A comprehensive compensation method for differential pressure transmitter based on kriging interpolation and cubic spline interpolation

Abstract

The application provides a differential pressure transmitter comprehensive compensation method based on Kriging interpolation and cubic spline interpolation, which comprises the following steps: measuring the calibration output voltage of a differential pressure transmitter at multiple temperature calibration points, static pressure calibration points and differential pressure calibration points to obtain data calibration points; fitting a variogram function theoretical model by using Kriging interpolation and obtaining a compensation matrix; establishing an output voltage model by using cubic spline interpolation; when the measured value of the ambient temperature is a temperature calibration point, the measured value of the static pressure is directly brought into the output voltage model to obtain a theoretical voltage, three calibration output voltages adjacent to the theoretical voltage are selected, a differential pressure function relationship is established by using cubic spline interpolation, and the measured output voltage is brought into the differential pressure function relationship to obtain a to-be-measured differential pressure; when the measured value of the ambient temperature is not a temperature calibration point, a compensation coefficient is determined by using the variogram function theoretical model, and the to-be-measured differential pressure is calculated by using the compensation coefficient. The application adopts cubic spline interpolation at the modeling temperature and adopts Kriging interpolation at the non-modeling temperature, so that the algorithm with large calculation amount can be used to improve the compensation precision, the repeated interpolation at each temperature and static pressure interval is avoided, the workload is reduced, and the real-time performance of the compensation is improved.

Description

Technical Field

[0001] This invention relates to the technical field of differential pressure transmitter compensation, and in particular to a comprehensive compensation method for differential pressure transmitters based on Kriging interpolation and cubic spline interpolation. Background Technology

[0002] Differential pressure transmitters, as pressure measurement and control instruments, are widely used in industrial testing fields such as aerospace, automotive, and industrial control. Due to the influence of silicon materials and the temperature characteristics of the encapsulating medium, as well as variations in diffusion resistance, differential pressure transmitters suffer from problems such as zero-point drift, sensitivity drift, and nonlinearity. Ambient temperature and other factors also affect the voltage variation of differential pressure transmitters, with ambient temperature having the greatest impact. Therefore, measures need to be taken to reduce the error caused by ambient temperature, i.e., temperature compensation. On the other hand, the object measured by the differential pressure transmitter is the pressure difference, and static pressure is the pressure it withstands during operation. When the ambient temperature is stable, the output of the differential pressure transmitter is affected by static pressure, resulting in static pressure error, which is also a significant factor affecting the measurement accuracy of the differential pressure transmitter. The actual voltage output of the differential pressure transmitter is affected by the coupling effect of ambient temperature and static pressure, severely degrading the measurement accuracy. Therefore, measures need to be taken to improve the measurement accuracy of the differential pressure transmitter, i.e., comprehensive compensation.

[0003] Currently, the main methods for temperature compensation in differential pressure transmitters are hardware compensation and software compensation. Hardware compensation mainly includes thermistor compensation and series diode compensation, adjusting the diffusion resistance value to compensate for the electrical signal loss due to temperature changes. However, hardware compensation suffers from complex circuit debugging, low accuracy, and high cost. Software compensation combines a microprocessor with the differential pressure transmitter, utilizing the microprocessor's built-in compensation algorithm to construct a temperature compensation model based on ambient temperature and output voltage. Software compensation includes artificial intelligence methods and numerical calculation methods. Artificial intelligence methods include BP neural networks, RBF neural networks, and extreme learning machines. These algorithms have high hardware requirements, large computational load, and complex model structures. Artificial intelligence methods require training node parameters and are prone to local minima. Particle swarm optimization, gray wolf algorithms, and genetic algorithms are often used to optimize these methods, making the model more complex, requiring more computation time, and increasing microprocessor memory consumption. Numerical calculation methods include cubic spline interpolation, Lagrange interpolation, and Newton interpolation. These algorithms have clear compensation structures, low computational load, and are easy to implement online. While there are many methods to suppress temperature drift in differential pressure transmitters, few involve comprehensive compensation that simultaneously considers ambient temperature and static pressure errors.

