A natural cooling kinetics-based dilution refrigerator thermometer in-situ calibration system

Abstract

The present application relates to dilution refrigerator temperature calibration technical field, and disclose a kind of dilution refrigerator thermometer in situ calibration system based on natural cooling dynamics, comprising: according to the dynamics equation of cooling power and temperature Curvature is calculated, according to the temperature corresponding to thermometer resistance value, the temperature is substituted into temperature curvature, and the calibration function of resistance value and temperature is obtained;Identify the multivalued region of temperature, and evolve multiple branch functions in multivalued region in calibration function, calculate the deviation measure of each branch function and calibration function;In multivalued region, the support degree of each branch function to calibration function is calculated, and real-time data is obtained by adjusting calculation load, to minimize the number of experiments to verify calibration function;According to the branch verification result of multivalued region, dynamically adjust the verification strategy of non-multivalued region, under the premise of not relaxing calibration accuracy, through dynamics branch and load guide, significantly reduce the repeated experiment cost of dilution refrigerator cryogenic calibration.

Description

Technical Field

[0001] This invention relates to the field of temperature calibration technology for dilution refrigerators, specifically to an in-situ calibration system for a dilution refrigerator thermometer based on natural cooling dynamics. Background Technology

[0002] Dilution refrigerators are widely used in low-temperature experiments to achieve milliKelvin-level cooling. Their thermometers are usually measured by changes in resistance. The cooling process in the low-temperature region has obvious dynamic characteristics, and the temperature changes nonlinearly with time. Moreover, the same resistance value may correspond to different temperature evolution paths, which poses challenges to in-situ calibration and real-time verification.

[0003] Existing thermometer calibration techniques for dilution refrigerators typically rely on a limited number of discrete calibration points or empirical curves to establish a resistance-temperature mapping relationship. This makes it difficult to continuously characterize the dynamic evolution of temperature, resistance, and their relationship during natural cooling, leading to decreased calibration accuracy in low-temperature regions where cooling rates change rapidly or thermal inertia is significant. Current techniques generally neglect the nonlinear dynamic characteristics between cooling power and temperature below 100 mK and fail to model the first and second derivatives of temperature, resulting in ineffective constraint on temperature curvature changes and impacting calibration accuracy in low-temperature regions. Existing techniques also face difficulties in verifying multi-value regions: the same resistance value may correspond to different temperatures under different cooling paths or experimental conditions, and single-point verification results are prone to large fluctuations and are difficult to reproduce. Furthermore, existing techniques lack methods for identifying the temperature evolution state in multi-value regions, making it impossible to determine the specific temperature branch corresponding to a given measurement point. This makes it difficult to use observational data from multi-value regions as reliable verification data, requiring verification of the calibration function through repeated experiments or extended stabilization times. This verification process is costly, time-consuming, and the results are significantly affected by the cooling path and initial conditions, failing to meet the needs for rapid in-situ calibration in low-temperature regions.

[0004] This proposal suggests an in-situ calibration system for a dilution refrigeration thermometer based on natural cooling dynamics. Summary of the Invention

[0005] This invention provides an in-situ calibration system for a dilution refrigeration thermometer based on natural cooling kinetics, which helps to solve the problems mentioned in the background art.

[0006] This invention provides the following technical solution: an in-situ calibration system for a dilution refrigeration thermometer based on natural cooling kinetics, comprising:

[0007] The temperature and cooling power mapping module is used to calculate the temperature curvature based on the dynamic equation of cooling power and temperature. Based on the temperature corresponding to the resistance value of the thermometer, the temperature is substituted into the temperature curvature to obtain the calibration function of resistance value and temperature.

[0008] The temperature evolution branch discrimination module is used to identify the multi-value region of temperature, and evolve the calibration function into multiple branch functions within the multi-value region, and calculate the deviation measure between each branch function and the calibration function;

[0009] The branch verification and load adjustment module is used to calculate the support of each branch function for the calibration function in the multi-value region, adjust the computational load to obtain real-time data, and minimize the number of experiments to verify the calibration function.

[0010] The non-multi-value area validation strategy optimization module is used to dynamically adjust the validation strategy for non-multi-value areas based on the branch validation results of multi-value areas, so as to reduce the number of repeated validations.

[0011] Optionally, the temperature and cooling power mapping module is used to calculate the temperature curvature based on the dynamic equations of cooling power and temperature, including:

[0012] The equation relating the cooling power of the dilution refrigerator to temperature exhibits nonlinear characteristics in the low-temperature region;

[0013] The low temperature region indicates the following;

[0014] ,in, To dilute the cooling power of the refrigeration unit, For temperature, These are constants related to the dilution refrigerator, used to represent the characteristics of the dilution refrigerator;

[0015] Calculate the curvature of temperature change over time: , and These are the thermal response constant and the heat capacity, respectively.

