A thin-film thermocouple error compensation method based on a recurrent neural network

CN116698217BActive Publication Date: 2026-08-11XI AN JIAOTONG UNIV
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-04-10
Publication Date
2026-08-11

AI Technical Summary

Technical Problem

[0005]薄膜热电偶的实际测试中,在热端温度较高,而热电偶传感器的尺寸较小的情况下,冷端的温度难以保持恒定,从而较大的影响了薄膜热电偶传感器的精度,所以对其进行冷端补偿是很有必要的,而传统的补偿方法如冰点法和补偿器法等可靠性低或难以与薄膜热电偶在刀具上集成

Benefits of technology

[0034] This invention corrects and compensates for thermoelectric signals, solving the measurement error problem caused by cold junction temperature variations and manufacturing deviations in thin-film thermocouples on alumina ceramic cutting tools. It corrects and compensates for thermoelectric signal deviations caused by cold junction temperature rises during testing, as well as random errors present in the screen printing process, thereby improving the accuracy of the thin-film thermocouple sensor.

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Abstract

This invention discloses a method for error compensation of thin-film thermocouples based on recurrent neural networks, comprising: fabricating thin-film thermocouples using screen printing; performing temperature tests on the thin-film thermocouples; collecting thermoelectric potential data of the thin-film thermocouples and standard K-type thermocouples, and processing the collected thermoelectric potential data in the integrated development environment PyCharm; constructing a recurrent neural network in PyCharm, loading the dataset, adjusting the initial state of the neural network, and defining hyperparameters. This invention corrects and compensates for thermoelectric signals, solving the measurement error problem caused by cold junction temperature changes and manufacturing deviations in thin-film thermocouples on alumina ceramic cutting tools. It corrects and compensates for thermoelectric signal deviations caused by the rise in cold junction temperature during testing, as well as random errors present in the screen printing process, thereby improving the accuracy of the thin-film thermocouple sensor.
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Description

Technical Field

[0001] This invention belongs to the field of thin-film temperature sensor technology and relates to a method for compensating for thin-film thermocouple errors based on a recurrent neural network. Background Technology

[0002] With the introduction of initiatives such as "Made in China 2025" and Germany's "Industry 4.0," traditional manufacturing has regained importance. High-speed machining, as a crucial method for material production across various fields, faces the challenge of significantly impacting the service life of cutting tools when processing high-strength and high-hardness materials. Cutting heat is a key parameter limiting machining quality and efficiency. To monitor and control the cutting process, researchers have fabricated thermocouples into thin films and deposited them onto the surface of small cutting tools. Thin-film thermocouples do not affect the tool's working environment and offer fast response and high accuracy, making them a superior choice for measuring cutting tool temperature.

[0003] The positive and negative electrodes of a thin-film thermocouple are composed of two conductors of different materials, which intersect and coincide at one end, called the hot end node, while the two nodes at the other end do not intersect, and are the positive and negative nodes of the cold end, respectively. According to the Seebeck effect, when there is a temperature gradient between the hot and cold ends, a current will appear in the circuit, and a thermoelectric potential will be generated accordingly.

[0004] To accurately monitor changes in the hot junction temperature, it is necessary to maintain a constant cold junction temperature, ideally with the thermoelectric potential being a single-valued function of the hot junction temperature. Mass-produced thin-film thermocouples of the same type require high manufacturing consistency; it is desirable that thin-film thermocouples composed of the same materials exhibit consistent performance.

[0005] In actual testing of thin-film thermocouples, when the hot junction temperature is high and the thermocouple sensor size is small, it is difficult to keep the cold junction temperature constant, which greatly affects the accuracy of the thin-film thermocouple sensor. Therefore, cold junction compensation is necessary. However, traditional compensation methods such as the freezing point method and the compensator method have low reliability or are difficult to integrate with thin-film thermocouples on the cutting tool.

[0006] At the same time, since screen printing is a manual manufacturing process, it requires a certain level of experience and skill from the experimenters. Due to random errors, the ratio of each component in the paste and the effect of heat treatment are never ideal, so the method of analyzing specific situations is no longer applicable. Summary of the Invention

[0007] The purpose of this invention is to solve the problems in the prior art and provide a thin-film thermocouple error compensation method based on a recurrent neural network.

[0008] To achieve the above objectives, the present invention employs the following technical solution:

[0009] A method for compensating for thin-film thermocouple errors based on recurrent neural networks includes the following steps:

[0010] S1, thin-film thermocouples are prepared using screen printing technology;

[0011] S2, temperature testing of the thin-film thermocouple;

[0012] S3 collects thermoelectric potential data of thin-film thermocouples and standard K-type thermocouples, and processes the collected thermoelectric potential data in the integrated development environment PyCharm.