[0004] Patent application number 202311397847.3 discloses a method for compensating voltage for temperature drift error based on a magnetic current sensor. The method includes: performing a temperature sensitivity test on the magnetic current sensor and acquiring test data; fitting the test data to construct a relationship between the sensitivity of the magnetic current sensor and temperature, and constructing a relationship curve based on this relationship; determining a sensitivity compensation coefficient at each temperature based on the relationship curve; and determining the compensated output voltage of the magnetic current sensor based on the sensitivity compensation coefficient and the temperature drift error. This invention can calculate the compensated output voltage of the magnetic current sensor based on the temperature drift error, improving the measurement performance and environmental adaptability of the magnetic current sensor. However, this invention only considers the influence of temperature on the magnetic current sensor and does not comprehensively consider the coupling effect of temperature and static pressure on the differential pressure sensor, thus failing to improve measurement accuracy when applied to differential pressure transmitters. Summary of the Invention

[0005] To address the technical problems of existing differential pressure transmitter temperature compensation methods, such as high hardware requirements, high computational complexity, and low measurement accuracy, this invention proposes a comprehensive compensation method for differential pressure transmitters based on Kriging interpolation and cubic spline interpolation, which can improve the measurement accuracy of differential pressure transmitters.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: a comprehensive compensation method for differential pressure transmitters based on Kriging interpolation and cubic spline interpolation, comprising the following steps:

[0007] Step 1, Offline Section: Measure the calibration output voltage of the differential pressure transmitter at multiple temperature calibration points, static pressure calibration points, and differential pressure calibration points to obtain data calibration points; based on the data calibration points, use Kriging interpolation to fit the variogram theoretical model and obtain the compensation matrix; use cubic spline interpolation to establish output voltage models at multiple static pressure calibration points and differential pressure calibration points under temperature calibration points.

[0008] Step 2: Determine whether the measured ambient temperature value is the temperature calibration point from Step 1. If it is, proceed to Step 3; otherwise, proceed to Step 4.

[0009] Step 3: Directly input the static pressure measurement value under the current ambient temperature into the output voltage model to obtain the theoretical voltage. Select three calibration output voltages adjacent to the theoretical voltage, and establish the differential pressure function relationship using cubic spline interpolation and the three calibration output voltages. Substitute the measured output voltage into the differential pressure function relationship to obtain the differential pressure to be measured.

[0010] Step 4: Combining the measured ambient temperature, static pressure, and output voltage, determine the compensation coefficient using the variogram theoretical model, and calculate the differential pressure to be measured using the compensation coefficient and the differential pressure calibration point.

[0011] Preferably, the method for fitting the theoretical model of the variogram is as follows: the variogram value is...

[0012]

[0013] Among them, the data pairs {Z(x) are divided by vector h. i ),Z(x i Z(x) + h)}(i=1,2,…,N(h)) can be viewed as a single, distinct realization of the data pair [Z(x), Z(x+h)], where N(h) is the number of data pairs separated by vector h; different lag distances h are used to calculate the corresponding variance value γ. * (h), for the variogram value γ * The theoretical model of the variogram γ(h) is obtained by fitting (h).

[0014] Preferably, the method for obtaining the compensation matrix is ​​as follows: calculate the Euclidean distance of all data calibration points, substitute the Euclidean distance into the variogram theoretical model γ(h) to obtain matrix K, and solve for the generalized inverse matrix [K]. + [ ] as the compensation matrix.

[0015] Preferably, the method for obtaining the data calibration points is as follows: at m temperature calibration points T i n static pressure calibration points SP j q differential pressure calibration points DP k The output voltage U of m×n×q differential pressure transmitters was measured. ijk i = 1, 2, ..., m, j = 1, 2, ..., n, k = 1, 2, ..., q; thus obtaining m × n × q data calibration points (T i SP j U ijk ,DP k ).

[0016] Preferably, the method for establishing the output voltage model at multiple static pressure calibration points and differential pressure calibration points using cubic spline interpolation at the temperature calibration point in step one is as follows: at m temperature calibration points T i Below, cubic spline interpolation is used to establish q differential pressure calibration points DP. k Lower static pressure calibration point SP j Output voltage model affecting output voltage: and:

[0017]

[0018] Among them, a jk b jk c jk d jkSP represents the cubic spline interpolation coefficients of the output voltage model at different static pressure calibration points, j = 1 = 1, 2, ..., n-1. c This is the static pressure measurement value.

