Multi-parameter weak coupling optimization temperature measuring method for constant-pressure gas refractive index benchmark temperature measuring device

Abstract

The application provides a kind of constant pressure gas refractive index benchmark temperature measuring device multi-parameter weak coupling optimization temperature measuring method, it is related to gas benchmark temperature measuring technical field, the method comprises: the measurement model of constant pressure gas refractive index benchmark temperature measuring device is established, and temperature control, pressure control and microwave resonance frequency measurement system are included in measurement model;Based on the contribution ratio model of measurement model, the contribution ratio of each influencing factor to thermodynamic temperature is calculated;According to each contribution ratio, the dominant factor is identified, and the temperature stability, pressure stability and microwave emission power are respectively optimized according to the dominant factor, and each single factor optimization result is obtained;Based on the measurement model and each single factor optimization result, a multi-parameter response surface model is established, and the best working parameter combination is determined by optimization method;The best working parameter combination is used for measurement, and the thermodynamic temperature measurement result and the uncertainty of thermodynamic temperature measurement result are output.The application improves the accuracy of thermodynamic temperature measurement.

Description

Technical Field

[0001] This invention relates to the field of gas reference temperature measurement technology, and in particular to a multi-parameter weak coupling optimization temperature measurement method for a constant pressure gas refractive index reference temperature measurement device. Background Technology

[0002] Constant-pressure gas refractive index reference temperature measurement is a method for measuring temperature based on the relationship between gas refractive index and thermodynamic temperature. The basic idea is to fill a microwave resonant cavity with the gas to be measured under known pressure conditions, obtain the gas refractive index by measuring the change in microwave resonant frequency, and then deduce the thermodynamic temperature by combining the gas's dielectric properties, pressure, molar polarizability, and relevant correction terms.

[0003] In this type of temperature measuring device, the thermodynamic temperature is usually not directly given by a single measured quantity, but is determined by multiple physical quantities. Typically, a constant-pressure gas refractive index reference temperature measuring device includes three core subsystems: (1) Temperature control system: used to establish a stable, uniform and traceable temperature environment, and to obtain a reference temperature through a standard thermometer or reference thermometer; (2) Pressure control system: used to provide a stable measurement pressure to the microwave resonant cavity and to realize pressure measurement, pressure regulation and pressure correction; (3) Microwave resonant frequency measurement system: used to excite a specific mode of microwave resonant cavity, measure the resonant frequency under vacuum and gas filling conditions, and thus obtain the frequency change related to the gas refractive index.

[0004] Ideally, the three systems can be optimized independently. For example, the temperature control system aims for smaller temperature fluctuations, the pressure control system for higher pressure stability, and the microwave resonant frequency measurement system for higher frequency resolution and a stronger signal-to-noise ratio. However, in actual integrated devices, the three systems are not completely independent but are significantly coupled. For example, temperature fluctuations in the temperature control system affect gas density, cavity size, microwave resonant frequency, and pressure stability; pressure changes in the pressure control system affect gas refractive index, thermodynamic temperature inversion results, and the correction of static pressure difference between the pressure sensor and the resonant cavity; and excessively low transmit power in the microwave frequency measurement system can lead to unstable frequency fitting, while excessively high transmit power may cause microwave power deposition, local thermal disturbances, or changes in the resonant peak shape, thus affecting the temperature inversion results.

[0005] Therefore, in high-accuracy thermodynamic temperature measurement, simply increasing the individual measurement parameters of temperature, pressure, and frequency may not necessarily yield optimal temperature results. If the coupling effects among these three parameters are not fully considered, the following problems may occur: mutual interference exists between temperature control, pressure control, and microwave frequency measurement, leading to decreased measurement repeatability and consequently, a decrease in the accuracy of thermodynamic temperature measurement. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a multi-parameter weak coupling optimization temperature measurement method for a constant-pressure gas refractive index reference temperature measuring device. This invention substantially improves the thermodynamic temperature measurement accuracy of the constant-pressure gas refractive index reference temperature measuring device.

[0007] In a first aspect, the present invention provides a multi-parameter weakly coupled optimized temperature measurement method for a constant-pressure gas refractive index reference temperature measuring device, the method comprising the following steps: A measurement model for a constant-pressure gas refractive index reference temperature measuring device is established, incorporating a temperature control system, a pressure control system, and a microwave resonant frequency measurement system into the measurement model. Based on the measurement model, an error propagation model and a contribution ratio model are established to calculate the contribution ratio of each influencing factor to the thermodynamic temperature; the influencing factors include temperature, pressure, frequency, and correction terms. Based on the contribution ratio of each of the aforementioned influencing factors, the dominant factor with the greatest impact on the thermodynamic temperature measurement is identified. Then, based on the dominant factor, single-factor optimization is performed on temperature stability, pressure stability, and microwave transmission power to obtain the optimization results for each single factor. Based on the measurement model and the optimization results of each single factor, a multi-parameter response surface model is established with the microwave transmission power, the pressure stability and the temperature stability as optimization variables, and the optimal combination of operating parameters that minimizes the standard uncertainty of thermodynamic temperature is determined by the optimization method. Weak coupling verification is performed using the optimal combination of operating parameters. If the verification is successful, the optimal combination of operating parameters is used for measurement, and the thermodynamic temperature measurement result and the uncertainty of the thermodynamic temperature measurement result are output.

[0008] According to the multi-parameter weakly coupled optimized temperature measurement method of the constant-pressure gas refractive index reference temperature measuring device provided by the present invention, the calculation of the contribution ratio of each influencing factor to the thermodynamic temperature includes: Calculate the sensitivity coefficient of each of the aforementioned influencing factors to the thermodynamic temperature; the sensitivity coefficient is obtained using the finite difference method. The contribution percentage is obtained by dividing the product of the square of each sensitivity coefficient and the square of the standard uncertainty of each sensitivity coefficient by the square of the standard uncertainty of the thermodynamic temperature.

[0009] According to the present invention, a multi-parameter weak coupling optimization temperature measurement method for a constant-pressure gas refractive index reference temperature measuring device is provided, wherein the weak coupling verification using the optimal combination of operating parameters includes: Calculate the optimized coupling strength and the unoptimized coupling strength; the coupling strength is evaluated in the following way: the coupling strength coefficient between any two influencing factors is the product of the absolute value of the second partial derivative of the two influencing factors and the standard uncertainty of each influencing factor; the overall coupling strength is the sum of the normalized coupling strength coefficients of all pairwise combinations of influencing factors, and the normalized coupling strength coefficient is the coupling strength coefficient divided by the thermodynamic temperature standard uncertainty; Verify whether the optimized coupling strength is less than the unoptimized coupling strength, and whether the optimized temperature measurement uncertainty is less than the unoptimized temperature measurement uncertainty.

[0010] According to the present invention, a multi-parameter weakly coupled optimized temperature measurement method for a constant-pressure gas refractive index reference temperature measuring device is provided. The method for determining the optimal combination of operating parameters that minimizes the standard uncertainty of thermodynamic temperature through an optimization approach includes: Determine the comprehensive objective function; the comprehensive objective function includes the square of the standard uncertainty of thermodynamic temperature, the square of the difference between the measured thermodynamic temperature and the reference temperature, the coupling strength function, and the single-point measurement time, and sums the terms after multiplying each term by its corresponding weighting coefficient; The combination of working parameters that minimizes the overall objective function is determined as the optimal combination of working parameters.

[0011] According to the present invention, a multi-parameter weakly coupled optimized temperature measurement method for a constant-pressure gas refractive index reference temperature measuring device includes identifying the dominant factor with the greatest influence on the thermodynamic temperature measurement among the influencing factors based on the contribution ratio of each influencing factor. The influencing factors are ranked according to their respective contribution percentages; Based on the ranking results, the dominant factors are identified.

[0012] According to the present invention, a multi-parameter weakly coupled optimized temperature measurement method for a constant-pressure gas refractive index reference temperature measuring device, wherein, after successful verification, the optimal combination of operating parameters is used for measurement, and the thermodynamic temperature measurement result and the uncertainty of the thermodynamic temperature measurement result are output, including: If the verification is successful, the optimal combination of operating parameters is used for measurement to obtain the thermodynamic temperature measurement result and the uncertainty of the thermodynamic temperature measurement result; Under the condition that the temperature stability criterion, pressure stability criterion, microwave signal stability criterion, and weak coupling criterion are satisfied, the thermodynamic temperature measurement result and the uncertainty of the thermodynamic temperature measurement result are output.

[0013] According to the multi-parameter weakly coupled optimized temperature measurement method of the constant-pressure gas refractive index reference temperature measuring device provided by the present invention, before establishing the error propagation model and contribution ratio model based on the measurement model and calculating the contribution ratio of each influencing factor to the thermodynamic temperature, the method further includes: Baseline data was acquired under initial operating conditions; the baseline data included reference temperature, measured pressure, measured frequency, signal-to-noise ratio, quality factor, temperature fluctuation, pressure fluctuation, and frequency repeatability. The measured pressure is corrected by static pressure difference, pipeline pressure drop, temperature gradient, dynamic disturbance, and pressure drift to obtain the effective pressure inside the resonant cavity; The measured frequency is corrected by resonant peak fitting, microwave power, mode, transmission line, and frequency drift to obtain the effective frequency; The gas refractive index is calculated based on the cavity frequency and the filling frequency. The thermodynamic temperature is obtained by inversion based on the gas refractive index, the effective pressure inside the resonant cavity, and the gas state model. Both the cavity frequency and the filling frequency are determined based on the effective frequency. The thermodynamic temperature is used to calculate each sensitivity coefficient and each contribution percentage.

[0014] According to the present invention, a multi-parameter weakly coupled optimized temperature measurement method for a constant-pressure gas refractive index reference temperature measuring device is provided. The effective pressure in the resonant cavity is expressed as the sum of the measured pressure and the static pressure difference correction, the pipeline pressure drop correction, the pressure correction caused by the temperature gradient, the dynamic disturbance correction, and the pressure gauge drift correction. The static pressure difference correction is determined based on the product of the measured gas density, the local gravitational acceleration, and the height difference between the pressure measurement point and the effective measurement center of the resonant cavity.

[0015] According to the present invention, a multi-parameter weakly coupled optimized temperature measurement method for a constant-pressure gas refractive index reference temperature measuring device is provided, which optimizes the microwave transmission power based on the dominant factors to obtain the single-factor optimization results, including: If the dominant factor is the frequency, establish a relationship model between the microwave transmission power and the frequency measurement uncertainty; the relationship model includes: a frequency fitting uncertainty term caused by insufficient signal-to-noise ratio when the power is too low, an uncertainty term caused by microwave disturbance or thermal effect when the power is too high, and a basic uncertainty term unrelated to the power; With the goal of minimizing the standard uncertainty of the thermodynamic temperature, the optimal microwave power that satisfies the constraints is determined by solving the relational model. The constraints include: the signal-to-noise ratio is not lower than the signal-to-noise ratio threshold, the quality factor is not lower than the quality factor threshold, and the power correction amount does not exceed the power correction threshold.

[0016] Secondly, the present invention also provides a multi-parameter weakly coupled optimized temperature measurement device for a constant pressure gas refractive index reference temperature measurement device, which includes the following modules: The measurement model establishment module is used to establish a measurement model for a constant-pressure gas refractive index reference temperature measuring device, and incorporates the temperature control system, pressure control system and microwave resonant frequency measurement system into the measurement model. The error propagation and contribution ratio model building module is used to build an error propagation model and a contribution ratio model based on the measurement model, and to calculate the contribution ratio of each influencing factor to the thermodynamic temperature; the influencing factors include temperature, pressure, frequency and correction terms; The single-factor optimization module is used to identify the dominant factor that has the greatest impact on the thermodynamic temperature measurement among the influencing factors according to the contribution ratio of each of the influencing factors, and to perform single-factor optimization on temperature stability, pressure stability and microwave transmission power according to the dominant factor to obtain the optimization results of each single factor. The parameter optimization module is used to establish a multi-parameter response surface model with the microwave transmission power, the pressure stability and the temperature stability as optimization variables based on the measurement model and the optimization results of each single factor, and to determine the optimal combination of operating parameters that minimizes the standard uncertainty of thermodynamic temperature through the optimization method. The weak coupling verification and output module is used to perform weak coupling verification using the optimal combination of operating parameters. If the verification is successful, the module performs measurement using the optimal combination of operating parameters and outputs the thermodynamic temperature measurement result and the uncertainty of the thermodynamic temperature measurement result.

