Optimal Control of the Thermistor Problem in Three Spatial Dimensions

This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness and continuity for the state system are derived by employing maximal parabolic regularity in the fundamental theorem of Pr\"uss. Global solutions are addressed, which includes analysis of the linearized state system via maximal parabolic regularity, and existence of optimal controls is shown if the temperature gradient is under control. The adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem in form of a qualified optimality system. The theoretical findings are illustrated by numerical results

Optimal Control of Nonlocal Thermistor Equations

We are concerned with the optimal control problem of the well known nonlocal thermistor problem, i.e., in studying the heat transfer in the resistor device whose electrical conductivity is strongly dependent on the temperature. Existence of an optimal control is proved. The optimality system consisting of the state system coupled with adjoint equations is derived, together with a characterization of the optimal control. Uniqueness of solution to the optimality system, and therefore the uniqueness of the optimal control, is established. The last part is devoted to numerical simulations.Comment: Submitted 21-March-2012; revised 11-June-2012; accepted 13-June-2012; for publication in the International Journal of Contro

Theoretical substantiation method and system diagnostics of mobile agricultural machinary

Побудована діагностична модель стану МСГТ у вигляді графу взаємозв’язку структурних параметрів з певними рівнями. Розглядається взаємозалежність технічного стану агрегатів і діагностичних систем. За кількісну оцінку діагностичної інформації взято різницю між повною і залишковою інформаційними ентропіями. За основу вибору діагностичних параметрів взято такі критерії, як повнота контролю і швидкість отримання інформації. Built diagnostic model MAM status as a graph of the relationship of structural parameters of a certain level. We consider the interdependence of technical condition units and diagnostic systems. For a quantitative assessment of diagnostic information taken distinction between full and residual information entropy. It is based on the choice of diagnostic parameters taken criteria such as completeness and speed control for information

Theoretical basing of the technical condition control points of systems and units of means of transport

В роботі для прогнозування залишкового ресурсу систем і агрегатів засобів транс- порту за їх фактичним технічним станом запропоновано ймовірнісно-фізичний підхід. На основі цього підходу, а також ймовірнісно-статистичного розроблено алгоритми оцінки між діагностичних інтервалів при незначному числі діагностик та визначення оптималь- ного значення першого інтервалу діагностики, а також розроблена методика оцінки пара- метрів ряду законів розподілу напрацювання по значеннях числових характеристик бази ді- агностичних даних. In this article for forecasting of a residual resource of elements of systems and units of means of transport for their actual technical condition is proposed probabilistic-physical approach. The essence of the approach is to use statistical information and an actual values resource defining diagnostic parameters. In the operation of means of transport two development options are considered: monotony when a parameter does not change through time, or the changes are minor and non-monotonic, when there are the increasing and decreasing of values of diagnostic parameters with preservation of tendencies of their development. The mathematical apparatus of determining the first interval control of technical condition and forecasting of runs until the next control using the ratio of the minimum intensity of operating costs, which takes into account the costs of restoration of the technical condition during unscheduled repairs and preventive costs during scheduled maintenance, is proposed. Based on the developed mathematical apparatus, a number of algorithms for its implementation are proposed. In predicting time to failure using the developed algorithms, we used the following distributions: inverse Gaussian, Weibull-Gnedenko, Birman-Saunders, truncated normal and generated for these methods of parameters estimation based on the procedure of isolation of decisions and parameters satisfying the property is almost an increasing function of the intensity of the operating costs. Features patterns between the parameters of the distribution laws, mathematical expectation of the run and its dispersion are shown. Determination of the parameters of the distribution laws allows to more accurately describe and identify the rational operating times for the first and subsequent intervals of control of technical condition of systems and and units of means of transport

Studying the Tribological Properties of Mated Materials C61900 - A48-25BC1.25BNo. 25 in Composite Oils Containing Geomodifiers

With the development of dispersed systems in tribology, there emerged a possibility to use effectively functional additives to lubricants in the form of geomodifiers. When introducing composite oils with geomodifiers, it is not necessary to perform constructive changes in mated machine parts, however, their wear resistance and alignment increase. This requires experimental tribological research.It was proposed to use geomodifiers KGМF-1+oleic acids as a functional additive to motor oil, fresh oil Monnol TS-5 UHPD 10W40 and composite oil Monnol TS-5 UHPD 10W40+XADO HighWay for Diesel Truck (2.0...2.3 %) were chosen for comparison. An increase in friction momentum of different mated samples in the studied oils was recorded on the friction machine of 2070 СМТ-1 model with the additional module "ring – ring". Wear intensity in the samples in the studied oils was determined using the method of measuring the amplitude of the acoustic signal directly from the friction zone with the help of the device produced by Brüel&Kjear company.It was found that an increase in effectiveness of the oil compositions is observed in the following order: Monnol TS-5 UHPD 10W4, Monnol TS-5 UHPD 10W40, Monnol TS-5 UHPD 10W40+XADO HighWay for Diesel Truck, Monnol TS-5 UHPD 10W4+KGМF-1+oleic acid. The indicator of wear of the metal samples in the medium of modified oil Monnol TS-5 UHPD 10W4+KGМF-1+oleic acid, in comparison with basic oil decreased by 11.5...14.3 %. The value of critical load increased by 17.2 % and welding load increased by 19.3 %, respectively. In turn, it was found that maximum intensity of wear of the sample when using modified oil Monnol TS-5 UHPD 10W4+KGМF-1+oleic acid decreased by 3.4...6.0 times.The obtained data are necessary for the formation of composite oils and substantiation of conditions of their further operation during the period of forced alignment of parts tribojunctio