First, the definition of measurement error The measurement error is the difference between the measurement result minus the measured true value, referred to as the error. Because the true value (also called the theoretical value) cannot be accurately obtained, the actual value is actually agreed. The agreed true value needs to be characterized by the measurement uncertainty, so the measurement error can not be accurately obtained.
Measurement Uncertainty: Indicates that the dispersibility of the measured value is reasonably given. It is related to the degree of knowledge of the person being measured, and is an interval obtained by analysis and evaluation.
Measurement error: It is the difference indicating that the measurement result deviates from the true value. It exists objectively but cannot be determined.
For example, the measurement result may be very close to the true value (that is, the error is small), but due to insufficient understanding, the value given by people falls within a large area (ie, the measurement uncertainty is large); Large, but due to insufficient analysis and estimation, the uncertainty given is too small. Therefore, in assessing the measurement uncertainty, various influencing factors should be fully considered, and the evaluation of the uncertainty should be verified as necessary.
Second, the error of error is divided into random error and system error error can be expressed as: error = measurement result - true value = random error + system error, therefore any error can be decomposed into algebraic sum of systematic error and random error
Random error: Random error is also called accidental error. Even in the ideal case of completely eliminating systematic error, repeated measurement of the same measurement object repeatedly will cause measurement error due to various accidental and unpredictable uncertain factors. Called random error.
The random error is characterized by repeated measurements on the same measurement object, and the error of the obtained measurement result shows irregular fluctuation, which may be positive (measurement is too large) or negative (measurement is too small), and the error is absolute. Value fluctuations are irregular. However, the distribution of errors obeys the statistical law, showing the following three characteristics: unimodality, that is, the error is smaller than the error; symmetry, that is, the positive error and the negative error probability are equal; boundedness, that is, the error is very large The probability is almost zero.
From the law of random error distribution, it is known that increasing the number of measurements and processing the measurement results according to statistical theory can reduce the random error.
Systematic error: The measurement error caused by the inherent error of the measuring tool (or measuring instrument), the measurement principle or the theoretical flaw of the measuring method itself, the experimental operation and the psychological and physiological conditions of the experimenter is called the systematic error.
The characteristic of system error is that under the same measurement conditions, the measurement results obtained by repeated measurement are always too large or too small, and the error value must be certain or change according to a certain law. The method of reducing the systematic error can usually change the measurement tool or measurement method, and can also consider the correction value for the measurement result.
3. Precision, accuracy and accuracy are measured multiple times under the same conditions using the same measuring tool and method. If the random error of the measured value is small, that is, the fluctuation of each measurement result is small, indicating that the measurement repeatability is good, called measurement precision. Goodness is also called good stability. Therefore, the magnitude of the measurement accidental error reflects the precision of the measurement.
According to the error theory, when the number of measurements is infinitely increased, the random error can be made to zero, and the degree of deviation between the obtained measurement result and the true value - the measurement accuracy will fundamentally depend on the magnitude of the systematic error. The magnitude of the systematic error reflects how accurately the measurement can be achieved.
Accuracy is the general term for the accuracy and precision of measurement. In actual measurement, the accuracy of influence may be mainly system error, or it may be mainly random error. Of course, the influence of both on measurement accuracy can not be ignored. In some measuring instruments, the concept of commonly used precision actually includes two aspects of system error and random error. For example, commonly used instruments often divide the instrument level with precision.
Instrument accuracy is referred to as accuracy, also known as accuracy. Accuracy and error can be said to be twin brothers, because of the existence of errors, the concept of precision. The accuracy of the meter is simply the accuracy of the meter's measured value close to the true value, usually expressed as a relative percentage error (also known as relative folding error). The relative percentage error formula is as follows: (omitted)
It can be seen from the formula that the accuracy of the meter is not only related to the absolute error, but also related to the measuring range of the meter. The absolute error is large, the relative percentage error is large, and the accuracy of the meter is low. If two instruments with the same absolute error have different measurement ranges, the relative percentage error of the meter with a large measurement range is small, and the accuracy of the meter is high. Accuracy is a quality indicator that is important for the instrument. It is commonly used to standardize and represent accuracy levels. The accuracy level is the maximum relative percentage error minus the sign and %. According to the national unified regulations, the grades are 0.05, 0.02, 0.1, 0.2, 1, 5, etc. The smaller the number, the higher the accuracy of the meter.
Fourth, the choice of application accuracy In the actual application process, according to the actual situation of the measurement to select the instrument's range and accuracy, and not necessarily the instrument with a small accuracy level, there must be the best measurement results. Take the application of the multimeter as an example, and use a multimeter with different accuracy to measure the error caused by the same voltage.
For example: there is a standard voltage of 10V, measured with two multimeters of 100V, 0.5 and 15V, and 2.5. Which one has a small measurement error?
Solution: The first block test: the maximum absolute allowable error ΔX1 = ± 0.5% × 100V = ± 0.50V.
The second block test: the maximum absolute allowable error ΔX2 = ± 2.5% × l5V = ± 0.375V.
Comparing â–³X1 and â–³X2, it can be seen that although the accuracy of the first block is higher than that of the second block, the error caused by the measurement of the first block is larger than the error caused by the measurement of the second block. Therefore, it can be seen that when selecting an instrument, the higher the accuracy, the better. Also choose the appropriate range. The potential accuracy of a universal instrument can only be achieved if the range is correctly selected.
V. Accuracy calibration method In addition to the nationally stipulated level, with the wide application of electronic technology, depending on the performance, there are several precision calibration methods as follows.
1) Display value ±X: Applied in an electronic display instrument, indicating that there is an error of X words at the lowest bit of the currently displayed value. If the display value is Y, the error △X=X/Y×100%
2) X% of the displayed value: Applied in the electronic display instrument, indicating that X% of the currently displayed value is the current error range. If the display value is Y error ΔX=X%, the error value is ±X%×Y
3) Segmented range calibration: applied to wide-range instruments. The instrument uses different error calibration methods in different measurement intervals. For example, when measuring 0.01-1 volts, the error is 5%, and the voltage is 1-10 volts. When the error is 1%, it is the segmentation calibration method. When applying the segmentation calibration instrument, it is necessary to select the appropriate range and carefully check the error calculation and calibration method of the range.
4) Error calibration of mathematical model: Give the error calculation formula F(X) of the instrument, and bring the current error â–³X=F(Y) according to the current measurement result Y of the instrument and other relevant conditions. The corresponding relationship between the error result and the measured value measured by this method is mostly a curve. Since the error of each point of this method is different, the application should pay special attention and be carefully calculated.
It is not difficult to conclude from the above conditions that the actual measurement accuracy of the results is different for different measurement values. When selecting, it is necessary to analyze the measurement conditions and the allowable error of the instrument at the measurement point. It is not necessary for the low-grade instrument to have the best measurement effect. The appropriate instrument and range should be selected according to the specific conditions to minimize the measurement error.
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