[0017] According to the present invention, a multi-parameter weakly coupled optimized temperature measurement device for a constant-pressure gas refractive index reference is provided, wherein the error propagation and contribution ratio model establishment module is specifically used for: Calculate the sensitivity coefficient of each of the aforementioned influencing factors to the thermodynamic temperature; the sensitivity coefficient is obtained using the finite difference method. The contribution percentage is obtained by dividing the product of the square of each sensitivity coefficient and the square of the standard uncertainty of each sensitivity coefficient by the square of the standard uncertainty of the thermodynamic temperature.

[0018] Thirdly, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the multi-parameter weak coupling optimization temperature measurement method of the constant pressure gas refractive index reference temperature measuring device as described above.

[0019] Fourthly, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the multi-parameter weakly coupled optimized temperature measurement method of the constant pressure gas refractive index reference temperature measuring device as described above.

[0020] Fifthly, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the multi-parameter weak coupling optimization temperature measurement method of the constant pressure gas refractive index reference temperature measuring device as described above.

[0021] The present invention provides a multi-parameter weakly coupled optimization method for a constant-pressure gas refractive index reference temperature measuring device. First, a measurement model of the constant-pressure gas refractive index reference temperature measuring device is established, incorporating the temperature control system, pressure control system, and microwave resonant frequency measurement system into the measurement model. Then, based on the measurement model, an error propagation model and a contribution ratio model are established to calculate the contribution ratio of each influencing factor to the thermodynamic temperature. Each influencing factor includes temperature, pressure, frequency, and correction terms. Further, based on the contribution ratio of each influencing factor, the dominant factor with the greatest impact on thermodynamic temperature measurement is identified. Single-factor optimization is then performed on temperature stability, pressure stability, and microwave transmission power based on the dominant factor, yielding the optimization results for each single factor. Based on the measurement model and the optimization results for each single factor, a multi-parameter response surface model is established with microwave transmission power, pressure stability, and temperature stability as optimization variables. An optimization method is used to determine the optimal combination of operating parameters that minimizes the standard uncertainty of the thermodynamic temperature. Finally, the optimal combination of operating parameters is used for weak coupling verification. If the verification is successful, the optimal combination of operating parameters is used for measurement, outputting the thermodynamic temperature measurement result and its uncertainty.

[0022] This invention integrates the temperature control system, pressure control system, and microwave resonant frequency measurement system into a unified measurement model, establishes an error propagation and contribution ratio model, identifies the dominant factors based on the contribution ratio, conducts single-factor optimization, constructs a multi-parameter response surface model for global optimization, and finally verifies the effectiveness of the optimization through weak coupling, forming a complete closed-loop process of modeling → quantification → identification → optimization → verification. This process restores and improves the thermodynamic temperature measurement accuracy that was originally reduced due to the coupling of the three systems. Specifically, the mutual interference between the three systems is quantified and suppressed, the dominant error source is accurately identified and optimized in a targeted manner, and finally, the temperature measurement uncertainty is minimized under the globally optimal combination of operating parameters. It transforms the negative factor of the three-system coupling that originally led to the decrease in temperature measurement accuracy into a controllable object that can be effectively identified, quantified, and suppressed through a systematic modeling, quantification, and optimization process, thereby substantially improving the thermodynamic temperature measurement accuracy of the constant-pressure gas refractive index reference temperature measurement device. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in this 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 some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0024] Figure 1 This is one of the flowcharts illustrating the multi-parameter weak coupling optimization temperature measurement method of the constant pressure gas refractive index reference temperature measurement device provided by the present invention.

[0025] Figure 2 This is a schematic diagram of the three-system coupling integration of the constant pressure gas refractive index reference temperature measuring device provided by the present invention.

[0026] Figure 3 This is a schematic diagram of the multi-parameter response surface optimization provided by the present invention.

[0027] Figure 4 This is the second flowchart illustrating the multi-parameter weak coupling optimization temperature measurement method of the constant pressure gas refractive index reference temperature measuring device provided by the present invention.

[0028] Figure 5 This is a schematic diagram of the structure of the constant pressure gas refractive index reference temperature measuring device and the multi-parameter weak coupling optimized temperature measuring device provided by the present invention.

[0029] Figure 6 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0031] The terms "first," "second," etc., used in the specification and claims of this application are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such terms can be used interchangeably where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first" and "second" are generally of the same class, not limited in number; for example, a first node can be one or more. Furthermore, in the specification and claims, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0032] To provide a clearer understanding of the various embodiments provided by the present invention, the technical content involved in the present invention will first be described as follows: The existing technology still has the following shortcomings: An inappropriate selection of microwave transmission power results in a tradeoff between frequency signal strength and microwave-added uncertainty. There may be a static pressure difference, temperature gradient or pipeline pressure drop between the pressure measurement point and the effective measurement area of ​​the resonant cavity, resulting in a deviation between the actual cavity pressure and the measured pressure. The contribution ratio of different error sources to the final thermodynamic temperature is unclear, making it impossible to reduce the dominant uncertainty component in a targeted manner; traditional experimental optimization relies heavily on empirical parameter tuning and lacks quantifiable, iterative, and verifiable multi-parameter optimization models.

[0033] Therefore, it is necessary to propose a multi-parameter weakly coupled optimization temperature measurement method for constant-pressure gas refractive index reference temperature measurement devices. By establishing a quantitative model between temperature, pressure, microwave frequency and thermodynamic temperature, the influence law and contribution ratio of different factors on the temperature measurement results are analyzed, and the optimal operating parameters are determined, thereby reducing the impact of system integration on the accuracy of thermodynamic temperature measurement.

[0034] The purpose of this invention is to provide a multi-parameter weak coupling optimization temperature measurement method for a constant pressure gas refractive index reference temperature measurement device, which solves the problem of mutual coupling and mutual influence between the temperature control system, pressure control system and microwave resonant frequency measurement system during integrated operation, leading to a decrease in the accuracy of thermodynamic temperature measurement.

[0035] The technical problems to be solved by this invention include: the difficulty in quantifying the impact of the temperature control, pressure control and microwave frequency measurement systems coupled and integrated in a constant pressure gas refractive index reference temperature measuring device on the thermodynamic temperature measurement results, the difficulty in identifying the dominant error sources, and the difficulty in determining the optimal combination of operating parameters. A multi-parameter influence analysis and weak coupling optimization method is proposed to improve the accuracy and repeatability of thermodynamic temperature measurement.

[0036] This invention establishes a temperature measurement error propagation model, a coupling effect model (measurement model), a contribution ratio model, and a multi-parameter optimization objective function to achieve synergistic optimization of temperature, pressure, and microwave frequency-related parameters, thereby obtaining the optimal combination of operating parameters under weak coupling conditions and improving the accuracy of thermodynamic temperature measurement.

[0037] The overall technical concept of this invention is as follows: This invention provides a multi-parameter weakly coupled optimization method for temperature measurement in a constant-pressure gas refractive index reference temperature measuring device. This method aims to minimize the uncertainty in thermodynamic temperature measurement. It models the temperature control system, pressure control system, and microwave resonant frequency measurement system as a coupled whole, establishes the influence relationship of temperature, pressure, frequency, and their correction terms on thermodynamic temperature, calculates the sensitivity coefficients and contribution ratios of each factor, and determines the optimal operating point through multi-parameter optimization. The core idea of ​​this method is: In the process of constant-pressure gas refractive index reference temperature measurement, thermodynamic temperature is expressed as a function of temperature reference quantity, pressure measurement quantity, microwave resonant frequency quantity, and several correction quantities: in, Thermodynamic temperature This is the reference temperature under the ITS-90 temperature scale. The effective pressure inside the resonant cavity. This is the microwave resonant frequency. For temperature-related correction terms, For pressure-related corrections, For frequency-dependent correction terms, These are model parameters such as gas dielectric constant, cavity deformation, gas non-ideality, and boundary conditions.

[0038] By constructing the objective function: in, This represents the standard uncertainty of thermodynamic temperature.

[0039] or: To obtain the optimal combination of operating parameters. For the optimal combination of operating parameters, Let be the parameter vector to be optimized. To allow for working parameter space, For the standard uncertainty of thermodynamic temperature, This is the coupling strength evaluation function. This is the temperature measurement deviation term. , , These are their respective weighting coefficients.

[0040] Parameter vector to be optimized It can be represented as: in, Let be the parameter vector to be optimized. For reference temperature stability, For pressure stability, i.e. pressure fluctuation, For frequency measurement stability, i.e. frequency fluctuation, This refers to microwave transmission power. The height difference between the pressure measurement point and the effective measurement center of the resonant cavity. For pressure correction residuals, For quality factor, For signal-to-noise ratio, and These are the characteristic time constants for temperature control and pressure control, respectively.

[0041] The following is combined with Figures 1 to 6 This invention describes a multi-parameter weak coupling optimization temperature measurement method for a constant-pressure gas refractive index reference temperature measuring device.

[0042] Figure 1 This is one of the flowcharts illustrating the multi-parameter weak coupling optimization temperature measurement method for the constant-pressure gas refractive index reference temperature measuring device provided by the present invention, such as... Figure 1 As shown, the method includes the following: Step 101: Establish a measurement model for a constant-pressure gas refractive index reference temperature measuring device, incorporating the temperature control system, pressure control system, and microwave resonant frequency measurement system into the measurement model.

[0043] The execution subject of the multi-parameter weak coupling optimization temperature measurement method of the constant pressure gas refractive index reference temperature measurement device provided by the present invention can be an electronic device, or any other subject that can realize the multi-parameter weak coupling optimization temperature measurement method of the constant pressure gas refractive index reference temperature measurement device.

[0044] The working gas of the constant pressure gas refractive index reference temperature measuring device is selected from any one of helium, neon, argon or hydrogen.

[0045] Figure 2 This is a schematic diagram of the three-system coupling and integration of the constant-pressure gas refractive index reference temperature measuring device provided by the present invention, as shown below. Figure 2 As shown, the constant pressure gas refractive index reference temperature measurement device mainly includes three core subsystems: temperature control system (for temperature control), pressure control system (for pressure control), and microwave resonant frequency measurement system (for microwave frequency measurement). The three subsystems are coupled and integrated around the microwave resonant cavity.

[0046] The temperature control system includes a temperature control module, a pulse tube refrigerator, and a temperature fluctuation attenuation structure.

[0047] The pressure control system includes a piston pressure gauge and a flow meter. The piston pressure gauge is connected to the resonant cavity via a pipeline to introduce the measuring gas into the resonant cavity and provide a stable measuring pressure. The flow meter is located on the pipeline between the piston pressure gauge and the resonant cavity to monitor the gas flow rate. The pressure control module detects the pressure in the resonant cavity and sends a feedback signal to the flow meter via the piston pressure gauge.

[0048] The microwave resonant frequency measurement system includes a microwave frequency measurement module connected to the resonant cavity. It is used to excite a specific mode of the microwave resonant cavity and measure the resonant frequency under vacuum and gas-filled conditions, thereby obtaining the frequency change related to the gas refractive index.

[0049] The three subsystems are physically coupled through a resonant cavity. The temperature control system affects the temperature environment of the resonant cavity, thus influencing the cavity size and gas density; the pressure control system affects the gas pressure and density within the resonant cavity; and the microwave resonant frequency measurement system infers the gas refractive index and thermodynamic temperature by measuring frequency changes. The coupling and integration relationship between the three is as follows: Figure 2 The interactive arrows around the resonant cavity are shown. Ultimately, the above three subsystems together constitute a constant-pressure gas refractive index reference temperature measuring device, which achieves reference-level measurement of thermodynamic temperature by measuring the gas refractive index.

[0050] The method provided in this embodiment includes: First, a measurement model for a constant-pressure gas refractive index reference temperature measuring device is established, incorporating the temperature control system, pressure control system, and microwave resonant frequency measurement system into the measurement model. The measurement model refers to integrating the temperature control system, pressure control system, and microwave resonant frequency measurement system into a unified mathematical description framework, determining the functional relationships between thermodynamic temperature and reference temperature, effective pressure within the resonant cavity, microwave resonant frequency, and correction terms.

