 1961-2019 (DL/T1961-2019)Description (Translated English): Calculation method of uncertainty in flow measurement of power plant Sector / Industry: Electricity & Power Industry Standard (Recommended) Classification of Chinese Standard: J75 Classification of International Standard: 27.060.30 Word Count Estimation: 30,32 Date of Issue: 2019-06-04 Date of Implementation: 2019-10-01 Quoted Standard: GB/T 27759-2011; ISO 772; ISO/TR-7066-1; ISO/TR-7066-2 Issuing agency(ies): National Energy Administration Summary: This standard specifies the uncertainty calculation methods for the linear and nonlinear relationships in the flow measurement of thermal power plants in the process of calibration and use. This standard applies to the flow measurement of various closed pipelines or open channels. DL/T 1961-2019: Calculation method of uncertainty in flow measurement of power plant---This is a DRAFT version for illustration, not a final translation. Full copy of true-PDF in English version (including equations, symbols, images, flow-chart, tables, and figures etc.) will be manually/carefully translated upon your order.Calculation method of uncertainty in flow measurement of power plant ICS 27.060.30 J 75 People's Republic of China Electric Power Industry Standard Calculation Method of Uncertainty of Flow Measurement in Thermal Power Plant Refractory materials for boilers in thermal power plants 2019-06-04 released 2019-10-01 implementation Issued by National Energy Administration Table of contentsForeword...II 1 Scope...1 2 Normative references...1 3 Terms and definitions...1 4 Parameter symbols...2 5 General principles of uncertainty evaluation...3 6 Calculation method of uncertainty in independent measurement...4 7 Linear fitting and uncertainty calculation method...5 8 Non-linear fitting and uncertainty calculation method...10 Appendix A (Normative Appendix) Calculation of Standard Deviation of General Function...13 Appendix B (Informative appendix) Calculation example of open channel calibration...14 Appendix C (informative appendix) Uncertainty calculation examples of closed pipeline flow calibration...19 Appendix D (Normative Appendix) Regression Method...26 Appendix E (Informative Appendix) Orthogonal Polynomial Curve Fitting...29ForewordThis standard was drafted in accordance with the rules given in GB/T 1.1-2009 "Guidelines for Standardization Work Part 1.Standard Structure and Compilation". Please note that certain contents of this document may involve patents. The issuing agency of this document is not responsible for identifying these patents. This standard was proposed by the China Electricity Council. This standard is under the jurisdiction of the Power Plant Steam Turbine Standardization Technical Committee. Drafting organizations of this standard. Xi'an Thermal Power Research Institute Co., Ltd., Xi'an Xire Energy Saving Technology Co., Ltd. The main drafters of this standard. Gao Dengpan, Zeng Lifei, Yang Rongzu, Qi Wenyu, Zhang Yonghai, Yu Xiaobing, Gu Weiwei, Zhu Pengbo, Shi Hui, Wang Ting, Gao Qing, Xue Chaonan, Mu Qiwei. This standard is formulated for the first time. The opinions or suggestions during the implementation of this standard are fed back to the Standardization Management Center of the China Electricity Council (Baiguang Road, Beijing) Two Article No. 1, 100761) Calculation Method of Uncertainty of Flow Measurement in Thermal Power Plant1 ScopeThis standard specifies the uncertainty calculation method for the linear and non-linear relationship of thermal power plant flow measurement during calibration and use. This standard applies to flow measurement of various closed pipelines or open channels.2 Normative referencesThe following documents are indispensable for the application of this standard. For dated reference documents, only the dated version applies to this standard. For undated reference documents, the latest version (including all amendments) is applicable to this standard. GB/T 27759-2011 fluid flow measurement uncertainty evaluation procedure ISO 772 Hydraulic Measurement-Vocabulary and Symbols ISO -TR-7066-1 Estimation of Uncertainty in the Calibration and Use of Flow Measuring Devices --Part 1.Linear calibration relationship ISO -TR-7066-2 Uncertainty Estimation of Calibration and Use Method of Flow Measuring Device--Part 2.Nonlinear Calibration Relation3 Terms and definitions3.1 Calibration graph Certain response parameters and flow functions of the flowmeter are points drawn from the coordinates. 3.2 Confidence limits The (confidence) upper and lower limits of the observed or calculated value, the estimated interval of the overall parameter constructed by the sample statistics. 