[0016] Substituting the cooling power into the curvature, we get: ;

[0017] The derivative of curvature is calculated to obtain: ;

[0018] right Differentiation yields: ;

[0019] Substituting the curvature formula, we get: This is used to indicate the rate at which temperature changes over time. For time.

[0020] Optionally, the step of substituting the temperature into the temperature curvature based on the temperature corresponding to the thermometer resistance value to obtain the calibration function of resistance value and temperature includes:

[0021] Obtain the relationship between the resistance and temperature of the thermometer when there is no external heating source: ,in, For temperature The corresponding resistance value at that time The resistance value at the reference temperature. The temperature coefficient of resistance;

[0022] Calculating temperature using resistance value: ;

[0023] The calibration function is used to describe the constraints on resistance and temperature during the cooling process using a dilution refrigerator;

[0024] Substituting the temperature into the curvature yields a calibration function for temperature and resistance. , and These are the first and second derivatives of temperature, respectively.

[0025] Optionally, the temperature evolution branch discrimination module is used to identify multi-value regions of temperature, and within these regions, evolve the calibration function into multiple branch functions, calculating the deviation metric between each branch function and the calibration function, including:

[0026] Real-time recording during the operation of the dilution refrigeration unit The resistance value of the thermometer at any time ;

[0027] Real-time recording Temperature of the thermometer ;

[0028] If a resistance value exists Corresponding to multiple temperatures and satisfying the calibration function If there are constraints, then determine the resistance value. The time interval in question is a multi-value region;

[0029] Obtain the resistance value at the starting point of the multi-value region. and corresponding multiple temperature values ,in, For the i-th temperature, according to The multiple branch functions for the evolution of the multivalued region are as follows:

[0030] Define any candidate first derivative ;

[0031] Construct a system of equations: , , Solving the system of equations in the multi-valued region yields the temperature that conforms to the calibration function. , which serves as the i-th branch function in the evolution of the calibration function;

[0032] calculate inverse mapping Obtain the resistance value Calculate the resistance deviation term This is used to describe the degree of deviation between the resistance of the branch function and the measured resistance value;

[0033] The first and second derivatives of the branch function are denoted as follows: and ;

[0034] Calculate the trend deviation term: , ;

[0035] Calculate the deviation measure based on the resistance deviation term and the trend deviation term. .

[0036] Optionally, the branch verification and load adjustment module is used to calculate the support of each branch function for the calibration function in the multi-value region, adjust the computational load to obtain real-time data, and minimize the number of experiments to verify the calibration function, including:

[0037] Set deviation measurement threshold ;

[0038] calculate Support of branch functions for calibration functions ,in, ;

[0039] Estimate the cost of adjusting computing load Specifically:

[0040] Set up multiple load adjustment modules and calculate the adjustment range as follows: Time-related behavioral costs ,in, This is the amplitude weighting coefficient; the higher the amplitude, the higher the cost.

[0041] Setting the risk of branch confusion caused by load adjustment ;

[0042] , The number of branch functions, These are the predictions for time s before load adjustment. The resistance values ​​of the two branch functions, Predicting the first load after load adjustment The resistance values ​​of the two branch functions, To prevent positive numbers with a denominator of zero;

[0043] ,in, Branch confusion risk to cost Influence weight;

[0044] Set cost threshold ,like If so, adjusting the computing load is prohibited;

[0045] like In the multi-value region, the computational load is adjusted to minimize the number of times the calibration function is repeatedly verified.

[0046] Optionally, adjusting the computational load to acquire real-time data to minimize the number of experiments required to verify the calibration function includes:

[0047] Acquire data from multiple sampling points recorded in real time within a multi-value region. Each data point includes temperature and resistance values. Obtain the highest temperature value. and minimum value ;

[0048] The branching function has a temperature range in the multi-value region, with the temperature range between and The branch function is denoted as the candidate function;

[0049] Define a binary function , This indicates that the candidate function is used to verify the calibration function; otherwise, ;

[0050] Calculation for candidate functions: , ;

[0051] Set probability threshold ;

[0052] The candidate functions used for verifying the calibration function must at least cover The percentage of sampling points, wherein the number of sampling points is fixed in each validation experiment;

[0053] The objective function is obtained by solving for it, and the objective function is used to verify the calibration function;

[0054] Calculate the load adjustment corresponding to the switching of the two objective functions, specifically as follows:

[0055] Obtain two objective functions that intersect. and Adjust the computational load through the intersection point from the objective function Switch to the target function Specifically:

[0056] set up The load adjustment amount at the intersection point is Calculate the first derivative ;

[0057] Objective function at the intersection point and The rates of temperature change are equal: .