[0013] S4. In PyCharm, build a recurrent neural network, load the dataset, adjust the initial state of the neural network, and define hyperparameters.

[0014] Furthermore, the specific method for preparing the thin-film thermocouple in S1 according to the present invention is as follows:

[0015] S101. The material composition for preparing the thin film thermocouple electrode is nano-sized powder of In2O3 and ITO, and the additives are terpineol, polyetheramine and high temperature glass powder, which are configured into a composite slurry of In2O3 and ITO.

[0016] S102. The prepared composite material slurry is coated on a photomask, and then the material of an electrode is printed onto the ceramic substrate through the corresponding position of the photomask using a squeegee to obtain a thin film with an electrode pattern.

[0017] S103. After leveling the printed film for 5-10 minutes, place it on a heating table at 120-150℃ and dry for 15-20 minutes to allow the paste to dry and set fully. After the sample cools down, repeat the above operation to prepare the second electrode.

[0018] S104. After completing the printing process, the thin film thermocouple sample is heat-treated at 1200-1300℃ to remove the binder and terpineol. The temperature is increased at a rate of 5℃ per minute, and the sample is kept at the preset temperature for 2-2.5 hours.

[0019] S105. Connect the external wires to the thin film thermocouple sample, and connect them to the two electrodes of the thin film thermocouple using high-temperature conductive silver paste DS3120 paste and copper wires with a diameter of 0.3 mm. Place the sample on a heating table at 100°C and dry for 1-2 hours.

[0020] Furthermore, in S2 of this invention, the prepared thin-film thermocouple is tested in a muffle furnace; a K-type standard thermocouple is selected and fixed relative to the hot junction of the prepared thin-film thermocouple, and the temperature of the hot junction of the thin-film thermocouple is calibrated. The maximum temperature that can be tested is 1800℃, and the accuracy is 1℃; under the initial condition of room temperature of 20℃, the muffle furnace temperature is set to 600℃, and the heating time is 2 to 2.5 hours.

[0021] Furthermore, in S3 of this invention, a multi-channel data collector is used to collect the thermoelectric potential of the prepared ITO-In2O3 thin-film thermocouple and the standard K-type thermocouple, with a sampling frequency of 2s. The obtained data is then processed in the integrated development environment PyCharm. The specific method is as follows:

[0022] S301. Perform thermoelectric experiments under the same conditions on multiple thin-film thermocouples prepared by screen printing process, and collect 61 sets of experimental results as sample data.

[0023] S302. 59 of the 61 experimental samples collected were used as the training set, and the other 2 experimental samples were used as test thermocouple a and test thermocouple b, respectively.

[0024] Furthermore, S4 in this invention uses Python to construct a recurrent neural network in PyCharm, load the dataset, adjust the initial state of the neural network, and define hyperparameters. The specific method is as follows:

[0025] S401. Each set of data in the training set has 61 features, each corresponding to a thermoelectric potential value in chronological order, which are used as the input of the 61 nodes of the input layer (input_size). The hidden layer (num_layer) is a two-layer RNN structure with 30 nodes (hidden_size) in each layer. The output layer (output_size) consists of 30 nodes, corresponding to the 30 thermoelectric potential values ​​of a standard K-type thermocouple in chronological order, which are used as the learned labels. The hidden layer and the output layer are connected linearly.

[0026] S402, learning rate lr is set to 0.02, initial hidden layer state h_state is the default 0, training epochs are 4000-5000, loss function is MSE, and optimizer is Adam.

[0027] Furthermore, the thermoelectric potential data of the thin-film thermocouple and the standard K-type thermocouple described in this invention are collected by setting the voltage and the K-type thermocouple signal category at a sampling frequency of 2 seconds, and then reading the thermoelectric potential and the corresponding temperature value.

[0028] The thermoelectric signal is read and the thermoelectric curve is preliminarily processed using the Kalman filter algorithm to obtain a smooth potential-temperature curve. Then, 61 potential values ​​are selected from this curve at equal intervals in order of temperature from low to high. At the same time, 30 values ​​are selected at equal intervals from the recorded standard K-type thermocouple thermoelectric potential values.

[0029] Furthermore, in the training of the recurrent neural network described in this invention, the training times are 4500 times, the loss function is MSE, the learning rate is 0.02, the hidden layer has a two-layer structure, and the hidden layer to the output layer is a linear connection.

[0030] Furthermore, in the training of the recurrent neural network described in this invention, test thermocouple a and test thermocouple b are used to test the trained RNN model. To quantify the error between the thermoelectric signal result after training and the thermoelectric signal curve of a standard K-type thermocouple, the maximum relative error is taken to reflect the error.

