Перевод заглавия: The restoration of temperature distribution in a two-dimensional domain by a tomographic method by using the results of measurements for electric resistance of oriented conductors
Кл.слова (ненормированные):
двумерное распределение температуры -- термометр сопротивления -- система линейных алгебраических уравнений -- решение томографической задачи -- two-dimensional temperature distribution -- resistance thermometer -- system of linear algebraic equations -- the solution of a tomographic problem
Аннотация: Рассмотрена возможность использования “термометра сопротивления” для измерения распределения температуры в двумерной области. Создана математическая модель датчика, сводящаяся к решению томографической задачи. Важной особенностью модели является то, что число уравнений в системе линейных алгебраических уравнений (СЛАУ) больше числа переменных. Это позволяет уменьшить ошибки в исходных данных. Создана программа для определения решения СЛАУ с плохо обусловленной матрицей, позволяющая обрабатывать результаты измерений в реальном масштабе времени. Выполнен тестовый расчет. При малом числе ракурсов измерений получена удовлетворительная точность восстановления температуры.
Purpose. To ensure a long period of active lifetime of space vehicles, it is necessary to use effective methods and means to control physical processes leading to premature failure of on-board radio electronic equipment both at the stage of ground testing and during active operation of the spacecraft in space. Long-term testing experience for electronic equipment shows that monitoring compliance with necessary temperature conditions of onboard equipment plays the main role in ensuring reliability. Ideally, the thermal control should be performed for all elements of radio electronic units in real time. Method. The possibility of using a “two-dimensional resistance thermometer” for recording the thermal field of a printed circuit board of an electronic unit is considered. The principle of operation of the thermometer is based on the measurement of integral resistances of extended mutually intersecting conductors in a medium with inhomogeneous temperature distribution. The registration of the integral resistances of individual conductors is possible with the help of an automated measuring system by solving the tomographic problem aimed to obtain the temperature distribution on the surface of the printed circuit board. Result. The design of the “two-dimensional temperature sensor” is considered. The sensor is technologically compatible with the design of the printed circuit board of the radio electronic unit. A mathematical model of the sensor is developed. It is reduced to the solution of a tomographic problem. A program for solving a system of linear equations with an ill-conditioned matrix is developed that provides the real-time processing for measurement results. The test calculation is performed. A satisfactory accuracy of the temperature restoration is achieved. Conclusion. A “two-dimensional resistance thermometer” can be used to measure a two-dimensional temperature field for a printed circuit board of a radio electronic unit in real time. The mathematical model allows adapting the thermometer design to a specific radio electronic unit and selecting the required accuracy of the temperature field restoration.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Институт теоретической и прикладной механики им. С.А. Христиановича СО РАН
Доп.точки доступа:
Деревянко, Валерий Александрович; Derevyanko Valery Aleksandrovich; Латыпов, Альберт Фатхиевич; Latypov Albert Fatkhievich