3.3 Correlation coefficient An index indicating the degree of linear relationship between two variables. 3.4 Variance Characterize the data distribution, measure the degree of deviation between the variable value and the expected value, defined as 3.5 Covariance The expectation of the overall error between two variables is defined as 3.6 Error of measurement The difference between the measured value and the true value, including systematic and random errors. 3.7 Random error The difference between the measurement result and the average result of a large number of repeated measurements for the same measurement. 3.8 Systematic error Under repeatability conditions, the difference between the average value and the true value of the measured result from an unlimited number of measurements on the same measured. 3.9 Spurious error The error under the specified conditions. 3.10 Residual Refers to the difference between the actual observed value and the estimated value. 3.11 Sample (experimental) standard deviation The dispersion measure of the average value of the same measured n times, defined as 3.12 Uncertainty uncertainty A parameter associated with the measurement result, used to characterize the dispersion of the measured value that is reasonably assigned. 3.13 Individual measurement Only need to measure a single variable measurement process. 3.14 Unbiased fitting The fitting curve can truly reflect the distribution trend of the data and is used to evaluate the excellent characteristics of the degree of fitting.4 Parameter symbol4.1 Parameter symbol definition The symbols and measurement value units in this standard shall meet the requirements of Table 1. 4.2 Definition of upper and subscripts of parameter symbols The definition of superscript and subscript of parameter symbols in this standard shall meet the requirements of Table 2.6 Calculation method of uncertainty in independent measurement6.1 Calculation of random uncertainty 6.1.1 List the source of uncertainty for each variable and make a table. The table should include all the errors in the measurement and list the random Error term and system error term. 6.1.2 For variable values determined by direct measurement, formula (2) or formula (3) can be used to calculate the standard deviation. 6.1.3 Substituting the standard deviation calculation result into equation (4), the random uncertainty of a specific t value of the measured x can be obtained. 6.1.4 In order to improve the accuracy of the assessment, sufficient data points must be taken. 6.1.5 When the variable is the sum or difference of multiple independent measurement results, calculate the overall standard deviation according to the following formula. 6.1.6 For more complex functions, such as the product or quotient between the dependent variable and the independent variable, the standard deviation should be calculated in accordance with Appendix A Calculate, and then substitute equation (4) to calculate the corresponding uncertainty. 6.2 Calculation of system uncertainty 6.2.1 The indeterminate component of the system error should be evaluated based on the past valid calibration data and historical records. 6.2.2 When the variable is the sum of multiple independent measurement results, and the sign of each component is uncertain, the system error is calculated by the following formula. 6.2.3 For more complex functional relations, the system error limit shall be applied to the method given in Appendix A, replacing the variance term in the formula with 2, eS i. 6.2.4 When the sources of all uncertainties are determined, and each variable is combined with random uncertainty and system uncertainty, complete The evaluation process. 6.2.5 Refer to Appendix B and Appendix C for calculation examples of uncertainty evaluation of flow measurement in open channels and closed pipelines.7 Linear fitting and uncertainty calculation method7.1 The linear judgment of the calibration chart In order to determine whether the fitted value and the measured value can fit unbiasedly, the measurement result and the residual error of the fitted straight line should be observed, and the following method should be used to obtain Get an approximate straight line. 7.2 Linearization method of calibration curve 7.2.1 If the linearity judgment in Section 7.1 shows that the calibration chart is in the form of a curve, consider the following two methods for linearization. a) The first method is variable replacement, which is only applicable to the nature of mathematical function relationships between variables, and the form of conversion depends on the mathematical expression The formula itself. For example, for open channel calibration, the relationship between water level and flow can be expressed as. 7.2.2 After the linearization is completed, the linear judgment of the calibration icon described in 7.1 shall be repeated. 