Adaptive conductivity measurement method and system

Abstract

Disclosed in the present invention are an adaptive conductivity measurement method and a system. The method comprises the following steps: 1) collecting in real time environmental temperature and illuminance data in a set period; 2) measuring the conductivity of a solution; 3) using a partial differential equation to simulate physical and chemical processes in the solution; and 4) calculating a conductivity compensation coefficient on the basis of the differential equation model obtained in step 3), and adjusting a conductivity measurement value in real time on the basis of the conductivity compensation coefficient. In the method of the present invention, temperature and illuminance changes are compensated on the basis of a partial differential equation model, so that measurement errors caused by environmental changes can be effectively eliminated, thereby improving the accuracy and reliability of conductivity measurement in experiments and industrial applications.

Description

An adaptive conductivity measurement method and system Technical Field

[0001] This invention relates to an adaptive conductivity measurement method, belonging to the field of conductivity measurement technology. Background Technology

[0002] Electrical conductivity measurement is an important analytical tool in scientific research and industrial applications, widely used in chemical analysis, environmental monitoring, biomedicine, and other fields. However, in practical applications, conductivity measurement results are often affected by changes in ambient temperature and light intensity, leading to measurement errors. Traditional conductivity measurement systems often ignore these environmental factors or use only simple compensation methods, which cannot meet the requirements for high-precision measurement.

[0003] Existing conductivity measurement systems mainly rely on single compensation methods, such as linear compensation models or simple temperature compensation coefficients. While these methods can reduce errors caused by environmental changes to some extent, their accuracy and reliability are greatly reduced under complex or rapidly changing environmental conditions. Furthermore, the influence of illumination on conductivity measurements is often overlooked, further affecting the accuracy of the measurement results.

[0004] To improve the accuracy and reliability of conductivity measurement, a conductivity measurement system that can comprehensively consider changes in temperature and illumination and compensate for them in real time is needed. Summary of the Invention

[0005] The technical problem to be solved by this invention is that, during the conductivity measurement process, it is necessary to automatically adapt to environmental changes and compensate for the effects of temperature and light, so as to improve the accuracy and reliability of conductivity measurement in experimental and industrial applications.

[0006] To address the aforementioned technical problems, this invention provides an adaptive conductivity measurement method, comprising the following steps:

[0007] 1) Collect ambient temperature and light intensity data in real time within a set period;

[0008] 2) Measure the conductivity of the solution;

[0009] 3) Partial differential equations are used to simulate physical and chemical processes in solution;

[0010] 4) Based on the differential equation model obtained in step 3), calculate the conductivity compensation coefficient, and adjust the conductivity measurement value in real time according to the conductivity compensation coefficient.

[0011] In the aforementioned adaptive conductivity measurement method, step 3) uses partial differential equations to simulate the physical and chemical processes in the solution. In this embodiment, the partial differential equations are convection-diffusion equations, expressed as follows:

[0012] in, ρ is the convection velocity, D is the diffusion coefficient, R is the reaction term dependent on temperature T and light intensity I, C is the solute concentration, and t is time. For concentration gradient, For the Laplace operator.

[0013] In the aforementioned adaptive conductivity measurement method, in step 4), the conductivity compensation coefficient is dynamically calculated based on the differential equation model, and the conductivity measurement value is adjusted in real time to adapt to environmental changes. The conductivity compensation coefficient is calculated using the following formula:

[0014] Where α and γ are weight parameter one and weight parameter two, respectively, adjusted according to real-time data;

[0015] κ t This represents the adjustment coefficient for the rate of concentration change calculated by partial differential equations. The weight of concentration change is adjusted using real-time data to reflect the response of concentration change in the time dimension.

[0016] λ t This represents the adjustment coefficient of the concentration gradient calculated by the partial differential equation. The weight of the concentration gradient is adjusted by real-time data to reflect the response of the concentration gradient in spatial distribution.