[0019] Preferably, the method for establishing the differential pressure function relationship is as follows: using cubic spline interpolation to establish three calibrated output voltages U x U y U z With the corresponding calibrated differential pressure [DP] x ,DP y ,DP z The functional relationship of ]:

[0020] Where a1, b1, c1, and d1 are the cubic spline interpolation coefficients under the calibrated output voltage, x, y, z ∈ {1, 2, ..., q}, U c This is the actual output voltage.

[0021] Preferably, the three calibrated output voltages U x U y U z The method for determining this is as follows: take the current ambient temperature measurement value T c Below, static pressure measurement value SP c Substitute the output voltage model: Obtain the current ambient temperature measurement value T c Compared with static pressure measurement value SP c The calibration differential pressure point DP k Corresponding theoretical voltage Based on the measured output voltage U c Selecting the theoretical voltage The three adjacent rated output voltages [U] x U y U z ].

[0022] Preferably, the method for determining the compensation coefficient is as follows: calculating the measured ambient temperature value T. c Static pressure measurement value SP c and output voltage U c The Euclidean distances to the data calibration points, which are composed of various temperature calibration points, static pressure calibration points, and differential pressure calibration points, are used to obtain the variogram matrix by substituting the Euclidean distances into the variogram function theoretical model. The compensation coefficients are then calculated based on the variogram matrix and the compensation matrix.

[0023] Preferably, the method for obtaining the variation matrix is ​​as follows: calculating the actual measurement data (T) c SP c U c ) and data calibration point (T) i SPj U ijk The Euclidean distance of γ(h) is calculated and substituted into the variogram model to obtain the variogram matrix M.

[0024] Preferably, the method for calculating the compensation coefficient is as follows: calculate the compensation coefficient matrix [λ] = [K] + [M]; The method for calculating the differential pressure to be measured using the compensation coefficient and differential pressure calibration point is as follows: Substitute the compensation coefficient matrix [λ] into the formula Calculate the differential pressure DP′ to be measured.

[0025] The beneficial effects of this invention are as follows: Addressing the coupling effect of temperature and static pressure errors in differential pressure transmitters, this invention proposes a comprehensive compensation method based on Kriging interpolation and cubic spline interpolation. Cubic spline interpolation is used under the modeling temperature, while Kriging interpolation is used under the non-modeling temperature. Utilizing the powerful computing capabilities of computers, the theoretical models of the cubic spline interpolation coefficients and the Kriging interpolation variogram are downloaded offline. This allows for the use of computationally intensive algorithms to improve compensation accuracy, effectively avoiding repeated interpolation in each temperature and static pressure range, significantly reducing the computational workload and improving the real-time performance of the compensation. Furthermore, this method has the following advantages:

[0026] (1) It can improve the measurement accuracy of differential pressure transmitters. After comprehensive compensation, the maximum full-range reference error, average error, and error variance of the differential pressure transmitter are 1.5×10⁻⁶. -3 3.79×10 -4 4.30×10 -7 This invention improves the measurement accuracy of differential pressure transmitters under different ambient temperatures and static pressures, and achieves ideal results in the comprehensive compensation of differential pressure transmitters.

[0027] (2) Reduce the computational load when the differential pressure transmitter is operated. The method of the present invention can store the interpolation coefficients of the comprehensive model compensation into the memory of the differential pressure transmitter, and calculate the comprehensive compensation differential pressure value based on the input ambient temperature measurement value, static pressure measurement value and the output voltage corresponding to the differential pressure measurement value. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a schematic diagram of the process of the present invention.

[0030] Figure 2 This is a block diagram illustrating the working principle of the differential pressure transmitter of the present invention.

[0031] Figure 3 The schematic diagram of the experimental setup for calibrating a differential pressure transmitter.

[0032] Figure 4 The static pressure error diagrams for differential pressure transmitters at various temperature conditions are shown, where (a) is -20℃, (b) is 20℃, and (c) is 70℃.

[0033] Figure 5 This is a temperature error diagram for a differential pressure transmitter.

[0034] Figure 6 The following are the comprehensive error surface plots of the differential pressure transmitter under various temperature conditions, where (a) is 10℃, (b) is 30℃, and (c) is 60℃.

