Conductivity measurement compensation method and system based on temperature field distribution modeling

Abstract

The invention discloses a conductivity measurement compensation method and system based on temperature field distribution modeling, and the method comprises the following steps: 1), building a to-be-measured medium temperature field model which is used for describing the temperature distribution in a medium; 2) establishing a conductivity temperature compensation model; 3) coupling the temperature field model and the conductivity temperature compensation model, and establishing a conductivity measurement compensation equation; 4) solving the conductivity measurement compensation equation to obtain compensated conductivity distribution; and 5) receiving data of the temperature sensor in real time, dynamically updating boundary conditions and initial conditions of the temperature field model, inputting temperature field distribution obtained by calculation into the conductivity compensation model, and compensating a conductivity measurement result in real time. According to the method, the influence of the temperature change on the conductivity is more accurately compensated by simulating the temperature distribution of the medium, the method adapts to the environment condition of rapid change, and the measurement precision of the conductivity can be obviously improved in the scene of large temperature gradient or rapid change.

Description

Technical Field

[0001] The invention relates to a method for compensating conductivity measurement errors based on temperature field distribution modeling, and belongs to the technical field of conductivity measurement. Background Art

[0002] In industrial and scientific research applications, conductivity can reflect the electrolyte concentration and type of the solution. However, the measurement of conductivity is often affected by temperature changes, because the conductivity of the solution changes with temperature. In the traditional conductivity measurement process, temperature compensation methods are usually used to correct this effect, but most compensation methods are based on the assumption that the temperature of the measurement environment or medium is uniform. This assumption is often not true in practical applications, especially in environments with large temperature gradients or rapid temperature changes, such as reactors or bioreactors. Therefore, in the prior art, temperature compensation usually uses a simple linear or nonlinear model, relying only on the temperature data of a single measurement point to adjust the conductivity reading, ignoring the complex temperature distribution that may exist inside the medium, which may lead to large measurement errors in practical applications.

[0003] Therefore, a new conductivity measurement compensation method is needed that can accurately reflect the changes in the complex temperature field inside the medium in real time to improve the accuracy and reliability of conductivity measurement, and can dynamically adjust the conductivity compensation according to the actual temperature distribution inside the medium, thereby adapting to rapidly changing environmental conditions and application scenarios with large temperature gradients. Summary of the invention

[0004] The technical problem to be solved by the present invention is: in the conductivity measurement process, how to compensate the conductivity measurement result in combination with the change of the complex temperature field inside the medium, so as to improve the accuracy of conductivity measurement in a complex temperature environment.

[0005] In order to solve the above technical problems, the present invention provides a conductivity measurement compensation method based on temperature field distribution modeling, comprising the following steps:

[0006] 1) Establish a temperature field model of the medium to be measured to describe the temperature distribution in the medium;

[0007] 2) Establish a conductivity temperature compensation model;

[0008] 3) Couple the temperature field model with the conductivity temperature compensation model to establish the conductivity measurement compensation equation;

[0009] 4) Solve the conductivity measurement compensation equation to obtain the conductivity distribution after compensation;

[0010] 5) Receive temperature sensor data in real time, dynamically update the boundary conditions and initial conditions of the temperature field model, and input the calculated temperature field distribution into the conductivity compensation model to compensate the conductivity measurement results in real time.

[0011] In the above conductivity measurement compensation method based on temperature field distribution modeling, in step 1), the temperature field model adopts the non-uniform heat conduction equation:

[0012]

[0013] in, is the temperature, For time, is the medium density, is the specific heat capacity, is the thermal conductivity coefficient, is the gradient operator, is the internal heat source term, indicating that the heat source is in space and time The distribution on .

[0014] In the above conductivity measurement compensation method based on temperature field distribution modeling, in step 2), the conductivity temperature compensation model adopts an improved nonlinear compensation model:

[0015]

[0016] in, is the reference temperature The conductivity under , , They are temperature coefficient one, temperature coefficient two, and temperature coefficient three. is the characteristic temperature difference.

[0017] In the above conductivity measurement compensation method based on temperature field distribution modeling, in step 2), the temperature coefficient in the conductivity temperature compensation model is obtained by measuring , Temperature coefficient 2 , Temperature coefficient three and characteristic temperature difference The specific methods include:

[0018] Under the target measurement environment, a standard solution with known conductivity is prepared, and conductivity measurements are performed under different temperature conditions. The temperature coefficient is determined by data fitting. , Temperature coefficient 2 , Temperature coefficient three and characteristic temperature difference The fitted model is as follows:

[0019] in, is the conductivity, is the temperature, is the reference temperature The conductivity under the condition of temperature coefficient is determined by nonlinear least square fitting method. , Temperature coefficient 2 , Temperature coefficient three and characteristic temperature difference The value of .

