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9УДК 681.518.9; 621.384.3
S. S. Antsyferov, K. N. Fazilova, K. E. Rusanov Moscow Technological University MIREA, c. Moscow, Russia Russia, 119454, c. Moscow, Vernadsky ave., 78
EVALUATION ALGORITHM OF COGNITIVE SYSTEMS NON-EQUILIBRIUM STABILITY
С. С. Анцыферов, К. Н. Фазилова, К. Е. Русанов Московский технологический университет МИРЭА, г. Москва, Россия 119454, Россия, г. Москва, пр. Вернадского, 78
АЛГОРИТМ ОЦЕНКИ НЕРАВНОВЕСНОЙ УСТОЙЧИВОСТИ КОГНИТИВНЫХ СИСТЕМ
С. С. Анциферов, К. Н. Фазтова, К. G. Русанов Московський технолопчний ушверситет М1РЕА, м. Москва, Роая Роая, 119454 , м. Москва, пр. Вернадського, 78
АЛГОРИТМ ОЦ1НКИ НЕР1ВНОВАЖНО1 СТ1ЙКОСТ1 КОГН1ТИВНИХ СИСТЕМ
Development and practical approbation of non-equilibrium stability evaluation algorithm of cognitive systems is carried out. Algorithm is based on operations of formation the initial database of properties and knowledge base about possible states of the system, identification of the system state and, if necessary, transformation the initial system database.
Keywords: cognitive system, stability of effective functioning, structural element, entropy indicators, database, knowledge base, transformation, identification.
Проведена разработка и практическая апробация алгоритма оценки неравновесной устойчивости. В основу алгоритма положены операции формирования исходной базы данных о свойствах и базы знаний о возможных состояниях системы, идентификации состояния системы и, в случае необходимости, - трансформация исходной системы базы данных. Ключевые слова: когнитивные системы, устойчивость эффективного функционирования, структурные элементы, энтропийный показатели, база данных, база знаний, трансформация, идентификация.
Проведена розробка i практична апроба^я алгоритму оцЫки нерiвноважноT стшкосп. В основу алгоритму покладено операци формування вихщнот бази даних про властивост i бази знань про можливi стани системи, щентифшацп стану системи i, в раз1 необхщносп, трансформа^я вихщнот системи бази даних.
Ключовi слова: когн1тивн1 системи, стмкють ефективного функцюнування, структуры елементи, ентропмний показники, база даних, база знань, трансформац1я, щентиф1кац1я.
Introduction
Because of increasingly widespread cognitive technologies implementation into sphere of processing information flows, characterized by a change intensity in a wide range, both in quantitative and qualitative (semantic) terms, task of developing feasible methods of evaluation such an important indicator as stability of effective functioning becomes urgent. The basis for the development of methods is, as a rule, a model of non-equilibrium stability of cognitive systems (CS). In works [1-5], a model based on probabilistic representation of effective functioning of system's interconnected structural elements (SE) was proposed and investigated. This model served as a basis for the development of nonequilibrium stability evaluation algorithm. Implementation of developed method in the form of algorithm with its subsequent practical testing is an important point.
Purpose of this work is the development and practical approbation of non-equilibrium stability estimation algorithm of cognitive systems.
Development of Nonequilibrium Stability Evaluation Algorithm of CS
The algorithm assumes following operations:
Data base creation
Based on previously proposed model, the main properties of SE should be considered probabilistic efficiency measures, functioning of each individual SE and their pairwise interaction.
Evaluation of SE indicators properties can be made on basis of calculation-analytical and expert methods. Calculation-analytical method based on usage of test information signals to assess correct decisions made on results of testing. The results obtained by testing should be subjected to analytical processing associated with the definition of probabilistic measures of information content.
The Bayesian ratio can be used to determine the measure of SE efficiency
g ^ p^jkhijk^jk^
m
where p - a posteriori probability density of the j-th SE on the k-th cycle of the system operation;
p^ijk - a priori probability density of the j-th SE on the k-th cycle of the system operation;
p \Mjk - likelihood function;
I jk - intensity of information flow at the input of the j-th SE at the k-th cycle of the system;
Mjk - measure of informativeness of the j-th SE at the k-th cycle of the system operation.
