another contribution to the problem of applying the information theory to measurement technology

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GENERAL PROBLEMS IN METROLOGY ANOTHER CONTRIBUTION TO THE PROBLEM OF APPLYING THE INFORMATION THEORY TO MEASUREMENT TECHNOLOGY* B. G. Kaduk Tramlated from Izmeritel'naya Tekhnika, No. 8, pp. 5-6, August, 1963 Measurement is a method of cognizing nature, a process of establishing the objective truth. In this case'the point of view of life, in practice, should be the first and main point of view of the theory of cognition" [1]. The achievements of the information theory and its mathematical techniques are being used increasingly in the application of measurement technology. As an example it is possible to cite the development of the spectral analyzer for low and infrasonic frequencies with the application of time compression of samples taken from the sig- nal according to Kotel'nikov's theory [2]. Methods for a substantial increase in the precision of measuring instru- ments by their repeated calibration during measurements have been suggested [3], complex automatic assemblies, whose existence provides the author's assertions with a certain authority, have been produced and are now in use [4]. Certain aspects in the practical application of the information theory to measurement technology can be con- sidered as promising means for its further development, but doubts can be expressed as to the advisability of recon- sidering metrological definitions and, in particular, the definition of the concept of measurements. We consider the definition provided in [4] as the most suitable to the present condition of measurement technology. "Measurement is a process of obtaining information which consists in comparing experimentally measured and known quantities and signals, in performing the required logical and computing operations and presenting the in:~ formation in a digital form." It is pointed out, in objecting to the above definition, that it does not stress the gnosiological aspect of the measuring process. However, this is not completely true. From the point of view of philosophical categories in- formation is an ordered reflection of matter, and the quantity of information is a measure of the ordering of this re- flection [5]. The peculiarity of this reflection as an attribute of matter consists in the fact that it is not a sensation, but it is a property which is capable in its development of leading to a sensation. We know that "the first premise of the theory of cognition consists, undoubtedly, in asserting that the only source of our knowledge are sensations" [1]. One argument against definition [ 4] refers to the ambiguity of defining measurement as consisting of "com- paring experimentally measured and known quantities or signals" instead of comparing measured quantities and units of measurement [6]. It should be noted that in one of the classical definitions of the concept of measurement [7] the measured quantity is also compared with a known quantity, "a certain value of that quantity taken as a unit of comparison." Comparison of the measured quantity with a known quantity or signal simply generalizes the concept of meas- urement. For instance, in nuclear physics,measurement of elementary particle charges is mainly expressed in terms of an elementary charge of an electron and not in a metrological unit of charge; the measurement of the coeffi- cient of nonlinear distortions, correlation functions, or the tolerance field of any quantity is carried out precisely by comparing the measured quantity with a known quantity or a signal. On the basis of cybernetic concepts new information characteristics of measuring instruments are suggested, such as information efficiency T/ and information margin of accuracy [8]. The above characteristics depend on one of the propositions which serve as a basis for applying information theory concepts to measurement technology, namely, the relation of the quantity of information to the relative or proportional error (the error referred to the measurement limits) [9]: *Continuation of a discussion. See "Izmeriternaya tekhnika', 1961, No. 12; 1962, Nos. 1, 8, and 9. 636

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GENERAL PROBLEMS IN METROLOGY

A N O T H E R C O N T R I B U T I O N TO THE PROBLEM OF APPLYING

THE I N F O R M A T I O N THEORY TO MEASUREMENT T E C H N O L O G Y *

B. G. K a d u k

Tramlated from Izmeritel'naya Tekhnika, No. 8, pp. 5-6, August, 1963

Measurement is a method of cognizing nature, a process of establishing the objective truth. In this case ' the point of view of life, in practice, should be the first and main point of view of the theory of cognition" [1].

The achievements of the information theory and its mathematical techniques are being used increasingly in the application of measurement technology. As an example it is possible to cite the development of the spectral analyzer for low and infrasonic frequencies with the application of time compression of samples taken from the sig- nal according to Kotel'nikov's theory [2]. Methods for a substantial increase in the precision of measuring instru- ments by their repeated calibration during measurements have been suggested [3], complex automatic assemblies, whose existence provides the author's assertions with a certain authority, have been produced and are now in use [4].

Certain aspects in the practical application of the information theory to measurement technology can be con- sidered as promising means for its further development, but doubts can be expressed as to the advisability of recon- sidering metrological definitions and, in particular, the definition of the concept of measurements. We consider the definition provided in [4] as the most suitable to the present condition of measurement technology.

"Measurement is a process of obtaining information which consists in comparing experimentally measured and known quantities and signals, in performing the required logical and computing operations and presenting the in:~ formation in a digital form."

It is pointed out, in objecting to the above definition, that it does not stress the gnosiological aspect of the measuring process. However, this is not completely true. From the point of view of philosophical categories in- formation is an ordered reflection of matter, and the quantity of information is a measure of the ordering of this re- flection [5]. The peculiarity of this reflection as an attribute of matter consists in the fact that it is not a sensation, but it is a property which is capable in its development of leading to a sensation. We know that "the first premise of the theory of cognition consists, undoubtedly, in asserting that the only source of our knowledge are sensations" [1].

One argument against definition [ 4] refers to the ambiguity of defining measurement as consisting of "com- paring experimentally measured and known quantities or signals" instead of comparing measured quantities and units of measurement [6].

It should be noted that in one of the classical definitions of the concept of measurement [7] the measured quantity is also compared with a known quantity, "a certain value of that quantity taken as a unit of comparison."