[0020] In the above-mentioned conductivity measurement compensation method based on temperature field distribution modeling, in step 3), the conductivity measurement compensation equation established is:

[0021]

[0022] in, is the conductivity after compensation, To measure conductivity, is the reference temperature, The local temperature calculated by the temperature field model;

[0023] In the above conductivity measurement compensation method based on temperature field distribution modeling, in step 4), the temperature field model and the conductivity compensation equation are discretized using the finite element method to obtain a discretized equation group:

[0024]

[0025] in, is the heat capacity matrix, is the heat conduction matrix, is the heat source vector, is the temperature vector, and are the conductivity value after compensation and the measured conductivity value, Denotes the Hadamard product, and the implicit time integration format is used in combination with the Newton-Raphson iteration method to solve the above nonlinear equations.

[0026] In the aforementioned conductivity measurement compensation method based on temperature field distribution modeling, in step 5), the specific steps are as follows:

[0027] Use high-precision temperature sensors to collect temperature data of the measurement environment in real time ;

[0028] Real-time temperature data Substitute into the conductivity temperature compensation model and calculate the conductivity compensation value :

[0029] The calculated conductivity compensation value With measured conductivity value Compare and get the conductivity value after compensation :

[0030] .

[0031] A computer device / equipment / system comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above method.

[0032] A computer-readable storage medium stores a computer program / instruction, which implements the steps of the above method when executed by a processor.

[0033] A computer program product comprises a computer program / instruction, which implements the steps of the above method when executed by a processor.

[0034] Beneficial effects achieved by the present invention: The conductivity measurement compensation method of the present invention comprehensively considers the non-uniformity of temperature distribution inside the medium and the nonlinear effect of temperature on conductivity. By coupling the temperature field model and the improved nonlinear conductivity compensation model, high-precision conductivity measurement compensation can be achieved in a complex temperature environment. At the same time, the finite element method is used for numerical solution, which can handle regions of arbitrary shapes and complex boundary conditions, and has strong applicability and flexibility. The method of the present invention can significantly improve the conductivity measurement accuracy in an environment with non-uniform temperature distribution, and more accurately compensate for the effect of temperature change on conductivity by simulating the temperature distribution of the medium, adapting to rapidly changing environmental conditions, and significantly improving the conductivity measurement accuracy in scenes with large temperature gradients or rapid changes. It is suitable for chemical industry, environmental monitoring, bioengineering and other occasions that require precise conductivity measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flow chart of the conductivity measurement compensation method based on temperature field distribution modeling of the present invention. DETAILED DESCRIPTION

[0036] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0037] Example 1

[0038] like Figure 1 As shown, this embodiment provides a conductivity measurement compensation method based on temperature field distribution modeling, comprising the following steps:

[0039] 1) Establish a temperature field model of the medium to be measured to describe the temperature distribution in the medium;

[0040] Considering the influence of the heat source inside the medium, the non-uniform heat conduction equation is adopted:

[0041]

[0042] in, is the temperature, For time, is the medium density, is the specific heat capacity, is the thermal conductivity coefficient, is the gradient operator, is the internal heat source term, indicating that the heat source is in space and time Distribution on;

[0043] 2) Establish a conductivity temperature compensation model;

[0044] Considering the nonlinear effect of temperature on conductivity, an improved nonlinear compensation model is established:

[0045]

[0046] in, is the reference temperature The conductivity under , , They are temperature coefficient one, temperature coefficient two, and temperature coefficient three. is the characteristic temperature difference; characteristic temperature difference It is a parameter used in the model to adjust the nonlinear part of the temperature compensation curve, reflecting the sensitivity of conductivity to temperature changes. With reference temperature When the gap between increases, the characteristic temperature difference The growth rate of the exponential term in the compensation term is controlled, thereby affecting the correction amplitude of the overall conductivity.