Functions in this ratio are selected according to the following assumptions:
* dependence of the likelihood function on the measure of informativeness Mj is linear;
* a priori probability p(M) is approximated by a uniform law.
Evaluation Algorithm Of Cognitive Systems Non-Equilibrium Stability
To clarify the approximation p(m) experimental determination is carried out m= f(flr), = r — where r- property metrics of some test message, r -evaluation of the performance characteristics of the test message structure element (fig. 1).
Fig. 1 - Functions of evaluation the measure of informativeness of an SE
The following operations are used to determine ffr (fig. 2): formation of test information message; Evaluation of properties indicators by structural element; comparison of obtained estimate with the true value r ; definition JJr.
Formation of test information message
Evaluation of properties indicators by structural element
r V
Ar
Fig. 2 - Definition scheme flr
This sequence of operations is applied to each structural element. If for some SE it turns out that the dependence m on ffr is nonlinear, then by differentiating this
dependence a new approximation of the distribution law is established p(m) and then the value of a posteriori probability is determined by the Bayes formula. In a similar way, efficiency of pairwise interaction of SE is evaluated.
Expert method is based on principle of consistent ranking of probabilistic properties of structural elements.
The generated database includes (fig. 3) two arrays:
* probability estimates of each SE effectiveness Pi} i=1,n;
* probability estimates of SE pairwise interaction effectiveness I',,, ij=l,n.
Fig. 3 - Database arrays Determination of system s entropy indicators
According to the model of CS non-equilibrium stability, entropy parameters can be determined using the following equations
H = Hj+H2 =
-YXPjlogPj
i j
№ ,2 MI'
(H-^-y-
2MJ 4MJ2
- system's entropy (2)
(3)
where № - increment of information flow intensity; MJ - increment of information flow processing intensity.
Roots of equation H0 = 0, Hl — are points of stability.
Knowledge base formation
Knowledge base (KB) is formed by two equations (2 and 3) for different combinations of signs of increments 0 <JJJ < 0 and 0 <JJJ <0, and is a set of phase portraits that characterize possible state of the system.
This set includes subsets of phase portraits characterizing stable and unstable functioning in the point area H0 and H}. Identification of system status
Identification is carried out by determining the position of the point with coordinates
H and H on the diagram. Based on identification results, a decision is made on the system's state. If system's state does not correspond to the required, then the transformation of matrix array is performed until the desired result is obtained. Evaluation algorithm
According to above operations, algorithm (fig. 4) can have the following form
on
Data base (Matrix array)
Fig. 4 - Block diagram of evaluation algorithm of cognitive systems nonequilibrium stability
Practical Testing of the Algorithm
To test the algorithm was used CS, which is a team of employees of a scientific laboratory, consisting of ten people. According to the results of expert evaluation, was formed matrix array:
N 1 2 3 4 5 6 7 8 9 10
Pi 0,1 0,1 0,1 0,2 0,8 0,7 0,8 0,8 0,6 0,1
N 1 2 3 4 5 6 7 8 9 10
1 0,1 0,1 0,1 0,2 0,1 0,2 0,1 0,1 0,1
2 0,1 x 0,1 0,1 0,2 0,1 0,1 0,1 0,1 0,1
3 0,1 0,1 x 0,1 0,2 0,1 0,1 0,1 0,1 0,1
4 0,1 0,1 0,1 0,2 0,1 0,1 0,1 0,1 0,1
5 0,1 0,1 0,1 0,1 x 0,7 0,8 0,7 0,7 0,1
6 0,1 0,1 0,1 0,1 0,7 0,7 0,7 0,6 0,1
7 0,1 0,1 0,1 0,1 0,8 0,7 x 0,6 0,7 0.1
8 0,1 0,1 0,1 0,1 0,8 0,6 0,6 0,5 0,1
9 0,1 0,1 0,1 0,1 0,7 0,5 0,5 0,5 x 0,1
10 0,1 0,1 0,1 0,1 0,1 0,1 0,1 0,1 0,1 x
Entropy indicators of the matrix array have values H = 16,5 u H = -254,9 (point 1, fig. 5). The identification results showed that the point 1 is sufficiently far from stable functioning zone and is located on the curve A of the phase portrait of stable functioning in the point Hj area.