[0058] Optionally, the step of adjusting the computational load to acquire real-time data in order to minimize the number of experiments required to verify the calibration function further includes:

[0059] according to The switching condition is solved as follows: , Let be the temperature at the intersection, where These are constants related to the dilution refrigerator when calculating the two objective functions;

[0060] By adjusting the load control Used to complete the task from the objective function Switch to target function , , for The sensitivity to load was fitted experimentally.

[0061] get .

[0062] Optionally, the non-multi-value region verification strategy optimization module is used to dynamically adjust the verification strategy for non-multi-value regions based on the branch verification results of multi-value regions, in order to reduce the number of repeated verifications, including:

[0063] In the multi-value region, if the calibration function constraint is satisfied... If the number of branch functions is 1, then perform non-multi-valued region verification;

[0064] Calculate the confidence level of the objective function against the calibration function. , , This represents the sum of the support of the objective function in this test. For scale parameters;

[0065] Adjust the verification frequency of non-multi-value regions based on the confidence level of multi-value regions. and error threshold Specifically:

[0066] , , This is the default verification frequency for non-multi-value regions. These are the weighting coefficients. Based on the basic error threshold, This is the adjustment coefficient.

[0067] The present invention has the following beneficial effects:

[0068] 1. This in-situ calibration system for dilution refrigerator thermometers based on natural cooling kinetics integrates cooling power, temperature evolution kinetics, and thermometer resistance characteristics into a unified calibration framework, achieving highly consistent and low-interventional in-situ calibration of thermometers in the low-temperature region. By introducing a temperature evolution branch discrimination mechanism, it avoids calibration ambiguity issues caused by traditional single-value fitting methods when multiple solutions exist in the temperature-power relationship. Combined with branch verification and load adjustment modules, it actively controls the system evolution path, causing measured data to converge to the valid branch function, thereby reducing the number of repeated experiments without compromising calibration accuracy. The non-multi-value region verification strategy optimization module can use the verification results from the multi-value region to guide subsequent verification strategies, realizing dynamic allocation of verification resources. It effectively solves the problems of difficult calibration, high verification cost, and unstable data in the low-temperature range of dilution refrigerators, significantly improving calibration efficiency and reliability, and is suitable for long-term online calibration needs in complex low-temperature experimental environments.

[0069] 2. This in-situ calibration system for a dilution refrigerator thermometer based on natural cooling kinetics effectively solves the problem of multiple temperature solutions corresponding to the same resistance during low-temperature cooling by real-time monitoring of thermometer resistance and temperature data and identifying multi-value regions in the resistance-temperature relationship based on calibration function constraints. By introducing a branch function construction mechanism in the multi-value region, multiple temperature evolution paths conforming to kinetic constraints are generated using different candidate values ​​of the first derivative, transforming the originally indistinguishable multi-value state into a quantifiable and comparable set of branches. Through the joint measurement of resistance deviation and trend deviation terms, not only static matching error is considered, but also the consistency of temperature change trends is taken into account, avoiding the instability caused by judging based on a single error index. This significantly improves the precision and reliability of calibration discrimination in the multi-value region, providing a solid data foundation for subsequent branch selection and load adjustment.

[0070] 3. This in-situ calibration system for a dilution refrigerator thermometer based on natural cooling kinetics achieves dynamic verification of the calibration function, rather than traditional static fitting verification, by constructing branch functions in a multi-value region and calculating their support for the calibration function. Within a multi-value region, the same resistance may correspond to multiple temperature branches. If verification relies solely on a single calibration function, the verification results are prone to instability due to path dependence or external disturbances, requiring numerous repeated experiments or extended stabilization times, significantly increasing verification costs. By introducing the concept of branch function support, the temperature evolution path within the multi-value region is treated as a selectable, legitimate evolution trajectory. By calculating the deviation metric between each branch function and the calibration function and converting it into support, the reliability of each branch for the calibration function can be quantified, allowing direct selection of the most meaningful branch for verification within the multi-value region. By adjusting the computational load to change the system's transient evolution conditions, the measured data is more likely to fall into a high-support branch, thus significantly reducing the number of repeated experiments and experimental time without compromising accuracy requirements, thereby improving the efficiency and reliability of in-situ calibration. It avoids the inefficient strategy of relaxing the error threshold or repeating experiments until compliance is achieved, has clear physical constraints and engineering feasibility, and is suitable for rapid and stable thermometer calibration and verification in low-temperature regions.

