A method for improving the calibration accuracy of thin-film thermocouples based on linear regression algorithm

Abstract

A method for improving the calibration accuracy of thin-film thermocouples based on a linear regression algorithm is disclosed, belonging to the field of thin-film thermocouples. The method includes: constructing a thin-film thermocouple calibration system; using the constructed system to begin calibrating the thin-film thermocouples; calculating the thermoelectric characteristic curves using a linear regression algorithm; and obtaining a thermoelectric characteristic calibration table for the thin-film thermocouples using linear interpolation. This invention can effectively improve the calibration accuracy of thin-film thermocouples. Addressing situations where the output temperature of thin-film thermocouples cannot be accurately controlled, this method provides a high-precision thermoelectric characteristic curve, offering advantages such as simple and rapid calculation, and high versatility, applicable to the dynamic / static calibration of thin-film thermocouples of various sizes and materials.

Description

Technical Field

[0001] This invention belongs to the field of thin-film thermocouple technology, specifically relating to a method for improving the calibration accuracy of thin-film thermocouples based on a linear regression algorithm. Background Technology

[0002] Thin-film thermocouples are small in size (approximately 1 μm thick) and have minimal interference with the measured temperature field, making them suitable for applications such as turbine blade temperature measurement. The Seebeck effect is the fundamental working principle of thin-film thermocouples. When a temperature difference occurs between the two ends of the thin-film thermocouple (generally the thermal junction and the voltage output terminal), a voltage is generated at the output terminal. The output voltage is related to the temperature at both ends of the thin-film thermocouple, i.e., V = f(T). 热节点 T 输出端 According to literature reports, the thermoelectric properties of thin-film thermocouples are generally not consistent (there may be significant differences even within the same batch), therefore each thin-film thermocouple needs to be calibrated before it can be used.

[0003] The calibration process for thin-film thermocouples requires strict control of the output temperature to 0°C before thermoelectric characteristics can be obtained. However, for small-sized thin-film thermocouples fabricated on rigid substrates (such as ceramics), the output temperature cannot be accurately controlled at 0°C. This is because thin-film thermocouples are typically small (~10 cm), and at higher calibration temperatures (>1000°C), heat is rapidly conducted from the hot junction to the output. According to literature review, the most common traditional approach is to ignore the fluctuation in the sensor's output temperature, which obviously leads to significant errors in the obtained thermoelectric characteristics. Currently, the calibration methods for thin-film thermocouples cannot obtain highly accurate thermoelectric characteristic curves. Summary of the Invention

[0004] To address the problems of existing technologies, namely obtaining highly accurate thermoelectric characteristic curves, this invention provides a method for improving the calibration accuracy of thin-film thermocouples based on a linear regression algorithm.

[0005] The technical solution adopted by this invention to solve the technical problem is as follows:

[0006] This invention provides a method for improving the calibration accuracy of thin-film thermocouples based on a linear regression algorithm, comprising the following steps:

[0007] Step S1: Set up a thin-film thermocouple calibration system;

[0008] Step S2: Using the constructed thin-film thermocouple calibration system, begin calibrating the thin-film thermocouples;

[0009] Step S3: Calculate the thermoelectric characteristic curve using a linear regression algorithm;

[0010] Step S4: Obtain the thermoelectric characteristic calibration table of thin film thermocouples using linear interpolation.

[0011] Furthermore, the thin-film thermocouple calibration system includes: a sintering furnace, a cooling device, leads, a voltage acquisition device, a thin-film thermocouple, a substrate, and a temperature sensor; the thin-film thermocouple is integrated on the surface of the substrate; the sintering furnace is installed on one side of the thin-film thermocouple; the cooling device is installed at the output end of the thin-film thermocouple; the output end of the thin-film thermocouple is connected to the voltage acquisition device via leads; a temperature sensor is installed at the thermal node and the output end of the thin-film thermocouple, respectively.

[0012] Furthermore, the voltage acquisition device is a voltmeter.

[0013] Furthermore, the temperature sensor is a type K thermocouple.