7.3 Best linear fit 7.3.1 According to the calculated value of the two standard deviations in 7.1, calculate the ratio according to formula (14), 7.3.2 Least Squares Method a) If the error of the independent variable is negligible compared with the error of the dependent variable, the least square method is used to fit the calibration straight line. The following formula is calculated. 7.4 Fitting the best weighted curve 7.4.1 When the variance of y changes with the value of x, a weighted regression analysis method is required. 7.4.2 When the variance of each variable is known, the weight coefficient ci can be calculated according to formula (30). 7.5 The method of determining the fitted straight line when y is independent of x 7.5.1 When the slope of the calibration curve is zero, that is, y is a constant within the variation range of x, the calibration curve becomes a horizontal straight line, and the calibration curve Simplify to the average value of yi. which is 7.6 Calculation of Random Uncertainty 7.6.1 The random uncertainty of the fitted straight line at x=xk is calculated as follows. 7.7 Calculation of system uncertainty 7.7.1 According to the principles given in Section 6, calculate the system uncertainty during the calibration process, and use equation (36) to calculate. 7.7.2 Random uncertainty and system uncertainty can be synthesized by the following two formulas. 7.8 Evaluation of Uncertainty of Measurement Results 7.8.1 The additional uncertainty caused by inaccurate positioning on the fitted straight line, and other additional uncertainty introduced by the increase or decrease of data The degree of certainty should be evaluated using the method given in GB/T 27759-2011. 7.8.2 Using the URSS model to synthesize the random uncertainty and the system uncertainty, the total uncertainty in the measurement process is expressed as URS(y�), which can be Calculate as follows. 7.8.3 When the slope of the fitted straight line is 0, the flow rate is obtained by the product of the output function of the flowmeter and the coefficient independent of the flow rate. In the additional uncertainty, equation (39) is simplified to. 7.8.4 When the slope of the fitted straight line is not equal to 0, the iterative method is required to calculate the flow rate. In order to iterate, the initial estimate of the fitting coefficient is used To obtain the initial calculation value of the flow rate, and then use the calculated flow rate to obtain a more accurate calibration coefficient. Repeat this process until the flow rate is preset The valuation no longer undergoes major changes. In this case, any measurement error of the flowmeter will introduce the error of the coefficient used. Therefore, the total The uncertainty of should be calculated according to equation (39). 7.8.5 When the use conditions are different from the calibration conditions, such as system measurement conditions, fluids, devices, etc., the measurement will be further increased The uncertainty. In this case, the confidence limit of each situation needs to be evaluated. 8 Non-linear fitting and uncertainty calculation method 8.1 Basic principles of nonlinear fitting methods 8.1.1 If the linear fitting method cannot be used, a polynomial method should be used to establish a nonlinear calibration curve between variables. For example, quadratic polynomials, The form is. 8.1.2 Use the least square method to calculate the coefficient bj, and use the following formula to minimize the sum of squares of the deviation between the calibration curve and the data point. 8.1.3 The highest power in the polynomial can be obtained based on past experience, otherwise it can be obtained by the method in 8.3. 8.1.4 Too many fitting polynomial terms may cause curve oscillation. In this case, the interval of x can be divided into a number of linear or low-order The interval of the polynomial fit. 8.1.5 Proper transformation of one or two variables can also achieve linear or low-order polynomial fitting. For example, converting the argument to its The reciprocal 1/x can linearize the original data. 8.1.6 When the random uncertainty er(x) of the given data xi cannot be ignored relative to the random uncertainty er(y) of yi, the minimum is no longer applicable Two multiplication. When the slope of the calibration curve is less than 1/5 of er(y)/er(x), the method can be considered effective. When the slope of the fitted curve exceeds this The mathematical processing methods described in this section will no longer be applicable. Therefore, in the actual calibration process, if the variable to be fitted does not satisfy The above conditions, the methods described in this section are no longer applicable. 