[0031]

[0032] In the formula, y and y K These represent the output potential of the sample thin-film thermocouple after training and the thermoelectric potential of the standard K-type thermocouple, respectively, at the same temperature.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] This invention corrects and compensates for thermoelectric signals, solving the measurement error problem caused by cold junction temperature variations and manufacturing deviations in thin-film thermocouples on alumina ceramic cutting tools. It corrects and compensates for thermoelectric signal deviations caused by cold junction temperature rises during testing, as well as random errors present in the screen printing process, thereby improving the accuracy of the thin-film thermocouple sensor. Attached Figure Description

[0035] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is the overall flowchart for error compensation of thin-film thermocouples;

[0037] Figure 2 This is the process of training the RNN model to compensate for the thin-film thermocouple a;

[0038] Figure 3 This is a comparison of the thermoelectric curves of thin-film thermocouple a before and after compensation;

[0039] Figure 4 This is the process of training the RNN model to compensate for the thin-film thermocouple b;

[0040] Figure 5 This is a comparison of the thermoelectric curves of thin-film thermocouple b before and after compensation. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0042] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0043] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0044] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0045] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0046] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0047] The present invention will now be described in further detail with reference to the accompanying drawings:

[0048] See Figure 1 This invention discloses a method for compensating for thin-film thermocouple errors based on a recurrent neural network, comprising the following steps:

[0049] S1. Prepare thin-film thermocouples using screen printing process;

[0050] S101. The material composition for preparing the thin-film thermocouple electrode is nano-sized powder of In2O3 and ITO, with additives including a certain mass fraction of terpineol, polyetheramine and high-temperature glass powder, etc., to form a composite slurry of In2O3 and ITO, ensuring that the prepared slurry is neither too thin nor too dry.

[0051] S102. The prepared paste is coated onto a photomask, and then the material of an electrode is printed onto the ceramic substrate through the corresponding position of the photomask using a squeegee to obtain a thin film with an electrode pattern.

[0052] S103. After leveling the printed film for 5 to 10 minutes, place it on a heating table at a temperature of 120 to 150°C to dry for 15 to 20 minutes to allow the paste to dry and set completely. After the sample cools, repeat the above steps to prepare the second electrode.

[0053] S104. After completing the printing process, the thin-film thermocouple sample is heat-treated at 1200 to 1300°C to remove the binder and terpineol. The temperature is increased at a rate of 5°C per minute, and the sample is kept at the preset temperature for 2 to 2.5 hours.

[0054] S105. Connect the external wires to the thin-film thermocouple sample. Use a copper wire with a diameter of 0.3mm made of high-temperature conductive silver paste DS3120 to connect the two electrodes of the thin-film thermocouple. Place it on a heating table at 100℃ and dry it for 1 to 2 hours. After the connection is stable, prepare to start the temperature test of the thin-film thermocouple.

[0055] S2. Test the prepared thin-film thermocouple in a muffle furnace;

[0056] S201. Select a type K standard thermocouple and fix its hot junction relative to the test sample. calibrate the temperature of the hot junction of the thin-film thermocouple; its maximum testable temperature is 1800℃, with an accuracy of 1℃. Under initial conditions of room temperature 20℃, set the muffle furnace temperature to 600℃, with a heating time of 2 to 2.5 hours.

[0057] S3. The thermoelectric potentials of the prepared ITO-In2O3 thin film thermocouple and the standard K-type thermocouple were collected using a multi-channel data collector (LR8410-30 Japan HIOKI) at a sampling frequency of 2s, and the obtained data were processed in the integrated development environment PyCharm.

[0058] S301. Repeat the experiment and conduct thermoelectric experiments under the same conditions on multiple thin-film thermocouples prepared by screen printing process, and collect 61 sets of experimental results as sample data.

[0059] S302. 59 of the 61 experimental samples collected were used as the training set, and the other 2 experimental samples were used as test thermocouple a and test thermocouple b, respectively.

[0060] S4. Using Python, build a recurrent neural network in PyCharm, load the dataset, adjust the initial state of the neural network, and define hyperparameters.

[0061] S401. Each set of data in the training set has 61 features, each corresponding to a thermoelectric potential value in chronological order, which are used as inputs to the 61 nodes of the input layer (input_size). The hidden layer (num_layer) is a two-layer RNN structure with 30 nodes in each layer (hidden_size). The output layer (output_size) consists of 30 nodes, corresponding to 30 thermoelectric potential values ​​of a standard K-type thermocouple in chronological order, which are used as learning labels. The hidden layer and the output layer are linearly connected.