[0035] Figure 7 This is a schematic diagram of the comprehensive compensation results of the pressure transmitter under various temperature conditions according to the present invention, wherein (a) is 10℃, (b) is 30℃, and (c) is 60℃. Detailed Implementation

[0036] 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] like Figure 1 As shown, a comprehensive compensation method for differential pressure transmitters based on Kriging interpolation and cubic spline interpolation is proposed. A compensation model is established using Kriging interpolation and cubic spline interpolation, and the compensation is based on the input ambient temperature measurement value T. c Static pressure measurement value SP c and differential pressure measurement value DP c The corresponding output voltage U c The differential pressure value DP′ after comprehensive compensation is calculated using the corresponding Kriging interpolation coefficients and cubic spline interpolation coefficients. The specific steps of this invention are as follows:

[0038] Step 1, Offline Section: Measure the calibration output voltage of the differential pressure transmitter at multiple temperature calibration points, static pressure calibration points, and differential pressure calibration points to obtain data calibration points; based on the data calibration points, use Kriging interpolation to fit the variogram theoretical model, calculate the Euclidean distance of all data calibration points, and substitute it into the variogram theoretical model to obtain the compensation matrix; use cubic spline interpolation to establish the output voltage model at the temperature calibration points, multiple static pressure calibration points, and differential pressure calibration points.

[0039] Step 1: At m temperature calibration points T i (i = 1, 2, ..., m), n static pressure calibration points SP j (j=1,2,…,n), q differential pressure calibration points DP k The output voltage U of m×n×q differential pressure transmitters was measured under (k=1,2,…,q) conditions. ijk .

[0040] Step 2: Calculate m×n×q data calibration points (T) i SP j U ijk ,DP k The variation value γ * (h), use Kriging interpolation to fit the variogram theoretical model γ(h), and store the variogram theoretical model γ(h) in the memory of the differential pressure transmitter.

[0041] Step 3: Calculate the Euclidean distance of all data calibration points, substitute it into the variogram theoretical model γ(h) to obtain matrix K, and solve for the generalized inverse matrix [K]. + The data is stored in the memory of the differential pressure transmitter.

[0042] Step 4: At m temperature calibration points T i Under the condition (i = 1, 2, ..., m), q differential pressure operating conditions, i.e., differential pressure calibration points DP, are established using cubic spline interpolation. k (k=1,2,…,q) Static pressure condition, i.e., static pressure calibration point SP j Output voltage model for the influence of (j=1,2,…,n) on output voltage: The cubic spline interpolation coefficients are stored in the differential pressure transmitter's memory. The output voltage model is as follows:

[0043]

[0044] Among them, a jk b jk c jk d jk SP represents the cubic spline interpolation coefficients of the output voltage model at different static pressure calibration points, j = 1 = 1, 2, ..., n-1. c This is the static pressure measurement value.

[0045] Step 2: Determine if the ambient temperature measurement value is the temperature calibration point from Step 1. If it is, proceed to Step 3; otherwise, proceed to Step 4.

[0046] Step 5: Determine the ambient temperature measurement value T c Is it a temperature calibration point, when the ambient temperature measurement value T cTo establish the temperature calibration point, proceed with steps 6 and 7; when the ambient temperature measurement value T... c If it is not the temperature calibration point, proceed to steps 8 and 9 to reduce the computational load of the differential pressure transmitter.

[0047] Step 3: Directly input the static pressure measurement value under the current ambient temperature into the output voltage model to obtain the theoretical voltage of the differential pressure calibration point. Select three calibration output voltages adjacent to the theoretical voltage, and establish a differential pressure function relationship using cubic spline interpolation and the three calibration output voltages. Input the measured differential pressure transmitter output voltage into the differential pressure function relationship to obtain the differential pressure to be measured.

[0048] Step 6: Record the current ambient temperature measurement value T c Below, the measured static pressure value SP c Substitute the output voltage model: The DP of the calibrated differential pressure under the given temperature and static pressure conditions was obtained. k The theoretical voltage corresponding to (k=1,2,…,q) Based on the actual output voltage U collected by the differential pressure transmitter under the current operating conditions c Selecting the theoretical voltage The three adjacent calibrated output voltages are denoted as [U x U y U z ], x, y, z∈{1,2,…,q}, where: U x c y z Or. U x y c z .