[0017] The concentration change rate calculated using partial differential equations. The concentration gradient is calculated for the partial differential equation.

[0018] In the aforementioned adaptive conductivity measurement method, step 4) involves constructing a compensation model based on temperature and illumination conditions to adjust the concentration change rate coefficient κ. t And the adjustment coefficient λ of the concentration gradient t Dynamic adjustment is performed, and the compensation model is expressed as: σ comp =σ meas ×exp(k T1 ·(TT ref )+k I1 ·(II ref )+k T2 ·(TT ref ) 2 +k I2 ·(II ref ) 2 )

[0019] Where, σ meas The measured conductivity is uncompensated, and T and I are temperature and light intensity, respectively.ref I ref For reference temperature and light intensity, k T1 k I1 k is the first-order temperature and illumination compensation coefficient. T2 k I2 σ is a second-order temperature and illumination compensation coefficient used to adjust for nonlinear effects of temperature and illumination. comp It is the conductivity after compensation.

[0020] The aforementioned adaptive conductivity measurement method includes the following steps in determining the compensation coefficient:

[0021] 1) Conductivity data σ were collected under different temperatures T and different light irradiance I. meas The data is then cleaned and standardized to form a sample set.

[0022] 2) Use multivariate regression analysis to determine the compensation coefficients, and determine the first-order temperature and light compensation coefficients k. T1 k I1 Second-order temperature and illumination compensation coefficient k T2 k I2 The multivariate regression analysis method used ordinary least squares, and the objective function was optimized as follows:

[0023] min∑(log(σ comp / σ meas )-[k T1 ·(TT ref )+k I1 ·(II ref )+k T2 ·(TT ref ) 2 +k I2 ·(II ref ) 2 ]) 2 .

[0024] The aforementioned adaptive conductivity measurement method further includes: verification and optimization of the compensation model, wherein the verification method includes residual analysis or the adjusted R-squared value method, and the optimization method includes gradient descent, Newton's method or quasi-Newton method.

[0025] A computer device / apparatus / system includes 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-described method.

[0026] A computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implement the steps of the above-described method.

[0027] A computer program product includes a computer program / instructions that, when executed by a processor, implement the steps of the above-described method.

[0028] The beneficial effects achieved by this invention are as follows: The method of this invention, through a partial differential equation model, compensates for changes in temperature and illumination, effectively eliminating measurement errors caused by environmental changes, thereby improving the accuracy and reliability of conductivity measurement in experimental and industrial applications. Attached Figure Description

[0029] Figure 1 is a flowchart of an adaptive conductivity measurement method according to the present invention. Detailed Implementation

[0030] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0031] Example 1

[0032] This embodiment provides an adaptive conductivity measurement method, including the following steps:

[0033] 1) Collect ambient temperature and light intensity data in real time within a set period;

[0034] 2) Measure the conductivity of the solution;

[0035] 3) Partial differential equations are used to simulate physical and chemical processes in solution;

[0036] 4) Based on the differential equation model obtained in step 3), calculate the conductivity compensation coefficient, and adjust the conductivity measurement value in real time according to the conductivity compensation coefficient.

[0037] In step 3), partial differential equations are used to simulate the physical and chemical processes in the solution. In this embodiment, the partial differential equations are convection-diffusion equations, expressed as follows:

[0038] in, ρ is the convection velocity, D is the diffusion coefficient, R is the reaction term dependent on temperature T and light intensity I, C is the solute concentration, and t is time. For concentration gradient, For the Laplace operator.

[0039] Through convection velocity Simulations of the diffusion coefficient D and the reaction term R, which depend on temperature T and light intensity I, accurately describe changes in solute concentration in the solution.

[0040] In step 4), the conductivity compensation coefficient is dynamically calculated based on the differential equation model, and the conductivity measurement value is adjusted in real time to adapt to environmental changes. The conductivity compensation coefficient is calculated using the following formula:

[0041] Where α and γ are weight parameter one and weight parameter two, respectively, adjusted according to real-time data;

[0042] κ t This represents the adjustment coefficient for the rate of concentration change calculated by partial differential equations. The weight of concentration change is adjusted using real-time data to reflect the response of concentration change in the time dimension.

