Soft Measurements and Computations

ISSN 2618-9976

Soft Measurements and Computations
Modern Intelligent Measurement Theory. Bayesian Intelligent Measurements

S.V. Prokopchina


The development of measurement theory is primarily associated with the creation of new types of measurements, such as intelligent, fuzzy, soft, cognitive, polysystem, entropy and other types of measurements. The distinctive features of these types of measurements is the possibility of using different knowledge in the implementation of measurements. In this regard, methods of measurement of these species include methods and models of artificial intelligence, fuzzy set theory, cognitive theory. From a methodological point of view, this diversity of new types of measurements together with classical ones determines the necessity of their systematization and classification for their effective and purposeful application. This issue is devoted to the article.

Key words: Measurement Theory, classification, intelligent, fuzzy, soft measurement

Introduction. Modern measurement tasks

The development of the General theory of measurements stimulated the expansion of metrological requirements and nomenclature of indicators of data quality, as well as the emergence of new types of measurements, metrological certification and control, in particular, Metrology algorithms, models, objects and measurement conditions.

As a rule, the practice of modern measurement tasks are accompanied by complex experimental conditions associated with the presence of a considerable a priori uncertainty about the properties of objects and of the factors affecting the environment of their functioning, the relationships between them, the inaccuracy and incompleteness of the experimental information, inaccessibility to direct observation of many properties of objects, or influencing factors, what distinguishes the cognitive function of the methodology of their solutions as fundamental. Therefore, the formulation of these problems as measuring causes the strengthening of the role of cognitive function of measurements and demands the results of their decisions in the form of knowledge (analytical expressions for models, as well as conclusions and decisions) on the basis of taking into account the entire amount of a priori information and information received during the measuring experiment, including non-numeric. Thus, the process of understanding the results of measurements in the form of numbers, as well as analytical conclusions and decision-making are included in the contour of the measuring processes. However, this is permissible only in the presence of metrological support at all stages of decision-making. Only under this condition, the processing of information can be attributed to the measuring.

We define this type of measurement tasks as a type of complex measurement tasks, understanding this complex dimension objects, which is a system of interrelated properties that are actively interacting with the ambient environment, complex and multi-step analytical measuring processes, difficult conditions of measurement for information uncertainty and instability as the objects themselves, and their environment.

The fulfillment of this requirement contributed to the attraction of the theory of artificial intelligence apparatus, optimal solutions, computer science to the creation of new information-measuring technologies for processing heterogeneous flows of experimental data by means of measuring equipment.

One of the main points of construction of measuring technologies is to determine the type of information situation in which measurements are made. There are three types of measurement information situations.

This is a situation with completely certain information, and the conditions of measurement (type I); the situation with incomplete certain information and stable measurement conditions (type II), but this situation with considerable uncertainty, and partial uncertainty can be removed in the iterative mode , adapting the model of the object of measurement according to the information received (type II) and situations with significant uncertainty, instability of the measurement conditions , the active influence of the external environment (type III).

Identifying this specificity of methods, there appeared, in addition to the existing direct measurements, which are implemented in the first information situation, the concept of:

- integrated measurement based on extended concepts of the measurement and thesauri, which are implemented as structures modelitem; (situation (type II);

- statistical measurements [based on the probability-theoretical approach; situation (type II);

- dynamic adaptive measurements, emphasizing the time characteristics of the properties of objects of measurement; situation (type II);

- adaptive measurements with correction of the result in the process of measurements by a given algorithm; situation (type II);

- interval measurements of the situation (type II) and (type III);

- processor measures that allocate the class of it tools necessary for their implementation; situation (type II);

- algorithmic measurements determining the relationship with the computational aspects of solving measurement problems; situation (type II);

- measure, reflecting their applied focus (industrial measurement, bioisoprene, radio astrophysics, aerobalance, social dimension, economic dimension, etc.) situation (type II), and intellectual dimensions of the situation (type III).

