Hits:Updated:2020-04-03 09:04:29【Print】
1 Definition of measurement error
Common error expressions are: absolute error, relative error, and reference error.
1. Absolute error:
Definition: The difference between the measured value x * and its measured true value x is called the absolute error of the approximate value x *, referred to as ε.
Calculation formula: absolute error = measured value-real value;
2. Relative error:
Definition: The value obtained by multiplying the ratio of the absolute error caused by the measurement to the measured (conventional) true value by 100%, expressed as a percentage.
Calculation formula: relative error = (measured value-true value) / true value × 100% (that is, the absolute error as a percentage of the true value);
3. Reference error
Definition: The ratio of the absolute error of the measurement to the full scale value of the meter is called the reference error of the meter, and it is often expressed as a percentage.
Calculation formula: reference error = (maximum absolute error / meter range) × 100%
The smaller the reference error, the higher the accuracy of the meter, and the reference error is related to the range of the meter. Therefore, when using a meter with the same accuracy, it is often to compress the range to reduce the measurement error.
01 Examples
Use a multimeter to measure the voltage of 1.005V. Assuming that the true voltage is 1V, the multimeter has a range of 10V, and the accuracy (reference error) is 0.1% F.S. Is the multimeter test error within the allowable range?
The analysis process is as follows:
Absolute error: E = 1.005V-1V = + 0.005V;
Relative error: δ = 0.005V / 1V × 100% = 0.5%;
Multimeter reference error: 10V × 0.1% F.S = 0.1V;
Because the absolute error is 0.005V <0.1V, the 10V range refers to a multimeter with an error of 0.1% F.S. The relative error of measuring 1V is 0.5%, which is still within the tolerance range.
2 Generation of measurement errors
The absolute error exists objectively, but people cannot determine it, and the absolute error is unavoidable. The relative error can be minimized.
Error components can be divided into random errors and system errors, that is: error = measurement result-true value = random error + system error
Therefore, any error can be decomposed into algebraic and systematic errors of systematic and random errors:
1.System error
Definition: Under repeatable conditions, the difference between the average of the results of infinite and multiple measurements of the same measured value and the true value of the measured value.
Cause: The measurement error caused by the inherent error of the measurement tool (or measuring instrument), the theoretical defect of the measurement principle or the measurement method itself, the experimental operation and the constraints of the experimental staff's own psychological and physiological conditions
Characteristics: Under the same measurement conditions, repeated measurement results are always large or small, and the error value is constant or changes according to a certain law.
Optimization method: The method can usually change the measurement tool or measurement method, and also consider the correction value for the measurement result.
2.Random error
Definition: Random error, also called accidental error, refers to the difference between the measurement result and the average result of a large number of repeated measurements of the same to be measured.
Cause: Even in the ideal case of completely eliminating system errors, repeated measurement of the same measurement object multiple times will still cause measurement errors due to various occasional and unpredictable uncertain factors.
Features: The measurement is repeated repeatedly for the same measurement object, and the error of the measurement results shows irregular fluctuations, which may be positive or negative deviations, and the absolute value of the errors fluctuates irregularly.
However, the distribution of errors obeys the statistical law and shows the following three characteristics:
Unimodality, that is, the error is smaller than the error;
Symmetry, that is, the probability of a positive error is equal to a negative error;
Boundedness, that is, the probability of a large error is almost zero.
Optimization method: According to the random error distribution rule, increasing the number of measurements and processing the measurement results according to statistical theory can reduce random errors.
3Precision, precision and accuracy
Precision and error can be said to be twin brothers, because of the existence of error, there is the concept of accuracy. In short, the accuracy of the meter is the accuracy of the meter's measured value close to the true value, which is usually expressed by a relative percentage error (also known as a relative reduction error).
1.The magnitude of the occasional measurement error reflects the precision of the measurement
Use the same measurement tool and method to measure multiple times under the same conditions. If the random error of the measurement value is small, that is, the fluctuation of each measurement result is small, it means that the measurement repeatability is good, which is called good measurement precision and good stability.
2.The size of the system error reflects the accuracy of the measurement
According to the error theory, when the number of measurements is infinitely increased, the random error can be brought to zero, and the degree of deviation between the obtained measurement result and the true value, the measurement accuracy, will ultimately depend on the size of the system error.
3.Accuracy is a general term for measurement accuracy and precision
In actual measurement, the accuracy may be mainly caused by systematic errors or random errors. Of course, the influence of the two on measurement accuracy may not be ignored. In some measuring instruments, the concept of commonly used accuracy actually includes two aspects of system error and random error. For example, commonly used instruments often divide the instrument level by accuracy.
4 Instrument accuracy level and range
Accuracy is a very important quality indicator of the instrument, and it is usually standardized and expressed by the accuracy level. The accuracy level is the maximum relative percentage error minus the sign and%. There are 0.05, 0.02, 0.1, 0.2, 1.5 and so on according to the unified national regulations. The smaller the number, the higher the accuracy of the instrument.
Instrument accuracy is not only related to the absolute error, but also to the measuring range of the instrument. If two instruments with the same absolute error have different measurement ranges, then the instrument with a large measurement range will have a relatively small percentage error and high instrument accuracy; and vice versa, two instruments with the same accuracy level will have a large range instrument. The absolute error is also greater.
5 selection of application accuracy
In the actual application process, the range and accuracy of the instrument should be selected according to the actual situation of the measurement. It is not necessarily an instrument with a small accuracy level, and it must have the best measurement effect.
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