[0049] Step 7: Establish three calibrated output voltages [U] using cubic spline interpolation. x U y U z [and corresponding differential pressure conditions [DP]] x ,DP y ,DP z The functional relationship is: DP′=S(U c The measured differential pressure transmitter output voltage U c Substitute the values ​​into the equation to obtain the differential pressure DP′ to be measured.

[0050]

[0051] Where a1, b1, c1, and d1 are the cubic spline interpolation coefficients under the calibrated output voltage.

[0052] ​​​​​​When the ambient temperature measurement value is taken at the temperature calibration point in step one of this invention, the theoretical voltage is selected. The differential pressure under the measured differential pressure transmitter output voltage is calculated by fitting the differential pressure function relationship of the three adjacent calibrated output voltages using cubic spline interpolation.

[0053] Step 4: Calculate the measured ambient temperature value T. c Static pressure measurement value SP c and output voltage U c The Euclidean distance from the data calibration point in step one is used to obtain the variogram matrix by substituting it into the variogram function theoretical model. The compensation coefficient is then calculated based on the variogram matrix and the compensation matrix, and the differential pressure to be measured is calculated using the compensation coefficient.

[0054] Step 8: Calculate the actual measurement data (T) c SP c U c ) and data calibration point (T) i SP j U ijk The Euclidean distance of γ(h) is calculated and substituted into the variogram model to obtain the variogram matrix M.

[0055] Step 9: Calculate the compensation coefficient matrix [λ] = [K] + [M], Substitute the compensation coefficient matrix [λ] into the formula Calculate the differential pressure DP′ to be measured.

[0056] When the ambient temperature measurement is not the temperature calibration point, the compensation coefficient is calculated using the variogram theoretical model and the compensation matrix.

[0057] Calibration experiment: The working principle diagram of the differential pressure transmitter is as follows Figure 2 As shown, the differential pressure transmitter operates in a temperature range of -20℃ to 70℃, with 10 temperature measurement conditions selected in 10℃ increments. The static pressure range is 0 kPa to 9000 kPa, with 10 static pressure measurement conditions selected in 1000 kPa increments. The high and low temperature test chamber (ACS-CH250TF) has an adjustable temperature range of -40℃ to +180℃. The differential pressure transmitter is calibrated within the high and low temperature test chamber. The structure of the calibration test setup is shown below. Figure 3 As shown. In Figure 3A nitrogen cylinder serves as the pressure source, connected to a pressure controller. The pressure controller controls the pressure input and is connected to the differential pressure transmitter. A temperature controller provides insulation and is also connected to the differential pressure transmitter. The differential pressure transmitter contains a differential pressure unit, a static pressure unit, and a temperature sensor. The differential pressure unit and the static pressure unit measure the differential pressure and static pressure values, respectively. The differential pressure transmitter outputs the measurement results via a multimeter and transmits the measured data to a host computer, which processes the collected data. For each temperature measurement condition, the transmitter is kept at a constant temperature for 2.5 hours to allow all components to reach equilibrium with the ambient temperature in the high and low pressure test chamber before pressurization testing begins. For each temperature and static pressure measurement condition, 17 pressure measurement points are selected within the range of -1000 kPa to 1000 kPa, with a step size of 125 kPa, resulting in 1700 sets of calibration data. The multimeter output voltage U is converted to the differential pressure output DP′. Some calibration data (20℃) are shown in Table 1. Using the differential pressure sensor output at a temperature of 20℃ and a static pressure of 0 kPa as a reference, the conversion relationship between voltage U and differential pressure DP is established. To evaluate the effectiveness of the comprehensive compensation, full-range reference error is introduced as a performance indicator. The full-range reference error is:

[0058]

[0059] Among them, DP FS This indicates the range of the differential pressure sensor.

[0060] Table 1. Calibration data for differential pressure transmitter (20℃)

[0061]

[0062] Using the output of the differential pressure transmitter at 0 kPa static pressure at each temperature as a reference, and calculating the full-range reference error using equation (3), the static pressure error surface of the differential pressure transmitter under each temperature condition is obtained as follows: Figure 4 As shown. By Figure 4 It can be seen that under the same temperature and input differential pressure conditions, the static pressure error changes significantly with the static pressure. Taking the output of the differential pressure transmitter at 20℃ and 0kPa static pressure as the reference, the error curves for each temperature under the static pressure of 0kPa are obtained by calculating the full-range reference error using equation (3). Figure 5 As shown. By Figure 5 It can be seen that under the same input differential pressure condition of 0 kPa static pressure, the temperature error changes significantly with temperature. When the differential pressure transmitter is affected by the coupled influence of static pressure error and temperature error, the combined error surface is as follows: Figure 6 As shown. By Figure 6 It is evident that the overall error significantly affects the measurement accuracy of the differential pressure transmitter. To ensure the measurement accuracy of the differential pressure transmitter, comprehensive compensation is necessary.