Fig. 5 - System functioning phase portrait
As transformations associated with the reduction in the number of structural elements N, a consistent approach to the stable zone operation occurs:
N 10 8 6 4
Point 1 Point 2 Point 3 Point 4
H 16,47 13,37 8,19 3,53
H -254,9 -165,5 -58,9 -8,9
It should be noted that at the obtained values, H and H it is likely that the system will not be able to meet conditions JJJ > 0 and JJJ > 0. At JJJ < 0 and JJJ < 0 position of the point 7'characterizing the system s state will be located on the curve B of unstable
operation. In this case, the transformation of original data array will not lead to desired result.
Evaluation Algorithm Of Cognitive Systems Non-Equilibrium Stability
Conclusion
An algorithm that allows to assess the CS state and if necessary, transformation aimed at achieving effective and sustainable operation.
Practical testing of the proposed algorithm on a real cognitive system has shown correctness of previously proposed theoretical model of CS nonequilibrium stability.
Based on the results of practical testing, it is possible to make a preliminary conclusion that in some cases CS effective functioning is achieved with a small number of participants with a sufficiently high level of efficiency of their functioning.
Список литературы
1. Анцыферов С. С. Определение показателей устойчивого функционирования нейроподобных систем [Текст] / С. С. Анцыферов, К. Н. Фазилова, К. Е. Русанов // Материалы XXV Всероссийского семинара «Нейроинформатика, её приложения и анализ данных», 29 сентября. - 1 октября 2017 г., Красноярск : Институт вычислительного моделирования СО РАН, - 2017. - С. 8-13.
2. Анцыферов С. С. Имитационная динамическая модель когнитивных систем [Текст] / С. С. Анцыферов, К. Н. Фазилова, К. Е. Русанов // Проблемы искусственного интеллекта. - 2017. - № 2 (5). - С. 32-39.
3. Antsyferov S. S. Building and functioning principles of intelligence information processing systems of spati-temporal fields [Text] / S. S. Antsyferov, K. N. Fazilova, K. E. Rusanov // Science Intensive Technologies. - 2018. - № 2. - P. 36-45.
4. Antsyferov S. S. Indicators of properties of intelligent systems of pattern recognition of space-time fields [Text] / S. S. Antsyferov, K. N. Fazilova, K. E. Rusanov // Гибридные и синергетические интеллектуальные системы : Материалы IV Всероссийской Поспеловской конференции с международным участием. Под ред. A. В. Колесникова. - Калининград, 2018. - С. 330-337.
5. Antsyferov S. S. Modeling of non-equilibrium stability of cognitive systems [Text] / S. S. Antsyferov, K. N. Fazilova, K. E. Rusanov // Моделирование неравновесных систем: Материалы XXI Всероссийского семинара, 5-7 октября 2018 г. - Красноярск : Институт вычислительного моделирования Сибирского отделения Российской академии наук, 2018. - С. 9-14.
6. Анцыферов С. С. Проблемы искусственного интеллекта [Текст] / С. С. Анцыферов // Проблемы искусственного интеллекта. - Донецк : ГУ ИПИИ. - 2015. - № 0(1). - С. 5-12.
7. Анцыферов С. С. Показатели неравновесной устойчивости когнитивных систем [Текст] / С. С. Анцыферов, К. Н. Фазилова, К. Е. Русанов // Проблемы искусственного интеллекта. - 2016. - № 2 (3). - С. 4-11.
References
1. Antsyferov S. S., Fazilova K. N., Rusanov K. E. Determination of indicators of stable functioning of neural-like systems. Materialy XXV Vserossijskogo seminara «Nejroinformatika, eyo prilozheniya i analiz dannyh», 29 sentyabrya - 1 oktyabrya 2017 g., Krasnoyarsk: Institut vychislitel'nogo modelirovaniya SO RAN. 2017. pp. 8-13.