[0047] The nonlinear compensation model adds an exponential term on the basis of the traditional nonlinear model, which can better describe the rapid change of conductivity in the high temperature area;

[0048] 3) Couple the temperature field model with the conductivity temperature compensation model to establish the conductivity measurement compensation equation;

[0049] The conductivity measurement compensation equation established is:

[0050]

[0051] in, is the conductivity after compensation, To measure conductivity, is the reference temperature, The local temperature calculated by the temperature field model;

[0052] 4) Solve the conductivity measurement compensation equation to obtain the conductivity distribution after compensation;

[0053] The finite element method is used to discretize the temperature field model and the conductivity compensation equation to obtain the discretized equation group:

[0054]

[0055] in, is the heat capacity matrix, is the heat conduction matrix, is the heat source vector, is the temperature vector, and are the conductivity value after compensation and the measured conductivity value, Denotes the Hadamard product, and the implicit time integration format is used in combination with the Newton-Raphson iteration method to solve the above nonlinear equations;

[0056] 5) Receive temperature sensor data in real time, dynamically update the boundary conditions and initial conditions of the temperature field model, and input the calculated temperature field distribution into the conductivity compensation model to compensate the conductivity measurement results in real time.

[0057] In step 2), the temperature coefficient in the conductivity temperature compensation model is obtained by measuring , Temperature coefficient 2 , Temperature coefficient three and characteristic temperature difference The specific methods include:

[0058] Under the target measurement environment, a standard solution with known conductivity is prepared, and conductivity measurements are performed under different temperature conditions. The temperature coefficient is determined by data fitting. , Temperature coefficient 2 , Temperature coefficient three and characteristic temperature difference The fitted model is as follows: in, is the conductivity, is the temperature, is the reference temperature The conductivity under the condition of temperature coefficient is determined by nonlinear least square fitting method. , Temperature coefficient 2 , Temperature coefficient three and characteristic temperature difference The value of .

[0059] In step 5), the ambient temperature is measured in real time, and the conductivity compensation value is calculated and applied to correct the effect of temperature on the conductivity measurement. The specific steps are as follows:

[0060] Real-time temperature acquisition: Use high-precision temperature sensors, such as platinum resistance thermometers or thermocouples, to collect temperature data of the measurement environment in real time ;

[0061] Calculate compensation value: Real-time temperature data Substitute into the conductivity temperature compensation model and calculate the conductivity compensation value :

[0062] Apply compensation value: Apply the calculated conductivity compensation value With measured conductivity value

[0063] Compare and get the conductivity value after compensation :

[0064] .

[0065] In practical applications, a high-precision temperature sensor, such as a platinum resistance thermometer or a thermocouple, is set in the conductivity measurement device to collect temperature data of the measurement environment in real time to ensure that the sensor and the electrode can accurately respond and measure the corresponding physical quantity.

[0066] In the control system of the conductivity measuring equipment, a temperature field modeling module and a conductivity compensation module are provided to realize real-time processing of temperature data and dynamic compensation of conductivity measurement values. The parameters of the compensation model are adjusted in real time through the optimization algorithm to adapt to rapidly changing temperature conditions or complex temperature distribution conditions, thereby ensuring compensation accuracy and stability.

[0067] Conduct conductivity measurement experiments under various temperature environments, record the original measurement data and compensated data, the experimental process is as follows:

[0068] Prepare experimental solutions: Prepare standard solutions with known conductivity to cover the target measurement range.

[0069] Set up a temperature gradient: Use a constant temperature water bath or a temperature controller to measure the conductivity of the experimental solution at different temperature conditions (e.g., 20°C, 25°C, 30°C, 35°C, 40°C).

[0070] Data recording: Use the conductivity measuring device to record the uncompensated and compensated conductivity measurements, and also record the corresponding temperature data.

[0071] Repeated measurement: To ensure the reliability of the data, the measurement was repeated multiple times under each temperature condition and the average value was taken as the final result.

[0072] Data analysis: Compare and analyze the original measurement data with the compensated data, calculate the mean square error (MSE) and mean absolute error (MAE) of the two sets of data, and evaluate the effectiveness and accuracy of the compensation method. The specific steps are as follows:

[0073] Data preprocessing: normalize or standardize the original measurement data and compensated data to eliminate the influence of dimension and scale;

[0074] Error calculation: for the uncompensated and compensated conductivity measurement values ​​under each temperature condition, the error between the conductivity measurement value and the standard conductivity value is calculated to obtain the error data set;

[0075] Mean Squared Error (MSE) calculation:

[0076] in, For the The standard conductivity value measured, For the The uncompensated or compensated conductivity value of the measurement, is the number of measurements;

[0077] Mean Absolute Error (MAE) calculation:

[0078] Comparison of results: MSE and MAE were calculated for the uncompensated and compensated conductivity measurement data, respectively. The effectiveness and accuracy of the compensation method were evaluated by comparing the two sets of error indicators.

[0079] Through the above data collection and analysis method, the performance of the conductivity measurement compensation method can be quantitatively evaluated, providing a basis for further optimizing the compensation model, and also verifying the superiority of the present invention in improving the accuracy of conductivity measurement.