[0014] Furthermore, during the calibration process, the sintering furnace temperature is increased to the calibration temperature, and the following data is recorded simultaneously: hot node temperature T h Output temperature T l The thin-film thermocouple outputs V; continue to raise the sintering furnace temperature to the next calibration temperature and record the data until all data corresponding to the set calibration temperature point has been collected; turn off the sintering furnace, allow it to cool naturally, and the calibration is complete.

[0015] Furthermore, the heating rate of the sintering furnace is 10-20℃ / min, and after reaching the calibrated temperature, it is held for 30-60 minutes.

[0016] Furthermore, when the output temperature of the thin-film thermocouple is fixed at 0°C, a polynomial is used... Representing its thermoelectric characteristic curve, when the output of the thin-film thermocouple is not fixed, the actual output of the thin-film thermocouple is: The coefficients A, B, and C of the thermoelectric property polynomial are calculated using a linear regression algorithm, where T h T represents the hot node temperature. l V represents the output temperature, and V represents the output voltage of the thin-film thermocouple.

[0017] Furthermore, the specific implementation process of step S3 is as follows:

[0018] Step S3.1: Denote the coefficients A, B, and C of the thermoelectric characteristic polynomial as k(1,3)=[A,B,C]; record the data as... y(1,n)=[V1,…,V n Therefore, y = kx;

[0019] Step S3.2: Use multiple linear regression to estimate the value of k. Using the least squares method as the optimization objective, we have an estimated value. Solve for the coefficients A, B, and C;

[0020] Step S3.3: Substitute the coefficients A, B, and C of the thermoelectric characteristic polynomial into... Obtain the thermoelectric characteristic curves.

[0021] Furthermore, substituting the coefficients A, B, and C of the thermoelectric characteristic polynomial into... Then, VT is recorded by linear interpolation using polynomials. h The correspondence between them, namely the correspondence between the output of the thin-film thermocouple and the output end temperature, forms the thermoelectric characteristic calibration table of thin-film thermocouples.

[0022] Furthermore, the specific implementation process of step S4 is as follows:

[0023] Step S4.1: Set the temperature vector to be interpolated;

[0024] Step S4.2: Use the linear interpolation function interp1 in Matlab to interpolate with T as the interpolation point to obtain the corresponding voltage vector; combine the temperature vector and voltage vector to form a calibration table of thermoelectric characteristics of thin film thermocouples.

[0025] The beneficial effects of this invention are:

[0026] 1. The present invention provides a method for improving the calibration accuracy of thin-film thermocouples based on a linear regression algorithm, which can effectively improve the accuracy of their thermoelectric characteristic curves. In fact, the method of the present invention can obtain a true thermoelectric characteristic curve of a thin-film thermocouple (fabricated on a rigid substrate), which is the biggest difference from traditional methods. Traditional thin-film thermocouple calibration schemes assume that the output temperature remains constant and directly use δT-V data as the thermoelectric characteristic curve (δT = T). h -T l Strictly speaking, this is not in accordance with regulations.

[0027] 2. This invention provides a method for improving the calibration accuracy of thin-film thermocouples based on a linear regression algorithm, which has the advantages of simple and fast calculation. Based on the calibration, only three sets of data need to be input (thermal node temperature T). h Output temperature T l The thermoelectric characteristic curve of the thin-film thermocouple can be quickly obtained by using a pre-programmed program (the output of the thin-film thermocouple is V).

[0028] 3. The present invention provides a method for improving the calibration accuracy of thin-film thermocouples based on a linear regression algorithm. This method is highly versatile and applicable to the dynamic / static calibration of thin-film thermocouples of various sizes and materials fabricated on rigid substrates. Even when the output temperature cannot be accurately controlled, the method of this invention can obtain highly accurate thermoelectric characteristic curves. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of a thin-film thermocouple calibration system.

