An optimized Kalman filtering method to improve the accuracy of thermocouple temperature measurement

Abstract

The present invention relates to an optimized Kalman filtering method for improving the temperature measurement accuracy of a thermocouple, comprising the following steps: S1, establishing a temperature state equation and an observation equation of a temperature measurement object; S2, determining thermal model parameter values ​​and optimizing Kalman filter parameter values; S3, collecting temperature measurement data of the thermocouple; S4, performing real-time standard Kalman filtering and real-time mean filtering on the temperature measurement data; S5, at each temperature measurement moment, performing information fusion on the real-time standard Kalman filtering and real-time mean filtering results, slightly converging the real-time standard Kalman filtering result to the real-time mean filtering result, obtaining an optimized Kalman filtering posterior estimation value of the temperature measurement data, and eliminating the deviation caused by error accumulation under the premise of maintaining the smoothness of the temperature measurement data curve. The beneficial effect is that when the thermal model parameters and the Kalman filter parameter values ​​are inaccurate, the thermocouple temperature measurement deviation is small, and the temperature measurement precision and accuracy are high.

Description

Technical field

[0001] The present invention relates to the field of satellite aerospace technology, and in particular to an optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples. [Background Technology]

[0002] The temperature measurement accuracy of a temperature measuring element includes indicators at two levels: precision and accuracy. Among them, temperature measurement accuracy represents its ability to resolve weak temperature signals, and accuracy represents the deviation of its measurement results from the true value.

[0003] Thermocouples, platinum resistance thermocouples, and thermistors are three common types of temperature measurement components. Thermocouples offer advantages such as no self-heating, rapid temperature response, no need for power supply, low cost, good component consistency, a wide temperature measurement range, and minimal temperature drift. However, their weak output signal is susceptible to high-intensity noise generated by environmental electromagnetic interference, significantly limiting their application in precise temperature measurement and control on spacecraft.

[0004] Signal post-processing through filtering can improve thermocouple temperature measurement accuracy to a certain extent. Common filtering methods include mean filtering, clipping filtering, and median filtering. However, the temperature measurement noise of thermocouples can reach tens of millikelvins or even over 100 millikelvins. These filtering methods are unable to effectively suppress the temperature measurement noise, reduce it to the millikelvin level, and thus fail to improve temperature measurement accuracy.

[0005] The Kalman filter method can modify measurement results based on the thermal model of the temperature measurement object, effectively suppressing noise. However, the practical application of this method is highly dependent on the accuracy of the thermal model and the appropriate values ​​of the Kalman filter parameters. In practical projects, it is often difficult to achieve high accuracy in the thermal model parameters and Kalman filter parameters of the temperature measurement object. Model deviation or parameter inaccuracy may occur during application. Inaccurate parameter values ​​can easily lead to poor noise suppression or deviation of the filter results from the true value, resulting in reduced temperature measurement accuracy or precision. Furthermore, parameter selection is challenging, and it is often difficult to simultaneously ensure both accuracy and precision.

[0006] Kalman filtering is an algorithm that uses the linear system state equation to optimally estimate the system state through system input and output observation data. Since the observation data includes the influence of noise and interference in the system, the optimal estimation can also be regarded as a filtering process.

[0007] The present invention aims to solve the technical problems in the prior art of low temperature measurement precision or accuracy and difficulty in ensuring both precision and accuracy, and makes technical improvements to the thermocouple temperature measurement Kalman filter method. [Summary of the invention]

[0008] The purpose of the present invention is to propose a Kalman filtering method which has small deviation in thermocouple temperature measurement and high temperature measurement precision and accuracy when the values ​​of thermal model parameters and Kalman filtering parameters are inaccurate.

[0009] To achieve the above object, the technical solution adopted by the present invention is an optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples, which includes the following steps:

[0010] S1. Establish the temperature state equation and observation equation of the temperature measurement object;

[0011] S2. Determine the thermal model parameter values ​​and optimize the Kalman filter parameter values;

[0012] S3, collecting temperature measurement data of thermocouples;

[0013] S4, performing real-time standard Kalman filtering and real-time mean filtering on the temperature measurement data;

[0014] S5. At each temperature measurement moment, the real-time standard Kalman filter and real-time mean filter results are fused, and the real-time standard Kalman filter results are slightly converged to the real-time mean filter results to obtain the optimized Kalman filter posterior estimate of the temperature measurement data, eliminating the deviation caused by error accumulation while maintaining the smoothness of the temperature measurement data curve.

