Діагностика раптових змін у динаміці об'єктів контролю

Abstract

У даній статті розглядається клас лінійних стохастичних систем, динаміка яких може зазнавати епізодичних змін, але настільки рідких, що статистичні дані про частоту цих змін відсутні. За таких умов методами оптимальної фільтрації та узагальненого відношення правдоподібності розв`язується задача сукупного оцінювання стану динамічної системи, виявлення моменту появи непередбачуваних змін та їх ідентифікації.

In this article the class of linear stochastic systems which dynamics can change incidentally and so seldom that statistical data on the frequency of changes are absent is considered. By results of the last researches and basic references analysis which is carried out in this direction it is revealed that used in such case the model conditional optimum Kalman`s filter adjusted on a rated operating mode of controlled object creates the current assessment of a dynamic system state vector on the basis of all previous history and over time becomes too careful, inertly reacts to fast changings of a trend in separate results of supervision. In the presence of additional, real restrictions: malfunctions happen time to time incidentally and so seldom that statistical data on the frequency of their emergence are absent; emergence of malfunctions has single character ­ cases of simultaneous emergence two and more malfunctions are excluded; at the disposal of the observer there is enough time for the analysis and decision­making, there is an actual problem of increase Kalman`s filter sensitivity to sudden changes and application of compensation schemes. In this case this rather prime and universal model allows considering malfunctions both in a management subsystem and in a sensors subsystem which are usually modelled by jumps, shifts, or drift in separate variables state. For the solution of the specified task the following stages are used: on the basis of the assumption that malfunctions are absent the Kalman`s filter is implemented; the secondary system of differential signal processing is implemented, due to emergence fault status monitoring of regarding change properties is its technical task; localization and the size caused loss estimation is carried out it for the introduction of compensation schemes in case of malfunction is detected. Use of a restriction data standard method of some last results in case of increase volume calculations in real time system. An assessment of emergence fault time to define within the data ive strobe is offered. The issue of the choice of acceptable width ive strobe is resolved by careful mathematical modelling. In such sequence methods of optimum filtering and the generalized likelihood ratio solve a problem of cumulative estimation camp of dynamic system, the emergence unforeseen changes of moment detection and identification.