A method for temperature calculation in platinum resistance temperature measurement systems

Abstract

This invention discloses a temperature calculation method for a platinum resistance thermometer system. Based on the nonlinear changes in platinum resistance with temperature and the nonlinear changes in the output voltage of the temperature measurement system, the method utilizes two-point calibration, linear interpolation, and nonlinear regression correction to calculate the temperature. Compared with the currently used multi-point calibration and piecewise interpolation methods for temperature calculation, its advantages are that only the boundary points of the temperature measurement range need to be calibrated within a wider temperature range. By performing nonlinear regression correction on the theoretical resistance value calculated by interpolation, the problems of nonlinear changes in the resistance of platinum resistance with temperature and nonlinear changes in the output voltage of the temperature measurement circuit can be overcome. This allows the temperature measurement accuracy of the system to be unrestricted by the hardware conditions of the temperature measurement system, and high-precision temperature measurement requirements can be met with minimal hardware resources. A regression relationship between the resistance and temperature of platinum resistance is established based on the resistance-temperature calibration table of platinum resistance, and the temperature can be directly calculated using this relationship based on the resistance value of the platinum resistance after regression correction.

Description

Technical Field

[0001] This invention belongs to the technical field of platinum resistance temperature measurement, and relates to a temperature calculation method for platinum resistance temperature measurement systems. Background Technology

[0002] Temperature measurement, as a general measurement technology, has a wide range of applications, especially in materials science, aerospace, and industrial control, where extremely high accuracy is required. Among various temperature sensors, platinum resistance temperature sensors are widely used due to their relatively higher stability and superior linearity. In temperature measurement systems, two-wire, three-wire, or four-wire temperature measurement circuits are typically used to convert the resistance value R of the platinum resistance, obtaining the corresponding voltage value. This voltage value is then obtained through an A / D converter to obtain the sampled value. Generally, in environments with a narrow temperature measurement range, the resistance value R at the boundary of the range and the A / D sampled value are calibrated, and the temperature can be approximated by interpolation. However, in environments with a wide temperature measurement range, the simple two-point calibration combined with linear interpolation becomes unsuitable due to the non-linear characteristics of the resistance of the platinum resistance changing with temperature and the non-linear characteristics of the resistance-voltage conversion in currently available two-wire, three-wire, and four-wire platinum resistance temperature measurement circuits. In such environments, the calculation error in the mid-temperature range will increase significantly, failing to meet the requirements for high-precision temperature measurement.

[0003] To address the above issues, a common approach is to calculate temperature using multi-point calibration combined with piecewise interpolation. This method assumes a linear relationship between all relevant quantities within the specified interval. Theoretically, this approach can improve measurement accuracy in the mid-temperature range, but it has the following drawbacks:

[0004] 1. Multiple calibrations and storage of calibration data are required to improve the solution accuracy, which consumes a lot of hardware storage resources.

[0005] 2. A large amount of storage space is required in the temperature measurement system to store the platinum resistance thermometer.

[0006] 3. The temperature measurement accuracy of the temperature measurement system is completely limited by the hardware resources of the temperature measurement system. Under the condition of limited hardware resources, it is impossible to achieve wide-range and high-precision temperature measurement. Summary of the Invention

[0007] The purpose of this invention is to provide a temperature calculation method for a platinum resistance temperature measurement system, which can calculate the temperature value with high accuracy by storing only two calibration values ​​in the temperature measurement system, with minimal hardware storage resources required.

[0008] This invention is achieved through the following technical solution:

[0009] A temperature calculation method for a platinum resistance temperature measurement system, based on the platinum resistance temperature measurement system, includes the following steps:

[0010] Step 1: Determine the temperature measurement range of the platinum resistance thermometer [T0, T...] M The corresponding resistance value range is [R0, R]. M ];

[0011] Step 2, connect the resistance values ​​R0 and R M A fixed resistor is connected to a platinum resistance temperature measurement system for calibration, and the sampling value range [S0, S] is obtained. M ];

[0012] Step 3: Based on the resistance value range [R0, R...] M ] and the sampling value interval [S0, S M The linear proportional relationship is used to calculate the temperature T of any medium using a linear interpolation formula. t The theoretical resistance value R under the given conditions t And record the temperature T of any medium. t Under certain conditions, the resistance value Zt of the actual resistor connected in the platinum resistance temperature measurement system as a substitute for the platinum resistance thermometer.