[0063] When using MATLAB to simulate and analyze differential pressure transmitter calibration data, to avoid proportional differences caused by inconsistent evaluation standards, the data needs to be normalized to the [-1,1] interval. A portion of this interval is selected as the modeling dataset, and another portion as the validation dataset. Within the operating temperature range of -20℃ to 70℃, -20℃, 0℃, 20℃, 40℃, and 70℃ are selected as temperature modeling conditions. Under these temperature modeling conditions, 0 kPa, 2000 kPa, 4000 kPa, 6000 kPa, and 9000 kPa are selected as static pressure modeling conditions. -1000 kPa, -750 kPa, -500 kPa, -250 kPa, 0 kPa, 250 kPa, 500 kPa, 750 kPa, and 1000 kPa are selected as differential pressure modeling conditions. A total of 225 (5*5*9) sets of calibration data are used as the modeling dataset, and the remaining 1475 sets constitute the validation dataset.

[0064] Based on the aforementioned comprehensive compensation method steps, interpolation calculations were performed using the modeling dataset, and the results were verified against the validation dataset. The comprehensive compensation results for the differential pressure transmitter are shown in Table 2. Within the operating range of the differential pressure transmitter, the maximum full-range reference error is 1.5 × 10⁻⁶. -3 The maximum full-range reference error occurred at a temperature of -10℃, a static pressure of 2000kPa, and a differential pressure of -1000kPa. At other temperatures, the maximum error reached 8.82×10⁻⁶. -4 The following is a summary of the results. After comprehensive compensation, the average error under various temperature conditions reaches 3.79 × 10⁻⁶. -4 Below, the error variance reaches 4.30 × 10⁻⁶. -7 The overall compensation effect is relatively stable. The overall compensation error surface is as follows: Figure 7 As shown, the comprehensive compensation effectively reduces the coupled effects of static pressure error and temperature error. Therefore, the method of this invention can meet the measurement requirements of high-precision differential pressure transmitters.

[0065] Table 2. Comprehensive Compensation Results for Differential Pressure Transmitters

[0066]

[0067] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A comprehensive compensation method for differential pressure transmitters based on Kriging interpolation and cubic spline interpolation, characterized in that, The steps are as follows: Step 1, Offline Section: Measure the calibration output voltage of the differential pressure transmitter at multiple temperature calibration points, static pressure calibration points, and differential pressure calibration points to obtain data calibration points; based on the data calibration points, use Kriging interpolation to fit the variogram theoretical model and obtain the compensation matrix; use cubic spline interpolation to establish output voltage models at multiple static pressure calibration points and differential pressure calibration points under temperature calibration points. Step 2: Determine whether the measured ambient temperature value is the temperature calibration point from Step 1. If it is, proceed to Step 3; otherwise, proceed to Step 4. Step 3: Directly input the static pressure measurement value under the current ambient temperature into the output voltage model to obtain the theoretical voltage. Select three calibration output voltages adjacent to the theoretical voltage, and establish the differential pressure function relationship using cubic spline interpolation and the three calibration output voltages. Substitute the measured output voltage into the differential pressure function relationship to obtain the differential pressure to be measured. Step 4: Combining the measured ambient temperature, static pressure, and output voltage, determine the compensation coefficient using the variogram theoretical model, and calculate the differential pressure to be measured using the compensation coefficient and the differential pressure calibration point.

2. The differential pressure transmitter integrated compensation method based on Kriging interpolation and cubic spline interpolation according to claim 1, characterized in that, The method for fitting the theoretical model of the variogram is as follows: variogram value Among them, the data pairs {Z(x) are separated by the lag distance h. i ),Z(x i The data pair [Z(x), Z(x+h)] is considered as a single distinct realization of the data pair [Z(x), Z(x+h)], where N(h) is the number of data pairs separated by lags h; for different lags h, the corresponding variogram value γ is calculated. * (h) Using Kriging interpolation to adjust the variogram value γ * The theoretical model of the variogram γ(h) is obtained by fitting (h).