Comparison of the measured quantity with a known quantity or signal simply generalizes the concept of meas- urement. For instance, in nuclear physics,measurement of elementary particle charges is mainly expressed in terms of an elementary charge of an electron and not in a metrological unit of charge; the measurement of the coeffi- cient of nonlinear distortions, correlation functions, or the tolerance field of any quantity is carried out precisely by comparing the measured quantity with a known quantity or a signal.

On the basis of cybernetic concepts new information characteristics of measuring instruments are suggested, such as information efficiency T/ and information margin of accuracy [8]. The above characteristics depend on one of the propositions which serve as a basis for applying information theory concepts to measurement technology, namely, the relation of the quantity of information to the relative or proportional error (the error referred to the measurement limits) [9]:

*Continuation of a discussion. See "Izmeriternaya tekhnika', 1961, No. 12; 1962, Nos. 1, 8, and 9.

636

where L is the measuring limit, Ax is the absolute error, 6 = Ax/L is the relative error.

The precision of an experiment is determined as the reciprocal of 6:

! A ~ ~ e

6

The information efficiencyof a measuring instrument indicates the ratio of the quantity of information at the out- put of the instrument to the entropy of the measured object:

l i

i.e., it is the coefficient of relative utilization of the received information. The information margin of accuracy X characterizes the total loss of information in the measuring instrument:

lnx = / o -- li

Caution in the evaluation of the above information characteristics of a measuring instrument is justified, since they are only tentative and depend on the conditions of the experiment. For instance, in measuring current the in- itial entropy

can vary according to the value of the carrier charge q (electrons, ions with different valences), currenti and meas- ing time t.

w

For a more rigorous determination of initial entropy it is necessary to take into consideration the wave nature of a charged particle, the charge carrier, and its interaction with the potential field of the measuring instrument, for instance, by means of Schr6dinger's equation

2m ~,+ -~ (w-u) ,=o,

where._w is the energy of the charge-carrying particle, u is the energy of the measuring instrument's potential field.

A rise in initial entropy is also due to the existence of Heisenberg's indeterminacy relationship, with this in- determinacy in actual instruments under practical conditions exceeding considerably its theoretical limit [10].

In applying the information characteristics of measuring instruments, i.e., the information efficiency and the information margin of accuracy, it is necessary to take into consideration their relationships, which makes inad- visable the application of one of the characteristics

lnx = I0 (I--IlL

Despite certain difficulties the application of the information theory concepts will not only provide a more general approach to the problems of measurement technology, but will also resolve a number of theoretical diffi- culties which arise in measuring at the physical boundaries of Observation (measurements of very small distances, microcurrents, etc.), and will determine the reliability of measurements not only from the point of view of the fault- less operation of measuring instruments, but also from the point of view of the authenticity of measurements.

L I T E R A T U R E C I T E D

1. V. I . Lenin, Materialism and Empirocriticism [in Russian], Gospolitizdat (State Political Literature Press)(1951). 2, W.R. Chynoweth and R. Page, M. Hat. Cony. Rec. Pt., 4 (1959). 3. P.V. Novitskii, Izmerit. tekh., No. 4 (1962). 4. K.B. Karandeev, V. I. Rabinovich, and M. P. Tsapenko, Izmerit. tekh., No. 12 (1961). 5. I .B. Novik, Voprosy filosofii, No. 6 (1962).

637

6. P.M. Tikhodeev, Outlines of Initial Measurements [in Russian], Moscow (1954). 7. M.F. Malikov, Foundations of Metrology. Part 1 [in Russian], Moscow (1949). 8. P.V. Novitskii, Izmerit. tekhn., No. 1 (1962). 9. L. Brillouin, Journal Applied Physics, Vol. 24, No. 9 (1953).

10. L. Brillouin, Science and the Theory of Information [Russian translation], Fizmatgiz (State Pre.~s for Physical and Mathematical Literature ) , Moscow (1960).

G R A P H I C O - A N A L Y T t C A L D E T E R M I N A T I O N OF THE M E A N - S Q U A R E

S Y S T E M A T I C ERROR IN D I S C R E T E MEASUREMENTS

I . M. S h e n b r o t

Translated from Izmeritel'naya Teldanika, No. 8, pp. 6-10, August, 1963

Several works [1, 2] deal with the analytical determination of the mean-square systematic error in discrete measurements. The relationships thus obtained are intended for evaluating errors for a given readout period, or for selecting that period for a given quadratic mean error. In this operation the measured quantity is considered as a stationary random function of time and is characterized by correlation function B(r) or by a power spectrum S(w).

The difficulty in calculating by means of these analytical relationships consists in the fact that the correla- tion function (or power spectrum) of the random process under investigation is almost always found experimentally in the form of a graph. It is usually difficult to represent analytically a correlation function which has been obtained graphically, and it introduces an additional computation error.

hT [k,OT [l~,2}r [It~3}r

~(o}d b

BrOil

Fig. 1 Fig. 2

Below we provide a more convenient graphico-analytical method of determining the quadratic mean error from a correlation function B(r) graph for several types of discrete measurements:

discrete measurements with replacement of the actual random process x(t) over the duration of each readout period T by its values x0(t ) = x(kT) at the instant of readout t = kT (stepped substitution of the process, Fig. 1);

discrete measurements with replacement of the process x(t) by segments whose value changes at a constant speed from x(kT) at the instant of readout t= kT up to x[(k+ 1)T] at the instant of the next readout t =(k+ 1)T (trape- zoidal substitution of the process, Fig. 1);

discrete integration with respect to stipulated ordinates measured at the readout instants kT.

Stepped substitution of the process (polygonal path abodefg in Fig. 1). The quadratic mean error of a stepped substitution of the process with a step T is

638