[0013] Step 4: Using the theoretical resistance value R t As the independent variable, the actual resistance value Z of the resistor is used. t A nonlinear regression was performed on the dependent variable to obtain the resistance value correction formula;

[0014] Step 5: Apply the resistance value correction formula to the theoretical resistance value R calculated in Step 3. t The corrected theoretical resistance value R is obtained by performing correction. t ';

[0015] Step 6: Using the actual resistance value Z of the resistor t As the independent variable, with arbitrary medium temperature T t The temperature correction formula is obtained by performing nonlinear regression on the dependent variable.

[0016] Step 7: Calculate the corrected theoretical resistance value R obtained in Step 5. t 'Substitute into the temperature correction formula to obtain the temperature of the correction medium T' t '.

[0017] The above-mentioned platinum resistance temperature measurement system is existing technology and is not an improvement of this invention, so its specific structure and usage will not be described in detail here.

[0018] To better realize the present invention, the linear interpolation formula in step 3 is further defined as follows:

[0019] ;

[0020] Where: R t For platinum resistance thermometers at any medium temperature Tt The theoretical resistance value under the given conditions; R0 is the resistance reading of the platinum resistance thermometer at temperature T0; R M For platinum resistance thermometers at T M The resistance reading corresponding to the temperature; S0 is the calibration value measured by connecting a fixed resistor with resistance R0 to the platinum resistance temperature measurement system; S M The resistance value is R M The fixed resistor is connected to the platinum resistance temperature measurement system to measure the calibration value; S t For platinum resistance thermometers at any medium temperature T t The sampled value output by the platinum resistance temperature measurement system under the given conditions.

[0021] To better realize the present invention, the resistance value correction formula in step 4 is further defined as follows:

[0022] ;

[0023] Among them: Z t The resistance value R is used to replace the actual resistor connected in the platinum resistance temperature measurement system. t For platinum resistance thermometers at any medium temperature T t The theoretical resistance value corresponding to the given conditions; a0-a n This is the correction factor.

[0024] To better realize the present invention, the temperature correction formula in step 6 is further defined as follows:

[0025] ;

[0026] Wherein: T t Z represents the temperature of any medium. t The resistance value used to replace the actual resistor connected in the platinum resistance temperature measurement system; A0-A n This is the correction factor.

[0027] To better realize the present invention, further, in step 7, the temperature T of the corrected medium is... t The specific formula for calculating ' is as follows:

[0028] ;

[0029] : To correct the medium temperature; To calibrate the resistance value of the actual resistor; To correct the theoretical resistance value.

[0030] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0031] This invention is based on the nonlinear changes in platinum resistance thermometers with temperature and the nonlinear changes in the output voltage of the temperature measurement system. It uses two-point calibration, linear interpolation, and nonlinear regression correction to calculate the temperature. Compared with the currently used multi-point calibration and piecewise interpolation methods for calculating temperature, its advantages are that it only requires calibration at the boundary points of the temperature measurement range over a wider range. By performing nonlinear regression correction on the theoretical resistance value calculated by interpolation, the problems of nonlinear changes in the resistance of platinum resistance thermometers with temperature and nonlinear changes in the output voltage of the temperature measurement circuit can be overcome. This makes the temperature measurement accuracy of the temperature measurement system not limited by the hardware conditions of the temperature measurement system, and can meet the high-precision temperature measurement requirements with minimal hardware resources. A regression relationship between the resistance value and temperature of platinum resistance thermometers is established based on the resistance-temperature calibration table of platinum resistance thermometers. The temperature can be directly solved using this relationship based on the resistance value of the platinum resistance thermometer after regression correction. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the process steps of the present invention. Detailed Implementation

[0033] Example 1:

[0034] This embodiment presents a temperature calculation method for a platinum resistance temperature measurement system, implemented based on the platinum resistance temperature measurement system, such as... Figure 1 As shown, it includes the following steps:

