How to calculate the uncertainty of college physics experiment (how to calculate the U value of uncertainty)

How to calculate the uncertainty of college physics experiment

Grade evaluation: standard uncertainty is evaluated by statistical analysis of observation columns. Grade b evaluation: the standard uncertainty is evaluated by a method different from the statistical analysis of the observation column. Class A evaluation is to obtain the standard deviation by observing the column data, and then calculate the standard uncertainty; Class B evaluation is to estimate the variation range of the evaluated quantity first.

Measurement uncertainty is a parameter associated with measurement results, which is used to reasonably characterize the dispersion of measurement values. It can be used in "uncertain" mode, or it can be the standard deviation or the half width of a given confidence interval. This parameter is often composed of multiple components, and its expression defines different methods to obtain uncertainty.

Measurement uncertainty is "a parameter that reasonably represents the dispersion of measured values and is related to the measurement results".

"Reasonable" in this definition means that the influence of various factors on the measurement should be considered, especially the measurement should be in the state of statistical control, that is, the correction in the process of random control. That is to say, the measurement is carried out under the condition of repeatability or reproducibility.

At this time, the dispersion of measurement results can be calculated according to Bessel formula in Article 5. 17, and expressed by repetitive standard deviation sr or reproducible standard deviation SR. ..

Usually, the quality of measurement results is measured by measurement error, but measurement error can only show the short-term quality of measurement. Whether the measurement process is continuously controlled, whether the measurement results are stable and consistent, and whether the measurement ability meets the requirements of production profitability need to be measured by measurement uncertainty.

The greater the measurement uncertainty, the worse the measurement ability; On the contrary, the stronger the measurement ability. However, no matter how small the measurement uncertainty is, the measurement uncertainty range must contain the true value, otherwise it means that the measurement process has failed.

Measurement uncertainty, understood from the meaning, refers to the degree of doubt or uncertainty about the reliability and effectiveness of measurement results, and is a parameter that quantitatively explains the quality of measurement results. In fact, due to the imperfection of measurement and people's ignorance, the measured values are scattered, that is, the results of each measurement are not the same value, but multiple values scattered in a certain area with a certain probability.

Although the objective system error is a constant value, we can only think that it exists in a certain area with a certain probability distribution, and this probability distribution itself is scattered. Measurement uncertainty is a parameter that describes the dispersion of measured values, and does not mean whether the measured results are close to the true value.

How to calculate the U value of uncertainty

U is the product of the standard uncertainty Uc of the combined uncertainty and the inclusion factor k, and the value of the extended uncertainty is generally 2 and sometimes 3.

The k- inclusion factor is a numerical factor multiplied by the combined standard uncertainty to obtain the extended uncertainty, sometimes called the coverage factor. The value of inclusion factor determines the confidence level of extended uncertainty. When =2, P = 95%; When =3, p=99%.

Example: There is a column number. A 1, A2, ..., An, and their average value is a, then the uncertainty is: max{|A-Ai|, i= 1, 2, ..., n}

Extended data:

The basic requirements for instrument calibration are as follows:

If the calibration of environmental conditions is carried out in the verification room, the environmental conditions should meet the requirements of the laboratory for temperature and humidity. If calibration is carried out in the field, the environmental conditions should be based on the conditions that can meet the field use of the instrument.

As a standard instrument for calibration, the error limit of the instrument should be1/3 ~110 of the error limit of the calibrated table.

Although personnel calibration is different from verification, the personnel who carry out calibration should also pass the effective examination and obtain the corresponding qualification certificate. Only certified personnel can issue calibration certificates and reports, and only such certificates and reports are considered valid.

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Class a and class b uncertainty formulas

The standard uncertainty is evaluated by statistical analysis of observation columns, which is called uncertainty A-level evaluation. The corresponding standard uncertainty is called Class A uncertainty component, which is represented by symbol uA. It is characterized by experimental standard deviation.

Calculation formula:

Ua = s of a measurement result An;

Uncertainty of average measurement result UA A = s/sqrt =

The uncertainty value is the maximum distance between each value and the average value.

Example: There is a column number. A 1, A2, ..., An, and their average value is a, then the uncertainty is: max{|A-Ai|, i= 1, 2, ..., n}

Extended data:

Extended uncertainty is the quantity that determines the interval of measurement results, and most of the value distributions reasonably given to the measured values are expected to be included in this interval. It is sometimes called distance uncertainty. The extended uncertainty is the measurement uncertainty expressed by the multiple of the combined standard uncertainty. It is usually represented by the symbol u: the product of the combined uncertainty and the inclusion factor k is called the total uncertainty.

The value of k here is generally 2 and sometimes 3. It depends on the measured importance, benefits and risks. The extended uncertainty is half the width of the range of measurement results, and it can be expected to include most of the distribution of measurement values. The percentage of the interval of the measurement result in the probability distribution of the measurement value is called the confidence probability, confidence level or confidence level of the interval.

At this time, the extended uncertainty is represented by the symbol U, and the representation interval can contain most possible values to be measured.

Calculation of Uncertainty in Physical Experiments

There are three kinds of uncertainties, Class A, Class B and Class C. ..

uA=

No.2 under the root symbol)

Xi is the data of each experiment, and n is the total number of experimental data.

Ub = instrument error, root number 3.

There are three kinds of instrument errors.

First: the instrument can't estimate, this is the minimum measurement.

Second, the measurable instrument is the minimum measured value ÷2.

Third: instruments with precision marks depend on precision marks.

Uc = under the root symbol

Examples of Seeking Uncertainty in College Physics Experiments