[0030] Figure 2 This figure shows a comparison between the thermoelectric characteristic curves of thin-film thermocouples obtained using the linear regression algorithm-based method for improving the calibration accuracy of thin-film thermocouples provided by this invention and those obtained using the most commonly used traditional method. In the figure, a: the thermoelectric characteristic curve of the thin-film thermocouple obtained using the most commonly used traditional method; b: the thermoelectric characteristic curve of the thin-film thermocouple obtained using the linear regression algorithm-based method for improving the calibration accuracy of thin-film thermocouples provided by this invention.

[0031] Figure 3 This is a comparison chart showing the results of back-deriving the thermoelectric characteristic curves of thin-film thermocouples obtained using the linear regression algorithm-based method for improving the calibration accuracy of thin-film thermocouples provided by this invention, and the results of back-deriving the thermoelectric characteristic curves of thin-film thermocouples obtained by the most commonly used traditional method.

[0032] In the diagram, 1 is the sintering furnace, 2 is the cooling device, 3 is the lead wire, 4 is the voltage acquisition device, and 5 is the thin-film thermocouple.

[0033] Substrate 6, temperature sensor 7, thermal node 8. Detailed Implementation

[0034] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0035] The present invention provides a method for improving the calibration accuracy of thin-film thermocouples based on a linear regression algorithm, the specific implementation steps of which are as follows:

[0036] Step S1: First, set up a thin-film thermocouple calibration system;

[0037] like Figure 1As shown, the thin-film thermocouple calibration system constructed by the present invention mainly includes: sintering furnace 1, cooling device 2, lead wire 3, voltage acquisition device 4, thin-film thermocouple 5, substrate 6, and temperature sensor 7.

[0038] The specific implementation process is as follows:

[0039] Step S1.1: Fabricate a thin-film thermocouple 5 on the surface of substrate 6.

[0040] In this invention, the material of the thin-film thermocouple 5 can be ITO-In2O3. In actual operation, the specific material of the thin-film thermocouple 5 is not limited.

[0041] In this invention, the size of the thin-film thermocouple 5 can be 150mm*40mm*1mm. In actual operation, the specific size of the thin-film thermocouple 5 is not limited.

[0042] In this invention, the substrate 6 can be made of ceramic material, and the specific material of the substrate 6 is not limited in actual operation.

[0043] Step S1.2: Use conductive adhesive to attach the lead wire 3 to the output pin of the thin film thermocouple 5, and then connect the output of the thin film thermocouple 5 to the voltage acquisition device 4 through the lead wire 3.

[0044] In this invention, the voltage acquisition device 4 can specifically use a voltmeter, but it is not limited to this.

[0045] Step S1.3: Fix a temperature sensor 7 near the hot node 8 (measuring point) and the output end of the thin-film thermocouple 5 respectively;

[0046] In this invention, the temperature sensor 7 can specifically be a type K thermocouple, but it is not limited to this.

[0047] Step S1.4: Fix a cooling device 2 near the output end of the thin-film thermocouple 5 to maintain the temperature of the output end of the thin-film thermocouple 5 at around room temperature. Under laboratory conditions, the cooling device 2 is typically attached to the output end of the thin-film thermocouple 5.

[0048] Step S1.5: Fix a sintering furnace 1 near the left side of the thin film thermocouple 5 to raise the temperature of the hot node 8 of the thin film thermocouple 5.

[0049] Step S2: Thin-film thermocouple calibration;

[0050] Using the constructed thin-film thermocouple calibration system, dynamic and static calibration processes were initiated. During calibration, the sintering furnace 1 was turned on to raise the temperature at the hot junction 8. Simultaneously, the cooling device 2 was turned on to lower the output temperature of the thin-film thermocouple 5. During the calibration process, n sets of data were measured / recorded, including: hot junction temperature T... hOutput temperature T l The thin-film thermocouple outputs V.

[0051] The specific implementation process is as follows:

[0052] Step S2.1: Raise the temperature of sintering furnace 1 to the calibrated temperature, wherein the preferred heating rate is 10-20℃ / min, and hold at the calibrated temperature for 30-60 minutes. Simultaneously record the following data: hot node temperature T. h Output temperature T l The thin-film thermocouple outputs V, wherein the preferred data acquisition frequency is 0.1-1 sets / s;

[0053] Step S2.2: Continue to raise the temperature of sintering furnace 1 to the next calibration temperature, and repeat step S2.1 until all data corresponding to the set calibration temperature point has been collected.