[0062] S402, learning rate (lr) is set to 0.02, initial hidden layer state (h_state) is the default 0, training epochs are 4000-5000, loss function is MSE, and optimizer is Adam.

[0063] The principle of this invention:

[0064] Data related to a sequential order is called sequential data, and the series of thermoelectric potential data generated by a thin-film thermocouple during temperature rise is sequential data. The reason for using a recurrent natural network (RNN) to process sequential data is due to the self-circulating structure of RNNs, which can connect neurons between hidden layers and greatly reduce the number of parameters by sharing parameters.

[0065] As a supervised learning algorithm, the entire learning process revolves around how to make the correction result closer to the target. Under the conditions of appropriate parameters and correct model, after training with a sufficient number of training sets, the recurrent neural network can perform good correction of the thermoelectric signal of the corresponding sensor, thereby achieving the purpose of error compensation.

[0066] In practical applications, the pre-trained RNN model can be deployed in a microcontroller to correct and compensate for the error of the thin-film thermocouple during high-temperature testing, resulting in more reliable test results.

[0067] The MSE loss function is used to reflect the quality of training a recurrent neural network model, such as... Figure 2-5 As shown, after 4500 training iterations, the training MSE loss of the model decreased to 1.1922937669044761e-14, while the actual test MSE loss was 1.4002194074506913e-08.

[0068] Furthermore, comparing the thermoelectric curves before and after training, the RNN significantly improves the linearity of the thin-film thermocouple potential signal output, largely compensating for errors caused by manufacturing processes and unstable cold junction temperatures.

[0069] Electrodes were printed on an alumina ceramic substrate using a screen printing process. After 3 minutes, the substrate was leveled and placed on a heating stage for drying for 20 minutes. The sample was then removed from the heating stage and allowed to cool naturally.

[0070] Next, the sample was subjected to annealing heat treatment at 1200℃ in air for 3 hours with a heating rate of 6℃ / min, and then held at 1200℃ for 2 hours. After the holding period, the sample was cooled to room temperature before being removed.

[0071] The two electrodes of the heat-treated thin-film thermocouple were connected to a copper wire with a diameter of 0.3 mm using conductive silver paste DS3120. The sample with the wire initially connected was then placed on a heating stage and dried at 150°C for 1 hour. A multimeter was used to test both ends of the wire to confirm that the thin-film thermocouple and the wire were connected.

[0072] The hot junction temperature of the sample thin-film thermocouple was tested using a standard K-type thermocouple. The sample thin-film thermocouple was fixed relative to the hot junction of the sample thermocouple and placed in a muffle furnace. The temperature of the muffle furnace was set to 600℃ and the heating time was 3 hours.

[0073] The two electrodes of the sample thin-film thermocouple and the electrodes of the standard K-type thermocouple were connected to a multi-channel data collector (LR8410-30 Japan HIOKI). The voltage and K-type thermocouple signal type were set at a sampling frequency of 2s, and the thermoelectric potential and corresponding temperature values ​​were read.

[0074] The thermoelectric signal is read and the thermoelectric curve is preliminarily processed using the Kalman filter algorithm to obtain a smooth potential-temperature curve. Then, 61 potential values ​​are selected from this curve at equal intervals in order of temperature from low to high. At the same time, 30 values ​​are selected at equal intervals from the recorded standard K-type thermocouple thermoelectric potential values.

[0075] In RNN training, the number of training iterations was 4500, the loss function was MSE, the learning rate was 0.02, the hidden layer had a two-layer structure, and the connection between the hidden layer and the output layer was linear.

[0076] The trained RNN model was tested using two different thermocouples, a and b, respectively. To quantify the error between the trained thermoelectric signal and the standard K-type thermocouple thermoelectric signal curve, the maximum relative error was used to reflect the error.

[0077]

[0078] In the formula, y and y K These represent the output potential of the sample thin-film thermocouple after training and the thermoelectric potential of the standard K-type thermocouple, respectively, at the same temperature.

[0079] For the two tested thin-film thermocouple samples, the final relative errors are as follows: the maximum relative error of a is 0.034803%, and the maximum relative error of b is 0.63619%.

