AS 2360.7.2-1993

Measurement of fluid flow in closed conduits Assessment of uncertainty in the calibration and use of flow measurement devices - Non-linear calibration relationships

Standards Australia

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1 - AS 2360.7.2-1993 MEASUREMENT OF FLUID FLOW IN CLOSED CONDUITS - ASSESSMENT OF UNCERTAINTY IN THE CALIBRATION AND USE OF FLOW
4 - PREFACE
7 - 0 Introduction
7 - 1 Scope and field of application
7 - 2 References
7 - 3 Definitions
7 - 3.1 method of least squares
7 - 3.2 polynomial (function)
7 - 3.3 regression analysis
7 - 3.4 standard deviation
7 - 3.5 variance
7 - 4 Symbols and abbreviations
8 - 5 Curve fitting
8 - 5.1 General
9 - 5.2 Computational methods
9 - 5.3 Selecting the optimum degree of fit
10 - 6 Uncertainty
11 - Annex A - Regression methods
11 - A.1 Introduction
11 - A.2 Multiple linear regression
12 - A.3 Polynomial (curvilinear) regression
12 - A.4 Computation of coefficients and variances
14 - A.5 Centred formulation
14 - A.6 Numerical techniques used in computer libraries
15 - Annex B - Orthogonal polynomial curve fitting
17 - Annex C - Computer program using orthogonal polynomials
17 - C.1 Input and output
17 - C.2 Program description
17 - C.3 Possible modifications
23 - Annex D - Examples
23 - D.1 Example 1: Calibration of a differential pressure flow-meter
24 - D.2 Example 2: Calibration of a turbine meter
25 - D.3 Example 3: Calibration of a stream flow station

Abstract

Deals with procedures for fitting a quadratic, cube or higher degree (integer powers) polynomial expressions to a non-linear (or linear) set of calibration data using the least-squares criterion and assessment of the uncertainty associated with the resulting calibration curve. Because it is generally not practical to carry out this assessment without using a computer with standard routines an alternative FORTRAN program listing is included as an Annex. It is identical with and has been reproduced from ISO 7066-2:1988.

Scope

This part of ISO 7066 describes the procedures for fitting a quadratic, cubic or higher degree polynomial expression to a non-linear 1)set of calibration data, using the least-squares criterion, and of assessing the uncertainty associated with the resulting calibration curve. It considers only the use of polynomials with powers which are integers.
Because it is generally not practicable to carry out this type of curve fitting and assessment of uncertainty without using a computer, it is assumed in this part of ISO 7066 that the user has access to one. In many cases it will be possible to use standard routines available on most computers; as an alternative the FORTRAN program listed in annex C may be used.
Examples of the use of these methods are given in annex D.
Extrapolation beyond the range of the data is not permitted.
Annexes A, B, C, D and E do not form integral parts of this part of ISO 7066.