[0080] In order to verify the effectiveness of the conductivity measurement compensation method proposed in the present invention, multiple groups of experiments were carried out under different temperature conditions, and the conductivity measurement results before and after compensation were compared. The experimental data are shown in Table 1:

[0081] Table 1 Comparison of conductivity measurement results under different temperature conditions

[0082]

[0083] From the experimental data in Table 1, it can be seen that at different ambient temperatures, there is a certain deviation between the original measured conductivity value and the standard conductivity value, and the error increases with the increase of temperature. At 20°C, the original error is 2.68%, while at 40°C, the original error is as high as 14.29%, indicating that the influence of temperature change on conductivity measurement is very significant.

[0084] After using the conductivity measurement compensation method proposed in the present invention, the error between the compensated conductivity value and the standard conductivity value is significantly reduced. In the temperature range of 20°C to 40°C, the absolute value of the error after compensation is less than 2.22%, which is significantly improved compared with the original error. In particular, the compensation effect is more obvious in an environment with large temperature changes. For example, at 40°C, the error after compensation is only 0.71%, while the original error is as high as 14.29%, and the error is reduced by about 95%.

[0085] In order to further quantify the effect of the compensation method, the average value of the measurement data error before and after compensation was calculated. The results showed that the measurement data error after compensation was reduced by about 80% on average, from 6.19% of the original error to 1.27% after compensation, which greatly improved the accuracy of conductivity measurement.

[0086] Through comparative analysis of experimental data, the conductivity measurement compensation method based on temperature field distribution modeling proposed in the present invention can effectively reduce the influence of temperature change on conductivity measurement, significantly improve the accuracy and reliability of conductivity measurement, especially in an environment with large temperature changes, the compensation effect is more obvious, and provides a practical solution for improving the accuracy of conductivity measurement.

[0087] Example 2

[0088] A computer device / equipment / system, comprising a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the following method:

[0089] A conductivity measurement compensation method based on temperature field distribution modeling comprises the following steps:

[0090] 1) Establish a temperature field model of the medium to be measured to describe the temperature distribution in the medium;

[0091] 2) Establish a conductivity temperature compensation model;

[0092] 3) Couple the temperature field model with the conductivity temperature compensation model to establish the conductivity measurement compensation equation;

[0093] 4) Solve the conductivity measurement compensation equation to obtain the conductivity distribution after compensation;

[0094] 5) Receive temperature sensor data in real time, dynamically update the boundary conditions and initial conditions of the temperature field model, and input the calculated temperature field distribution into the conductivity compensation model to compensate the conductivity measurement results in real time.

[0095] In the above conductivity measurement compensation method based on temperature field distribution modeling, in step 1), the temperature field model adopts the non-uniform heat conduction equation:

[0096]

[0097] in, is the temperature, For time, is the medium density, is the specific heat capacity, is the thermal conductivity coefficient, is the gradient operator, is the internal heat source term, indicating that the heat source is in space and time The distribution on .

[0098] In the above conductivity measurement compensation method based on temperature field distribution modeling, in step 2), the conductivity temperature compensation model adopts an improved nonlinear compensation model:

[0099]

[0100] in, is the reference temperature The conductivity under , , They are temperature coefficient one, temperature coefficient two, and temperature coefficient three. is the characteristic temperature difference; the nonlinear compensation model adds an exponential term on the basis of the traditional nonlinear model, which can better describe the rapid change of conductivity in the high temperature area.

[0101] In the above conductivity measurement compensation method based on temperature field distribution modeling, in step 2), the temperature coefficient in the conductivity temperature compensation model is obtained by measuring , Temperature coefficient 2 , Temperature coefficient three and characteristic temperature difference The specific methods include:

[0102] Under the target measurement environment, a standard solution with known conductivity is prepared, and conductivity measurements are performed under different temperature conditions. The temperature coefficient is determined by data fitting. , Temperature coefficient 2 , Temperature coefficient three and characteristic temperature difference The fitted model is as follows: in, is the conductivity, is the temperature, is the reference temperature The conductivity under the condition of temperature coefficient is determined by nonlinear least square fitting method. , Temperature coefficient 2 , Temperature coefficient three and characteristic temperature difference The value of .

