Journal Paper Format CHEMICAL ENGINEERING TRANSACTIONS VOL. 46, 2015 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Peiyu Ren, Yanchang Li, Huiping Song Copyright © 2015, AIDIC Servizi S. r. l. , ISBN 978-88-95608-37-2; ISSN 2283-9216 Research on the Application of Polynomial Direct Fitting to Platinum High-precision Temperature Measurement Zhixiang Wu, Xiangcai Zhou, Gong Chen* Changzhou Institute of Technology, Changzhou, 213002, China. 376366375@qq.com Although many methods can be used to conduct platinum resistor non-linear rectification, they cannot be put into wide use because of shortcomings such as narrow temperature range and complicated calculation of rectification. This article conducts fitting algorism based on three temperature ranges of platinum resistor within temperature range and obtains cubic and quartic polynomial coefficients via the method of adjusting weight function using least square method after a brief summary of the regular method and problems existing in platinum resistor non-linear function inversion calculation. Meanwhile, fitting algorism error distribution graph is also demonstrated. The maximum error is only ±0. 003℃ when applying quartic multinomial fitting algorism within the range of 0-650℃. Finally, the advantages of multinomial direct fitting is further testified an analysis of C language calculation precision and data instances. 1. Introduction Temperature is a physical quantity that represents objects’ degree of hotness or coldness. It serves as an important parameter in industrial production and scientific experiments. Characterized by features such as stable performance, wide range of temperature measurement, easy calibration and good interchangeability, platinum resistor has been widely used in temperature measurement. Stipulated in International Temperature Scale ITS-90, specially structured platinum resistor is used as standard thermometer between -259℃ and 961. 78℃. Because non-linear relationship exists between platinum resistor’s resistance value and temperature, non- linear operation (non-linear rectification) is required when temperature is reappeared. Based on scaling function and scaling table, non-linear operation is an indispensable part of high-accuracy temperature measurement with various methods. Although Newton Iteration Method can be used to solve platinum resistor scaling function and satisfactory results can be obtained after second iteration, iteration takes too long and internal memory is occupied too much. When Neural Network Approach is applied to conduct polynomial fitting for three times between 0℃ and 600℃ divided into six parts, the error is less than 0. 02℃. The temperature is calculated on the basis of the resistor value via radical sign operation’s analytic expression [Ping Yang]. The error 0. 02℃ is obtained within the range of 0℃-150℃ via symmetric function non-linear method and the error 0. 05℃is achieved within the range of 48℃-50℃ via least square method. Intelligent digital instrument whose core unit is an 8 bit single-byte-character single chip microcomputer is generally used to conduct high-accuracy temperature measurement. Therefore, the simple and direct algorithm used in studying the relationship between platinum resistor and temperature occupies little space and is valuable. 2. Non-linearity of Platinum Resistor (PT100) Pt100 is the most frequently used temperature repetition element among Pt 10, Pt 100 and Pt 1000. The relationship between platinum resistor and temperature within the range of 0℃-850℃ is: 2 0 (1 )   t R R at bt (1) In the equation a=3. 90 802E-3/℃ DOI: 10.3303/CET1546060 Please cite this article as: Wu Z.X., Zhou X.C., Chen G., 2015, Research on the application of polynomial direct fitting to platinum high- precision temperature measurement, Chemical Engineering Transactions, 46, 355-360 DOI:10.3303/CET1546060 355 b=-5. 80195E-7/℃ R (100℃) ／R (0℃) =1. 385 00 Factor (1) indicates the relationship between the temperature and the resistor. Therefore, the temperature calculated via resistor value is an inversion process. If resistor value RF is set corresponding to upper limit of temperature range tF and the temperature and resistor value within the measurement range is linear, the non-linear error is: 2 0 0 0 0 (1 )            F R F R R e R at bt t R t t (2) Derivatives of formula (2) are calculated and ordered to be 0: 0 0 0 0 2 0          FR F R Rde aR bR t dt t t then: 0 0 0 0 [( ) / ( ) ] / 2    F F t R R t t aR bR The highest temperatures and resistor values of non-linear errors are 325℃/6. 127Ω and 425℃/ 10.478Ω within the temperature ranges of 0-650℃ and 0-850℃, respectively. As is shown in graph 1, the reduced non- linear is about 27℃. Figure 1: Non-linear errors distribution diagram within the range of 0-650℃ and 0-850℃ 3. Least Square Method and Weight Function Discrete points (xi, yi) (i=0, 1, 2, ……, m) . Approximate function curve S (x) is constructed and the inherent law of the data is described, that is, selecting appropriate function class (collection) Φ { } 0 1 2 n span , , , ,    { , }     0 0 1 1 2 2 n n i a a a a a R    0, 1, 2, ……, n is n+1 linearly independent continuous function on [a, b]. Find a function * 0 * ( ) ( )    n i i i S x a x (n