[0035] Step 1: Determine the temperature measurement range of the platinum resistance thermometer [T0, T...] M The corresponding resistance value range is [R0, R]. M ];

[0036] Step 2, connect the resistance values ​​R0 and R M A fixed resistor is connected to a platinum resistance temperature measurement system for calibration, and the sampling value range [S0, S] is obtained. M ];

[0037] Step 3: Based on the resistance value range [R0, R...] M ] and the sampling value interval [S0, S M The linear proportional relationship is used to calculate the temperature T of any medium using a linear interpolation formula. t The theoretical resistance value R under the given conditions t And record the temperature T of any medium. t Under certain conditions, the resistance value Zt of the actual resistor connected in the platinum resistance temperature measurement system as a substitute for the platinum resistance thermometer.

[0038] Step 4: Using the theoretical resistance value R t As the independent variable, the actual resistance value Z of the resistor is used. t A nonlinear regression was performed on the dependent variable to obtain the resistance value correction formula;

[0039] Step 5: Apply the resistance value correction formula to the theoretical resistance value R calculated in Step 3. t The corrected theoretical resistance value R is obtained by performing correction. t ';

[0040] Step 6: Using the actual resistance value Z of the resistor t As the independent variable, with arbitrary medium temperature T t The temperature correction formula is obtained by performing nonlinear regression on the dependent variable.

[0041] Step 7: Calculate the corrected theoretical resistance value R obtained in Step 5. t 'Substitute into the temperature correction formula to obtain the temperature of the correction medium T' t '.

[0042] The linear interpolation formula in step 3 is as follows:

[0043] ;

[0044] Where: R t For platinum resistance thermometers at any medium temperature T t The theoretical resistance value under the given conditions; R0 is the resistance reading of the platinum resistance thermometer at temperature T0; R M For platinum resistance thermometers at T M The resistance reading corresponding to the temperature; S0 is the calibration value measured by connecting a fixed resistor with resistance R0 to the platinum resistance temperature measurement system; S M The resistance value is R M The fixed resistor is connected to the platinum resistance temperature measurement system to measure the calibration value; S t For platinum resistance thermometers at any medium temperature T t The sampled value output by the platinum resistance temperature measurement system under the given conditions.

[0045] The resistance value correction formula in step 4 is as follows:

[0046] ;

[0047] Among them: Z t The resistance value R is used to replace the actual resistor connected in the platinum resistance temperature measurement system. t For platinum resistance thermometers at any medium temperature T t The theoretical resistance value corresponding to the given conditions; a0-a n This is the correction factor.

[0048] The temperature correction formula in step 6 is as follows:

[0049] ;

[0050] Wherein: T tZ represents the temperature of any medium. t The resistance value used to replace the actual resistor connected in the platinum resistance temperature measurement system; A0-A n This is the correction factor.

[0051] In step 7, the temperature of the correcting medium T t The specific formula for calculating ' is as follows:

[0052] ;

[0053] : To correct the medium temperature; To calibrate the resistance value of the actual resistor; To correct the theoretical resistance value.

[0054] Example 2:

[0055] This embodiment presents a temperature calculation method for a platinum resistance temperature measurement system, taking the measurement of a PT1000 type platinum resistance thermometer using a three-wire constant current temperature measurement system as an example, with the temperature measurement range [T0, T...]. M [-100℃, 100℃].

[0056] Based on the required temperature range [-100℃, 100℃], consult the calibration table for the PT1000 platinum resistance thermometer. The corresponding resistance values ​​at the temperature boundaries of the measurement range are 602.56Ω and 1385.06Ω, respectively. Therefore, the resistance range [R0, R...] is obtained. M [602.56Ω, 1385.06Ω].