3. The differential pressure transmitter integrated compensation method based on Kriging interpolation and cubic spline interpolation according to claim 2, characterized in that, The method for obtaining the compensation matrix is ​​as follows: calculate the Euclidean distance of all data calibration points, substitute the Euclidean distance into the variogram theoretical model γ(h) to obtain matrix K, and solve for the generalized inverse matrix [K]. + [ ] as the compensation matrix.

4. The differential pressure transmitter integrated compensation method based on Kriging interpolation and cubic spline interpolation according to any one of claims 1-3, characterized in that, The method for obtaining the data calibration points is as follows: at m temperature calibration points T i n static pressure calibration points SP j q differential pressure calibration points DP k The output voltage U of m×n×q differential pressure transmitters was measured. ijk i = 1, 2, ..., m, j = 1, 2, ..., n, k = 1, 2, ..., q; thus obtaining m × n × q data calibration points (T i SP j U ijk ,DP k ).

5. The differential pressure transmitter integrated compensation method based on Kriging interpolation and cubic spline interpolation according to claim 4, characterized in that, The method for establishing the output voltage model at multiple static pressure calibration points and differential pressure calibration points using cubic spline interpolation at the temperature calibration point in step one is as follows: at m temperature calibration points T i Below, cubic spline interpolation is used to establish q differential pressure calibration points DP. k Lower static pressure calibration point SP j Output voltage model affecting output voltage: and: Among them, a jk b jk c jk d jk SP represents the cubic spline interpolation coefficients of the output voltage model at different static pressure calibration points, j = 1 = 1, 2, ..., n-1. c This is the static pressure measurement value.

6. The differential pressure transmitter integrated compensation method based on Kriging interpolation and cubic spline interpolation according to claim 5, characterized in that, The method for establishing the differential pressure function relationship is as follows: Three calibrated output voltages U are established using cubic spline interpolation. x U y U z With the corresponding calibrated differential pressure [DP] x ,DP y ,DP z The functional relationship of ]: Where a1, b1, c1, and d1 are the cubic spline interpolation coefficients under the calibrated output voltage, x, y, z ∈ {1, 2, ..., q}, U c This is the actual output voltage.

7. The differential pressure transmitter integrated compensation method based on Kriging interpolation and cubic spline interpolation according to claim 6, characterized in that, The three calibrated output voltages U x U y U z The method for determining this is as follows: take the current ambient temperature measurement value T c Below, static pressure measurement value SP c Substitute the output voltage model: Obtain the current ambient temperature measurement value T c Compared with static pressure measurement value SP c The calibration differential pressure point DP k Corresponding theoretical voltage Based on the measured output voltage U c Selecting the theoretical voltage The three adjacent rated output voltages [U] x U y U z ].

8. The differential pressure transmitter integrated compensation method based on Kriging interpolation and cubic spline interpolation according to any one of claims 5-7, characterized in that, The method for determining the compensation coefficient is as follows: calculate the measured ambient temperature value T. c Static pressure measurement value SP c and output voltage U c The Euclidean distances to the data calibration points, which are composed of various temperature calibration points, static pressure calibration points, and differential pressure calibration points, are used to obtain the variogram matrix by substituting the Euclidean distances into the variogram function theoretical model. The compensation coefficients are then calculated based on the variogram matrix and the compensation matrix.

9. The differential pressure transmitter integrated compensation method based on Kriging interpolation and cubic spline interpolation according to claim 8, characterized in that, The method for obtaining the variation matrix is ​​as follows: calculate the actual measurement data (T) c SP c U c ) and data calibration point (T) i SP j U ijk The Euclidean distance of γ(h) is calculated and substituted into the variogram model to obtain the variogram matrix M.

10. The differential pressure transmitter integrated compensation method based on Kriging interpolation and cubic spline interpolation according to claim 9, characterized in that, The method for calculating the compensation coefficient is as follows: Calculate the compensation coefficient matrix [λ] = [K] + [M]; The method for calculating the differential pressure to be measured using the compensation coefficient and differential pressure calibration point is as follows: Substitute the compensation coefficient matrix [λ] into the formula Calculate the differential pressure DP′ to be measured.

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