[0051] Specifically, thermodynamic temperature is expressed as a composite function of reference temperature, effective pressure within the resonant cavity, microwave resonant frequency, temperature-related correction terms, pressure-related correction terms, frequency-related correction terms, and model parameters (such as gas dielectric constant, cavity deformation, gas non-ideality, boundary conditions, etc.): in, Thermodynamic temperature This is the reference temperature under the ITS-90 temperature scale. The effective pressure inside the resonant cavity. This is the microwave resonant frequency. For temperature-related correction terms, For pressure-related corrections, For frequency-dependent correction terms, These are model parameters such as gas dielectric constant, cavity deformation, gas non-ideality, and boundary conditions.

[0052] More specifically, this invention expresses thermodynamic temperature as a composite function of pressure and frequency: in, Thermodynamic temperature The effective pressure inside the resonant cavity. The resonant frequency in the cavity state. The resonant frequency after gas is filled. , , These are the first-order, second-order, and third-order dielectric virial coefficients of the gas, respectively. The gas compressibility factor, Correction for changes in cavity size. To correct for cavity wall conductivity or surface impedance. For microwave mode related corrections, This is a correction for gas non-ideal properties.

[0053] This expression provides the foundation for subsequent error propagation, coupling analysis, and multi-parameter optimization.

[0054] Step 102: Based on the measurement model, establish an error propagation model and a contribution ratio model, and calculate the contribution ratio of each influencing factor to the thermodynamic temperature; each influencing factor includes temperature, pressure, frequency and correction terms.

[0055] Specifically, an error propagation model and a contribution ratio model are established based on the measurement model to calculate the contribution ratio of each influencing factor (including temperature, pressure, frequency, and correction terms) to the thermodynamic temperature.

[0056] An error propagation model is a mathematical model that describes how the measurement uncertainties of various influencing factors propagate and affect the final standard uncertainty of thermodynamic temperature. The contribution percentage is the proportion of each influencing factor's contribution to the thermodynamic temperature measurement uncertainty, used to identify the dominant error source.

[0057] This invention decomposes the uncertainty of thermodynamic temperature into a temperature reference term, a pressure term, a microwave frequency term, and a coupling term. The fundamental uncertainty propagation relationship is as follows: in, For the standard uncertainty of thermodynamic temperature, Thermodynamic temperature This is the reference temperature under the ITS-90 temperature scale. The effective pressure inside the resonant cavity. This is the microwave resonant frequency. The uncertainty of the reference temperature under the ITS-90 temperature scale. The uncertainty of the effective pressure inside the resonant cavity. This represents the uncertainty of the microwave resonant frequency, which is also the uncertainty of the effective frequency. For the first Several influencing factors, such as temperature, pressure, frequency, and static pressure difference correction, etc. For the first One influencing factor Standard uncertainty This refers to the number of influencing factors.

[0058] When considering the correlation between temperature, pressure, and frequency, a covariance term is introduced: in, For the standard uncertainty of thermodynamic temperature, The number of influencing factors, For the first The sensitivity coefficients of each influencing factor to thermodynamic temperature. For the first The sensitivity coefficients of each influencing factor to thermodynamic temperature. For the first The first influencing factor and the second The correlation coefficients between the influencing factors For the first Standard uncertainty of each influencing factor For the first Standard uncertainty of each influencing factor Thermodynamic temperature For the first One influencing factor, For the first One influencing factor.

[0059] The contribution percentage of each influencing factor to the temperature measurement uncertainty is defined as follows: in For the first One influencing factor The percentage of contribution, This represents the standard uncertainty of thermodynamic temperature.

[0060] When considering coupling terms, the first One influencing factor The overall contribution can be defined as: For the first One influencing factor The overall contribution.

[0061] pass or The magnitude of the error can be used to determine which factors among temperature, pressure, microwave frequency, and their correction terms are the dominant error sources, thereby determining the direction of optimization.

[0062] This step can quantitatively evaluate the degree of influence of different factors on the thermodynamic temperature measurement results.

[0063] Step 103: Identify the dominant factor that has the greatest impact on thermodynamic temperature measurement among the various influencing factors based on the contribution ratio of each influencing factor, and perform single-factor optimization on temperature stability, pressure stability and microwave transmission power according to the dominant factor to obtain the optimization results of each single factor.

[0064] Specifically, based on the contribution ratio of each of the aforementioned influencing factors, the dominant factor that has the greatest impact on the thermodynamic temperature measurement is identified. Then, based on the dominant factor, single-factor optimization is performed on temperature stability, pressure stability, microwave transmission power, and static pressure difference correction to obtain the optimization results of each single factor.

[0065] Among these factors, the dominant factor is the one that contributes the most to the uncertainty of thermodynamic temperature measurement, which is among multiple influencing factors such as temperature, pressure, frequency, and correction terms.

[0066] This step avoids blindly increasing a single indicator and instead determines the most effective optimization direction based on the actual contribution ratio.

[0067] Step 104: Based on the measurement model and the optimization results of each single factor, establish a multi-parameter response surface model with microwave transmission power, pressure stability and temperature stability as optimization variables, and determine the optimal combination of operating parameters that minimizes the standard uncertainty of thermodynamic temperature through optimization methods.

[0068] Specifically, based on the measurement model and the results of each single-factor optimization, a multi-parameter response surface model is established with the microwave transmission power, the pressure stability, and the temperature stability as optimization variables.

[0069] Among them, the response surface model is a mathematical surface model with multiple optimization variables as independent variables and thermodynamic temperature standard uncertainty as dependent variable, used to find the optimal operating point (corresponding to the best combination of operating parameters).

[0070] This invention further establishes a multi-parameter response surface model to find the optimal combination of operating parameters. Using microwave transmission power... Pressure Corrected Residual Reference temperature stability As the primary optimization variable, a thermodynamic temperature uncertainty response surface is constructed: This is the thermodynamic temperature uncertainty response surface. For the standard uncertainty of thermodynamic temperature, This refers to microwave transmission power. For pressure correction residuals, For reference temperature stability, For response surface model functions.

[0071] The optimal operating point is defined as: in, For optimal microwave transmission power, Correcting residuals for optimal pressure For optimal temperature stability.

[0072] The parameter vector to be optimized can also be Expanded to: in, For the optimal combination of operating parameters, To allow for working parameter space, Thermodynamic temperature Let be the parameter vector to be optimized. In the parameter vector to be optimized The standard uncertainty of thermodynamic temperature.

[0073] The parameter vector to be optimized It can be represented as: The response surface can be represented using a quadratic polynomial model: in, For the standard uncertainty of thermodynamic temperature, , , , These are the fitting coefficients. For the first One influencing factor, For the first One influencing factor, The number of influencing factors, cross terms Used to describe the coupling effects between different systems.

[0074] If temperature measurement deviation and stability are taken into account, a comprehensive objective function can be further established. : in, For the standard uncertainty of thermodynamic temperature, Let be the parameter vector to be optimized. For the standard uncertainty of thermodynamic temperature, The parameter vector to be optimized Thermodynamic temperature below, This is the coupling strength evaluation function. To compare temperatures, For single-point time measurement, , , , where is the respective weighting coefficient, and is the coefficient used to adjust the relative importance of each item in the overall objective function.

[0075] The optimal working point is: in, For the optimal combination of operating parameters, Let be the parameter vector to be optimized. To allow for working parameter space, This is the overall objective function.

[0076] This model can minimize temperature measurement uncertainty while ensuring measurement stability and efficiency.

[0077] The optimal combination of operating parameters that minimizes the standard uncertainty of thermodynamic temperature is determined by an optimization method. The optimization method is selected from any one of the following: grid search, least squares response surface methodology, gradient descent, genetic algorithm, particle swarm optimization, Bayesian optimization algorithm, or neural network surrogate model.

[0078] This step allows the device to move beyond single-factor local optimization and achieve an overall optimal operating state oriented towards the final temperature measurement results.

[0079] Figure 3 This is a schematic diagram of the multi-parameter response surface optimization provided by the present invention, as shown below. Figure 3 As shown, this invention establishes a multi-parameter response surface model to find the optimal combination of operating parameters (optimal operating point). ). With microwave transmission power Pressure Corrected Residual Reference temperature stability To optimize the variables, a response surface for the standard uncertainty of thermodynamic temperature is constructed. It should be noted that... Figure 3 Pressure Correction Residual That is, the aforementioned static pressure difference correction amount The abbreviated form of .

[0080] The figure shows the combined thermodynamic temperature uncertainty (also known as the standard thermodynamic temperature uncertainty). / μ k (micro Kelvin) varies with microwave transmission power / dBm (decibels and milliwatts) and pressure-corrected residuals / Pa (Pa) A three-dimensional surface plot of the response surface under varying conditions. The response surface exhibits a undulating shape, with convex regions corresponding to high uncertainty areas and concave regions corresponding to low uncertainty areas. The lowest point on the response surface is the optimal operating point. The corresponding thermodynamic temperature standard uncertainty is at its minimum value. .

[0081] The diagram indicates the optimization direction, showing the path from the initial operating point to the optimal operating point. The optimal path is shown in the figure, which also indicates the high uncertainty region and the low uncertainty region, as well as the optimal operating point. The projection onto the microwave transmission power axis corresponds to the optimal microwave transmission power. The projection onto the pressure-corrected residual axis corresponds to the optimal pressure-corrected residual. .

[0082] This response surface model allows for the intuitive identification of the region of minimum uncertainty in the three-dimensional parameter space. Furthermore, methods such as grid search, gradient optimization, response surface optimization, or Bayesian optimization can be used to determine the optimal parameter combination that minimizes the standard uncertainty of the thermodynamic temperature. Optimize variables: , , Objective function: Result: Optimal parameter combination determined. Step 105: Perform weak coupling verification using the optimal combination of operating parameters. If the verification is successful, perform measurement using the optimal combination of operating parameters and output the thermodynamic temperature measurement results and the uncertainty of the thermodynamic temperature measurement results.

[0083] Specifically, after obtaining the optimal combination of operating parameters, weak coupling verification is performed using the optimal combination of operating parameters. Weak coupling verification is a step to verify whether the coupling strength between the three systems of temperature control, pressure control and microwave frequency measurement has decreased after optimization.

[0084] If the verification is successful, the measurement is performed using the optimal combination of operating parameters, and the thermodynamic temperature measurement result and its uncertainty are output. The uncertainty of the thermodynamic temperature measurement result is a parameter characterizing the dispersion of the measurement result, and is usually expressed as standard uncertainty or expanded uncertainty.

[0085] The method provided in this invention first establishes a measurement model for a constant-pressure gas refractive index reference temperature measuring device, incorporating a temperature control system, a pressure control system, and a microwave resonant frequency measurement system into the measurement model. Then, based on the measurement model, an error propagation model and a contribution ratio model are established to calculate the contribution ratio of each influencing factor to the thermodynamic temperature. Each influencing factor includes temperature, pressure, frequency, and a correction term. Further, based on the contribution ratio of each influencing factor, the dominant factor with the greatest impact on thermodynamic temperature measurement is identified, and single-factor optimization is performed on temperature stability, pressure stability, and microwave transmission power according to the dominant factor, obtaining the optimization results for each single factor. Based on the measurement model and the optimization results for each single factor, a multi-parameter response surface model is established with microwave transmission power, pressure stability, and temperature stability as optimization variables, and the optimal combination of operating parameters that minimizes the standard uncertainty of the thermodynamic temperature is determined through an optimization method. Then, weak coupling verification is performed using the optimal combination of operating parameters. If the verification passes, measurement is performed using the optimal combination of operating parameters, outputting the thermodynamic temperature measurement result and its uncertainty.

[0086] This invention integrates the temperature control system, pressure control system, and microwave resonant frequency measurement system into a unified measurement model, establishes an error propagation and contribution ratio model, identifies dominant factors based on contribution ratios, conducts single-factor optimization, constructs a multi-parameter response surface model for global optimization, and finally verifies the effectiveness of optimization through weak coupling, forming a complete closed-loop process of modeling → quantification → identification → optimization → verification. This process restores and improves the thermodynamic temperature measurement accuracy that was originally reduced due to the coupling of the three systems. Specifically, the mutual interference between the three systems is quantified and suppressed, the dominant error source is accurately identified and optimized in a targeted manner, and finally, the temperature measurement uncertainty is minimized under the globally optimal combination of operating parameters. It transforms the negative factor of "three-system coupling," which originally led to a decrease in temperature measurement accuracy, into a controllable object that can be effectively identified, quantified, and suppressed through a systematic modeling, quantification, and optimization process, thereby substantially improving the thermodynamic temperature measurement accuracy of the constant-pressure gas refractive index reference temperature measurement device.

