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GB/T 29820.2-2024 English PDF

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GB/T 29820.2-2024: Assessment of uncertainty in the calibration and use of flow measurement devices - Part 2: Non-linear calibration relationships
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Basic data

Standard ID GB/T 29820.2-2024 (GB/T29820.2-2024)
Description (Translated English) Assessment of uncertainty in the calibration and use of flow measurement devices - Part 2: Non-linear calibration relationships
Sector / Industry National Standard (Recommended)
Classification of Chinese Standard N12
Classification of International Standard 17.120.10
Word Count Estimation 34,367
Date of Issue 2024-12-31
Date of Implementation 2025-07-01
Issuing agency(ies) State Administration for Market Regulation, China National Standardization Administration

GB/T 29820.2-2024: Assessment of uncertainty in the calibration and use of flow measurement devices - Part 2: Non-linear calibration relationships


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ICS 17.120.10 CCSN12 National Standard of the People's Republic of China Evaluation of the uncertainty in calibration and use of flow measurement devices Part 2.Nonlinear calibration relationships (ISO 7066-2.1988,MOD) Released on 2024-12-31 2025-07-01 Implementation State Administration for Market Regulation The National Standardization Administration issued

Table of Contents

Preface III Introduction V 1 Scope 1 2 Normative references 1 3 Terms and Definitions 1 4 Symbols 2 5 Curve Fitting 2 5.1 General Principles 2 5.2 Calculation method 3 5.3 Select the best fit number 3 6 Uncertainty 4 Appendix A (Informative) Computer Program Examples Using Orthogonal Polynomials 5 A.1 Input and Output 5 A.2 Program Description 5 A.3 Possible modifications 5 Appendix B (Informative) Example 12 Appendix C (Informative) Regression Method 21 C.1 Introduction 21 C.2 Multiple Linear Regression 21 C.3 Polynomial (curve) regression 21 C.4 Calculation of coefficients and variances 21 C.5 Concentrated expression 23 C.6 Mathematical methods used in computer program libraries 23 Appendix D (Informative) Orthogonal Polynomial Curve Fitting 24 Appendix E (Informative) Finite Difference Method 25 Reference 27

Foreword

This document is in accordance with the provisions of GB/T 1.1-2020 "Guidelines for standardization work Part 1.Structure and drafting rules for standardization documents" Drafting. This document is part 2 of GB/T 29820 "Evaluation of uncertainty in calibration and use of flow measurement devices". GB/T 29820 has been The following parts have been published. --- Part 1.Linear calibration relationship; --- Part 2.Non-linear calibration relationship. This document is modified from ISO 7066-2.1988 "Evaluation of uncertainty in the calibration and use of flow measurement devices - Part 2.Nonlinearity" Calibration Relationship. This document has the following structural adjustments compared to ISO 7066-2.1988. --- Appendix A corresponds to Appendix C of ISO 7066-2.1988; --- Appendix B corresponds to Appendix D of ISO 7066-2.1988; --- Appendix C corresponds to Appendix A of ISO 7066-2.1988; --- Appendix D corresponds to Appendix B of ISO 7066-2.1988. The technical differences between this document and ISO 7066-2.1988 and their reasons are as follows. --- Changed the concepts of "random uncertainty" and "systematic uncertainty" according to the provisions of GUM and ISO 5168.2005. In order to classify according to the uncertainty assessment method, it is divided into Class A standard uncertainty and Class B standard uncertainty; --- Changed the symbols in Chapter 4, replacing the symbol “eR()” with the symbol “u()” The symbol "random uncertainty of the quantity" and the symbol "systematic uncertainty of the variable in brackets" are represented by "uc(y ∧) The synthesis of calibration coefficients is not Degree of certainty" replaces the symbol "e(y c) Total uncertainty of calibration coefficients”, adding the symbol “uA() The variables in brackets are of type A standard Uncertainty”, the symbol “Type B standard uncertainty of the variable in the brackets of uB()” was added to adapt to my country’s technical conditions; --- ISO 7066-1 (see Chapter 5) has been replaced by the normative reference GB/T 29820.1 to adapt to my country's technical conditions. The following editorial changes were made to this document. --- Added a note on the term "regression analysis" (see 3.3); --- Replaced ISO 5168 with the informative reference GB/T 27759 and included the document in the references; --- Modified the contents of the diagram in the informative Appendix B; --- Modified the incorrect symbols and formulas in the informative appendix D, and changed Δ(1), Δ(2), Δ(3), Δ(1), Δ(2), Δ(3) to Δ1, Δ2, Δ3, Δ1, Δ2, Δ3, b0=y (n2-1)Δ(2) twenty four - Δ(1)x dx Δ2x2 2dx2 Modify to b0=y- Δ1x dx Δ2x2 2dx2 ,y ∧= 3313.12 6384.74x-20312.5x2 modified to y ∧=3258.45 6384.74x-20312.5x2; --- Move the references in informative Appendix E to the references of this document. Please note that some of the contents of this document may involve patents. The issuing organization of this document does not assume the responsibility for identifying patents. This document was proposed by the China Machinery Industry Federation. This document is under the jurisdiction of the National Industrial Process Measurement, Control and Automation Standardization Technical Committee (SAC/TC124). This document was drafted by. Shanghai Instrument and Control System Inspection and Testing Institute Co., Ltd., Shanghai Industrial Automation Instrumentation Research Institute Co., Ltd. Shenzhen Wanxun Automation Co., Ltd., Metso Instruments (Changzhou) Co., Ltd., Jiangsu Institute of Metrology, University of Shanghai for Science and Technology, Shenyang Xingya Measurement and Calibration Technology Co., Ltd., Shanghai Eco Gas Measurement and Control Equipment Co., Ltd., Jinka Smart Group Co., Ltd., Beijing Municipal Institute of Metrology and Testing Science, Hunan University of Science and Technology, Tianxin Instrument Group Co., Ltd., Zhejiang Institute of Metrology Science, Cologne Measuring Instruments (Shanghai) Co., Ltd., Guangzhou Energy Testing Institute, Dandong Tongbo Measurement and Control Engineering Technology Co., Ltd., Endress+Hauser (China) Automation Co., Ltd. Co., Ltd., Dandong Beite Automation Engineering Instrument Co., Ltd., Kaifeng Instrument Co., Ltd., Jiangyin Furen Hi-Tech Co., Ltd., Chengdu An Dickson Measurement Co., Ltd., Shengli Oilfield Dayuan Energy Saving Equipment Co., Ltd., and Chongqing Derun Automation Equipment Co., Ltd. The main drafters of this document are. Song Yanyong, Xiao Honglian, Zou Jing, Yang Di, Cao Jiuying, Su Mingxu, Sun Yuxin, Zhao Miyue, Zhao Zhuoshi, Ding Yuanming, Weiming Yan, Youtao Yang, Zuguo Chen, Chaojian Tao, Lei Xiang, Haojun Chen, Yong Wan, Changjiang Shi, Lian Yu, Lin Zhong, Haining Xu, Dongcheng Xu, Jie Liu, Sashuang Li, Gong Daoxia, Chao Kan.