8.1.7 If a variable is transformed before fitting, the uncertainty is related to the new variable. Random inaccuracy due to variable transformation The fixed degree er(y) cannot be regarded as a constant in the range of x, and the weighted least square method should be used for fitting. 8.2 Non-linear fitting calculation method 8.2.1 The method of fitting a straight line described in this standard is also called linear or simple linear regression. Similarly, the fitting polynomial can be called It is a polynomial or curvilinear regression, which is a special form of multiple linear regression. See Appendix D for the calculation method of data regression processing. 8.2.2 As an alternative to the regression method, the orthogonal polynomial method described in Appendix E can be used. This method is especially suitable for The number of times together. 8.2.3 When x is not evenly distributed, the finite difference method can be used to quickly predict the number of times the appropriate data fits the polynomial, and calculate the For the coefficients of the term, the finite difference method can refer to Appendix E in ISO -TR-7066-2.The uncertain calculation of this method is beyond the scope of this standard. Surrounding. 8.3 Selection of the best fit times 8.3.1 The principle of determining the number of best fits. further increase the number of fittings, and the highest degree of the polynomial when the fitting results are not significantly improved The number is the number of best fit. For each number of fitting times, the following formula should be used to calculate the standard deviation sr of the fitting deviation. 8.3.2 The degree m of the fitted polynomial should be much smaller than the number n of data points. 8.3.3 If the data can be better fitted with a polynomial of degree m, when the degree reaches m, sr will be significantly reduced. Almost stay the same. If the change of sr is not significant, other significance checking methods should be used to determine the best fit times or seek a more significant target To determine the optimal polynomial degree. 8.3.4 In the process of increasing the degree of the polynomial from m-1 to m, if the new coefficient bm is obviously not equal to zero, 8.3.5 For the calculation of the coefficient gm of the orthogonal polynomial, refer to Appendix E. 8.3.6 When increasing the degree of the polynomial for the first time does not improve the fitting result, increase the degree of the polynomial again to check the degree of polynomial Whether the number of fitting results has obvious changes. 8.3.7 When the highest degree of polynomial improves the fitting result to 95% confidence level, it can be considered as the optimal degree. Select this number of times Before as the optimal expression of the data to be fitted, the expected shape of the curve, the interval to be fitted, and the accuracy of the fitting should be considered. influences. Try to avoid overly complicated forms of fitting polynomials. Draw the data points and possible fitting curves. Can display data points more intuitively The true relationship of, gives a reasonable polynomial form. 8.4 Uncertainty calculation in the process of nonlinear fitting 8.4.1 At the 95% confidence level, the random uncertainty of the fitted predicted value is given by the following equation. 8.4.2 For the y value, the 95% random confidence limit is. The uncertainty of the calibration coefficient is. 8.4.3 If the dependent variable has been converted, all the above uncertainty calculations should be calculated based on the converted parameters.Appendix A(Normative appendix) Calculation of standard deviation of general function A.1 If the total variance is the product or quotient of two or more constituent variables, then formula (5) cannot be used, and the general function should be used instead. The corresponding more complex standard deviation expression. ......Tips & Frequently Asked Questions:Question 1: How long will the true-PDF of DL/T 1961-2019_English be delivered?Answer: Upon your order, we will start to translate DL/T 1961-2019_English as soon as possible, and keep you informed of the progress. The lead time is typically 3 ~ 5 working days. The lengthier the document the longer the lead time.Question 2: Can I share the purchased PDF of DL/T 1961-2019_English with my colleagues?Answer: Yes. 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