[0087] It should be noted that each implementation method of this application can be freely combined, rearranged, or executed individually, and does not need to rely on or depend on a fixed execution order.

[0088] According to the multi-parameter weakly coupled optimized temperature measurement method of the constant pressure gas refractive index reference temperature measuring device provided by the present invention, the contribution ratio of each influencing factor to the thermodynamic temperature is calculated, including: Calculate the sensitivity coefficients of each influencing factor to thermodynamic temperature; the sensitivity coefficients are obtained using the finite difference method. The contribution percentage is obtained by dividing the product of the square of each sensitivity coefficient and the square of the standard uncertainty of each sensitivity coefficient by the square of the standard uncertainty of the thermodynamic temperature.

[0089] Specifically, in some embodiments, the specific methods for calculating the contribution percentage of each influencing factor to the thermodynamic temperature include the following: First, the sensitivity coefficients of each of the aforementioned influencing factors to the thermodynamic temperature are calculated. The sensitivity coefficient represents the degree of change in thermodynamic temperature caused by a unit change in a certain influencing factor, reflecting the sensitivity of that factor to the temperature measurement result. The finite difference method refers to approximately calculating the sensitivity coefficient of a parameter by measuring the thermodynamic temperature corresponding to a parameter under positive and negative offset conditions, and dividing the difference between the two by twice the offset.

[0090] The sensitivity coefficient is obtained using the difference method, that is, for any influencing factor The thermodynamic temperature corresponding to the influencing factor was measured under positive and negative offset conditions, and the difference between the two was divided by twice the offset to obtain the sensitivity coefficient of the influencing factor. in, For the first The sensitivity coefficients of each influencing factor to thermodynamic temperature. Influencing factors In positive offset The corresponding thermodynamic temperature under the conditions, Influencing factors Negative offset The corresponding thermodynamic temperature under the conditions, This is the offset.

[0091] Then, the contribution percentage of each sensitivity coefficient is obtained by dividing the product of the square of each sensitivity coefficient and the square of the standard uncertainty of each sensitivity coefficient by the square of the standard uncertainty of the thermodynamic temperature. When considering coupling terms, the first The combined contribution of each influencing factor can be defined as: By comparison or The magnitude of the error can be used to determine which factors among temperature, pressure, microwave frequency, and their correction terms are the dominant error sources, thus determining the priority optimization direction. For example, if the calculated contribution of the frequency term is greater than that of the pressure term, and the contribution of the pressure term is greater than that of the temperature term, it indicates that the microwave frequency term is the dominant error source, and the microwave frequency measurement system should be optimized first.

[0092] The method provided in this invention employs the finite difference method to calculate the sensitivity coefficient. The contribution percentage is obtained by dividing the product of the squared sensitivity coefficient and the squared standard uncertainty by the squared thermodynamic temperature standard uncertainty. By quantifying the influence of each factor on the temperature measurement result using the finite difference method, the contribution percentage becomes calculable and comparable, providing a data foundation for accurately identifying the dominant error source.

[0093] According to the present invention, a multi-parameter weak coupling optimization temperature measurement method for a constant-pressure gas refractive index reference temperature measuring device is provided, which uses the optimal combination of operating parameters for weak coupling verification, including: Calculate the optimized coupling strength and the original coupling strength; the coupling strength is evaluated as follows: the coupling strength coefficient between any two influencing factors is the product of the absolute value of the second partial derivatives of the two influencing factors and the standard uncertainty of each influencing factor; the overall coupling strength is the sum of the normalized coupling strength coefficients of all pairwise combinations of influencing factors, and the normalized coupling strength coefficient is the coupling strength coefficient divided by the standard uncertainty of thermodynamic temperature. Verify whether the optimized coupling strength is less than the unoptimized coupling strength, and whether the optimized temperature measurement uncertainty is less than the unoptimized temperature measurement uncertainty.

[0094] In some embodiments, the specific methods for performing weakly coupled verification using the optimal combination of operating parameters include the following: First, calculate the optimized coupling strength and the original coupling strength.

[0095] To evaluate the coupling degree among the temperature control, pressure control, and microwave frequency measurement systems, this invention defines a coupling strength coefficient. The coupling strength is evaluated as follows: the coupling strength coefficient between any two influencing factors is the product of the absolute values ​​of the second-order partial derivatives of the two influencing factors and the standard uncertainty of each influencing factor. in, For the first The first influencing factor and the second The coupling strength coefficient between the influencing factors and They represent the first The first influencing factor and the second One influencing factor, such as temperature, pressure, frequency, or their correction terms. For the first One influencing factor Standard uncertainty For the first One influencing factor Standard uncertainty It is the thermodynamic temperature.

[0096] To facilitate comparison of factors with different dimensions, a normalized coupling coefficient can be used. The normalized coupling coefficient is the coupling strength coefficient divided by the standard uncertainty of the thermodynamic temperature. in, For the first The first influencing factor and the second Normalized coupling strength coefficients among the influencing factors Thermodynamic temperature and They represent the first The first influencing factor and the second One influencing factor, For the first One influencing factor Standard uncertainty For the first One influencing factor Standard uncertainty This represents the standard uncertainty of thermodynamic temperature.

[0097] The overall coupling strength is the sum of the normalized coupling coefficients of all pairwise combinations of influencing factors. The overall coupling strength function is defined as follows: in, This is the coupling strength evaluation function. The number of influencing factors, For the first The first influencing factor and the second Normalized coupling strength coefficients among the influencing factors.

[0098] Then, it is verified whether the optimized coupling strength is less than the unoptimized coupling strength, and whether the optimized temperature measurement uncertainty is less than the unoptimized temperature measurement uncertainty.

[0099] The objective of weak coupling optimization is: in, This is the coupling strength evaluation function.

[0100] At the same time, it is guaranteed that: in, For the target temperature measurement uncertainty, This represents the standard uncertainty of thermodynamic temperature.

[0101] For example, repeating measurements at the optimal operating point verifies whether the coupling strength between temperature, pressure, and frequency decreases, i.e., verification: And verify: in, and These represent the coupling strength and temperature measurement uncertainty before optimization, respectively. and These represent the optimized coupling strength and temperature measurement uncertainty, respectively.

[0102] If the optimized coupling strength is less than the unoptimized coupling strength, and the optimized temperature measurement uncertainty is less than the unoptimized temperature measurement uncertainty, then the optimization is effective, the coupling effect between the three systems has been significantly reduced, and the weak coupling verification is passed.

[0103] The method provided in this invention quantitatively verifies the effectiveness of optimization through the coupling strength index, ensuring that the mutual interference of the three systems has indeed been reduced, rather than relying solely on experience.

[0104] According to the present invention, a multi-parameter weakly coupled optimized temperature measurement method for a constant-pressure gas refractive index reference temperature measuring device determines the optimal combination of operating parameters that minimizes the standard uncertainty of thermodynamic temperature through an optimization method, including: Determine the comprehensive objective function; the comprehensive objective function includes the square of the standard uncertainty of thermodynamic temperature, the square of the difference between the measured thermodynamic temperature and the reference temperature, the coupling strength function, and the single-point measurement time. The combination of working parameters that minimizes the overall objective function is determined as the optimal combination of working parameters.

[0105] In some embodiments, the specific methods for determining the optimal combination of operating parameters that minimizes the standard uncertainty of thermodynamic temperature through an optimization method include the following: First, determine the comprehensive objective function. The comprehensive objective function is a mathematical function that comprehensively considers multiple optimization objectives (such as temperature measurement uncertainty, temperature measurement deviation, coupling strength, and measurement time). The comprehensive objective function includes a term representing the square of the standard uncertainty of thermodynamic temperature, a term representing the square of the difference between the measured thermodynamic temperature and the reference temperature, a coupling strength function term, and a single-point measurement time term. Each term is multiplied by its corresponding weighting coefficient and then summed. Then, the combination of working parameters that minimizes the comprehensive objective function is determined as the optimal combination of working parameters: Parameter vector to be optimized It can be represented as: The following is a detailed embodiment: With microwave transmission power Pressure Corrected Residual and reference temperature stability To optimize variables, set the range of values ​​for each optimization variable (e.g., ...). -40dBm to 0dBm -10 Pa to 10 Pa, (The weighting coefficients range from 0.1 mK to 1.0 mK). Weighting coefficients are set according to actual requirements. Combined experiments are conducted on each parameter within the allowable parameter space to obtain the comprehensive objective function values ​​at different operating points. The parameter combination that minimizes the comprehensive objective function is determined as the optimal operating parameter combination.

[0106] The method provided in this invention constructs a comprehensive objective function that includes temperature measurement uncertainty, temperature measurement deviation, coupling strength, and measurement time, and uses the parameter combination corresponding to its minimum value as the optimal operating parameters. This achieves optimal overall performance while ensuring accuracy and measurement efficiency.

[0107] According to the multi-parameter weak coupling optimization temperature measurement method of the constant pressure gas refractive index reference temperature measuring device provided by the present invention, the dominant factor with the greatest influence on thermodynamic temperature measurement is identified among the various influencing factors based on the contribution ratio of each influencing factor, including: The influencing factors are ranked according to their respective contribution percentages; Based on the ranking results, identify the dominant factors.

[0108] Specifically, in some embodiments, the methods for identifying the dominant factor based on the contribution ratio of each influencing factor include: First, the influencing factors are ranked according to their respective contribution percentages. Specifically, according to... or The temperature, pressure, frequency, and correction terms are arranged in descending order.

[0109] Then, based on the ranking results, the dominant factors are identified. The factors with the largest contribution in the ranking are determined as the dominant factors with the greatest impact on thermodynamic temperature measurement.

[0110] The following is a detailed embodiment: Detailed Implementation Examples: After calculating the contribution percentage of each influencing factor, for example, we obtain... , , , (in The contribution percentage of the frequency term, The percentage of contribution to stress items. The contribution percentage of the temperature term, If the contribution percentage of the correction term is considered, the ranking result is: frequency term > pressure term > temperature term > correction term, with the frequency term being the dominant factor. This indicates that the uncertainty in microwave frequency measurement is currently the main constraint on temperature measurement accuracy, and the microwave frequency measurement system should be optimized first.

[0111] The method provided in this invention sorts the influencing factors from largest to smallest contribution percentage, identifying the factor with the largest contribution percentage as the dominant factor. This sorting process enables the visual identification of the dominant factor, making the optimization direction clear and evidence-based, and avoiding blind parameter tuning.

[0112] According to the multi-parameter weakly coupled optimized temperature measurement method of the constant-pressure gas refractive index reference temperature measuring device provided by the present invention, under the condition of successful verification, the optimal combination of operating parameters is used for measurement, and the thermodynamic temperature measurement result and the uncertainty of the thermodynamic temperature measurement result are output, including: If the verification is successful, the optimal combination of operating parameters is used for measurement to obtain the thermodynamic temperature measurement results and the uncertainty of the thermodynamic temperature measurement results; Under the condition that the temperature stability criterion, pressure stability criterion, microwave signal stability criterion, and weak coupling criterion are satisfied, output thermodynamic temperature measurement results and the uncertainty of thermodynamic temperature measurement results.

[0113] In some embodiments, if verification is successful, the specific methods for performing measurements using the optimal combination of operating parameters and outputting measurement results include the following: First, assuming the verification is successful, measurements are performed using the optimal combination of operating parameters to obtain the measurement results.

[0114] Then, if the measurement results satisfy the temperature stability criterion, pressure stability criterion, microwave signal stability criterion, and weak coupling criterion, the thermodynamic temperature measurement results and the uncertainty are output.

[0115] Among them, the temperature stability criterion is used to determine whether the temperature has reached a stable state. The pressure stability criterion is used to determine whether the pressure has reached a stable state. The microwave signal stability criterion is used to determine whether the microwave signal has reached a stable state. The weak coupling criterion is used to determine whether the coupling strength of the three systems has decreased to an acceptable level.