2. Antsyferov S. S., Fazilova K. N., Rusanov K. E. Simulated dynamic model of cognitive systems. Problems of Artificial Intelligence. 2017. 2 (5). pp. 32-39.
3. Antsyferov S. S., Fazilova K. N., Rusanov K. E. Building and functioning principles of intelligence information processing systems of spati-temporal fields. Science Intensive Technologies. 2018. no. 2. pp. 36-45.
4. Antsyferov S. S., Fazilova K. N., Rusanov K. E. Indicators of properties of intelligent systems of pattern recognition of space-time fields. Gibridnye i sinergeticheskie intellektual'nye sistemy / Materialy IV Vserossijskoj Pospelovskoj konferencii s mezhdunarodnym uchastiem. Pod red. A.V. Kolesnikova, Kaliningrad, 2018, pp. 330-337.
5. Antsyferov S. S., Fazilova K. N., Rusanov K. E. Modeling of non-equilibrium stability of cognitive systems. Modelirovanie neravnovesnyh sistem: Materialy XXI Vserossijskogo seminara, 5-7 oktyabrya 2018 g., Krasnoyarsk: Institut vychislitel'nogo modelirovaniya Sibirskogo otdeleniya Rossijskoj akademii nauk, 2018, pp. 9-14.
6. Antsyferov S.S. Problemy iskusstvennogo intellekta [Problems of Artificial Intelligence]. Problems of Artificial Intelligence, 2015, no. 0(1), pp. 5-12.
7. Antsyferov S. S., Fazilova K. N., Rusanov K. E. Pokazateli neravnovesnoi ustoichivosti kognitivnykh sistem [Indicators of Non-Equilibrium Stability of Cognitive Systems]. Problems of Artificial Intelligence, 2016, no. 2(3), pp. 4-11.
RESUME
S. S. Antsyferov, K. N. Fazilova, K. E. Rusanov
Evaluation Algorithm of Cognitive Systems Non-Equilibrium Stability
Background: because of increasingly widespread cognitive technologies implementation into sphere of processing information flows, characterized by a change intensity in a wide range, both in quantitative and qualitative (semantic) terms, task of developing feasible methods of evaluation such an important indicator as stability of effective functioning becomes urgent.
Materials and methods: evaluation of SE indicators properties can be made on basis of calculation-analytical and expert methods.
Results: practical testing of the proposed algorithm on a real cognitive system has shown correctness of previously proposed theoretical model of cognitive system nonequilibrium stability. Based on the results of practical testing, it is possible to make a preliminary conclusion that in some cases cognitive systems effective functioning is achieved with a small number of participants with a sufficiently high level of efficiency of their functioning.
Conclusion: an algorithm that allows to assess the cognitive system state and determine the probabilistic indicators of the structural element, providing effective sustainable operation.
РЕЗЮМЕ
С. С. Анцыферов, К. Н. Фазилова, К. Е. Русанов
Алгоритм оценки неравновесной устойчивости когнитивных систем
История вопроса, исходные данные: в связи со все более широким внедрением когнитивных технологий в сферу обработки информационных потоков, характеризующихся изменением интенсивности в широком диапазоне, как в количественном, так и в качественном (смысловом) отношении, актуальной становится задача разработки практически реализуемых методов оценки такого важного показателя когнитивной системы, как их устойчивость эффективного функционирования.
Материалы и методы: оценка показателей свойств структурного элемента может производитьсь на основании расчетно-аналитического и экспертного методов.
Результаты: практическая апробация предложенного алгоритма на реальной когнитивной системе показала правильность предложенной ранее теоретической модели неравновесной устойчивости когнитивных систем. По результатам практической апробации можно сделать предварительное заключение о том, что в ряде случаев эффективное функционирование когнитивных систем достигается при небольшом числе участников с достаточно высоким уровнем эффективности их функционирования.
Заключение: разработан алгоритм, позволяющий производить оценку состояния когнитивной системы и в случае необходимости трансформации, направленные на достижение эффективно-устойчивого функционирования.
Статья поступила в редакцию 06.08.2018.