[0071] 4. This in-situ calibration system for a dilution refrigerator thermometer based on natural cooling kinetics faces the challenge of branch confusion due to the presence of multiple branches in the multi-value region. Blindly adjusting the load could lead to branch confusion, where the system abruptly jumps from one branch to another, distorting the verification results. To address this, a cost function is proposed, quantifying the behavioral costs associated with load adjustment and the risk of branch confusion. A cost threshold is set as a constraint on adjustment decisions. If the threshold is exceeded, load adjustment is prohibited to avoid risk; when within an acceptable range, adjustment is allowed, and the optimal adjustment range is selected to minimize the number of repeated verifications. On one hand, limiting the load adjustment range avoids excessive disturbance to the system, thus maintaining the physical consistency between the calibration function and the branch function. On the other hand, assessing the risk of branch confusion ensures that adjustment does not introduce incorrect branch selection, guaranteeing the repeatability and interpretability of the verification results. This improves verification efficiency, achieving a balance between efficiency and reliability in in-situ calibration in the low-temperature multi-value region and reducing reliance on human experience.

[0072] 5. This in-situ calibration system for a dilution refrigerator thermometer based on natural cooling kinetics achieves global optimization of the calibration process by feeding back the verification results of the multi-value region branch to the verification strategy in the non-multi-value region. When the calibration function in the multi-value region has achieved high confidence, the system can automatically reduce the verification frequency or adjust the error threshold in the non-multi-value region, thereby avoiding unnecessary repeated verification. Conversely, when the confidence is insufficient, a stricter verification strategy is maintained to ensure overall calibration accuracy. This adjustment mechanism allows verification resources to be rationally allocated according to the actual level of uncertainty, significantly improving the efficiency and robustness of the overall calibration process. Compared with fixed-strategy calibration schemes, this method can adapt to different experimental stages and system state changes, reduce reliance on human experience, and improve calibration consistency and automation under long-term operating conditions. Attached Figure Description

[0073] Figure 1 This is a schematic diagram of the system modules of the present invention.

[0074] Figure 2 This is a schematic diagram of the sampling points for the calibration function of this invention.

[0075] Figure 3 This is a schematic diagram of sampling point two for the calibration function of the present invention. Detailed Implementation

[0076] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0077] Example 1, refer to Figure 1 An in-situ calibration system for a dilution refrigerator thermometer based on natural cooling kinetics, comprising:

[0078] In the low-temperature region of a dilution refrigerator, the cooling power and absolute temperature typically follow a power-law relationship. When the system is under natural cooling or quasi-steady-state conditions, the change in cooling power with temperature can be approximated as a deterministic relationship, thus providing a dynamic constraint for temperature-time evolution. Thermometer resistance values ​​only reflect the local temperature of the sensor, and the resistance-temperature relationship in the low-temperature region is highly nonlinear, easily affected by material batches, thermal hysteresis, thermal gradients, self-heating of the measurement, and the external environment. This results in the same resistance value potentially corresponding to different temperatures under different experimental conditions. Therefore, relying solely on thermometer resistance is insufficient to obtain accurate low-temperature temperatures. To achieve accurate temperature measurement in the low-temperature region, the accurately measurable thermometer resistance value is mapped to the absolute temperature of the low-temperature region of the dilution refrigerator, and the thermometer is calibrated and verified in situ in conjunction with the dynamic relationship between cooling power and temperature.

[0079] All temperatures in this plan refer to absolute temperatures;

[0080] The temperature and cooling power mapping module is used to calculate the temperature curvature based on the dynamic equation of cooling power and temperature. Based on the temperature corresponding to the resistance value of the thermometer, the temperature is substituted into the temperature curvature to obtain the calibration function of resistance value and temperature.

[0081] The equation relating the cooling power of the dilution refrigerator to temperature exhibits nonlinear characteristics in the low-temperature region;

[0082] The low temperature region indicates the following;

[0083] ,in, To dilute the cooling power of the refrigeration unit, For temperature, These are constants related to the dilution refrigerator, used to represent the characteristics of the dilution refrigerator;

[0084] Calculate the curvature of temperature change over time: , and These are the thermal response constant and the heat capacity, respectively.

[0085] Substituting the cooling power into the curvature, we get: ;

[0086] The derivative of curvature is calculated to obtain: ;

[0087] right Differentiation yields: ;

[0088] Substituting the curvature formula, we get: This is used to indicate the rate at which temperature changes over time. For time.

[0089] Obtain the relationship between the resistance and temperature of the thermometer when there is no external heating source: ,in, For temperature The corresponding resistance value at that time The resistance value at the reference temperature. The temperature coefficient of resistance;

[0090] Calculating temperature using resistance value: ;

[0091] The calibration function is used to describe the constraints on resistance and temperature during the cooling process using a dilution refrigerator;

[0092] Substituting the temperature into the curvature yields a calibration function for temperature and resistance. , and These are the first and second derivatives of temperature, respectively. The calibration function is a mathematical relationship that maps the resistance value measured by the thermometer to the corresponding absolute temperature. It is used to convert the measurable resistance into a true temperature value and to provide a basis for subsequent temperature measurements in the low-temperature region.