[0015] Preferably, step S1:

[0016] The temperature state equation of the temperature measurement object is T k =T k-1 +u k-1 +w k ,

[0017] Among them, T k Represents the temperature of the temperature measurement object at the kth moment, T k-1 represents the temperature of the temperature measurement object at the k-1th moment, u k-1 The temperature change trend between k-1 and k is calculated based on the heating power P. heat and heat leakage power P loss The difference between the two and the total heat capacity C of the temperature measurement object is determined, that is, u k-1 =dt*(P heat,k-1 -P loss,k-1 ) / C, where dt is the sampling time interval for temperature measurement, P heat,k-1 Usually determined according to the power of the heating source, P loss,k-1 It can be calculated based on the temperature difference between the temperature measurement object and the environment and the thermal resistance, that is, P loss,k-1 =(T k-1 -T atm,k-1 ) / R, where T atm,k-1 is the ambient temperature, R is the thermal resistance between the temperature measurement object and the environment;

[0018] w k is the white noise error of the temperature state equation, which obeys Gaussian distribution and has a variance of W k ;

[0019] The temperature observation equation of the temperature measurement object is Z k =X k +v k , where Z k is the temperature measurement value, X k is the display value of the temperature measuring instrument, v k To measure white noise, its variance is V k .

[0020] Preferably, step S2:

[0021] The thermal model parameters that need to be determined include the total heat capacity C of the temperature measurement object, the thermal resistance R between the temperature measurement object and the environment, and the sampling time interval dt. The total heat capacity C of the temperature measurement object is determined based on the geometric parameters and physical parameters of the temperature measurement object, the thermal resistance R between the temperature measurement object and the environment is determined through experimental testing, and the sampling time interval dt is determined based on the data acquisition frequency.

[0022] The optimized Kalman filter parameters that need to be determined include the mean square error of the measurement error V k , the mean square error of the system error W k , and regression coefficient B; where the measurement error mean square error V k Determine according to the mean square error of temperature measurement data under constant temperature conditions; k After that, we try to find the appropriate mean square error W of the system error by multiple attempts. k The temperature measurement noise is made small enough; the regression coefficient B is used to reduce the temperature measurement deviation value without significantly reducing the noise suppression effect.

[0023] Preferably, step S3:

[0024] Arrange temperature measuring thermocouples on the temperature measurement object according to requirements, set the sampling time interval dt in the data acquisition system, start the data acquisition system, and save the temperature measurement data to the storage.

[0025] Preferably, step S4:

[0026] At the kth moment, the measured data X k Perform standard Kalman filtering and mean filtering;

[0027] Among them, the mean filter is

[0028] In the standard Kalman filtering process, the temperature prior estimate is first calculated

[0029] Then calculate the temperature prior estimated covariance and the Kalman gain coefficient

[0030] Afterwards, update the temperature posterior estimated covariance

[0031] Finally, calculate the standard Kalman filter temperature posterior estimate

[0032] Preferably, step S5:

[0033] When W k If the value is too small, the standard Kalman filter method tends to over-rely on the inaccurate state equation, resulting in temperature estimation errors;

[0034] At each temperature measurement moment, the standard Kalman filter result is converged to the mean filter result in a small range of information fusion in, To optimize the temperature posterior estimate of the Kalman filter, B is the regression coefficient of the mean filter result.

