ДОСЛІДЖЕННЯ ВПЛИВУ МЕТОДИЧНОЇ ТА ІНСТРУМЕНТАЛЬНОЇ СКЛАДОВИХ ПОХИБКИ НА ТОЧНІСТЬ РЕКОНСТРУКЦІЇ ТЕМПЕРАТУРНОГО ПОЛЯ НА ПОВЕРХНІ СТІНКИ
Journal Title: Вимірювальна техніка та метрологія - Year 2016, Vol 1, Issue 77
Abstract
In the paper the reconstruction of temperature distribution based on resistance measurements of linear sensing elements using tomography method are considered. The methodical and instrumental errors of temperature distribution are investigated and analyzed. In particular the first component depends on number of sensors and degree of used approximation of temperature distribution and the second component depends on the level of random and systematic additive and multiplicative components in measurements. Two schemes of placing of the linear temperature resistivity sensors on the investigation object are researched in the paper (Fig. 1). Also, three approximation models of the temperature distribution in the form of two-dimensional cosine, asymmetrical cosine and Gaussian with initial temperature Θ0 = 100 ºС and different maximal change temperature Θm = 25; 10 and 5 ºС are investigated. The spatial resistivity distribution can be approximated by known two-dimensional basic functions are presented by formula (3). The resistances of linear resistive temperature sensors depend on resistivity are represented by formula (5). Coefficients' vector of the basic functions was calculated using the method of least squares with regularization (formula (22)). Then approximated spatial temperature distribution can be calculated on the basis of approximation model of the spatial distribution of resistivity (formula (14)). In the article proposed method is investigated for sensitive elements with the following parameters: resistivity ρ0 = 0.01724 μΩ m, temperature coefficient of resistance α = 4.3∙10-3 1/ºС, diameter of sensitive element d = 0.2 mm is simulated. The temperature distribution on the wall size of 2×2 m×m is investigated. The normalized to the maximum temperature error of reconstructed temperature distribution and root mean square error are calculated (formula (15), (16)). By using Monte-Carlo method (number of simulations M = 104 ) was performed simulation and in each simulation the surface average value, its standard deviations, minimum and maximum errors were determined by formulas (18) and (19). The characteristics of methodical error of reconstruction of temperature distribution for connection points on the side k = 6; 8; 12, algebraic polynomial of order p = 2 and different schemes (Fig. 1(a) and (b)) are presented in Fig. 2 and 3 respectively. The characteristics of methodical error of reconstruction of temperature distribution for scheme (Fig. 1(b)), approximation model 1(b), connection points on the side k = 6; 8; 12 and algebraic polynomial of order p = 2; 3 is presented in Fig. 4. The characteristics of instrumental error of reconstruction of temperature distribution for scheme (Fig. 1(b)), approximation model 3 (a) and (b), connection points on the side k = 8 and algebraic polynomial of order p = 2 are presented in Fig. 5. The results of this investigation showed that methodical component the most depends on approximation model and order of algebraic polynomial. The influence of additive systematic component of approximation is twice smaller than the influence of random. The influence of multiplicative systematic component of approximation is close to the influence of additive systematic component. The influence of additive random is amplified in 5–10 times.
Authors and Affiliations
Михайло Дорожовець, Мар'яна Бурдега
Keywords
Related Articles
- EP ID EP180601
- DOI -
- Views 119
- Downloads 0
АДАПТАЦІЯ ВИЩОГО НАВЧАЛЬНОГО ЗАКЛАДУ В УМОВАХ ВПРОВАДЖЕННЯ СИСТЕМИ УПРАВЛІННЯ ЯКІСТЮ У ВІДПОВІДНОСТІ СТАНДАРТУ ДСТУ ISO СЕРІЇ 9001:2009 (НА ПРИКЛАДІ УКРАЇНСЬКОЇ ІНЖЕНЕРНО-ПЕДАГОГІЧНОЇ АКАДЕМІЇ)
In the article examined the improvement of the management system of the educational organization process ISO 9001:2009. The analysis of problems is conducted retentive development and introduction of the system of manage...
ЕЛЕМЕНТИ МЕТОДОЛОГІЇ ВИМІРЮВАННЯ ГІДРОХІМІЧНИХ ХАРАКТЕРИСТИК ВОДНИХ ЕКОСИСТЕМ
Recommendations concerning measurement of hydrochemical characteristics in lakes of biological Shatsk reserve on the basis of a series of international standards ISO 14000, ISO/IEC 17025 in view of mathematical model of...
БАГАТОРІВНЕВА МЕТРОЛОГІЧНА ПЕРЕВІРКА КІБЕР-ФІЗИЧНИХ СИСТЕМ
This article presents the features of functioning the cyber-physical systems and their components. The cyber-physical systems are complex systems which components may be located at great distance from one another. The cy...
Проектування нейроконтролерів для керування нелінійними об’єктами другого порядку
Some issues concerning the neural networks application in automatic control of non-linear objects are presented in this paper. Several teaching sequences configuration creation, and their efficiency, i.e. the reaction ti...
ПОХИБКИ АЛГОРИТМІВ НЕЧІТКОЇ ЛОГІКИ, ЯКІ ПОБУДОВАНІ ЗА МЕТОДАМИ SUGENO ТА MAMDANI
It was considered the opportunity of making intelligent measurement devices using the technology of «plug and play», whose work is based on mathematical fuzzy logic. It was performed the investigation of recreating the f...