[0093] By calculating the first and second derivatives of temperature, the rate of temperature change and curvature can be obtained, thereby imposing dynamic constraints on the temperature evolution path.

[0094] The temperature evolution branch discrimination module is used to identify the multi-value region of temperature, and evolve the calibration function into multiple branch functions within the multi-value region, and calculate the deviation measure between each branch function and the calibration function;

[0095] Real-time recording during the operation of the dilution refrigeration unit The resistance value of the thermometer at any time ;

[0096] Real-time recording Temperature of the thermometer ;

[0097] If a resistance value exists Corresponding to multiple temperatures and satisfying the calibration function If there are constraints, then determine the resistance value. The time interval in question is a multi-value region;

[0098] The multi-value region originates from the path dependence of thermodynamic state. First, temperature is not the only factor determining resistance. Under different cooling paths or different initial conditions, even if the same temperature is reached, the resistance of the thermometer may be different. Second, the nonlinear effect in the low-temperature region causes the system to branch. In the low-temperature region, the relationship between cooling power and temperature is nonlinear. In addition, the thermal resistance and heat capacity change with temperature, resulting in a nonlinear dynamic process in the temperature evolution.

[0099] The actual measured resistance value may not match the calibration function because the sensor's thermal hysteresis and self-heating are inconsistent, and different cooling paths lead to different thermodynamic states. Therefore, the measured data may deviate from the calibration function in the multi-value region, but this does not mean that the calibration function is wrong. Rather, it shows that the thermometer resistance is not a function of temperature alone, but a function of "temperature + dynamic state".

[0100] This scheme uses not useless data from the deviation calibration, but useful data containing branching information within the deviation calibration data. In other words, even when deviating from the calibration function, the data still evolves within the same physical system, just falling on different branches. These branch data satisfy the same dynamic constraints (e.g., the relationship between cooling power and temperature, and the variation law of the temperature derivative), and therefore can be used to construct branch functions. The branch function gives the true temperature variation law of a certain evolution path, which can be used for:

[0101] By constructing the branch function, a set of legal temperature evolution paths under a given cooling power constraint is predefined for subsequent measured data. When the measured data deviates from the calibration function in the multi-value region, there is no need to restart the verification experiment. Instead, the verification is performed by determining whether the measured data falls within the range of the constructed branch function. This is because, under the condition of keeping the cooling power constant, the temperature deviation from the calibration function often stems from thermal hysteresis, differences in initial conditions, or other non-critical constraint factors. Even if the experiment is restarted, these constraints may still exist, and it cannot be guaranteed that the measured data will necessarily fit the calibration function. By treating the branch function as other reasonable evolution paths under the premise that the cooling power-temperature relationship holds, the waste of time and resources caused by repeated experiments can be avoided, thereby significantly reducing the verification cost while ensuring the effectiveness of the calibration function.

[0102] In this embodiment, refer to Figure 2 The relationship between the sampling point region and the calibration function position is not entirely the same before entering the multi-value region. Due to the difference between the initial thermal state and thermal hysteresis, the legal branch shift is caused by the difference between the initial thermal state and thermal hysteresis. Even if the cooling power is kept consistent, the transient evolution path of the system in the multi-value region may still be different.

[0103] In this embodiment, refer to Figure 3 The relationship between the sampling point region and the calibration function position, the equal power multipath evolution under the superposition of secondary constraint perturbations, the core logic: cooling power determines the dominant dynamic constraint, but there are still a number of secondary constraints in the actual system, such as thermometer self-heating, small fluctuations in measurement current, changes in thermal contact impedance, and external micro-vibrations or electromagnetic disturbances. These factors will not change the cooling power model, but will change the local path of temperature evolution.

[0104] Although the two sampling results differ significantly in numerical distribution, both are legitimate temperature evolution paths formed under the same calibration function and cooling power constraints. They represent specific manifestations of different branch functions within a multi-value region.

[0105] Obtain the resistance value at the starting point of the multi-value region. and corresponding multiple temperature values ,in, For the i-th temperature, according to The evolutionary multi-branch function for the multi-valued region is as follows:

[0106] Define any candidate first derivative ;

[0107] Construct a system of equations: , , Solving the system of equations in the multi-valued region yields the temperature that conforms to the calibration function. , which serves as the i-th branch function in the evolution of the calibration function;

[0108] calculate inverse mapping Obtain the resistance value Calculate the resistance deviation term This is used to describe the degree of deviation between the resistance of the branch function and the measured resistance value;

[0109] The first and second derivatives of the branch function are denoted as follows: and ;

[0110] Calculate the trend deviation term: , ;

[0111] Calculate the deviation measure based on the resistance deviation term and the trend deviation term. .