[0103] In the above-mentioned conductivity measurement compensation method based on temperature field distribution modeling, in step 3), the conductivity measurement compensation equation established is:

[0104]

[0105] in, is the conductivity after compensation, To measure conductivity, is the reference temperature, The local temperature calculated by the temperature field model;

[0106] In the above conductivity measurement compensation method based on temperature field distribution modeling, in step 4), the temperature field model and the conductivity compensation equation are discretized using the finite element method to obtain a discretized equation group:

[0107]

[0108] in, is the heat capacity matrix, is the heat conduction matrix, is the heat source vector, is the temperature vector, and are the conductivity value after compensation and the measured conductivity value, Denotes the Hadamard product, and the implicit time integration format is used in combination with the Newton-Raphson iteration method to solve the above nonlinear equations.

[0109] In the aforementioned conductivity measurement compensation method based on temperature field distribution modeling, in step 5), the specific steps are as follows:

[0110] Use high-precision temperature sensors to collect temperature data of the measurement environment in real time ;

[0111] Real-time temperature data Substitute into the conductivity temperature compensation model and calculate the conductivity compensation value :

[0112] The calculated conductivity compensation value With measured conductivity value Compare and get the conductivity value after compensation :

[0113] .

[0114] A computer-readable storage medium stores a computer program / instruction, which implements the steps of the above method when executed by a processor.

[0115] A computer program product comprises a computer program / instruction, which implements the steps of the above method when executed by a processor.

[0116] The above is only a preferred implementation of the present disclosure / application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present disclosure / application, and these improvements and modifications should also be regarded as the scope of protection of the present disclosure / application.

Claims

1. A conductivity measurement compensation method based on temperature field distribution modeling, characterized in that: The following steps are involved: 1) Establish a temperature field model of the medium to be measured to describe the temperature distribution in the medium; 2) Establish a conductivity temperature compensation model; 3) Couple the temperature field model with the conductivity temperature compensation model to establish the conductivity measurement compensation equation; 4) Solve the conductivity measurement compensation equation to obtain the conductivity distribution after compensation; 5) Receive temperature sensor data in real time, dynamically update the boundary conditions and initial conditions of the temperature field model, and input the calculated temperature field distribution into the conductivity compensation model to compensate the conductivity measurement results in real time.

2. The conductivity measurement compensation method based on temperature field distribution modeling according to claim 1 is characterized in that: In step 1), the temperature field model adopts the non-uniform heat conduction equation: in, is the temperature, For time, is the medium density, is the specific heat capacity, is the thermal conductivity coefficient, is the gradient operator, is the internal heat source term, indicating that the heat source is in space and time The distribution on .

3. According to the conductivity measurement compensation method based on temperature field distribution modeling according to claim 2, in step 2), the conductivity temperature compensation model adopts an improved nonlinear compensation model: in, is the reference temperature The conductivity under , , They are temperature coefficient one, temperature coefficient two, and temperature coefficient three. is the characteristic temperature difference.

4. The conductivity measurement compensation method based on temperature field distribution modeling according to claim 3 is characterized in that: In step 2), the temperature coefficient in the conductivity temperature compensation model is obtained by measuring , Temperature coefficient 2 , Temperature coefficient three and characteristic temperature difference The specific methods include: Under the target measurement environment, a standard solution with known conductivity is prepared, and conductivity measurements are performed under different temperature conditions. The temperature coefficient is determined by data fitting. , Temperature coefficient 2 , Temperature coefficient three and characteristic temperature difference The fitted model is as follows: in, The temperature coefficient is determined by the nonlinear least squares fitting method. , Temperature coefficient 2 , Temperature coefficient three and characteristic temperature difference The value of .

5. The conductivity measurement compensation method based on temperature field distribution modeling according to claim 4 is characterized in that: In step 3), the conductivity measurement compensation equation established is: in, is the conductivity after compensation, To measure conductivity, is the reference temperature, The local temperature calculated by the temperature field model.

6. The conductivity measurement compensation method based on temperature field distribution modeling according to claim 5 is characterized in that: In step 4), the temperature field model and the conductivity compensation equation are discretized using the finite element method to obtain the discretized equation group: in, is the heat capacity matrix, is the heat conduction matrix, is the heat source vector, is the temperature vector, and are the conductivity value after compensation and the measured conductivity value, Denotes the Hadamard product, and the implicit time integration format is used in combination with the Newton-Raphson iteration method to solve the above nonlinear equations.

7. The conductivity measurement compensation method based on temperature field distribution modeling according to claim 6 is characterized in that: In step 5), the specific steps are as follows: Use high-precision temperature sensors to collect temperature data of the measurement environment in real time ; Real-time temperature data Substitute into the conductivity temperature compensation model and calculate the conductivity compensation value : The calculated conductivity compensation value With measured conductivity value Compare and get the conductivity value after compensation : 。 8. A computer device / equipment / system comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

Images