[0043] λ t This represents the adjustment coefficient of the concentration gradient calculated by the partial differential equation. The weight of the concentration gradient is adjusted by real-time data to reflect the response of the concentration gradient in spatial distribution.

[0044] The concentration change rate calculated using partial differential equations. The concentration gradient calculated for the partial differential equation;

[0045] In step 4), a compensation model is constructed based on temperature and light conditions to adjust the concentration change rate by a coefficient κ. t And the adjustment coefficient λ of the concentration gradient t Dynamic adjustments are made to reduce the impact of these two environmental factors on the accuracy of solution conductivity measurements. The compensation model is expressed as: σ comp =σ mea s ×exp(k T1 ·(TT ref )+k I1 ·(II ref )+k T2 ·(TT ref ) 2 +k I2 ·(II ref ) 2 )

[0046] Where, σ meas The measured conductivity is uncompensated, and T and I are temperature and light intensity, respectively. ref I ref For reference temperature and light intensity, T is usually taken. ref =25℃, I ref =500 lux, k T1 k I1 k is the first-order temperature and illumination compensation coefficient. T2 k I2 σ is a second-order temperature and illumination compensation coefficient used to adjust for nonlinear effects of temperature and illumination. comp It is the conductivity after compensation.

[0047] The process of determining the compensation coefficients, including data collection, regression analysis, and model validation and optimization, includes the following steps:

[0048] 1) Conductivity data σ were collected under different temperatures T and different light irradiance I. meas The data is then cleaned and standardized to form a sample set.

[0049] 2) Use multivariate regression analysis to determine the compensation coefficients, and determine the first-order temperature and light compensation coefficients k. T1 k I1 Second-order temperature and illumination compensation coefficient k T2 k I2 In this embodiment, the multivariate regression analysis method uses ordinary least squares (OLS), and the objective function is: min∑(log(σ) comp / σ meas )-[k T1 ·(TT ref )+k I1 ·(II ref )+k T2 ·(T-T) ref ) 2 +k I2 ·(II ref ) 2 ]) 2 ;

[0050] 3) Use cross-validation, model tuning, and sensitivity analysis to validate and optimize the compensation model, thereby improving the accuracy of the compensation model under various environmental conditions.

[0051] During model validation and optimization, cross-validation and model diagnostic methods, such as residual analysis or the adjusted R-squared method, are used to verify the accuracy of the compensation model. Based on the validation results, the parameters of the compensation model are adjusted so that the formula of the compensation model can provide accurate conductivity prediction under various environmental conditions.

[0052] During the experimental verification and optimization process, the computational complexity of the algorithm of this invention is analyzed and compared with that of existing algorithms to evaluate the performance of the compensation model and illustrate the practicality and accuracy of the compensation method of this invention.

[0053] Under different temperature and light conditions, conductivity data were collected, and the following steps were performed in a controlled laboratory environment using high-precision conductivity detection equipment and environmental sensors:

[0054] Data collection: Set the temperature range from 20℃ to 40℃, with one sample point every 5℃; set the illumination range from 200 lux to 1000 lux, with one sample point every 200 lux; collect data; repeat the measurement 3 times under each environmental setting to improve the reliability of the data.

[0055] An integrated conductivity measurement system, including a heater, a xenon lamp parallel light source, conductivity detection electrodes, illuminance and temperature sensors, is used, along with computing devices to acquire and analyze data in real time and execute compensation algorithms.

[0056] Data analysis and optimization, including:

[0057] Data preprocessing: The collected conductivity data are standardized to eliminate the influence of scale and dimensions, and outliers are detected and removed;

[0058] Performance evaluation of the compensation algorithm: The compensation coefficient is calculated using the proposed compensation model, and the measured data is compensated to evaluate the conductivity data before and after compensation. The compensation effect is analyzed by calculating the average error and standard deviation.