[0035] The present invention discloses an optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples. The method can significantly improve the temperature measurement accuracy compared to the mean filtering method. Compared to the standard Kalman filtering method, the method can eliminate the temperature measurement deviation by correcting the mean filtering results when the thermal model parameters and the filter parameters are inaccurate, thereby reducing the risk of temperature measurement deviation. In addition, the method can obtain higher temperature measurement accuracy than the standard Kalman filtering by selecting reasonable values. Specifically:

[0036] 1. Use thermocouples to measure the precise temperature data of the target object. The thermocouples are in a strong and variable electromagnetic interference environment, and the temperature measurement accuracy must reach the mK level;

[0037] 2. It is necessary to establish the temperature state equation and observation equation of the temperature measurement object, and perform preliminary filtering on the temperature data through standard Kalman filtering;

[0038] 3. It is necessary to perform mean filtering on the temperature data at the same time, use the mean filtering result to correct the standard positive Kalman filter result, and output the information fusion result as the best estimate in real time;

[0039] 4. When the thermal model deviation is large, the system error mean square error W of the Kalman filter is allowed to be k Selecting a smaller value can improve the suppression of temperature measurement glitches without significantly increasing the temperature measurement deviation.

Brief Description of the Drawings

[0040] Figure 1This is a diagram of the implementation steps of the optimized Kalman filter method to improve the accuracy of thermocouple temperature measurement.

[0041] Figure 2 This is a schematic diagram of the prototype of the thermocouple precision temperature measurement and control principle.

[0042] Figure 3 This is a schematic diagram of the filtering effect in the rapid heating section of the prototype of the thermocouple precision temperature measurement and control principle.

[0043] Figure 4 This is a schematic diagram of the filtering effect of the small temperature fluctuation section of the prototype of the thermocouple precision temperature measurement and control principle. [Specific implementation method]

[0044] The present invention will be further described below in conjunction with embodiments and with reference to the accompanying drawings.

[0045] Example

[0046] This embodiment implements an optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples.

[0047] The method of this embodiment belongs to the field of spacecraft temperature measurement technology, and can effectively reduce the deviation of filtering results caused by inaccurate thermal model parameters, thereby improving the temperature measurement precision and accuracy of thermocouples.

[0048] The method of this embodiment optimizes the standard Kalman filter method, reduces the temperature measurement deviation when the thermal model parameters and Kalman filter parameters are inaccurate, improves the temperature measurement accuracy, and the adaptability and stability of the temperature measurement system in complex and changeable engineering application environments.

[0049] The specific technical features of the method in this embodiment are as follows:

[0050] 1) Use thermocouples to measure the precise temperature data of the target object. The thermocouples are in a strong and variable electromagnetic interference environment, and the temperature measurement accuracy must reach the mK level;

[0051] 2) It is necessary to establish the temperature state equation and observation equation of the temperature measurement object, and perform preliminary filtering on the temperature data through standard Kalman filtering;

[0052] 3) It is necessary to perform mean filtering on the temperature data at the same time, use the mean filtering result to correct the standard positive Kalman filter result, and output the information fusion result as the best estimate in real time;

[0053] 4) When the thermal model deviation is large, the method of this embodiment allows the system error mean square error W of the Kalman filter to be k Selecting a smaller value can improve the suppression of temperature measurement glitches without significantly increasing the temperature measurement deviation.

[0054] Figure 1This is a diagram of the implementation steps of the optimized Kalman filter method to improve the accuracy of thermocouple temperature measurement. Figure 1 As shown, the specific implementation steps of the method in this embodiment are as follows:

[0055] 1. Establish the temperature state equation and observation equation of the temperature measurement object

[0056] The temperature state equation of the temperature measurement object is:

[0057] T k =T k-1 +u k-1 +w k

[0058] Where T k Represents the temperature of the temperature measurement object at the kth moment, T k-1 Represents the temperature of the temperature measurement object at the k-1th moment. k-1 The temperature change trend between k-1 and k is calculated based on the heating power P. heat and heat leakage power P loss The difference between and the total heat capacity C of the temperature measurement object is determined, that is,

[0059] u k-1 =dt*(P heat,k-1 -P loss,k-1 ) / C

[0060] Where dt is the sampling time interval for temperature measurement.

[0061] P heat,k-1 Usually determined according to the power of the heating source, P loss,k-1 It can be calculated based on the temperature difference between the temperature measurement object and the environment and the thermal resistance, that is,

[0062] P loss,k-1 =(T k-1 -T atm,k-1 ) / R

[0063] Where T atm,k-1 is the ambient temperature, and R is the thermal resistance between the temperature measurement object and the environment.