[0116] The temperature stability criterion can be written as: in, For the standard deviation of temperature fluctuation, This is to count the number of temperature data points collected within a given time period. For the first time period in the statistics One temperature measurement value, The average temperature over the statistical period. This is the temperature stability threshold. Simultaneously, it is required that: in, For statistical windows, This is the temperature stability threshold. The temperature drift threshold, This represents the temperature drift rate.

[0117] The pressure stability criterion can be written as: in, The standard deviation of pressure fluctuation, This refers to the number of pressure data points collected within a given time period. For the first time period in the statistics One pressure measurement value, The average pressure over the statistical period. This is the pressure stability threshold.

[0118] And satisfy: in, For statistical windows, This is the pressure stability threshold. The pressure drift rate threshold, This represents the pressure drift rate.

[0119] For example, after the weak coupling verification is passed, actual measurements are performed using the optimal combination of operating parameters. During the measurement process, temperature, pressure, microwave signal stability, and coupling strength are continuously monitored. When all criteria are met, including that the standard deviation of temperature fluctuation is no greater than the temperature stability threshold and the temperature drift rate is no greater than the temperature drift rate threshold, the standard deviation of pressure fluctuation is no greater than the pressure stability threshold and the pressure drift rate is no greater than the pressure drift rate threshold, the signal-to-noise ratio is no less than the signal-to-noise ratio threshold and the quality factor is no less than the quality factor threshold, and the optimized coupling strength is less than the unoptimized coupling strength, the measurement results are read and recorded, and the thermodynamic temperature is output. and thermodynamic temperature expansion uncertainty : The thermodynamic temperature expansion uncertainty is: ： in, As a inclusion factor, This represents the standard uncertainty of thermodynamic temperature.

[0120] The method provided in this invention outputs measurement results only when four criteria—temperature, pressure, microwave signal, and weak coupling—are simultaneously met. This multi-criteria linkage ensures that measurement data is collected only when the system is fully stable, guaranteeing the reliability and repeatability of the output results.

[0121] According to the multi-parameter weakly coupled optimized temperature measurement method of the constant-pressure gas refractive index reference temperature measuring device provided by the present invention, before establishing an error propagation model and a contribution ratio model based on the measurement model and calculating the contribution ratio of each influencing factor to the thermodynamic temperature, the method further includes: Baseline data was collected under initial operating conditions; the baseline data included reference temperature, measured pressure, measured frequency, signal-to-noise ratio, quality factor, temperature fluctuation, pressure fluctuation, and frequency repeatability. The measured pressure is corrected by static pressure difference, pipeline pressure drop, temperature gradient, dynamic disturbance, and pressure drift to obtain the effective pressure inside the resonant cavity; The effective frequency is obtained by performing resonance peak fitting correction, microwave power correction, mode correction, transmission line correction and frequency drift correction on the measured frequency; The gas refractive index is calculated based on the cavity frequency and the filling frequency. The thermodynamic temperature is obtained by inversion based on the gas refractive index, the effective pressure in the resonant cavity, and the gas state model. Both the cavity frequency and the filling frequency are determined based on the effective frequency. The thermodynamic temperature is used to calculate each sensitivity coefficient and each contribution percentage.

[0122] In some embodiments, the preprocessing steps before establishing the error propagation and contribution ratio model include the following: First, baseline data is acquired under initial operating conditions. This baseline data includes a reference temperature. Actual pressure Measured frequency Signal-to-noise ratio (SNR) and quality factor Temperature fluctuations Pressure fluctuations and frequency fluctuations .

[0123] Then, the measured pressure is corrected for static pressure difference, pipeline pressure drop, temperature gradient, dynamic disturbance, and pressure drift to obtain the effective pressure inside the resonant cavity. That is, the effective pressure inside the resonant cavity is calculated based on factors such as static pressure difference, pipeline pressure drop, temperature gradient, and pressure drift. in, The effective pressure inside the resonant cavity. To measure the actual pressure, For static pressure difference correction, For pipeline pressure drop correction, Pressure correction due to temperature gradient For dynamic disturbance correction, For pressure gauge drift correction.

[0124] After applying resonant peak fitting correction, microwave power correction, mode correction, transmission line correction, and frequency drift correction to the measured frequency, the effective frequency is obtained. .

[0125] To improve the reliability of the frequency measurement model, the measured frequency can be... Corrected to effective frequency That is, the microwave resonant frequency: in, The effective frequency, also known as the microwave resonant frequency, This is the measured frequency. Correction for resonant peak fitting. Correction for microwave power. For pattern recognition and pattern coupling correction, Corrections introduced for transmission lines or connectors, This is for frequency drift correction.

[0126] Calculate the gas refractive index based on the cavity frequency and the filling frequency. The thermodynamic temperature is obtained by inversion based on the gas refractive index, the effective pressure inside the resonant cavity, and the gas state model. Both the cavity frequency and the inflation frequency are determined based on the effective frequency. The thermodynamic temperature is used to calculate each sensitivity coefficient and each contribution percentage.

[0127] Based on the above relationships, this invention expresses thermodynamic temperature as a composite function of pressure and frequency: in, Thermodynamic temperature The effective pressure inside the resonant cavity. The resonant frequency in the cavity state (cavity frequency). The resonant frequency after gas is introduced (gas filling frequency). , , These are the first-order, second-order, and third-order dielectric virial coefficients of the gas, respectively. The gas compressibility factor, Correction for changes in cavity size. To correct for cavity wall conductivity or surface impedance. For microwave mode related corrections, This is a correction for gas non-idealities. This expression provides the foundation for subsequent error propagation, coupling analysis, and multi-parameter optimization.

[0128] The following is a detailed embodiment: After establishing the measurement model, the device was started under initial operating conditions. Once the temperature stabilized, a reference temperature was collected using a reference thermometer. The measured pressure is collected by a pressure gauge. The measured frequency was collected using a network analyzer. Signal-to-noise ratio (SNR) and quality factor And record temperature fluctuations Pressure fluctuations and frequency fluctuations .

[0129] The measured pressure is corrected to obtain the effective pressure inside the resonant cavity. The measured frequency is corrected to obtain the effective frequency. That is, the microwave resonant frequency.

[0130] The resonant frequency (cavity frequency) in the cavity state. And the resonant frequency after gas is introduced (inflation frequency). Calculate the refractive index of a gas : in, For the refractive index of the gas, The resonant frequency in the cavity state (cavity frequency). The resonant frequency after gas is introduced (gas filling frequency). Correction for changes in cavity size. To correct for cavity wall conductivity or surface impedance. For microwave mode related corrections, This is a correction for gas non-ideal properties.

[0131] The gas density is obtained by inversion using the following Lorentz-Lorentz relation. : in, For the refractive index function of the gas, , , These are the first-order, second-order, and third-order dielectric virial coefficients of the gas, respectively. For gas density, is the refractive index of the gas.

[0132] The final thermodynamic temperature is obtained as follows: Under isobaric conditions, thermodynamic temperature can be expressed as: in Thermodynamic temperature The effective pressure inside the resonant cavity. Boltzmann's constant, Let Avogadro's constant be 1. This refers to the gas compressibility factor. If the molar gas constant is used... It can also be written as: in, Thermodynamic temperature The effective pressure inside the resonant cavity. For gas molar mass, For mass density, It is the gas compressibility factor.

[0133] The obtained thermodynamic temperature is used in subsequent steps to calculate the sensitivity coefficients and contribution percentages.

[0134] The method provided in this invention first acquires baseline data, then performs multiple corrections on the measured pressure and frequency, and finally retrieves the thermodynamic temperature from the effective frequency and effective pressure. By acquiring baseline data and performing multi-stage corrections, systematic errors in the measurement process are eliminated, ensuring the accuracy and reliability of the initial thermodynamic temperature value used for contribution percentage calculation.

[0135] According to the multi-parameter weak coupling optimization temperature measurement method of the constant pressure gas refractive index reference temperature measurement device provided by the present invention, the effective pressure in the resonant cavity is expressed as the sum of the measured pressure and the static pressure difference correction, the pipeline pressure drop correction, the pressure correction caused by the temperature gradient, the dynamic disturbance correction, and the pressure gauge drift correction; the static pressure difference correction is determined based on the product of the measured gas density, the local gravitational acceleration, and the height difference between the pressure measurement point and the effective measurement center of the resonant cavity.

[0136] Specifically, the effective pressure inside the resonant cavity is expressed as follows.

[0137] The effective pressure inside the resonant cavity is expressed as the sum of the measured pressure and the corrections for static pressure difference, pipeline pressure drop, pressure caused by temperature gradient, dynamic disturbance, and pressure gauge drift: The static pressure difference correction is determined based on the product of the measured gas density, the local gravitational acceleration, and the height difference between the pressure measurement point and the effective measurement center of the resonant cavity. in, For static pressure difference correction, To measure gas density, For local gravitational acceleration, This is the height difference between the pressure measurement point and the effective measurement center of the resonant cavity.

[0138] The method provided in this invention represents the effective pressure as the sum of the measured pressure and five correction factors, wherein the static pressure difference correction factor is determined by the product of density, gravitational acceleration, and height difference. By structurally decomposing the pressure correction factors, the determination of the effective pressure within the cavity becomes verifiable, and each correction is traceable, thereby improving the accuracy of the pressure input.

[0139] According to the present invention, a multi-parameter weakly coupled optimization temperature measurement method for a constant-pressure gas refractive index reference temperature measuring device is provided. This method optimizes microwave transmission power using a single factor based on the dominant factor, yielding the single-factor optimization result, including: If the dominant factor is frequency, establish a relationship model between microwave transmission power and frequency measurement uncertainty; the relationship model includes: frequency fitting uncertainty term caused by insufficient signal-to-noise ratio when the power is too low, uncertainty term caused by microwave disturbance or thermal effect when the power is too high, and basic uncertainty term unrelated to power; With the goal of minimizing the standard uncertainty of thermodynamic temperature, the optimal microwave power that satisfies the constraints is determined by solving the relational model. The constraints include: signal-to-noise ratio not lower than the signal-to-noise ratio threshold, quality factor not lower than the quality factor threshold, and power correction not exceeding the power correction threshold.

[0140] The specific method for single-factor optimization of microwave transmission power based on the dominant factors.

[0141] Specifically, in some embodiments, the single-factor optimization process includes the following: First, determine whether the dominant factor is the frequency. If the dominant factor is the frequency, then establish a relationship model between the microwave transmission power and the frequency measurement uncertainty.

[0142] Microwave frequency measurement systems obtain the gas refractive index by measuring the frequency of the resonant cavity. Microwave transmission power. It is an important parameter affecting the quality of frequency measurement. If If the frequency is too low, the resonant signal is weak, the signal-to-noise ratio is insufficient, and the frequency fitting uncertainty increases; if... Excessive power may cause microwave power deposition, resonant peak deformation, local thermal effects, or mode perturbation, leading to increased additional uncertainty.

[0143] Therefore, the frequency uncertainty is expressed as follows: in, This refers to the effective frequency uncertainty, which is also the uncertainty of the microwave resonant frequency. The fitting uncertainty of the resonance peak, For repeatability uncertainty, For the uncertainty of frequency measuring instruments, For microwave power-related uncertainties, For pattern recognition or pattern coupling uncertainty, This represents the frequency drift uncertainty.

[0144] The relational model includes: a frequency fitting uncertainty term caused by insufficient signal-to-noise ratio when the power is too low, an uncertainty term caused by microwave disturbance or thermal effects when the power is too high, and a fundamental uncertainty term unrelated to power. in, Indicates microwave transmission power Effective frequency uncertainty under the following conditions This indicates the frequency fitting uncertainty caused by insufficient signal-to-noise ratio when the power is too low. This indicates the uncertainty caused by microwave disturbances or thermal effects when the power is too high. This represents the fundamental uncertainty, which is independent of power.

[0145] Therefore, the theoretical optimal point of microwave power can be obtained: Right now: in, Indicates microwave transmission power Uncertainty at the lower effective frequency, This refers to microwave transmission power. For optimal microwave transmission power, This indicates the frequency fitting uncertainty caused by insufficient signal-to-noise ratio when the power is too low. This indicates the uncertainty caused by microwave disturbances or thermal effects when the power is too high.

