Measurement as an elementary metrological system

2.2 Physical-metrological fundamentals of constructing the RUTS systemsthe RUTS systems

2.2.3 Foundations of the description of RUTS systems

2.2.3.2 Measurement as an elementary metrological system

A rather fruitful approach for studying and describing various metrological systems is the use of measurement components as an elementary metrological system. An ap- proach of this kind is sufficiently “natural”, since it uses the main object of studying by metrology, i.e., a measurement, and is rather efficient for studying various metrological systems from the single positions, which is very important in systemic investigations.

Let us consider a general description of measurement to be the process of measure- ment problem solution outlined in [390]. Since a measurement in the most general form is understood to be one of a variety of perceptions at which information is always transformed, then an initial equation for describing the measurement can be written in the form

J :Ia !Ip, (2.2.1)

whereJ is the operator of transformation,Iais a priori information, andIpis a pos- teriori information.

Specification of this rather abstract expression takes place in the process of intro- ducing the concept “measurement problem” (see Section 2.2.3.1), i.e., the problem of finding the value of a PQ under definite conditions. It should be noted that this is an important moment for carrying out any measurement. Without the formulation of a specific measurement problem the measurement becomes meaningless. To meet this demand it is necessary to indicate the kind of the PQ, the object, and the conditions of measurement, time (and so on) within which the measurement should be carried out, i.e., to assign parameters (components) of a specific measurement problemzi:

zi D.'i,oi, i,ı'i,gi,ti,ti,pi,: : :/, (2.2.2) where

'iis the measurand as the quality (by definition);

oiis the object of the study (the carrier of the measurand);

iare the measurement conditions (the totality of the given influencing factors);

ı'i is the given measurement error;

giis the given form of presenting a measurement result;

ti is the moment of time at which the measurement is realized;

ti is the time interval within which it is necessary to perform the measurement;

piare the coordinates of a place (of space) where the measurement is performed.

This collection of components forms a set of given (i.e., uncontrollable in the pro- cess of a given measurement) parameters of measurement as a system. It should be noted that the collection indicated is sufficiently general (universal) and can be ap- plied for any measurement problem.

After formulating the measurement problem, it is naturally possible to consider any measurement as aprocess of solving a measurement problem,which can be divided into three stages.

At the first stage, according to a measurement problem (reflecting the question “what has to be done?”) a plan for a measurement experiment is developed (answering the question “in what way must it be done?”). At this stage a method and the required measuring instruments are selected, an observer (an operator who is able to carry out the measurement experiment) is chosen, a procedure (algorithm) for using selected measuring instruments and the methods and means of processing experimental data

Section 2.2 Physical-metrological fundamentals of constructing the RUTS systems 111 are defined more accurately (and so on). The development of this plan is realized on the basis of a priori information (accumulated before posing the given measurement problem), reasoning from the content of the problem itself.

This first stage of the measurement process can be represented by the following equation of transformation:

Jv.z/:.Ia,zi/!Iz, (2.2.3) where

Jv(z) is the corresponding transformation function realized by an operator (a subject) v, processing initial information (in a general case it may differ from an observer);

Izis information corresponding to the received plan of measurement experiment (here the space-time parameters are omitted for simplicity):

Iz D

'i,oi, i,ı'i,gi, ˇˇˇŒ'i ,mi,si,vi,wi,: : :

, (2.2.4)

where

Œ'i is the selected measurand unit;

mi is the chosen measurement method;

si ạskºis the totality of measuring instruments used to solve a given measurement problem;

viis the observer (operator) realizing the plan of measurement experiment;

wi is the means for processing measurement experiment results.

All these parameters located on the right of a vertical line in equation (2.2.4) are thecontrollable components of measurement(as of the system), which can be varied within the time of developing the measurement experiment plan. In Figure 2.3a the first stage of the measurement process is shown in diagram form.

At the second stagea process of real (physical) transformations takes place. These transformations are connected with a physical interaction of the selected measuring instruments with the object, external conditions and observer (Figure 2.3b). Usually, this process is compared with the concept “measurement”; however such an interpre- tation appears to be insufficient for revealing all THE components of measurement as the system and also of the process of the measurement problem solution, it also presents difficulties for describing the measurements different from the direct and sin- gle ones. In terms of the designations accepted here this stage in the general form can be expressed by the equation

JOs.Iz/: .o, /!hsi, (2.16) where hsi is the indications of measuring instrumentssi obtained as a result of the measurement experiment.

At the third stage the processing of the obtained measurement informationhsi is performed on the basis of the measurement experiment plan using in the general case

Vz

Zi Iz

Ia

Jv(z)

{S}i

Oi Vi Iz

{Ψ}i

hs

a)

b)

Js(Iz)

Vi

Iz

hs Wi Ip

c) Jw(Iz)

Figure 2.3.Stages of measurement as the process of the measurement problem solution.

an auxiliary computer techniquewi (Figure 2.3c).This stage, by analogy to the pre- ceding ones, can be described by the equation

Jw.Iz/: .hs,Iz/!Ip. (2.2.6) The a posteriori informationIpis the measurement resultQin accordance with the given form of its presentation. These forms are indicated in GOST 8.011. An algorithm of transition fromhstoIp DQdepends not only on the form of the presentation of the result but also on the measurement method. So, for direct single measurements the result is a value of the measurand'.meas/, according to a readouthsof the measuring instrument:

'.meas/Dh'osDnsŒ' s, (2.2.7) where'osis the constant of the given measuring instrument for a selected digital scale (scale-division value)ns, and's are the numerical value of the measurand and “true”

(or assigned) value of the unit realized in the given measuring instrument.

In a more general case the measurand value obtained as a result of a specific mea- surement has to be presented in the form

'.meas/.zi/Dn'r.Izi/Œ'rIzi (2.2.7)

Section 2.2 Physical-metrological fundamentals of constructing the RUTS systems 113 This means that both the numerical value and the measurand value'of the dimen- sionr are determined by the whole totality of parameters of the measurement system Izi, with the help of which the given measurement problemziis solved. In other words, this means that for the measurement system on the whole there are some “metrological characteristics” (much as now they are traditionally introduced for measuring instru- ments).