A multi-state plasma temperature field measurement method

Abstract

The application relates to the technical field of plasma temperature measurement, in particular to a multi-state plasma temperature field measurement method, which comprises the following steps: injecting plasma into a temperature control container; obtaining the plasma temperature value measured by each measuring point at each sampling time to obtain a plasma temperature distribution; obtaining the pressure value in the temperature control container at each sampling time to obtain a container pressure value change curve; according to the plasma temperature distribution, adopting a spatial residual fitting method to obtain a residual spatial distribution; averaging the residual spatial distribution at each sampling time to obtain a first error; according to the plasma temperature distribution and the container pressure value change curve, adopting a joint fitting method to obtain the deviation of the plasma temperature value measured by each measuring point as a second error; and obtaining the total error of the temperature sensor array according to the first error and the second error. The joint correction of the pressure and temperature measurement values can comprehensively reflect the temperature sensor error.

Description

Technical Field

[0001] This invention relates to the field of plasma temperature measurement technology, specifically a multi-state plasma temperature field measurement method. Background Technology

[0002] Plasma freezers are widely used in blood banks and medical institutions for the rapid freezing of plasma products. Plasma needs to be rapidly frozen into blocks at below -30 degrees Celsius after whole blood collection to maximize the preservation of clotting factors and other effective components. To monitor temperature changes during the freezing process, temperature sensors are installed in the plasma freezer for temperature measurement.

[0003] Existing plasma freezers typically employ one or two analog sensors to measure temperature changes at the center of the plasma. This single-point or dual-point measurement method only reflects the local temperature conditions of the plasma and is insufficient to obtain information on the temperature distribution across the entire plasma space. To obtain the spatial distribution of plasma temperature, a sensor array consisting of multiple temperature sensors needs to be arranged within the temperature control container, constructing a plasma temperature field using the temperature values ​​collected at each measurement point. However, due to the inherent error characteristics of multiple temperature sensors, the temperature data measured at different points at the same time may exhibit logical inconsistencies in spatial distribution. Using spatial surface fitting to process the temperature values ​​at each measurement point yields the residuals of each measurement point relative to the fitted surface, reflecting the relative deviations of each sensor. However, spatial fitting methods only reflect the differential deviations between sensors and cannot reflect the systematic deviations that occur in the sensor array under low-temperature conditions. Especially in the cryogenic stage where plasma temperatures drop below -30 degrees Celsius, temperature sensors from the same batch may deviate from the true temperature values ​​as a whole; such systematic deviations cannot be captured by simple spatial fitting methods.

[0004] During the phase transition of plasma from a liquid to a solid state, the plasma volume expands, causing pressure changes within a sealed, temperature-controlled container. These pressure changes are physically related to the plasma's solid-liquid state and average temperature. Current technologies do not utilize pressure change information during the plasma solid-liquid phase transition for joint calibration of sensor arrays, nor do they combine spatial fitting residuals with pressure-temperature joint fitting bias to obtain individual and systematic errors in the sensor array. This makes it difficult to comprehensively characterize and correct the measurement errors of the sensor array. Therefore, a multi-state plasma temperature field measurement method is needed to jointly correct the measured temperature values ​​using both temperature and pressure measurement data. Summary of the Invention

[0005] (1) Technical problems to be solved

[0006] The purpose of this invention is to provide a multi-state plasma temperature field measurement method to realize the error calculation of the temperature sensor used to measure plasma temperature.

[0007] (2) Technical solution To achieve the above objectives, the present invention provides a method for measuring the temperature field of multi-state plasma, the method comprising the following steps: S1, inject plasma into a temperature control container; a temperature sensor array is pre-arranged inside the temperature control container; a cooling source is installed at the bottom of the temperature control container; the temperature of the cooling source is controlled to decrease linearly from high to low; a pressure sensor is installed at the top of the temperature control container.

[0008] S2, set the sampling time according to the preset sampling time interval; at each sampling time, acquire the plasma temperature value measured by each measuring point of the temperature sensor array to obtain the plasma temperature distribution; at each sampling time, acquire the pressure value in the temperature control container through the pressure sensor and fit the container pressure value change curve; the pressure sensor is not submerged in plasma.

[0009] S3. Based on the plasma temperature distribution, a spatial residual fitting method is used to obtain the residual of the plasma temperature value measured at each measurement point at the same sampling time relative to the fitted temperature distribution surface, i.e., the spatial distribution of the residual; the average of the spatial distribution of the residual at each sampling time is used to obtain the first error; based on the plasma temperature distribution and the container pressure value change curve, a joint fitting method is used to obtain the overall deviation of the plasma temperature value measured at each measurement point as the second error.

[0010] S4. The total error of the temperature sensor array is obtained based on the first error and the second error.

[0011] Furthermore, the method of injecting plasma into a temperature-controlled container includes: Plasma is injected into the temperature control container through an injection port located at the top of the container; after the plasma is injected into the temperature control container, the injection port is sealed with a sealing element to form a closed space inside the temperature control container.

[0012] Furthermore, the method for obtaining the residuals of the plasma temperature values ​​measured at each measurement point at the same sampling time relative to the fitted temperature distribution surface, i.e., the spatial distribution of the residuals, based on the plasma temperature distribution, using a spatial residual fitting method, includes: A three-dimensional spatial coordinate system is established with the center of the bottom of the temperature control container as the origin; the spatial position coordinates of each measurement point of the temperature sensor array in the three-dimensional spatial coordinate system are obtained; the plasma temperature values ​​measured at each measurement point at the same sampling time are extracted from the plasma temperature distribution; a polynomial surface fitting method is used to perform least squares fitting on the spatial position coordinates of all measurement points at the same sampling time and the plasma temperature values ​​to obtain a fitted temperature distribution surface; based on the fitted temperature distribution surface, the fitted temperature value corresponding to the spatial position coordinates of each measurement point is calculated; the fitted temperature value corresponding to the spatial position coordinates is subtracted from the plasma temperature value measured at each measurement point to obtain the temperature residual of each measurement point, i.e., the residual spatial distribution.