[0112] The branch verification and load adjustment module is used to calculate the support of each branch function for the calibration function in the multi-value region, adjust the computational load to obtain real-time data, and minimize the number of experiments to verify the calibration function.

[0113] Set deviation measurement threshold ;

[0114] calculate Support of branch functions for calibration functions ,in, Branch functions with low deviation metrics are selected for verification of calibration functions to improve the accuracy of verification.

[0115] Estimate the cost of adjusting computing load Specifically:

[0116] Set up multiple load adjustment modules and calculate the adjustment range as follows: Time-related behavioral costs ,in, This is the amplitude weighting coefficient; the higher the amplitude, the higher the cost.

[0117] Setting the risk of branch confusion caused by load adjustment ;

[0118] , The number of branch functions, These are the predictions for time s before load adjustment. The resistance values ​​of the two branch functions, Predicting the first load after load adjustment The resistance values ​​of the two branch functions, To prevent positive numbers with a denominator of zero;

[0119] ,in, Branch confusion risk to cost Influence weight;

[0120] Set cost threshold ,like If so, adjusting the computing load is prohibited;

[0121] like In the multi-value region, the computational load is adjusted to minimize the number of times the calibration function is repeatedly verified.

[0122] The computational load is the external thermal / electrical load applied to the thermometer or sample platform, including but not limited to resistance heating power, self-consumption power caused by the measurement current, power consumption of external devices, or thermal coupling strength.

[0123] Acquire data from multiple sampling points recorded in real time within a multi-value region. Each data point includes temperature and resistance values. Obtain the highest temperature value. and minimum value ;

[0124] The branching function has a temperature range in the multi-value region, with the temperature range between... and The branch functions are denoted as candidate functions. The purpose of screening candidate functions is to reduce the verification complexity, improve the verification reliability, and ensure that the verification covers the temperature range of the measured data, thereby achieving efficient and reliable calibration function verification in the multi-value region.

[0125] Define a binary function , This indicates that the candidate function is used to verify the calibration function; otherwise, ;

[0126] Calculation for candidate functions: , ;

[0127] Set probability threshold ;

[0128] The candidate functions used for verifying the calibration function must at least cover The percentage of sampling points, wherein the number of sampling points is fixed in each validation experiment;

[0129] The objective function is obtained by solving for it, and the objective function is used to verify the calibration function;

[0130] Calculate the load adjustment corresponding to the switching of the two objective functions, specifically as follows:

[0131] Obtain two objective functions that intersect. and Adjust the computational load through the intersection point from the objective function Switch to target function Specifically:

[0132] set up The load adjustment amount at the intersection point is Calculate the first derivative ;

[0133] Objective function at the intersection point and The rates of temperature change are equal: .

[0134] according to The switching condition is solved as follows: , Let be the temperature at the intersection, where These are constants related to the dilution refrigerator when calculating the two objective functions;

[0135] By adjusting the load control Used to complete the task from the objective function Switch to target function , , for The sensitivity to load was fitted experimentally.

[0136] Switching the objective function at the intersection point can ensure the continuity of the system state, satisfy the calibration function constraints, reduce experimental costs, and ensure controllable load adjustment, making it the most reasonable path to achieve efficient verification in multi-value regions.

[0137] get Unlike amplified errors, this scheme does not expand the error tolerance of the calibration function during load adjustment. Instead, it maintains the original accuracy requirements and verifies the results by guiding the system to evolve along different branch functions. This reduces the number of repeated experiments without sacrificing calibration accuracy.

[0138] Adjusting the computational load is a controllable and repeatable experimental input. Under the premise of keeping the cooling power constant, the system is guided to evolve along different branches, thereby achieving effective verification of the calibration function in the multi-value region. Adjusting the cooling power will change the main constraint conditions, resulting in incomparable verification results and introducing more systematic errors.

[0139] The non-multi-value area validation strategy optimization module is used to dynamically adjust the validation strategy for non-multi-value areas based on the branch validation results of multi-value areas, so as to reduce the number of repeated validations.

[0140] In the multi-value region, if the calibration function constraint is satisfied... If the number of branch functions is 1, then perform non-multi-value region verification, and temperature and resistance calibration functions. The theoretical calibration function constraints describe the strict relationships satisfied by temperature evolution under the ideal dynamic model. However, in actual experimental environments, temperature measurements are subject to noise; resistance measurements have errors; and heat capacity and cooling power fluctuate. Therefore, it is impossible to require strict compliance with these constraints. Set calibration function constraints This is used to determine whether the calibration function constraint is met when measurement error exists; the two correspond to the theoretical model and the actual verification stage, respectively.