[0146] In practical measurements, microwave power is usually expressed in dBm. If the linear microwave transmission power is... dBm power is The relationship between the two is: Therefore, within a given power range, for example to Within the range of other suitable devices, the resonant frequency repeatability, signal-to-noise ratio, and resonant peak fitting residuals are measured point by point to establish... Response curves to determine the optimal microwave transmission power .

[0147] The temperature disturbance caused by microwave power can be expressed as: in, Temperature disturbance caused by microwave power. For equivalent thermal resistance, The microwave power deposition coefficient is... Let be the microwave transmission power. The corresponding temperature uncertainty contribution is: Contribution to the temperature uncertainty of microwave power Thermodynamic temperature For temperature, Temperature disturbance caused by microwave power. The uncertainty is the temperature disturbance.

[0148] Then, the microwave power optimization objective is to minimize the thermodynamic temperature uncertainty (not just to maximize the signal-to-noise ratio). By minimizing the relational model, the optimal microwave power is determined to satisfy the constraints that the signal-to-noise ratio is not lower than the signal-to-noise ratio threshold, the quality factor is not lower than the quality factor threshold, and the power correction amount does not exceed the power correction threshold.

[0149] Specifically, the goal should be to minimize the uncertainty of thermodynamic temperature. in, For optimal microwave transmission power, This refers to microwave transmission power. For the parameter space of microwave power, Thermodynamic temperature The effective frequency, also known as the microwave resonant frequency, microwave transmission power Effective frequency uncertainty under the following conditions For the uncertainty of temperature disturbance, This refers to the temperature disturbance caused by microwave power.

[0150] Simultaneously, the following requirements must be met: in For power The signal-to-noise ratio is below. It is the lower limit threshold of the signal-to-noise ratio, that is, the minimum signal-to-noise ratio required to ensure that the resonance peak can be stably identified and the frequency can be reliably fitted.

[0151] in To achieve a microwave transmission power of At that time, the quality factor of the corresponding resonant mode of the microwave resonant cavity; This is the lower limit threshold of the resonant cavity quality factor, which is the minimum quality factor required to ensure the stability of the resonant mode and the accurate fitting of the resonant peak.

[0152] in, Correction for microwave power. This is the upper limit of the allowable microwave power-related frequency offset, i.e., the threshold that ensures the microwave power will not introduce excessive additional errors to the resonant frequency measurement. By meeting these conditions, the optimal transmit power can be obtained that both guarantees microwave signal strength and reduces microwave-related uncertainties.

[0153] The method provided in this invention establishes a microwave power-frequency uncertainty relationship model only when frequency is the dominant factor, and solves for the optimal microwave power with the goal of minimizing the thermodynamic temperature standard uncertainty. This directly links power optimization under frequency-dominant conditions with the thermodynamic temperature standard uncertainty, avoiding the neglect of temperature perturbation effects while solely focusing on maximizing the signal-to-noise ratio.

[0154] Modeling and optimization of temperature control factors include the following: Temperature control system mainly affects The invention considers the uniformity of cavity temperature, the stability of gas temperature, and the stability of cavity dimensions. The reference temperature... Represented as: in, For reference temperature, This is the reading from a standard thermometer. For thermometer calibration correction, For thermometer self-heating correction, For lead wire thermal leakage correction, For temperature gradient correction, This is for long-term drift correction.

[0155] The uncertainty of the temperature reference term is expressed as: in, The uncertainty of the reference temperature under the ITS-90 temperature scale. Correcting the uncertainty for thermometer calibration For the measurement uncertainty of the bridge, To correct the uncertainty of the thermometer's self-heating function, To correct for lead wire thermal leakage uncertainty, To correct the uncertainty of the temperature gradient, To correct for long-term drift uncertainty, This represents the uncertainty of repeated measurements.

[0156] The effect of temperature fluctuations on microwave resonant frequency can be expressed as: Microwave resonant frequency fluctuations caused by temperature fluctuations ， For temperature-related correction terms, For effective frequency, For temperature.

[0157] The effect of temperature fluctuations on pressure can be expressed as: Pressure fluctuations caused by temperature fluctuations ， For temperature-related correction terms, The effective pressure inside the resonant cavity. For temperature.

[0158] Therefore, the temperature control system not only directly affects Also through and This indirectly affects refractive index and pressure measurements. To reduce this coupling effect, this invention sets a temperature optimization target: in, The uncertainty of the reference temperature under the ITS-90 temperature scale. and These are the weighting coefficients for the coupling effect of temperature on frequency and pressure. The coupling effect of temperature on frequency, This represents the coupled effect of temperature on pressure.

[0159] Practical optimization measures for temperature control include: improve To improve measurement accuracy and reduce thermometer calibration uncertainty; to reduce temperature control fluctuations, ensuring that the standard deviation of temperature fluctuations is below a set threshold; to reduce the temperature gradient between different locations in the resonant cavity; to adopt a temperature stability criterion, only collecting frequency and pressure data after the stability conditions are met; and to incorporate the effects of temperature fluctuations on frequency and pressure into the thermodynamic temperature inversion model.

[0160] The modeling and optimization of pressure control factors include the following: The core task of the pressure control system is to obtain the true pressure within the effective measurement area of ​​the resonant cavity. Because there may be height differences, pipeline pressure drops, temperature gradients, and gas density changes between the pressure measurement point and the effective measurement center of the resonant cavity, the measured pressure... Not necessarily equal to the effective pressure inside the resonant cavity .

[0161] This invention will reduce the effective pressure inside the resonant cavity Represented as: in, For actual pressure For static pressure difference correction, For pipeline pressure drop correction, Pressure correction due to temperature gradient For dynamic disturbance correction, For pressure gauge drift correction.

[0162] Static pressure difference correction It can be represented as: in, To measure gas density, For local gravitational acceleration, This is the height difference between the pressure measurement point and the effective measurement center of the resonant cavity.

[0163] The uncertainty of the static pressure difference correction can be expressed as: in, Uncertainty corrected for static pressure difference. For local gravitational acceleration, The height difference between the pressure measurement point and the effective measurement center of the resonant cavity. To measure the uncertainty of gas density, To measure gas density ， The uncertainty is the height difference between the pressure measurement point and the effective measurement center of the resonant cavity. This represents the uncertainty of the local gravitational acceleration.

[0164] The total uncertainty of the pressure term is: in, The uncertainty of the effective pressure inside the resonant cavity. Uncertainty of measured pressure Uncertainty corrected for static pressure difference. Uncertainty for pipeline pressure drop correction, The uncertainty in pressure correction caused by the temperature gradient. Uncertainty for dynamic disturbance correction, Uncertainty for pressure gauge drift correction.

[0165] The effect of pressure on thermodynamic temperature is as follows: Effective pressure inside the resonant cavity Thermodynamic temperature uncertainty under the given conditions The uncertainty of the effective pressure inside the resonant cavity. Thermodynamic temperature This represents the effective pressure inside the resonant cavity.

[0166] Under the ideal gas approximation, if: This represents the effective pressure inside the resonant cavity.

[0167] Then we have: Therefore, the relative pressure error will be directly converted into the relative temperature error: The pressure optimization objective in this invention is: in, The uncertainty of the effective pressure inside the resonant cavity. For static pressure difference correction, For pressure drift rate, The weighting factor for static pressure difference correction. This is the weighting coefficient for the pressure drift rate.

[0168] Actual optimization measures include: Try to keep the pressure measurement point at the same height as the effective measurement center of the microwave resonant cavity to reduce... ; when When unavoidable, adopt Perform static pressure difference correction; Employing a high-stability pressure control mode reduces pressure instability. ; Establish a pressure stability criterion and collect frequency data only when the pressure drift rate meets the requirements; The pressure sensor readings, static pressure difference correction, pipeline pressure drop, and pressure drift are all incorporated into the pressure uncertainty model.

[0169] The following is a detailed embodiment: Step 1: Temperature Measurement Optimization Based on Three-System Coupling Model In a constant-pressure gas refractive index reference temperature measuring device, the temperature control system is first activated to bring the microwave resonant cavity to near the target temperature. The temperature is then obtained using a reference thermometer. It continuously collects temperature data over a period of time and calculates the average temperature, standard deviation of temperature fluctuation, and temperature drift rate.

[0170] When the temperature stability criterion is met: Temperature fluctuation standard deviation Not greater than the temperature stability threshold And the absolute value of the temperature drift rate Not greater than the temperature drift threshold At that point, the temperature control system is considered to have reached a stable state.

[0171] Temperature fluctuation standard deviation Represented as: in, For the standard deviation of temperature fluctuation, This is to count the number of temperature data points collected within a given time period. For the first time period in the statistics One temperature measurement value, The average temperature over the statistical period. This is the temperature stability threshold. This is a statistics window.

[0172] The pressure control system is then activated, introducing the measuring gas into the microwave resonant cavity and controlling the pressure to the target pressure point. The measured pressure is then obtained using a pressure gauge. The static pressure difference correction is calculated based on the height difference between the pressure measurement point and the effective measurement center of the resonant cavity. : in To measure gas density, For local gravitational acceleration, The effective pressure inside the resonant cavity is obtained by calculating the height difference between the pressure measurement point and the effective measurement center of the resonant cavity. : in To measure the actual pressure, For pipeline pressure drop correction, Pressure correction due to temperature gradient For dynamic disturbance correction, For pressure gauge drift correction.

[0173] Then start the microwave resonant frequency measurement system and select the initial microwave transmission power P. μ,0 Measure the resonant frequency in the cavity state, i.e., the cavity frequency. The resonant frequency after gas is introduced, also known as the inflation frequency. The frequency values ​​and frequency fitting uncertainty are obtained by fitting the resonance peaks. Effective frequency. (That is, the microwave resonant frequency) is determined by the measured frequency. The result was obtained after corrections for resonance peak fitting, microwave power, mode, transmission line, and frequency drift. The gas refractive index is expressed as follows: Gas refractive index function for: Then by Inversion yields gas density Ultimately, it was decided by... Obtain the thermodynamic temperature.

[0174] If the molar gas constant is used It can also be written as: 2. Contribution ratio analysis and identification of dominant error sources After obtaining the initial measurement results, perturbation analyses were performed on temperature, pressure, frequency, and correction terms. For any influencing factor (parameter)... The sensitivity coefficient was calculated using the finite difference method: Then calculate the contribution percentage of each factor: For example, when calculated In this case, the microwave frequency term is the dominant error source, and the microwave frequency measurement system should be optimized first, for example, by improving the signal-to-noise ratio, optimizing the transmit power, improving the resonant peak fitting quality, or reducing the influence of mode coupling. The contribution percentage of the frequency term, The percentage of contribution to stress items. The percentage contribution of temperature.

[0175] When calculated If the pressure term is the dominant source of error, priority should be given to reducing pressure fluctuations, decreasing static pressure difference, or improving the accuracy of pressure correction.

[0176] When calculated If the temperature term is the dominant source of error, then priority should be given to improving temperature stability, temperature uniformity, and the accuracy of reference temperature measurements.

[0177] This step avoids blindly increasing a single indicator and instead determines the most effective optimization direction based on the actual contribution ratio.

[0178] 3. Microwave transmission power optimization During microwave frequency measurement, multiple candidate microwave transmission power points are set: This is the first microwave transmission power point. This is the second microwave transmission power point. For the first One microwave transmission power point.

[0179] The signal-to-noise ratio was obtained by repeatedly measuring the resonant frequency at each power point. Quality Factor Frequency fluctuation and fitting residuals.

[0180] Establish a power-dependent frequency uncertainty model: in, Indicates microwave transmission power Effective frequency uncertainty under the following conditions This indicates the frequency fitting uncertainty caused by insufficient signal-to-noise ratio when the power is too low. This indicates the uncertainty caused by microwave disturbances or thermal effects when the power is too high. This represents the fundamental uncertainty, which is independent of power.

[0181] Based on the fitting of experimental data, the following was obtained. , , Then calculate the optimal microwave transmission power. : If the microwave power in the actual device is expressed in dBm, then... Convert to: The optimal microwave power is expressed in dBm. This is the optimal microwave transmission power.