[0054] Step S2.3: Turn off sintering furnace 1, allow it to cool naturally, and the calibration is complete.

[0055] Step S3: Calculate the thermoelectric characteristic curve using a linear regression algorithm;

[0056] The thermoelectric characteristic curve of thin-film thermocouple 5 was calculated using a linear regression algorithm. When the output terminal temperature of thin-film thermocouple 5 is fixed at 0℃, the thermoelectric characteristic curve can be expressed using a polynomial. This indicates that when the output of the thin-film thermocouple 5 is not fixed, the actual output of the thin-film thermocouple 5 is... The coefficients A, B, and C of the thermoelectric property polynomial need to be calculated using a linear regression algorithm.

[0057] The specific implementation process is as follows:

[0058] Step S3.1: Denote the coefficients A, B, and C of the thermoelectric characteristic polynomial as k(1,3)=[A,B,C]; record the data as... y(1, n) = [V1, ..., V n Therefore, y = kx;

[0059] Step S3.2: Use multiple linear regression to estimate the value of k. Using the least squares method as the optimization objective, we have an estimated value. Solve for the coefficients A, B, and C;

[0060] Step S3.3: Substitute the coefficients A, B, and C of the thermoelectric characteristic polynomial into... Obtain the thermoelectric characteristic curves.

[0061] Step S4: Obtain the thermoelectric characteristic calibration table of thin-film thermocouple 5 using linear interpolation;

[0062] Substitute the coefficients A, B, and C of the thermoelectric property polynomial into... Then, VT can be recorded by linear interpolation using the thermoelectric characteristic polynomial. h The correspondence between them, namely the correspondence between the output of the thin-film thermocouple 5 and the output end temperature, forms the thermoelectric characteristic calibration table of the thin-film thermocouple 5.

[0063] The specific implementation process is as follows:

[0064] Step S4.1: Set the temperature vector to be interpolated, such as T = [0, 1, 2, 3....., 1000]. It can be set arbitrarily within the temperature range, but according to the usual requirements of the thermoelectric characteristic calibration table, it is generally an arithmetic sequence.

[0065] Step S4.2: Use the linear interpolation function interp1 in Matlab to interpolate with T as the interpolation point to obtain the corresponding voltage vector; combine the temperature vector and voltage vector to form the thermoelectric characteristic calibration table of thin film thermocouple 5, as shown in Table 1.

[0066] Table 1. Thin-film thermocouple calibration table obtained using the method of the present invention.

[0067]

[0068]

[0069] The core innovation of this invention, a method for improving the calibration accuracy of thin-film thermocouples based on a linear regression algorithm, is that it first uses a pre-built thin-film thermocouple calibration system to acquire data such as the output and the temperatures at both ends of the thin-film thermocouple. Then, it uses a linear regression algorithm to calculate the thermoelectric characteristic curve of the thin-film thermocouple (mainly calculating the coefficients of the polynomial).

[0070] The thermoelectric characteristic curve of thin-film thermocouple 5 obtained using the linear regression algorithm-based method for improving the calibration accuracy of thin-film thermocouples provided by this invention is compared with the thermoelectric characteristic curve of thin-film thermocouple 5 obtained by the most commonly used traditional method, as shown in the following figure. Figure 2 As shown. The most common traditional approach is to directly use V = A*

[0071] (T h -T l ) 3 +B*(T h -T l ) 2 +C*(T h -T l () serves as the thermoelectric characteristic curve.