[0057] With the obtained R0 = 602.56Ω, R M Using 1385.06Ω as the calibration point, fixed resistors with resistances of 602.56Ω and 1385.06Ω were connected to a three-wire constant current temperature measurement system for calibration. The sampled values ​​obtained after 16-bit A / D conversion by the temperature measurement system were S0=100 and S... M =65500, and R0=602.56Ω, R are stored in the memory of the temperature measurement system. M =1385.06Ω, S0=100, S M =65500, T0=-100℃, T M =100℃ several data points;

[0058] The data in the resistance range [602.56Ω, 1385.06Ω] shows a linear proportional relationship with the data in the sampling range [100, 65500]. This can be determined using the linear interpolation formula:

[0059] ;

[0060] After substituting the corresponding data, we have:

[0061] R t =602.56+(S t -100) The temperature T of any medium is calculated using (1385.06-602.56) / (65500-100). t The corresponding theoretical resistance value R t Here, the temperature measurement range [-100℃, 100℃] is divided into 10 equally spaced segments, resulting in 11 temperature groups T within the measurement range. t The theoretical resistance value R under the given conditions t And record the temperature T t The resistance value Z of the 11 sets of actual resistors connected under the given conditions t .

[0062] The 11 sets of theoretical resistance values ​​R obtained t The resistance values ​​Z of the actual resistors corresponding to {602.56Ω, 683.75Ω, 764.16Ω, 843.85Ω, 923.22Ω, 1003.24Ω, 1080.94Ω, 1159.51Ω, 1235.27Ω, 1310.14Ω, 1385.06Ω} are respectively. t= {602.56Ω, 683.25Ω, 763.28Ω, 842.71Ω, 921.6Ω, 1000Ω, 1077.94Ω, 1155.41Ω, 1232.42Ω, 1308.97Ω, 1385.06Ω}, with R t Z is the independent variable. t A cubic polynomial regression was performed with the dependent variable as the dependent variable, and the resulting relationship is as follows:

[0063] Z t =0.0000000568×R t 3 +0.0001510067×R t 2 +1.1236307962×R t -32.29 (1)

[0064] The regression equation (1) is taken as the platinum resistance thermometer measured by the temperature measuring system at any medium temperature T. t The corresponding theoretical resistance value R under the condition t The correction calculation formula will be used to calculate the theoretical resistance value R. t Substitute into equation (1) to calculate the corrected theoretical resistance value R. t´={602.36Ω, 683.54Ω, 763.50Ω, 842.48Ω, 921.05Ω, 1000.34Ω, 1077.58Ω, 1156.09Ω, 1232.33Ω, 1308.35Ω, 1385.23Ω}.

[0065] According to the calibration table of PT1000 platinum resistance thermometers, the resistance value range [R0, R...] can be determined. M Data within [T0, T] and temperature measurement interval [T0, T] M The data was subjected to univariate cubic polynomial regression, with Z... t T is the independent variable. t A total of 202 sets of data were used for the regression, and the regression equation is as follows:

[0066] T t =1.04952×10 -9 ×Z t 3 -1.34185×10 -5 ×Z t 2 +2.32198×10 -1 ×Z t -244.575 (2)

[0067] Using equation (2) as the arbitrary medium temperature T t The calculation formula for R t Substituting ´={602.36Ω, 683.54Ω, 763.50Ω, 842.48Ω, 921.05Ω, 1000.34Ω, 1077.58Ω, 1156.09Ω, 1232.33Ω, 1308.35Ω, 1385.23Ω} into equation (2) yields the corrected medium temperature. ={-100.07℃, -79.92℃, -59.94℃, -40.06℃, -20.14℃, 0.08℃, 19.9℃, 40.18℃, 59.98℃, 79.84℃, 100.03℃}.

[0068] The maximum error between the calculated corrected medium temperature and the actual medium temperature is 0.18℃, and the average error is 0.09℃. If higher solution accuracy is required, it is necessary to increase the power of equations (1) and (2) and increase the number of data samples involved in the model derivation, which can effectively improve the system solution accuracy.

[0069] The following example only uses increasing the power; the number of data samples used in the model derivation remains unchanged.

[0070] If we set the regression power to 5, then we have:

[0071] Zt =-6.02855×10 -13 ×R t 5 +3.011624×10 -9 ×R t 4 -5.844019×10 -6 ×R t 3 +5.509965×10 -3 ×R t 2 -1.532333×R t +454.7904

[0072] Calculate the corrected theoretical resistance value R t ´={602.607Ω, 683.083Ω, 763.431Ω, 842.791Ω, 921.368Ω, 1000.370Ω, 1077.340Ω, 1155.860Ω, 1232.440Ω, 1308.791Ω, 1385.120Ω}.