Introduction

GB/T 29820 "Evaluation of uncertainty in calibration and use of flow measurement devices" is intended to consist of two parts. --- Part 1.Linear calibration relationship. The purpose is to determine the calibration diagrams and The process of evaluating the uncertainty of such a calibration. This section only considers the uncertainty evaluation of the linear relationship. --- Part 2.Nonlinear calibration relationships. The purpose is to determine the relationship using the least squares criterion using quadratic, cubic or higher order polynomials. The process of fitting a set of nonlinear calibration data and estimating the uncertainty associated with the resulting calibration curve. Evaluation of the uncertainty in calibration and use of flow measurement devices Part 2.Nonlinear calibration relationships

1 Scope

This document describes the use of the least squares criterion to fit a set of nonlinear calibration data using a quadratic, cubic or higher order polynomial and to evaluate The uncertainty associated with the generated calibration curve is calculated using only polynomials raised to integer powers. Since this type of curve fitting and uncertainty assessment usually requires the use of a computer, in most cases, A standard procedure is provided; a reference procedure is given in Appendix A. Examples of the use of these methods are given in Appendix B. Extrapolation beyond the data range is not permitted.

2 Normative references

The contents of the following documents constitute the essential clauses of this document through normative references in this document. For referenced documents without a date, only the version corresponding to that date applies to this document; for referenced documents without a date, the latest version (including all amendments) applies to This document. GB/T 29820.1 Evaluation of calibration and use uncertainty of flow measurement devices Part 1.Linear calibration relationship (GB/T 29820.1-2013,ISO /T R7066-1.1997, MOD)

3 Terms and definitions

The following terms and definitions apply to this document. 3.1 method of least squares When a particular form of equation is chosen to fit a curve to the data, the technique used to calculate the coefficients of that equation is to use The sum of squares of the deviations of the data of the open curve is the minimum. 3.2 polynomial(function) For a variable x, a series of terms raised to increasing powers of x. 3.3 Regression analysis A method of quantitatively expressing the dependence of one variable on one or more other variables. Note 1 to entry. Regression is the process of determining the unknowns of a proposed model in such a way that the predictions of the model come as close as possible to the data. Usually "as close as possible" means that the sum of squared deviations is minimized. NOTE 2 Many computer programs suitable for curve fitting have the word "regression" in their names. For the purpose of this document, the terms regression and least squares are considered synonymous. The laws are interchangeable. 3.4 Standard Deviation The positive square root of the variance.

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