[0080] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for compensating for thin-film thermocouple errors based on a recurrent neural network, characterized in that, Includes the following steps: S1, Thin-film thermocouples are prepared using screen printing technology; the specific method is as follows: S101. The material composition for preparing the thin film thermocouple electrode is nano-sized powder of In2O3 and ITO, and the additives are terpineol, polyetheramine and high temperature glass powder, which are configured into a composite slurry of In2O3 and ITO. S102. The prepared composite material slurry is coated on a photomask, and then the material of an electrode is printed onto the ceramic substrate through the corresponding position of the photomask using a squeegee to obtain a thin film with an electrode pattern. S103. After leveling the printed film for 5-10 minutes, place it on a heating table at 120-150℃ and dry for 15-20 minutes to allow the paste to dry and set fully. After the sample cools, repeat the above operation to prepare the second electrode. S104. After completing the printing process, the thin film thermocouple sample is heat-treated at 1200~1300℃ to remove the binder and terpineol. The temperature is increased at a rate of 5℃ per minute, and the sample is kept at the preset temperature for 2~2.5 hours. S105. Connect the external wires to the thin film thermocouple sample, and connect them to the two electrodes of the thin film thermocouple using high-temperature conductive silver paste DS3120 paste and copper wires with a diameter of 0.3 mm. Place the sample on a heating platform at 100°C and dry for 1~2 hours. S2, temperature testing of the thin-film thermocouple; S2 is performed in a muffle furnace to test the prepared thin-film thermocouple; a K-type standard thermocouple is selected and fixed relative to the hot junction of the prepared thin-film thermocouple, and the temperature of the hot junction of the thin-film thermocouple is calibrated. The maximum temperature that can be tested is 1800℃, and the accuracy is 1℃; under the initial condition of room temperature of 20℃, the muffle furnace temperature is set to 600℃, and the heating time is 2~2.5h. S3 involves collecting thermoelectric potential data from the thin-film thermocouple and the standard K-type thermocouple, and processing the collected thermoelectric potential data in the PyCharm integrated development environment. S3 employs a multi-channel data collector to collect the thermoelectric potential of the prepared ITO-In2O3 thin-film thermocouple and the standard K-type thermocouple at a sampling frequency of 2 seconds, and processes the obtained data in the PyCharm integrated development environment. The specific method is as follows: S301. Perform thermoelectric experiments under the same conditions on multiple thin-film thermocouples prepared by screen printing process, and collect 61 sets of experimental results as sample data. S302. 59 of the 61 experimental samples collected were used as the training set, and the other 2 experimental samples were used as test thermocouple a and test thermocouple b, respectively. S4. Build a recurrent neural network in PyCharm, load the dataset, adjust the initial state of the neural network, and define hyperparameters; The S4 method involves using Python in PyCharm to build a recurrent neural network, load the dataset, adjust the initial state of the neural network, and define hyperparameters. The specific method is as follows: S401. Each set of data in the training set has 61 features, each corresponding to a thermoelectric potential value in chronological order, which are used as the input of the 61 nodes of the input layer (input_size). The hidden layer (num_layer) is a two-layer RNN structure with 30 nodes (hidden_size) in each layer. The output layer (output_size) consists of 30 nodes, corresponding to the 30 thermoelectric potential values ​​of a standard K-type thermocouple in chronological order, which are used as the learned labels. The hidden layer and the output layer are connected linearly. S402, learning rate lr is set to 0.02, initial hidden layer state h_state is the default 0, training epochs are 4000~5000, loss function is MSE, and optimizer is Adam.

2. The thin-film thermocouple error compensation method based on recurrent neural networks according to claim 1, characterized in that, The thermoelectric potential data of the thin-film thermocouple and the standard K-type thermocouple are collected by setting the voltage and the K-type thermocouple signal type at a sampling frequency of 2 seconds, and then reading the thermoelectric potential and the corresponding temperature value. The thermoelectric signal is read and the thermoelectric curve is preliminarily processed using the Kalman filter algorithm to obtain a smooth potential-temperature curve. Then, 61 potential values ​​are selected from this curve at equal intervals in order of temperature from low to high. At the same time, 30 values ​​are selected at equal intervals from the recorded standard K-type thermocouple thermoelectric potential values.

3. The thin-film thermocouple error compensation method based on recurrent neural networks according to claim 2, characterized in that, The recurrent neural network was trained 4500 times, with MSE as the loss function and a learning rate of 0.

02. The hidden layers were of a two-layer structure, and the connection between the hidden layers and the output layer was linear.

4. The thin-film thermocouple error compensation method based on recurrent neural networks according to claim 3, characterized in that, When training the recurrent neural network, the trained RNN model is tested using test thermocouple a and test thermocouple b, respectively. To quantify the error between the trained thermoelectric signal result and the standard K-type thermocouple thermoelectric signal curve, the maximum relative error is taken to reflect the error. In the formula, and These represent the output potential of the sample thin-film thermocouple after training and the thermoelectric potential of the standard K-type thermocouple, respectively, at the same temperature.

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