[0073] Calculate the temperature of the correction medium ={-100.008℃, -80.038℃, -59.954℃, -39.978℃, -20.065℃, 0.080℃, 19.850℃, 40.120℃, 60.010℃, 79.962℃, 100.002℃}. The maximum error between the calculated and actual temperature values ​​is 0.158℃, and the average error is only 0.055℃.

[0074] After increasing the power of the correction model, the temperature calculation accuracy of the temperature measurement system was significantly improved.

[0075] The other parts of this embodiment are the same as those in Embodiment 1, so they will not be described again.

[0076] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications or equivalent changes made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A temperature calculation method for a platinum resistance temperature measurement system, implemented based on the platinum resistance temperature measurement system, characterized in that, Includes the following steps: Step 1: Determine the temperature measurement range of the platinum resistance thermometer [T0, T...] M The corresponding resistance value range is [R0, R]. M ]; Step 2, connect the resistance values ​​R0 and R M A fixed resistor is connected to a platinum resistance temperature measurement system for calibration, and the sampling value range [S0, S] is obtained. M ]; Step 3: Based on the resistance value range [R0, R...] M ] and the sampling value interval [S0, S M The linear proportional relationship is used to calculate the temperature T of any medium using a linear interpolation formula. t The theoretical resistance value R under the given conditions t And record the temperature T of any medium. t The resistance value Z of the actual resistor used to replace the platinum resistance thermometer in the platinum resistance temperature measurement system under certain conditions. t ; Step 4: Using the theoretical resistance value R t As the independent variable, the actual resistance value Z of the resistor is used. t A nonlinear regression was performed on the dependent variable to obtain the resistance value correction formula; Step 5: Apply the resistance value correction formula to the theoretical resistance value R calculated in Step 3. t The corrected theoretical resistance value R is obtained by performing correction. t '; Step 6: Using the actual resistance value Z of the resistor t As the independent variable, with arbitrary medium temperature T t The temperature correction formula is obtained by performing nonlinear regression on the dependent variable. Step 7: Calculate the corrected theoretical resistance value R obtained in Step 5. t 'Substitute into the temperature correction formula to obtain the temperature of the correction medium T' t '.

2. The temperature calculation method for a platinum resistance temperature measurement system according to claim 1, characterized in that, The linear interpolation formula in step 3 is as follows: ； Where: R t For platinum resistance thermometers at any medium temperature T t The theoretical resistance value under the given conditions; R0 is the resistance reading of the platinum resistance thermometer at temperature T0; R M For platinum resistance thermometers at T M The resistance reading corresponding to the temperature; S0 is the calibration value measured by connecting a fixed resistor with resistance R0 to the platinum resistance temperature measurement system; S M The resistance value is R M The fixed resistor is connected to the platinum resistance temperature measurement system to measure the calibration value; S t For platinum resistance thermometers at any medium temperature T t The sampled value output by the platinum resistance temperature measurement system under the given conditions.

3. The temperature calculation method for a platinum resistance temperature measurement system according to claim 2, characterized in that, The resistance value correction formula in step 4 is as follows: ； Where: Z t The resistance value R is used to replace the actual resistor connected in the platinum resistance temperature measurement system. t For platinum resistance thermometers at any medium temperature T t The theoretical resistance value corresponding to the given conditions; a0-a n This is the correction factor.

4. The temperature calculation method for a platinum resistance temperature measurement system according to claim 3, characterized in that, The temperature correction formula in step 6 is as follows: ； Wherein: T t Z represents the temperature of any medium. t The resistance value used to replace the actual resistor connected in the platinum resistance temperature measurement system; A0-A n This is the correction factor.

5. The temperature calculation method for a platinum resistance temperature measurement system according to claim 4, characterized in that, In step 7, the temperature of the correcting medium T t The specific formula for calculating ' is as follows: ； : To correct the medium temperature; To calibrate the resistance value of the actual resistor; To correct the theoretical resistance value.

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