[0182] At the optimal microwave transmission power, the following should be satisfied: in for The signal-to-noise ratio is below. It is the lower limit threshold of the signal-to-noise ratio, that is, the minimum signal-to-noise ratio required to ensure that the resonance peak can be stably identified and the frequency can be reliably fitted. To achieve optimal microwave transmission power At that time, the quality factor of the corresponding resonant mode of the microwave resonant cavity; This is the lower limit threshold of the quality factor, which is the minimum quality factor required to ensure the stability of the resonant mode and the accurate fitting of the resonant peak. To achieve optimal microwave transmission power Effective frequency uncertainty at time To achieve a microwave transmission power of Effective frequency uncertainty at time.

[0183] By applying the above conditions, the optimal transmission power can be obtained that ensures both microwave signal strength and reduces microwave-related uncertainties.

[0184] This method can avoid insufficient signal caused by excessively low microwave power, and can also avoid additional disturbances caused by excessively high microwave power.

[0185] 4. Pressure Static Pressure Difference Correction Optimization In a pressure measurement system, if there is a height difference between the pressure measurement point and the effective measurement center of the resonant cavity... Then calculate the static pressure difference correction. : in To measure gas density, For local gravitational acceleration, The effective pressure inside the resonant cavity is obtained by considering the height difference. : If structural optimization makes: but: At this time, the static pressure difference The effect on thermodynamic temperature is significantly reduced.

[0186] If the height difference cannot be eliminated structurally, then it can be addressed by raising the height. , and To reduce correction uncertainty by ensuring the accuracy of the determination: Uncertainty corrected for static pressure difference. For local gravitational acceleration, For height difference, To measure the uncertainty of gas density, To measure gas density, The uncertainty is the height difference between the pressure measurement point and the effective measurement center of the resonant cavity. This represents the uncertainty of the local gravitational acceleration.

[0187] Incorporate it into the final pressure uncertainty: in, The uncertainty of the effective pressure inside the resonant cavity. To account for the uncertainty of the measured pressure, Uncertainty corrected for static pressure difference. To correct for uncertainty in pipeline pressure drop, The pressure uncertainty is corrected for by the temperature gradient. Uncertainty for dynamic disturbance correction, To correct for pressure gauge drift uncertainty.

[0188] This implementation method can improve the accuracy of the effective pressure inside the resonant cavity and reduce the influence of pressure factors on the thermodynamic temperature measurement results.

[0189] 5. Finding the optimal operating point using a three-dimensional response surface Three main optimization variables are selected: in, This refers to microwave transmission power. For pressure correction residuals, For reference temperature stability.

[0190] Establish a three-dimensional response surface: Combined experiments were conducted on various parameters to obtain the thermodynamic temperature uncertainty at different operating points. The lowest point on the response surface is the optimal operating point. If a quadratic response surface model is used, then: in, For response surface model functions, , , , , , , , , , These represent the weight coefficients of each item and the interaction term, respectively. , , It reflects the coupling effect between microwave power, pressure correction and temperature stability.

[0191] When the optimal point satisfies: When the constraints of temperature stability, pressure stability, and microwave signal stability are met, the optimal operating parameters of the device are determined.

[0192] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention models and optimizes the temperature control system, pressure control system, and microwave resonant frequency measurement system as a unified measurement system, rather than adjusting temperature, pressure, or frequency separately. By establishing functional relationships between thermodynamic temperature and reference temperature, effective pressure within the resonant cavity, microwave resonant frequency, temperature-related correction terms, pressure-related correction terms, and frequency-related correction terms, the combined effect of these three measurement factors on the thermodynamic temperature result can be described, thereby improving the completeness and reliability of the overall measurement model of the constant-pressure gas refractive index reference temperature measurement device.

[0193] 2. This invention can quantitatively evaluate the contribution of different influencing factors to thermodynamic temperature measurement results. By establishing an uncertainty propagation model and calculating the sensitivity coefficients and contribution ratios of factors such as temperature, pressure, frequency, static pressure difference correction, microwave power influence, and resonance peak fitting error, the primary and secondary relationships of each error source in the final thermodynamic temperature uncertainty can be clarified, avoiding relying solely on experience to determine the optimization direction and improving the pertinence of temperature measurement system parameter optimization.

[0194] 3. This invention can reduce the mutual interference caused by the coupling and integration of the temperature control, pressure control, and microwave frequency measurement systems. By introducing a coupling strength evaluation function, the cross-influence between temperature and pressure, temperature and frequency, and pressure and frequency is analyzed. By adjusting the operating parameters with weak coupling as the optimization goal, the mutual interference between the subsystems after system integration can be reduced, allowing the device to carry out thermodynamic temperature measurement in a more stable and coordinated state.

[0195] 4. This invention can reasonably determine microwave transmission power. Addressing the issues of insufficient signal strength and unstable frequency fitting when microwave power is too low, and the potential introduction of microwave thermal disturbances, mode disturbances, or additional frequency shifts when microwave power is too high, this invention establishes a relationship model between microwave transmission power and frequency measurement uncertainty. While ensuring the resonant signal strength and signal-to-noise ratio, it reduces the additional uncertainty introduced by microwave power to the temperature measurement results, thereby obtaining more reasonable microwave frequency measurement parameters.

[0196] 5. This invention can improve the accuracy of determining the effective pressure within the resonant cavity. By incorporating factors such as pressure gauge readings, static pressure difference, pipeline pressure drop, temperature gradient, and pressure drift into the effective pressure correction model, the error caused by the inconsistency between the pressure measurement point and the effective measurement area of ​​the resonant cavity can be reduced, thus mitigating the impact of insufficient pressure correction on the thermodynamic temperature inversion results.

[0197] 6. This invention can determine the optimal operating point through multi-parameter response surface optimization. By incorporating key parameters such as microwave transmission power, pressure correction parameters, and temperature stability into the same optimization space, a thermodynamic temperature uncertainty response surface is established. The optimal parameter combination is determined with the goal of minimizing temperature measurement uncertainty. This allows the device to move beyond single-factor local optimization and achieve an overall optimal operating state oriented towards the final temperature measurement result.

[0198] 7. This invention can improve the accuracy, repeatability, and traceability of thermodynamic temperature measurements. After contribution ratio analysis, dominant factor identification, single-factor optimization, multi-parameter response surface optimization, and weak coupling verification, it can effectively reduce the influence of major error sources and system coupling terms on the temperature measurement results, resulting in lower uncertainty and better repeatability of the output thermodynamic temperature results. It is suitable for high-accuracy thermodynamic temperature measurement, low-temperature scale reproduction, temperature value traceability, and international temperature scale revision experiments.

[0199] This invention is not limited to the specific embodiments described above, and may also have the following alternatives and extended uses: 1. The working gas applicable to this invention is not limited to helium. Neon, argon, hydrogen, or other high-purity gases suitable for refractive index-based temperature measurement can also be selected depending on the temperature measurement zone, pressure range, dielectric properties, and experimental conditions. For different working gases, only the corresponding dielectric virial coefficient, gas law, compressibility factor model, and related correction parameters need to be replaced according to their physical properties to extend the temperature measurement model and uncertainty analysis method of this invention to the corresponding gas system.

[0200] 2. The microwave resonant cavity structure used in this invention is not limited to a spherical microwave resonant cavity. Quasi-spherical microwave resonant cavities, cylindrical microwave resonant cavities, or other microwave cavity structures with stable resonant modes and accurate characterization of the cavity's electromagnetic properties can also be used. As long as the cavity can provide a repeatable resonant frequency and an effective resonant frequency can be obtained through appropriate cavity deformation, boundary conditions, electromagnetic losses, and mode perturbation corrections, it can be used to realize the gas refractive index measurement and thermodynamic temperature inversion described in this invention.

[0201] 3. The pressure measurement method described in this invention is not limited to piston-type pressure gauges; capacitive diaphragm pressure gauges, resonant pressure gauges, or other high-accuracy pressure sensors can also be used for pressure measurement. Different pressure measurement devices can establish corresponding pressure correction models based on their range, accuracy, stability, and calibration methods. As long as the pressure measurement value, pressure correction term, and its uncertainty can be obtained, they can be incorporated into the effective pressure calculation and uncertainty propagation analysis process described in this invention.

[0202] 4. The temperature measurement method used for reference or auxiliary measurement in this invention is not limited to a single type of low-temperature thermometer. Standard platinum resistance thermometers, rhodium-iron resistance thermometers, ruthenium oxide resistance thermometers, capsule-type standard platinum resistance thermometers, or other thermometers suitable for the corresponding low-temperature range can be used. Different thermometers can be selected based on factors such as their calibration results, temperature range applicability, stability, and self-heating effect. Their measurement results can be used as reference temperatures, temperature control feedback quantities, or auxiliary correction quantities to improve the system's measurement stability and the reliability of model inversion.

[0203] 5. The method for determining the optimal operating point described in this invention is not limited to a specific optimization algorithm. Methods such as grid search, least squares response surface methodology, gradient descent, genetic algorithm, particle swarm optimization, Bayesian optimization algorithm, or neural network surrogate model can be selected based on experimental complexity, computational resources, and the form of the objective function. All of the above algorithms can be used to establish the response relationship between measurement parameters and thermodynamic temperature uncertainty, and to search for the optimal operating point while satisfying stability, weak coupling conditions, and experimental constraints.

[0204] 6. The optimization objective described in this invention is not limited to minimizing the uncertainty of thermodynamic temperature measurement. It can also incorporate indicators such as measurement time, system settling time, energy consumption, signal-to-noise ratio, quality factor of the resonance peak, pressure stability, frequency repeatability, and temperature control stability, based on actual application requirements, to construct a single-objective or multi-objective optimization model. By weighting, constraining, or performing Pareto optimality analysis on each optimization indicator, comprehensive optimization of measurement accuracy, measurement efficiency, and system operational stability can be achieved.

[0205] 7. In addition to its application in isobaric gas refractive index reference temperature measurement, this invention can also be extended to fields such as isovolic gas refractive index temperature measurement, microwave cavity gas density measurement, low-temperature dielectric constant measurement, pressure reference comparison, gas equation of state verification, and low-temperature temperature scale reproduction. By establishing and correcting the functional relationship between gas refractive index, pressure, temperature, and microwave resonant frequency, this invention can provide a highly accurate measurement method for low-temperature thermodynamic temperature measurement, gas property research, and metrological reference comparison.

[0206] Figure 4 This is the second flowchart illustrating the multi-parameter weak coupling optimization temperature measurement method for the constant-pressure gas refractive index reference temperature measurement device provided by this invention. Figure 4 As shown, the method includes: The process begins by establishing a measurement model for a constant-pressure gas refractive index reference temperature measuring device; collecting baseline data such as temperature, pressure, and frequency; calculating the corrected effective pressure and effective frequency; inverting the gas refractive index and thermodynamic temperature; establishing an error propagation and contribution ratio model; identifying the dominant influencing factors based on the uncertainty ratio; optimizing the temperature control, pressure control, and microwave frequency measurement parameters respectively; establishing a multi-parameter response surface model; and determining the optimal operating point.

[0207] Then proceed to the judgment step: determine whether the weak coupling and uncertainty meet the requirements.

[0208] If the judgment result is not satisfied, then return to optimize the temperature control, pressure control and microwave frequency measurement parameters respectively.

[0209] If the judgment result is satisfied, the thermodynamic temperature and its uncertainty are output.

[0210] The process is complete.

[0211] The following describes the multi-parameter weak coupling optimization temperature measurement device for constant pressure gas refractive index reference temperature measurement provided by the present invention. The multi-parameter weak coupling optimization temperature measurement device for constant pressure gas refractive index reference temperature measurement described below and the multi-parameter weak coupling optimization temperature measurement method for constant pressure gas refractive index reference temperature measurement described above can be referred to in correspondence with each other.