[0064] w k is the white noise error of the temperature state equation, which obeys Gaussian distribution and has a variance of W k .

[0065] The temperature observation equation of the temperature measurement object is:

[0066] Z k =X k +v k

[0067] where Z k is the temperature measurement value, Xk is the display value of the temperature measuring instrument, v k To measure white noise, its variance is V k .

[0068] 2. Determine the thermal model parameter values ​​and optimize the Kalman filter parameter values

[0069] The thermal model parameters that need to be determined include the total heat capacity C of the temperature measurement object, the thermal resistance R between the temperature measurement object and the environment, and the sampling time interval dt. R needs to be determined through experimental testing, the total heat capacity C is determined based on the geometric parameters and physical properties of the temperature measurement object, and the sampling time interval dt is determined based on the data acquisition frequency.

[0070] The optimized Kalman filter parameters that need to be determined include the mean square error of the system error W k , measurement error mean square error V k , and regression coefficient B. Among them, the measurement error mean square error V k Determine it based on the mean square error of the temperature measurement data under constant temperature conditions. k After that, we try to find the appropriate mean square error W of the system error by multiple attempts. k Make the temperature measurement noise small enough. Generally speaking, by increasing W k , can increase the stability of Kalman filtering and make it less likely to produce deviations, but it will reduce the noise suppression effect. k A high value can improve the suppression of temperature measurement noise, but it can easily cause temperature measurement deviation. The regression coefficient B is used to reduce the temperature measurement deviation without significantly reducing the noise suppression effect. The recommended value is 0.01. You can increase this value to improve stability or decrease it to improve noise suppression.

[0071] 3. Collect temperature measurement data of thermocouples

[0072] Place thermocouples on the temperature measurement object as needed and set the sampling interval dt in the data acquisition system. Start the data acquisition system and save the temperature measurement data to storage.

[0073] 4. Perform real-time standard Kalman filtering and real-time mean filtering on temperature measurement data

[0074] At the kth moment, the measured data X k Perform standard Kalman filtering and mean filtering. Among them, the mean filtering method is

[0075]

[0076] In the standard Kalman filtering process, the prior estimate is first calculated

[0077]

[0078] Then calculate the prior estimated covariance and the Kalman gain coefficient K k

[0079]

[0080]

[0081] Afterwards, the posterior estimated covariance is updated

[0082]

[0083] Finally, the standard Kalman filter posterior estimate is calculated

[0084]

[0085] 5. Perform information fusion on the filtering results to obtain the filtering result at the kth moment

[0086] When W k If the value is too small, the standard Kalman filter method tends to over-rely on an inaccurate state equation, resulting in temperature estimation errors. This error will accumulate during the temperature measurement process, causing the temperature measurement results to deviate from the actual temperature and reducing temperature measurement accuracy.

[0087] Therefore, at each temperature measurement moment, the method of this embodiment converges the standard Kalman filter result to the mean filter result by a small margin, eliminating the deviation caused by error accumulation while maintaining the smoothness of the curve, so that the final filter result is always close to the measured value. The information fusion method of this part is

[0088]

[0089] in, That is, the posterior estimation value of the optimized Kalman filtering method described in the method of this embodiment, and B is the regression coefficient of the mean filtering result. When it is 0, the optimized Kalman filtering will be restored to the standard Kalman filtering.

[0090] The following is an introduction to the temperature control measurement experiment of the thermocouple principle prototype.

[0091] Figure 2 This is a schematic diagram of the prototype of the thermocouple precision temperature measurement and control principle. Figure 2As shown, the temperature measurement target is the internal temperature of a 6cm-long cubic copper block. A small hole with a diameter of 6mm and a depth of 3cm is located in the center of the top surface of the copper block. The temperature measuring tips of the thermocouple and thermistor are placed at the bottom of the hole and secured with thermal adhesive. The thermocouple is used for temperature measurement, and its real-time temperature measurement results serve as the basis for temperature control. The high-precision thermistor has been calibrated and used to compare and analyze the temperature measurement and control performance of the thermocouple. The copper block is placed on a foam insulation board, with a thin film heater on the bottom and an acrylic windshield covering the outside. The temperature data from the thermocouple is collected by a data logger and temporarily stored in memory. The temperature data is collected every 1s. In the figure, 1 is the thermocouple, 2 is the thermistor, 3 is the copper cube, 4 is the thin film heater, 5 is the foam insulation board, and 6 is the acrylic windshield.