[0059] By comparing the computational complexity of the algorithm of this invention with that of the traditional Nelder-Mead algorithm, the effectiveness of this invention is demonstrated. The following statistics are presented regarding the number of executions of the basic operations:

[0060] Computational complexity test results: Table 1 shows the number of addition and multiplication operations performed by the two algorithms, indicating that the computational complexity of the algorithm of the present invention is significantly lower than that of the Nelder-Mead algorithm under the same conditions.

[0061] Table 1. Number of addition and multiplication operations performed by the method of this invention and the Nelder-Mead algorithm.

[0062] Adjust k using gradient descent method T1 k I1 k T2 k I2 To minimize the compensated error, besides gradient descent, other optimization algorithms can be used, including:

[0063] Newton's method:

[0064] θ n The parameter vector at the nth iteration contains the compensation coefficients to be optimized, i.e., θ. n =[k T1 ,k I1 ,k T2 ,k I2 ] n ;

[0065] η: Learning rate (step factor), which controls the step size of each parameter update, and is usually a positive number;

[0066] H -1 H is the inverse of the Hessian matrix of the objective function J(θ) with respect to the parameter θ. The Hessian matrix H is a matrix composed of the second-order partial derivatives of the objective function with respect to the parameter, expressed as:

[0067] Where m is the number of parameters, in this example m = 4.

[0068] The objective function J(θ) in parameter θ n The gradient vector at point O, containing the first-order partial derivatives of the objective function with respect to each parameter, is expressed as:

[0069] J(θ) is the objective function, defined as the sum of squared errors between the predicted and actual conductivity values ​​after compensation, i.e.:

[0070] N is the sample size, σ comp,i Let σ be the conductivity calculated by the compensation model for the i-th sample. actual,i This represents the actual conductivity measurement value of the i-th sample.

[0071] The Hessian matrix H reflects the curvature information of the objective function, and its elements H ij This indicates that the objective function with respect to the parameter θ i and θ j Second-order partial derivatives:

[0072] Calculating the Hessian matrix requires taking the second derivative of the objective function, which is computationally expensive in high-dimensional applications. Therefore, in practical applications, approximation methods can be used to reduce computational complexity.

[0073] Quasi-Newton method: To avoid directly calculating the inverse of the Hessian matrix, a quasi-Newton method can be used, and its update formula is as follows:

[0074] B n For an approximate matrix of the Hessian matrix H, updates are performed in the nth iteration. Commonly used quasi-Newton methods include the BFGS method and the DFP method. These methods update B iteratively. n To gradually approximate the true Hessian matrix.

[0075] Newton's method: By utilizing the second derivative information of the objective function, the optimal solution can be approximated faster during the iteration process. However, the computational cost of calculating the Hessian matrix and its inverse matrix is ​​relatively large. It is suitable for cases with low dimension or where the Hessian matrix can be calculated efficiently.

[0076] Quasi-Newton method: By approximating the Hessian matrix, the computational cost is reduced while still retaining the information of the second derivative, thus improving optimization efficiency. It is suitable for optimization problems of higher dimensions.

[0077] In this invention, by using these optimization algorithms, the optimal parameter k in the compensation model can be determined more effectively. T1 k I1 k T2 k I2 This improves the accuracy and reliability of conductivity measurements. A computer device / apparatus / system includes 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-described method.

[0078] Example 2

[0079] A computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implement the steps of the above-described method.

[0080] Example 3

[0081] A computer program product includes a computer program / instructions that, when executed by a processor, implement the steps of the above-described method.

[0082] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in one or more blocks of the flowchart illustrations and / or one or more blocks of the block diagrams.

[0083] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more flowcharts and / or one or more block diagrams.

[0084] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, such that the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions specified in one or more flowcharts and / or one or more block diagrams.