[0212] Figure 5 This is a schematic diagram of the multi-parameter weakly coupled optimized temperature measurement device for a constant-pressure gas refractive index reference temperature measurement device provided by the present invention, as shown below. Figure 5 As shown, the multi-parameter weakly coupled optimized temperature measuring device 500 for a constant-pressure gas refractive index reference temperature measuring device includes: The measurement model establishment module 510 is used to establish a measurement model of the constant pressure gas refractive index reference temperature measuring device, and incorporates the temperature control system, pressure control system and microwave resonant frequency measurement system into the measurement model. The error propagation and contribution ratio model establishment module 520 is used to establish an error propagation model and a contribution ratio model based on the measurement model, and to calculate the contribution ratio of each influencing factor to the thermodynamic temperature; the influencing factors include temperature, pressure, frequency and correction terms; The single-factor optimization module 530 is used to identify the dominant factor that has the greatest impact on the thermodynamic temperature measurement among the various influencing factors according to the contribution ratio of each of the influencing factors, and to perform single-factor optimization on temperature stability, pressure stability and microwave transmission power according to the dominant factor, so as to obtain the optimization results of each single factor. The parameter optimization module 540 is used to establish a multi-parameter response surface model with the microwave transmission power, the pressure stability and the temperature stability as optimization variables based on the measurement model and the optimization results of each single factor, and to determine the optimal combination of operating parameters that minimizes the standard uncertainty of thermodynamic temperature through the optimization method. The weak coupling verification and output module 550 is used to perform weak coupling verification using the optimal combination of operating parameters. If the verification is successful, the module performs measurement using the optimal combination of operating parameters and outputs the thermodynamic temperature measurement result and the uncertainty of the thermodynamic temperature measurement result.

[0213] This invention integrates the temperature control system, pressure control system, and microwave resonant frequency measurement system into a unified measurement model, establishes an error propagation and contribution ratio model, identifies dominant factors based on contribution ratios, conducts single-factor optimization, constructs a multi-parameter response surface model for global optimization, and finally verifies the effectiveness of optimization through weak coupling, forming a complete closed-loop process of "modeling → quantification → identification → optimization → verification". This process restores and improves the thermodynamic temperature measurement accuracy that was originally reduced due to the coupling of the three systems. Specifically, the mutual interference between the three systems is quantified and suppressed, the dominant error source is accurately identified and optimized in a targeted manner, and finally, the temperature measurement uncertainty is minimized under the globally optimal combination of operating parameters. It transforms the negative factor of "three-system coupling" that originally led to the decrease in temperature measurement accuracy into a controllable object that can be effectively identified, quantified, and suppressed through a systematic modeling, quantification, and optimization process, thereby substantially improving the thermodynamic temperature measurement accuracy of the constant-pressure gas refractive index reference temperature measurement device.

[0214] Figure 6 This is a schematic diagram of the structure of the electronic device provided by the present invention, such as... Figure 6As shown, the electronic device may include a processor 610, a communication interface 620, a memory 630, and a communication bus 640. The processor 610, communication interface 620, and memory 630 communicate with each other via the communication bus 640. The processor 610 can call logic instructions from the memory 630 to execute a multi-parameter weakly coupled optimized temperature measurement method for a constant-pressure gas refractive index reference temperature measurement device.

[0215] Furthermore, the logical instructions in the aforementioned memory 630 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0216] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer is able to execute the multi-parameter weakly coupled optimized temperature measurement method of the constant pressure gas refractive index reference temperature measuring device provided by the above methods.

[0217] In another aspect, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the multi-parameter weakly coupled optimized temperature measurement method of the constant pressure gas refractive index reference temperature measuring device provided by the above methods.

[0218] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0219] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0220] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-parameter weakly coupled optimized temperature measurement method for a constant-pressure gas refractive index reference temperature measuring device, characterized in that, include: A measurement model for a constant-pressure gas refractive index reference temperature measuring device is established, incorporating a temperature control system, a pressure control system, and a microwave resonant frequency measurement system into the measurement model. Based on the measurement model, an error propagation model and a contribution ratio model are established to calculate the contribution ratio of each influencing factor to the thermodynamic temperature; the influencing factors include temperature, pressure, frequency, and correction terms. Based on the contribution ratio of each of the aforementioned influencing factors, the dominant factor with the greatest impact on the thermodynamic temperature measurement is identified. Then, based on the dominant factor, single-factor optimization is performed on temperature stability, pressure stability, and microwave transmission power to obtain the optimization results for each single factor. Based on the measurement model and the optimization results of each single factor, a multi-parameter response surface model is established with the microwave transmission power, pressure stability, and temperature stability as optimization variables. An optimization method is then used to determine the optimal combination of operating parameters that minimizes the thermodynamic temperature standard uncertainty. This determination includes: determining a comprehensive objective function; the comprehensive objective function includes a square term for the thermodynamic temperature standard uncertainty, a square term for the difference between the measured thermodynamic temperature and the reference temperature, a coupling strength function term, and a single-point measurement time term; the operating parameter combination that minimizes the comprehensive objective function is determined as the optimal operating parameter combination. Weak coupling verification is performed using the optimal combination of operating parameters. If the verification is successful, the measurement is performed using the optimal combination of operating parameters, and the thermodynamic temperature measurement result and the uncertainty of the thermodynamic temperature measurement result are output.

2. The multi-parameter weak coupling optimized temperature measurement method for the constant-pressure gas refractive index reference temperature measuring device according to claim 1, characterized in that, The calculation of the contribution percentage of each influencing factor to the thermodynamic temperature includes: Calculate the sensitivity coefficient of each of the aforementioned influencing factors to the thermodynamic temperature; the sensitivity coefficient is obtained using the finite difference method. The contribution percentage is obtained by dividing the product of the square of each sensitivity coefficient and the square of the standard uncertainty of each sensitivity coefficient by the square of the standard uncertainty of the thermodynamic temperature.

3. The multi-parameter weak coupling optimized temperature measurement method for the constant-pressure gas refractive index reference temperature measuring device according to claim 1, characterized in that, The weak coupling verification using the optimal combination of operating parameters includes: Calculate the optimized coupling strength and the unoptimized coupling strength; the coupling strength is evaluated in the following way: the coupling strength coefficient between any two influencing factors is the product of the absolute value of the second partial derivative of the two influencing factors and the standard uncertainty of each influencing factor; the overall coupling strength is the sum of the normalized coupling strength coefficients of all pairwise combinations of influencing factors, and the normalized coupling strength coefficient is the coupling strength coefficient divided by the thermodynamic temperature standard uncertainty; Verify whether the optimized coupling strength is less than the unoptimized coupling strength, and whether the optimized temperature measurement uncertainty is less than the unoptimized temperature measurement uncertainty.

4. The multi-parameter weak coupling optimized temperature measurement method for the constant-pressure gas refractive index reference temperature measuring device according to claim 1, characterized in that, The process of identifying the dominant factor with the greatest impact on the thermodynamic temperature measurement among the various influencing factors based on their contribution ratio includes: The influencing factors are ranked according to their respective contribution percentages; Based on the ranking results, the dominant factors are identified.

5. The multi-parameter weak coupling optimized temperature measurement method for the constant-pressure gas refractive index reference temperature measuring device according to claim 1, characterized in that, If the verification is successful, the optimal combination of operating parameters is used for measurement, and the thermodynamic temperature measurement result and the uncertainty of the thermodynamic temperature measurement result are output, including: If the verification is successful, the optimal combination of operating parameters is used for measurement to obtain the thermodynamic temperature measurement result and the uncertainty of the thermodynamic temperature measurement result; Under the condition that the temperature stability criterion, pressure stability criterion, microwave signal stability criterion, and weak coupling criterion are satisfied, the thermodynamic temperature measurement result and the uncertainty of the thermodynamic temperature measurement result are output.

6. The multi-parameter weak coupling optimized temperature measurement method for the constant-pressure gas refractive index reference temperature measuring device according to claim 1, characterized in that, Before establishing the error propagation model and contribution ratio model based on the measurement model, and calculating the contribution ratio of each influencing factor to the thermodynamic temperature, the method further includes: Baseline data was acquired under initial operating conditions; the baseline data included reference temperature, measured pressure, measured frequency, signal-to-noise ratio, quality factor, temperature fluctuation, pressure fluctuation, and frequency repeatability. The measured pressure is corrected by static pressure difference, pipeline pressure drop, temperature gradient, dynamic disturbance, and pressure drift to obtain the effective pressure inside the resonant cavity; The measured frequency is corrected by resonant peak fitting, microwave power, mode, transmission line, and frequency drift to obtain the effective frequency; The gas refractive index is calculated based on the cavity frequency and the filling frequency. The thermodynamic temperature is obtained by inversion based on the gas refractive index, the effective pressure inside the resonant cavity, and the gas state model. Both the cavity frequency and the filling frequency are determined based on the effective frequency. The thermodynamic temperature is used to calculate each sensitivity coefficient and each contribution percentage.

7. The multi-parameter weak coupling optimized temperature measurement method for the constant-pressure gas refractive index reference temperature measuring device according to claim 6, characterized in that, The effective pressure inside the resonant cavity is expressed as the sum of the measured pressure and the static pressure difference correction, the pipeline pressure drop correction, the pressure correction caused by the temperature gradient, the dynamic disturbance correction, and the pressure gauge drift correction; the static pressure difference correction is determined based on the product of the measured gas density, the local gravitational acceleration, and the height difference between the pressure measurement point and the effective measurement center of the resonant cavity.

8. The multi-parameter weak coupling optimized temperature measurement method for the constant-pressure gas refractive index reference temperature measuring device according to claim 1, characterized in that, Based on the aforementioned dominant factors, single-factor optimization of microwave transmission power is performed to obtain the single-factor optimization results, including: If the dominant factor is the frequency, establish a relationship model between the microwave transmission power and the frequency measurement uncertainty; the relationship model includes: a frequency fitting uncertainty term caused by insufficient signal-to-noise ratio when the power is too low, an uncertainty term caused by microwave disturbance or thermal effect when the power is too high, and a basic uncertainty term unrelated to the power; With the goal of minimizing the standard uncertainty of the thermodynamic temperature, the optimal microwave power that satisfies the constraints is determined by solving the relational model. The constraints include: the signal-to-noise ratio is not lower than the signal-to-noise ratio threshold, the quality factor is not lower than the quality factor threshold, and the power correction amount does not exceed the power correction threshold.

9. A multi-parameter weakly coupled optimized temperature measurement device for a constant-pressure gas refractive index reference temperature measurement device, characterized in that, include: The measurement model establishment module is used to establish a measurement model for a constant-pressure gas refractive index reference temperature measuring device, and incorporates the temperature control system, pressure control system and microwave resonant frequency measurement system into the measurement model. The error propagation and contribution ratio model building module is used to build an error propagation model and a contribution ratio model based on the measurement model, and to calculate the contribution ratio of each influencing factor to the thermodynamic temperature; the influencing factors include temperature, pressure, frequency and correction terms; The single-factor optimization module is used to identify the dominant factor that has the greatest impact on the thermodynamic temperature measurement among the influencing factors according to the contribution ratio of each of the influencing factors, and to perform single-factor optimization on temperature stability, pressure stability and microwave transmission power according to the dominant factor to obtain the optimization results of each single factor. The parameter optimization module is used to establish a multi-parameter response surface model with the microwave transmission power, pressure stability, and temperature stability as optimization variables based on the measurement model and the optimization results of each single factor. It then uses an optimization method to determine the optimal combination of operating parameters that minimizes the standard uncertainty of thermodynamic temperature. Specifically, the parameter optimization module is used to determine the comprehensive objective function. This comprehensive objective function includes a square term for the standard uncertainty of thermodynamic temperature, a square term for the difference between the measured thermodynamic temperature and the reference temperature, a coupling strength function term, and a single-point measurement time term. The combination of operating parameters that minimizes the comprehensive objective function is determined as the optimal combination of operating parameters. The weak coupling verification and output module is used to perform weak coupling verification using the optimal combination of operating parameters. If the verification is successful, the module performs measurement using the optimal combination of operating parameters and outputs the thermodynamic temperature measurement result and the uncertainty of the thermodynamic temperature measurement result.

10. The multi-parameter weakly coupled optimized temperature measuring device for a constant-pressure gas refractive index reference temperature measuring device according to claim 9, characterized in that, The error propagation and contribution ratio model establishment module is specifically used for: Calculate the sensitivity coefficient of each of the aforementioned influencing factors to the thermodynamic temperature; the sensitivity coefficient is obtained using the finite difference method. The contribution percentage is obtained by dividing the product of the square of each sensitivity coefficient and the square of the standard uncertainty of each sensitivity coefficient by the square of the standard uncertainty of the thermodynamic temperature.

11. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the multi-parameter weak coupling optimization temperature measurement method of the constant pressure gas refractive index reference temperature measuring device as described in any one of claims 1 to 8.

12. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the multi-parameter weak coupling optimization temperature measurement method of the constant pressure gas refractive index reference temperature measuring device as described in any one of claims 1 to 8.

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