[0092] The model parameters can be determined based on the above information and experimental results. Among them, the sampling time interval dt = 1s, the total heat capacity of the temperature measurement object C = 754.8J / K, and the thermal resistance R between the temperature measurement object and the indoor air environment is 11K / W. The standard deviation of the thermocouple temperature measurement noise is about 35mK, so the measurement mean square error V K The value is 1.225E-3.

[0093] Figure 3 This is a schematic diagram of the filtering effect in the rapid heating section of the prototype of the thermocouple precision temperature measurement and control principle. Figure 4 This is a schematic diagram of the filtering effect of the small temperature fluctuation section of the prototype of the thermocouple precision temperature measurement and control principle. Figure 3 、 Figure 4 As shown, after trying, the system error mean square error W k When the temperature is 1E-8 or less, the burr structure of the standard Kalman filter result curve can be as low as the mK level; however, due to the accumulation of state equation errors, the Kalman filter results at this time have obvious deviations. Correspondingly, the mean filter and standard Kalman filter results are shown in the figure. In the rapid heating period and the small temperature fluctuation period, the standard deviation of the noise of the mean filter result is 19.9mK and 22.2mK respectively. k =1E-8, the standard Kalman filter noise is very small, but the result deviation is as high as about 20mK. After information fusion, the deviation of the filtering result is greatly reduced, and the standard deviation of the noise is as low as 2.7mK and 2.2mK respectively. At the same time, compared with W k =1E-7 curve shows that compared with the standard Kalman simply by increasing W k The method of this embodiment has a smaller burr structure and a smaller filtering deviation, and can achieve higher-precision temperature measurement.

[0094] In summary, the method of this embodiment overcomes the shortcomings of the above-mentioned prior art and achieves the above-mentioned technical effects through the following principles:

[0095] Thermocouples have a series of advantages such as low cost, fast response, good consistency, no self-heating, and no need for power supply. However, the temperature measurement is easily interfered by the external environment, which produces large temperature measurement noise and is difficult to use for precise temperature control in complex environments. Mean filtering, median filtering, limiting filtering and other filtering methods as well as W k The standard Kalman filter with a larger value cannot suppress the temperature measurement noise well. k If the value is too small, the temperature measurement result will easily rely too much on the inaccurate state equation, resulting in temperature estimation error. This error will continue to accumulate during the temperature measurement process, causing the temperature measurement result to deviate from the actual temperature.

[0096] In this embodiment, the method first adopts a smaller W k The standard Kalman filter is applied to the thermocouple temperature measurement data to obtain a good noise suppression effect; then, at each temperature measurement moment, the standard Kalman filter result is slightly converged to the mean filter result to eliminate the deviation caused by error accumulation, so that the final filter result is always close to the measured value; the information fusion method for this part is

[0097]

[0098] in, That is, the posterior estimation value of the optimized Kalman filtering method described in the method of this embodiment.

[0099] Compared with the mean filtering method, the method of this embodiment can greatly improve the temperature measurement accuracy; compared with the standard Kalman filtering method, when the thermal model parameters and filtering parameters are inaccurate, the temperature measurement deviation can be eliminated by correcting the mean filtering results, thereby reducing the risk of temperature measurement deviation; and, by reasonably selecting values, higher temperature measurement accuracy can be obtained than that of the standard Kalman filtering.

[0100] Those skilled in the art will appreciate that all or part of the steps for implementing the above embodiments may be accomplished by hardware, or may be accomplished by a program instructing the relevant hardware, and the program may be stored in a computer-readable storage medium, wherein the storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM), etc.

[0101] The above is only a preferred embodiment of the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements and supplements without departing from the principles of the present invention. These improvements and supplements should also be regarded as the scope of protection of the present invention.

