# Evaluate flowmeter measurement errors and uncertainties

A. Measurement error and measurement result correction

(I) Measurement error

The difference between the flowmeter measurement result minus the true value being measured is called the measurement error, referred to as the error. The result of measurement is the result of people's recognition. It is not related to quantity itself, but also relates to measurement procedures, measurement instruments, measurement environment, and measurement personnel. The measured true value is a value consistent with the measured definition. It is a complete representation of the definition of the quantity. It is a value that is exactly the same as the definition of a given specific quantity. Only through perfect or perfect measurement can obtain. Truth is inherently uncertain. However, in practice, for a given purpose, it is not necessary to obtain a specific amount of "truth" but only a value sufficiently close to "true value". This value is the agreed-upon true value, which can be used instead of the true value for a given purpose. For example, the value of a certain amount obtained by calibration or verification, or the value measured by a measuring instrument with a higher accuracy level, or the value determined by the result of multiple measurements can be used as the agreed-upon true value of the quantity. .

The error of the measurement result is often composed of several components. According to their characteristics, these components can be divided into two categories: random error and system error, and the algebraic sums of the components are taken without exception. In other words, any error can be decomposed into algebraic sums of systematic errors and random errors, which can be expressed by the following formula:

Error = measurement result - true value = (measurement result - population mean) + (overall mean - true value) = random error + systematic error

The difference between the measurement result and the average value of the results of an infinite number of measurements on the same measurement under repeatability conditions is called random error. Random errors are mostly derived from changes in the influence quantity. This change is unpredictable or random in time and space. It will cause changes in the measured repeated observations, so it is called â€œrandom effectsâ€. It can be considered that it is this random effect that leads to the dispersion in repeated observations.

The difference between the average value of the result of an infinite number of measurements made on the same meter and the true value being measured under the condition of repeatability is called system error. Since only a limited number of repeated measurements can be performed, the true value can only be replaced by the agreed value. Therefore, the possible systematic error is only its estimated value, and it has a certain degree of uncertainty. The system error is mostly derived from the amount of influence. If its effect on the measurement result has been identified, it can be quantified. Therefore, it is called the "system effect." If the magnitude of this effect is significant, it can be compensated by the estimated correction value.

(B) Correction of measurement results Measurement results that have not been corrected for system errors are called uncorrected results. When only a single indication is obtained by the measuring instrument, the indication is usually an uncorrected result, and when several indications are obtained, the uncorrected result is usually obtained from the arithmetic average of the indications.

For example: When measuring the diameter of a cylinder with a ruler, the observed value of a single observation is 14.7 mm, and the measured value is an uncorrected result. If 10 measurements are taken, the resulting indications are 14.9, 14.6, 14.8, 14.6, 14.9, 14.7, 14.7, 14.8, 14.9, 14.8 (mm), respectively, and the uncorrected result of the measurement column is the arithmetic mean. That is (14.9+14.6+...+14.8)/10=14.77â‰ˆ14.8(mm).

The corrected measurement results for system errors are called corrected results. The algebraic method and the uncorrected measurement result are added to compensate for the value of the system error, called the correction value. In the above example, if the scale is calibrated by a gage block, its correction value is -0.1mm, then the corrected result of a single measurement is (14.7-0.1)mm=14.6mm; and the corrected results of 10 measurements are: (14.8-0.1) mm=14.7 mm.

The correction value is equal to the negative system error, that is, adding a certain correction value is like deducting a systematic error, and the effect is the same. which is:

Truth = Measurement Result + Correction Value = Measurement Result - Error

It should be emphasized that: Systematic errors can be estimated and compensated by appropriate corrections, but this compensation is incomplete, ie, the correction itself contains uncertainty. When the measurement result is algebraically summed with the correction value, the absolute value of the system error will be smaller than before the correction, but it cannot be zero, that is, the correction value can only compensate the system error to a limited extent.

Second, the measurement uncertainty

(a) The basic concepts

The purpose of the measurement is to determine the amount to be measured. The quality of measurement results (quality) is the most important basis for measuring the credibility of measurement results. Measurement uncertainty is the quantitative representation of the quality of measurement results. The availability of measurement results depends largely on the degree of uncertainty. Therefore, the expression of the measurement result must include both the value assigned to the measurement and the measurement uncertainty associated with the value, which is complete and meaningful.

Characterization A parameter that reasonably assigns the measured value to the dispersibility and the measurement result is called measurement uncertainty. In terms of lexical meaning, â€œuncertaintyâ€ is doubtful or not. Therefore, in a broad sense, measurement uncertainty means the degree of doubt or uncertainty about the credibility and validity of the measurement results. In fact, due to imperfect measurement and people's lack of recognition, the measured values â€‹â€‹obtained are dispersive, that is, each measured result is not the same value, but is dispersed in a certain area with a certain probability. Although the objective systematic error is a relatively definite value, but because we can not fully understand or grasp it, we can only think that it is distributed in a certain probability with some probability, and this kind of probability distribution is also scattered Sex. Measurement uncertainty is a parameter that describes the dispersion of measured values. The uncertainty of the measurement results reflects the lack of accurate understanding of measured values. Even after the correction of the determined systematic error, the measurement result is still only an estimate of the measured value, because not only the random factors existing in the measurement will generate uncertainty, but also the incomplete system factor correction. There is also uncertainty.

Do not confuse error with uncertainty. Uncertainty of measurement indicates the degree of dispersion imparted to the measured value. It is an interval obtained by the analysis and evaluation of the measurement process. The measurement error is the difference between the measurement result and the true value. The corrected measurement result may be very close to the true value (ie, the error is small), but due to lack of understanding, the value assigned to it falls within a large interval (ie, the measurement uncertainty is large).

To characterize the dispersion imparted to the measured value, the measurement uncertainty is often expressed as a standard deviation. In practical use, since people often want to know the confidence interval of the measurement result, the measurement uncertainty can also be expressed as a multiple of the standard deviation or as a half-width representation of the interval of the confidence level. In order to distinguish these two different representations, they are called standard uncertainty and extended uncertainty, respectively. Http://

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