[0072] like Figure 3 As shown, the error of the thermoelectric characteristic curve of a thin-film thermocouple obtained by the linear regression algorithm-based method for improving the calibration accuracy of thin-film thermocouples provided by this invention is compared with that obtained by the most commonly used traditional method. The thermoelectric characteristic curve of the thin-film thermocouple obtained by the linear regression algorithm-based method provided by this invention matches the output of thin-film thermocouple 5 perfectly, showing good matching and high accuracy. In contrast, the thermoelectric characteristic curve (δT-V curve) of the thin-film thermocouple obtained by the most commonly used traditional method does not match the output of thin-film thermocouple 5, showing poor accuracy. The comparison results show that the linear regression algorithm-based method for improving the calibration accuracy of thin-film thermocouples provided by this invention can effectively obtain high-precision thermoelectric characteristic curves.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. However, these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for improving the calibration accuracy of a thin-film thermocouple based on a linear regression algorithm, characterized in that, The method comprises the following steps: Step S1: build a thin-film thermocouple calibration system; The thin-film thermocouple calibration system comprises a sintering furnace, a cooling device, a lead wire, a voltage acquisition device, a thin-film thermocouple, a substrate and a temperature sensor; the thin-film thermocouple is integrated on the surface of the substrate; the sintering furnace is installed on one side of the thin-film thermocouple; the cooling device is installed at the output end of the thin-film thermocouple; the output end of the thin-film thermocouple is connected with the voltage acquisition device through the lead wire; one temperature sensor is installed at the hot node and the output end of the thin-film thermocouple respectively; Step S2: start calibrating the thin-film thermocouple by using the built thin-film thermocouple calibration system; During the calibration process, the sintering furnace temperature is raised to the calibration temperature, and the following data are recorded: hot node temperature T h , output end temperature T l , and thin film thermocouple output V; the sintering furnace temperature is continuously raised to the next calibration temperature, and data are recorded until the data corresponding to the set calibration temperature points are all collected; the sintering furnace is closed, and natural cooling is performed, and the calibration is completed; Step S3: calculate the thermoelectric characteristic curve by using a linear regression algorithm; The output end temperature of the thin film thermocouple is fixed at 0°C, and the polynomial represents the thermoelectric characteristic curve thereof, so when the output voltage of the thin film thermocouple is not fixed, the actual output of the thin film thermocouple is The coefficients A, B, and C of the thermoelectric characteristic polynomial are calculated using a linear regression algorithm, where T h represents the hot node temperature, T l represents the output end temperature, and V represents the output voltage of the thin film thermocouple; Step S4: obtain the thin-film thermocouple thermoelectric characteristic scale table by using linear interpolation.

2. The method of claim 1, wherein the method is characterized by, The voltage acquisition device adopts a voltmeter.

3. The method of claim 1, wherein the method is characterized by: The temperature sensor adopts a K-type thermocouple.

4. The method of claim 1, wherein the method is characterized by: The heating rate of the sintering furnace is 10-20 ℃ / min, and the temperature is kept for 30-60 min after reaching the calibration temperature.

5. The method of claim 1, wherein the method is characterized by: The specific implementation process of step S3 is as follows: Step S3.1: The coefficients A, B, C of the thermoelectric characteristic polynomial are noted k(1,3) = [A, B, C]; the recorded data are noted y(1,n) = [V1,..., Vn], so that y = kx. y(1,n) = [V1,..., Vn], so that y = kx. n ], so that y = kx. Step S3.2: Solving the estimated value of k using the method of multiple linear regression Using the least square method as the optimization objective, there is an estimated value Solving the coefficients A, B, C; Step S3.3: Bring the coefficients A, B, C of the thermoelectric characteristic polynomial into The thermoelectric characteristic curve is obtained.

6. The method of claim 5, wherein the method is characterized by: The coefficients A, B, C of the thermoelectric characteristic polynomial are substituted into After that, the corresponding relationship between V and T is recorded by linear interpolation h between the output of the thin-film thermocouple and the temperature of the output terminal, to form a thermoelectric characteristic scale table of the thin-film thermocouple.

7. The method of claim 6, wherein the method is characterized by, The specific implementation process of step S4 is as follows: Step S4.1: set the temperature vector to be interpolated; Step S4.2: use the linear interpolation function interp1 in Matlab to interpolate the temperature vector T to obtain the corresponding voltage vector; combine the temperature vector and the voltage vector to form the thin-film thermocouple thermoelectric characteristic scale table.

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