In further works of the author of the given article concepts were offered, theoretical bases, the principles and information technologies and means of the following types of measurements which are realized in situations are developed (type III):

- Bayesian intelligent measurements based on the Bayesian regularization approach;

- fuzzy measurements in the form of a set of alternative solutions with varying degrees of reliability;

- soft measurements with flexible logic output measurement solutions;

- the cognitive dimension with the inclusion of the subject of the probe in the measuring technology;

- polysystem measurements with the object of measurement in the form of complex Autonomous systems. actively interacting with each other and external environment for this population;

- entropy measurements in which the object of measurement is the amount of information received;

- retrospective measurement on the basis of the deferral and technologies BII;

- prospective measurement on the basis of Bayesian intelligent technologies.

For the above mentioned new types of measurements it is possible to derive the corresponding equations of measurement explaining their methodology, similarities and differences.

The object of the measurement entropy measurement Gt(H) is the amount of information It(H), obtained at each new measurement of properties of the observed real object Gt. The difference between the a priori value of the amount of information It-1(H), and again received It(H), allows you to define a change in conditional entropy ΔHt(G)| Dt(G) assuming the existence of solutions for the selected dynamic compact measurement solutions Dt(G) at a certain point in time t. The amount of information obtained in the experiment is determined by the difference between a priori and a posteriori regularized Bayesian estimators (mles) on a scale of dynamic constraints.

Thus, the equation for entropy measurements has the following form:

ΔHt (G)| Dt (G) = 1 - (It(H), - It-1(H),), (1)

It(H), - the amount of Fisher information for the corresponding a priori and a posteriori regularized Bayesian estimators of the observed Gt object properties, the Calculation of these parameters is not difficult, since RBOs are essentially an estimate of the discrete distribution law of the observed object properties. According to the approximation algorithm estimates distribution laws of the model laws of The system of curves K. Pearson, proposed in, estimates can be approximated and the habit of the amount of information formula for these laws can be used to improve the accuracy of calculations.

In the works of the author on Bayesian statistical measurements and Bayesian mathematical statistics [38,53,45 and others], theoretical bases, methodology, information technologies are developed and applied problems of measurement of numerical characteristics of random variables and processes, correlation measurements, measurements of test hypotheses are solved. measurement of risks and potentials, functional measurements of the distribution laws, measurement of trends, the regression of measurements, entropy measurements in conditions of uncertainty.

For processing of archive data and measurement of events of the past time has developed a methodological framework for retrospective measurement on the basis of the deferral. Historical dimensions allow you to determine estimates of an object's properties at past times or to restore its dynamic model if you have current and archived information of any type about the object and external factors.

For perspective measurements (measurements for future periods and situations), the basic equation of measurements is constructed taking into account the forecast values associated with the measured other properties of the object and environment Gt+1(OE)

It is obvious that the above types of measurements are different for objects, methods and application-specific measurement tasks. The systematization and classification of these types of measurements will improve the efficiency of using the full range of types of measurements. Figure 1.the variant of such classification is offered.

As features of the classification are the following:

1. On the method of using knowledge in the measuring process:

- classical measurements based on current experimental numerical data;

- intelligent measurements using different types of knowledge along with the incoming measurement information in the measurement process.

2. By the method of output of the measuring solution:

- probabilistic approach (statistical measurements, Bayesian intelligent measurements);

- with flexible output logic (soft measurements).

3. According to the method of organization of the measuring process:

- without the inclusion of the subject of the probe in the measuring process;

- with the inclusion of the subject-meter in the contour of the measuring process (cognitive measurement).

4. If possible, the implementation of algorithmic processing:

- without the possibility of implementing algorithmic processing (direct measurements);

- with the possibility of implementing algorithmic processing (indirect measurements, algorithmic measurements).

5. On the complexity of the measurement object:

- simple property;

- complex system (system measurements, combined, joint measurements);

- a set of systems (polysystem measurements).

6. On the complexity of the measurement conditions:

- stable measurement conditions;

- instability conditions (dynamic measurements);

- conditions of uncertainty and instability (retrospective, prospective intellectual measurements).

7. The type of application-specific measurement tasks:

Different types of applied measurements (for example, listed above).

This classification, as well as a brief historical review of the development of modern measurement theory, certainly do not claim completeness. Therefore, the author would be grateful to colleagues for discussions and continuation of this topic.

Figure 1. Classification of modern types of measurements


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