Claims

1. An optimized Kalman filter method for improving the accuracy of thermocouple temperature measurement, characterized in that The following steps are involved: S1. Establish the temperature state equation and observation equation of the temperature measurement object; S2. Determine the thermal model parameter values ​​and optimize the Kalman filter parameter values; S3, collecting temperature measurement data of thermocouples; S4, performing real-time standard Kalman filtering and real-time mean filtering on the temperature measurement data; S5. At each temperature measurement moment, the real-time standard Kalman filter and real-time mean filter results are fused, and the real-time standard Kalman filter results are slightly converged to the real-time mean filter results to obtain the optimized Kalman filter posterior estimate of the temperature measurement data, eliminating the deviation caused by error accumulation while maintaining the smoothness of the temperature measurement data curve.

2. The optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples according to claim 1 is characterized in that Step S1: The temperature state equation of the temperature measurement object is T k =T k-1 +u k-1 +w k , Among them, T k Represents the temperature of the temperature measurement object at the kth moment, T k-1 represents the temperature of the temperature measurement object at the k-1th moment, u k-1 The temperature change trend between k-1 and k is calculated based on the heating power P. heat and heat leakage power P loss The difference between the two and the total heat capacity C of the temperature measurement object is determined, that is, u k-1 =dt*(P heat,k-1 -P loss,k-1 ) / C, where dt is the sampling time interval for temperature measurement, P heat,k-1 Usually determined according to the power of the heating source, P loss,k-1 It can be calculated based on the temperature difference between the temperature measurement object and the environment and the thermal resistance, that is, P loss,k-1 =(T k-1 -T atm,k-1 ) / R, where T atm,k-1 is the ambient temperature, R is the thermal resistance between the temperature measurement object and the environment; w k is the white noise error of the temperature state equation, which obeys Gaussian distribution and has a variance of W k ; The temperature observation equation of the temperature measurement object is Z k =X k +v k , where Z k is the temperature measurement value, X k is the display value of the temperature measuring instrument, v k To measure white noise, its variance is V k .

3. The optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples according to claim 2 is characterized in that Step S2: The thermal model parameters that need to be determined include the total heat capacity C of the temperature measurement object, the thermal resistance R between the temperature measurement object and the environment, and the sampling time interval dt. The total heat capacity C of the temperature measurement object is determined based on the geometric parameters and physical parameters of the temperature measurement object, the thermal resistance R between the temperature measurement object and the environment is determined through experimental testing, and the sampling time interval dt is determined based on the data acquisition frequency. The optimized Kalman filter parameters that need to be determined include the mean square error of the measurement error V k , the mean square error of the system error W k , and regression coefficient B; where the measurement error mean square error V k Determine according to the mean square error of temperature measurement data under constant temperature conditions; k After that, we try to find the appropriate mean square error W of the system error by multiple attempts. k The temperature measurement noise is made small enough; the regression coefficient B is used to reduce the temperature measurement deviation value without significantly reducing the noise suppression effect.

4. The optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples according to claim 3 is characterized in that Step S3: Arrange temperature measuring thermocouples on the temperature measurement object according to requirements, set the sampling time interval dt in the data acquisition system, start the data acquisition system, and save the temperature measurement data to the storage.

5. The optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples according to claim 4 is characterized in that Step S4: At the kth moment, the measured data X k Perform standard Kalman filtering and mean filtering; Among them, the mean filter is In the standard Kalman filtering process, the temperature prior estimate is first calculated Then calculate the temperature prior estimated covariance and the Kalman gain coefficient Afterwards, update the temperature posterior estimated covariance Finally, calculate the standard Kalman filter temperature posterior estimate 6. The optimized Kalman filtering method for improving the temperature measurement accuracy of thermocouples according to claim 5 is characterized in that Step S5: When W k If the value is too small, the standard Kalman filter method tends to over-rely on the inaccurate state equation, resulting in temperature estimation errors; At each temperature measurement moment, the standard Kalman filter result is converged to the mean filter result in a small range of information fusion in, To optimize the temperature posterior estimate of the Kalman filter, B is the regression coefficient of the mean filter result.

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