1.2. Measurement error

It is known that the measurement can not be performed exactly and always contain some error. Despite the variety of causes, nature and the nature of measurement errors, all errors are divided into two main types: objective and subjective:

Objective errors resulting from imperfections adopted the method of measurement, instrument design features as the impact of external factors on the measurement process. This distinction error: static observed when measured in constant time values and dynamic observed when measured variables for time values.

Static and dynamic errors form the category of so–called systematic errors.

The objective also includes the category of random errors.

Static errors consist of: first, with errors related to the properties of materials, processing technology, quality manufacturing and assembly of parts of the device and other parameters of the device–instrument; secondly, with errors related only to the method of measuring underlying the construction of this device. Because of this shared static error pas instrumental and methodological.

To include instrumental errors arising from friction in the bearings unnecessary gaps, inaccuracies manufacture, assembly and regulation units, changes in the elastic properties and linear dimensions of parts over time due to congestion and changes in temperature and so on.

To reduce the instrumental error in the devices used special materials injected joints, shielding, sealing and usually slander working limits of external conditions.

Methodical errors are caused by the principle of the device structure. They are not related to numerous factors give rise to instrumental error. Therefore, to reduce or eliminate their possible only by changing or replacement procedures and methods underlying parts of the measuring device.

Dynamic errors are caused inertial properties of the device. The presence of mechanical, thermal and other types of inertia leads to the fact that the readings are delayed by changing input values or reach new meaning after a long damped oscillations (sedation) or increasing (decreasing) in proportion to the rate of change of the input variable.

The oscillatory motion of moving parts of the appliance generates amplitude and phase errors due to moving the system to a new equilibrium. While oscillatory movement is not stopped or not the oscillation amplitude decreased to an acceptable limit, do not be counting.

Properties gear quickly suspend or reduce fluctuations in mobile parts to a certain value estimate time spent in comfort, which is calculated from the time of inclusion on the device for a half measurement range, until the mobile part it comes in relatively equilibrium state and fluctuations it does not exceed 1% of the entire range of the scale.

Amplitude and phase errors that are made to measure inertia mechanical elements of the device in the dynamic mode, it is possible to understand the example of the converter (Fig.1.1.2). Converters of this type are used in measuring pressure in different vibrators and so on.

Fig. 1.2.1: Schematic diagram of the converter of mechanical quantities

The external force F (t) has in it the mass m, connected with the body via the elastic element has stiffness with, and damper, providing reassurance factor g. Provided that: mass spring small compared with the mass m; weight t has only one degree of freedom (along the axis x); pacifier resists proportional to the speed of the first degree (viscous friction) and the initial time the movement's moving parts and speed dx/dt zero, the equation of motion takes the form of a system:

where force that causes movement's moving parts.

The final solution of the equation:

where – degree of sedation , the ratio of the angular frequency ω the frequency of forced oscillations natural oscillations.

First term of the right side of the equation expresses their system damped oscillations occurring at a frequency and amplitude . Due to the availability factor amplitude of natural oscillations of the system decreases and eventually vanishes. So after some time deflection device is fully described by the second term. For example, the values of β> 0, damped oscillations at all for the first few periods and practically can not be taken into account.

The second term on the right side of the equation describes the forced oscillations occurring at a frequency of change of the measured force and amplitude:

Since the static application of force:

then forced oscillations with amplitude, as opposed to moving the movable part in a static mode time.

Consequently, the value of M describes the amplitude error forced oscillations . When amplitude error can be up to an 1% calculated using the formula:

Patterns of changes of M depending on λ for different values of the degree of sedation was shown in Fig. 1.2.2.

Consequently, the value of M describes the amplitude error forced oscillations:

Fig. 1.2.2: Change the value of M depending on λ = ω / ω0 at different values of the degree of sedation β

Analysis of these graphs shows that for small values of β maximum amplitude error is at λ = ω/ω₀ = 1, ie in the case of resonance. Sensors operating in dynamic mode for the circuit shown in Fig. 1.2.1 should therefore have λ <1. In practice, their natural frequency ω0 should be greater than the frequency of the measured process at least 2–3 times. Amplitude error has a minimum value at β = 0,6 – 0,7.

The phase difference between the amount of anger and power that it is, in the above situation is characterized by a factor which periodically over time varies from 0 to 1.

This phase error in the registration process of forced oscillations is determined by the angle:

The phase error ψ at β = 0,65 – 0,70 almost linearly depends on the frequency, so the delay forced oscillations of the movable portion of changes in the measured value for each frequency in the same time.

Systematic errors arise naturally, so they can be quantified and excluded from the measurement results by amendments to the readings, numerically equal values of errors, taken with the opposite sign, or removed under the method of measurements.

Fig.1.2.3: Modifications needle indicator devices: I – scale; 2 – needle; 3 – mirror; 4 – a sign that indicates the class of accuracy of the instrument

Before processing the measurement results, they should be free from systematic errors.

Random error can not be predicted in advance and the likelihood of measurement errors of any sign about the same, they are volatile in absolute value. Therefore, unlike regular, random errors are eliminated and can not be excluded from the measurement results amendment. Their influence on outcomes measurement study methods of mathematical statistics and probability theory.

Subjective uncertainty arising from physiological characteristics tester, quality of work and experience.

Physiological characteristics observer related to his weight issues–ness, as of,. hearing and t. e., they are shown in the reaction rate signals while performing teams before the start and the end–metering in, blunders in reference records, and so on. n. Therefore, it is desirable that certain observations entrusted as possible, and one the same person.

Subjective error also depends on the individual, evaluations readings and, in particular, the position of the observer on the unit at the time of departure. As the arrow pointer is often not identical with the plane of the scale, in cases where the line of sight of the observer is not directed along the normal, and at an angle to scale, possible additional reference error.