[0141] Calculate the confidence level of the objective function against the calibration function. , , This represents the sum of the support of the objective function in this test. For scale parameters;

[0142] Adjust the verification frequency of non-multi-value regions based on the confidence level of multi-value regions. and error threshold Specifically:

[0143] , , This is the default verification frequency for non-multi-value regions. These are the weighting coefficients. Based on the basic error threshold, This is the adjustment coefficient.

[0144] Experimental results show that this invention can significantly improve the verification efficiency and reliability of in-situ calibration of thermometers for dilution refrigerators. Taking multiple independent cooling experiments of a certain model of dilution refrigerator in the low-temperature region (20 mK~100 mK) as an example, the average verification deviation of the traditional single calibration function in the multi-value region is usually in the range of ΔT≈(0.5~2.0) mK (or ΔR≈(0.3~1.2)%), with a verification pass rate of about 40%~60%, and 10~20 repeated experiments are required to achieve acceptable verification results, with verification time usually exceeding 3~6 hours. However, after adopting the branch function verification method of this invention, the average deviation in the multi-value region can be reduced to ΔT≈(0.1~0.4) mK (or ΔR≈(0.05~0.3)%), the verification pass rate is increased to 80%~95%, the average number of repeated experiments is reduced to 2~5, the verification time is shortened to 1~2 hours, and the average number of repeated experiments is reduced by about 60%~80%. By guiding the system along the target branch through load adjustment, the stability of this invention in the multi-value region verification is further improved, and the sensitivity of the verification results to initial conditions and cooling paths is significantly reduced. Therefore, this invention can achieve rapid in-situ calibration in the low-temperature region without compromising calibration accuracy, significantly reducing experimental costs and improving repeatability.

[0145] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0146] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. An in-situ calibration system for a dilution refrigerator thermometer based on natural cooling kinetics, characterized in that: include: The temperature and cooling power mapping module is used to calculate the temperature curvature based on the dynamic equation of cooling power and temperature. Based on the temperature corresponding to the resistance value of the thermometer, the temperature is substituted into the temperature curvature to obtain the calibration function of resistance value and temperature. The temperature evolution branch discrimination module is used to identify the multi-value region of temperature, and evolve the calibration function into multiple branch functions within the multi-value region, and calculate the deviation measure between each branch function and the calibration function; The branch verification and load adjustment module is used to calculate the support of each branch function for the calibration function in the multi-value region, adjust the computational load to obtain real-time data, and minimize the number of experiments to verify the calibration function. The non-multi-value area validation strategy optimization module is used to dynamically adjust the validation strategy for non-multi-value areas based on the branch validation results of multi-value areas, so as to reduce the number of repeated validations.

2. The in-situ calibration system for a dilution refrigerator thermometer based on natural cooling kinetics according to claim 1, characterized in that: The temperature and cooling power mapping module is used to calculate the temperature curvature based on the dynamic equations of cooling power and temperature, including: The equation relating the cooling power of the dilution refrigerator to temperature exhibits nonlinear characteristics in the low-temperature region; The low temperature region indicates the following; ,in, To dilute the cooling power of the refrigeration unit, For temperature, These are constants related to the dilution refrigerator, used to represent the characteristics of the dilution refrigerator; Calculate the curvature of temperature change over time: , and These are the thermal response constant and the heat capacity, respectively. Substituting the cooling power into the curvature, we get: ; The derivative of curvature is calculated to obtain: ; right Differentiation yields: ; Substituting the curvature formula, we get: This is used to indicate the rate at which temperature changes over time. For time.

3. The in-situ calibration system for a dilution refrigerator thermometer based on natural cooling kinetics according to claim 2, characterized in that: The step of substituting the temperature corresponding to the thermometer resistance value into the temperature curvature to obtain the calibration function of resistance value and temperature includes: Obtain the relationship between the resistance and temperature of the thermometer when there is no external heating source: ,in, For temperature The corresponding resistance value at that time The resistance value at the reference temperature. The temperature coefficient of resistance; Calculating temperature using resistance value: ; The calibration function is used to describe the constraints on resistance and temperature during the cooling process using a dilution refrigerator; Substituting the temperature into the curvature yields a calibration function for temperature and resistance. , and These are the first and second derivatives of temperature, respectively.