[0085] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

A method of adaptive conductivity measurement, characterized in that, The method comprises the following steps: 1) collecting the environmental temperature and light intensity data in a set period in real time; 2) measuring the conductivity of the solution; 3) simulating the physical and chemical processes in the solution by using partial differential equations; 4) calculating the conductivity compensation coefficient based on the differential equation model obtained in step 3), and adjusting the conductivity measurement value in real time according to the conductivity compensation coefficient. A self-adapting conductivity measurement method according to claim 1, characterized in that In step 3) the physical and chemical processes in the solution are simulated using partial differential equations, in this embodiment the convection-diffusion equation, which is expressed as follows: wherein is the convection velocity, D is the diffusion coefficient, R is a reaction term dependent on temperature T and light intensity I, C is the solute concentration, t is time, for the concentration gradient, is a Laplace operator. A self-adapting conductivity measurement method according to claim 2, characterized in that In step 4), the conductivity compensation coefficient is dynamically calculated according to the differential equation model, the conductivity measurement value is adjusted in real time, and the conductivity compensation coefficient is calculated through the following formula: wherein α and γ are weight parameter one and weight parameter two respectively adjusted according to real-time data; Kappa t a regulation coefficient representative of the rate of change of concentration calculated by means of a partial differential equation; λ t a regulation coefficient representative of the concentration gradient calculated by the partial differential equation; a rate of change of concentration calculated for a partial differential equation, is a concentration gradient calculated by the partial differential equation. A self-adapting conductivity measurement method as claimed in claim 3, characterized in that In step 4), a compensation model is constructed for the adjustment coefficient K of the rate of change of concentration, as a function of temperature and light conditions t and the adjustment coefficient λ of the concentration gradient t The compensation model is expressed as: σ comp = σ meas x exp(k T1 ·(T-T ref )+k I1 ·(I-I ref )+k T2 ·(T-T ref ) 2 +k I2 • (I-I ref ) 2 ) where σ meas is the uncompensated measured conductivity, T, I are the temperature and light intensity, respectively, T ref , I ref are the reference temperature and light intensity, k T1 , k I1 are the first order temperature and light compensation coefficients, k T2 , k I2 are the second order temperature and light compensation coefficients, used to adjust for non-linear effects of temperature and light, σ comp is the compensated conductivity. A self-adapting conductivity measurement method according to claim 4, characterized in that In the process of determining the compensation coefficient, the following steps are included: 1) Collect conductivity data σ under different temperature T and different light I conditions meas and perform data cleaning and standardization to form a sample set; 2) using a multivariate regression analysis method to determine the compensation coefficients, determining the first order temperature and illumination compensation coefficient k T1 , k I1 , the second order temperature and illumination compensation coefficient k T2 , k I2 ; the multivariate regression analysis method uses the ordinary least squares method, and the optimization objective function is: min∑(log(σ comp / σ meas )-[k T1 ·(T-T ref )+k I1 ·(I-I ref )+k T2 ·(T- T ref ) 2 +k I2 ·(I-I ref ) 2 ]) 2 . A self-adapting conductivity measurement method as claimed in claim 5, characterized in that, Also included are: The compensation model is verified and optimized, the verification method includes residual analysis or adjusted R-square value method, and the optimization method includes using gradient descent method, Newton method or quasi-Newton method. A computer apparatus / device / system comprising a memory, a processor and a computer program stored on the memory, characterised in that, The processor executes the computer program to implement the steps of the method of any one of claims 1-6. A computer readable storage medium having stored thereon computer programs / instructions, characterized in that, The computer program / instruction is executed by the processor to implement the steps of the method of any one of claims 1-6. A computer program product comprising computer programs / instructions, characterized in that, The computer program / instruction is executed by the processor to implement the steps of the method of any one of claims 1-6. The computer program / instruction is executed by the processor to implement the steps of the method of any one of claims 1-6.

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