4. The in-situ calibration system for a dilution refrigerator thermometer based on natural cooling kinetics according to claim 3, characterized in that: The temperature evolution branch discrimination module is used to identify multi-value regions of temperature, and within these regions, evolve the calibration function into multiple branch functions, calculating the deviation metric between each branch function and the calibration function, including: Real-time recording during the operation of the dilution refrigeration unit The resistance value of the thermometer at any time ; Real-time recording Temperature of the thermometer ; If a resistance value exists Corresponding to multiple temperatures and satisfying the calibration function If there are constraints, then determine the resistance value. The time interval in question is a multi-value region; Obtain the resistance value at the starting point of the multi-value region. and corresponding multiple temperature values ,in, For the i-th temperature, according to The multiple branch functions for the evolution of the multivalued region are as follows: Define any candidate first derivative ; Construct a system of equations: , , Solving the system of equations in the multi-valued region yields the temperature that conforms to the calibration function. , which serves as the i-th branch function in the evolution of the calibration function; calculate inverse mapping Obtain the resistance value Calculate the resistance deviation term This is used to describe the degree of deviation between the resistance of the branch function and the measured resistance value; The first and second derivatives of the branch function are denoted as follows: and ; Calculate the trend deviation term: , ; Calculate the deviation measure based on the resistance deviation term and the trend deviation term. .

5. The in-situ calibration system for a dilution refrigerator thermometer based on natural cooling kinetics according to claim 4, characterized in that: The branch verification and load adjustment module is used to calculate the support of each branch function for the calibration function in the multi-value region, adjust the computational load to obtain real-time data, and minimize the number of experiments to verify the calibration function, including: Set deviation measurement threshold ; calculate Support of branch functions for calibration functions ,in, ; Estimate the cost of adjusting computing load Specifically: Set up multiple load adjustment modules and calculate the adjustment range as follows: Time-related behavioral costs ,in, This is the amplitude weighting coefficient; the higher the amplitude, the higher the cost. Setting the risk of branch confusion caused by load adjustment ; , The number of branch functions, These are the predictions for time s before load adjustment. The resistance values ​​of the two branch functions, Predicting the first load after load adjustment The resistance values ​​of the two branch functions, To prevent positive numbers with a denominator of zero; ,in, Branch confusion risk to cost Influence weight; Set cost threshold ,like If so, adjusting the computing load is prohibited; like In the multi-value region, the computational load is adjusted to minimize the number of times the calibration function is repeatedly verified.

6. The in-situ calibration system for a dilution refrigerator thermometer based on natural cooling kinetics according to claim 5, characterized in that: The adjustment of computational load to acquire real-time data, in order to minimize the number of experiments required to verify the calibration function, includes: Acquire data from multiple sampling points recorded in real time within a multi-value region. Each data point includes temperature and resistance values. Obtain the highest temperature value. and minimum value ; The branching function has a temperature range in the multi-value region, with the temperature range between and The branch function is denoted as the candidate function; Define a binary function , This indicates that the candidate function is used to verify the calibration function; otherwise, ; Calculation for candidate functions: , ; Set probability threshold ; The candidate functions used for verifying the calibration function must at least cover The percentage of sampling points, wherein the number of sampling points is fixed in each validation experiment; The objective function is obtained by solving for it, and the objective function is used to verify the calibration function; Calculate the load adjustment corresponding to the switching of the two objective functions, specifically as follows: Obtain two objective functions that intersect. and Adjust the computational load through the intersection point from the objective function Switch to the target function Specifically: set up The load adjustment amount at the intersection point is Calculate the first derivative ; Objective function at the intersection point and The rates of temperature change are equal: .

7. The in-situ calibration system for a dilution refrigerator thermometer based on natural cooling kinetics according to claim 6, characterized in that: The method of adjusting the computational load to acquire real-time data in order to minimize the number of experiments required to verify the calibration function also includes: according to The switching condition is solved as follows: , Let be the temperature at the intersection, where These are constants related to the dilution refrigerator when calculating the two objective functions; By adjusting the load control Used to complete the task from the objective function Switch to the target function , , for The sensitivity to load was fitted experimentally. get .

8. The in-situ calibration system for a dilution refrigerator thermometer based on natural cooling kinetics according to claim 5, characterized in that: The non-multi-value region verification strategy optimization module is used to dynamically adjust the verification strategy for non-multi-value regions based on the branch verification results of multi-value regions, in order to reduce the number of repeated verifications, including: In the multi-value region, if the calibration function constraint is satisfied... If the number of branch functions is 1, then perform non-multi-valued region verification; Calculate the confidence level of the objective function against the calibration function. , , This represents the sum of the support of the objective function in this test. For scale parameters; Adjust the verification frequency of non-multi-value regions based on the confidence level of multi-value regions. and error threshold Specifically: , , This is the default verification frequency for non-multi-value regions. These are the weighting coefficients. Based on the basic error threshold, This is the adjustment coefficient.

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