[0013] Furthermore, the method for averaging the spatial distribution of the residuals at each sampling time to obtain the first error includes: By iterating through all sampling times, the average of the spatial distribution of the residuals corresponding to each sampling time is taken to obtain the first error.

[0014] Furthermore, the method of obtaining the overall deviation of the plasma temperature values ​​measured at each measurement point as the second error by using a joint fitting method based on the plasma temperature distribution and container pressure value change curves includes: The average value of the plasma temperature measured by all measurement points of the temperature sensor array at each sampling time is obtained as the average temperature at that sampling time. Based on the container pressure change curve, a method for identifying abrupt changes in pressure rate is used to obtain the average temperature at the start of plasma coagulation and the average temperature at the end of plasma coagulation, respectively, as the average temperature at the start of coagulation and the average temperature at the end of coagulation. Based on the average temperature at the start of coagulation and the average temperature at the end of coagulation, the average temperature is divided into a liquid zone, a phase transition zone, and a solid zone. Within each of the liquid, phase transition, and solid zones, a fitting relationship between the average temperature and the pressure value is established to obtain the average temperature fitting curves for the liquid zone, phase transition, and solid zones. These curves are then sequentially connected to obtain the overall average temperature fitting curve. The overall deviation of the plasma temperature measured by all measurement points at each sampling time is calculated based on the average temperature at each sampling time and the overall average temperature fitting curve. A second error is obtained based on the overall deviation of the plasma temperature measured by all measurement points at all sampling times.

[0015] Furthermore, the method of obtaining the average temperature corresponding to the start of plasma coagulation and the average temperature corresponding to the complete coagulation of plasma based on the pressure change curve of the container using a pressure change rate abrupt change point identification method, and using these as the average temperature at the start of coagulation and the average temperature at the end of coagulation, respectively, includes: The pressure change curve of the container is differentiated according to a pre-set sliding time window to obtain a pressure change rate curve. The sampling time when the absolute value of the pressure change rate on the pressure change rate curve first exceeds a pre-set first threshold is identified in the order of sampling time from front to back and recorded as the first abrupt change time. From the first abrupt change time, the sampling time when the absolute value of the pressure change rate on the pressure change rate curve last exceeds the first threshold is recorded as the second abrupt change time. The average temperature corresponding to the first abrupt change time is obtained as the solidification start average temperature, and the average temperature corresponding to the second abrupt change time is obtained as the solidification end average temperature.

[0016] Furthermore, the method for dividing the average temperature into a liquid state range, a phase transition range, and a solid state range based on the average solidification initiation temperature and the average solidification end temperature includes: The average temperature above the average temperature at the start of solidification is divided into the liquid phase range; the average temperature below or equal to the average temperature at the start of solidification and above or equal to the average temperature at the end of solidification is divided into the phase transition range; and the average temperature below the average temperature at the end of solidification is divided into the solid phase range.

[0017] Further, the method of establishing fitting relationships between average temperature and pressure values ​​in the liquid region, phase transition region, and solid region respectively, to obtain average temperature fitting curves for the liquid region, phase transition region, and solid region, and then sequentially connecting these average temperature fitting curves to obtain the overall average temperature fitting curve includes: Within the liquid region, a first fitting function is constructed; the first fitting function is expressed as: ; in, Denotes the first fitted function. Indicates the container pressure value. Indicates the first variable to be fitted. This indicates the average temperature at which solidification begins. This represents the container pressure value corresponding to the first abrupt change in the container pressure value change curve.

[0018] Within the phase transition range, a second fitting function is constructed; the second fitting function is expressed as: ; in, This represents the second fitting function. Indicates the second variable to be fitted. This represents the third variable to be fitted.

[0019] Within the solid-state region, a third fitting function is constructed; the third fitting function is expressed as: ; in, This represents the third fitting function. This represents the fourth variable to be fitted. This indicates the average temperature at which solidification ends. This represents the container pressure value corresponding to the second abrupt change moment on the container pressure value change curve.

[0020] Based on the average temperature and pressure data at all sampling times within the liquid region, the first fitting function is applied at point... The residual at point 0 is taken as the first constraint condition. Using the first constraint condition as a constraint, the least squares fitting method is used to obtain the result. The optimal value is denoted as Based on the average temperature and pressure data at all sampling times within the phase transition interval, the second fitting function is used at point... place and point The residuals at each point are all zero, which serves as the second constraint. Using this second constraint as a constraint, the least squares fitting method is employed to obtain the desired result. , The optimal values ​​are denoted as follows: , Based on the average temperature and pressure data at all sampling times within the solid-state region, the third fitting function is used at point... Using the constraint that the residual at point 0 is zero, a constrained least squares fitting method is employed to obtain the result. The optimal value is denoted as ;according to , , , The average temperature fitting curves for the liquid phase, phase transition, and solid phases are obtained, and then sequentially connected to obtain the overall average temperature fitting curve, which is expressed as follows: ; in, This represents the fitted curve of the overall average temperature.

[0021] Further, the method for calculating the overall deviation of the plasma temperature values ​​measured at all measurement points at each sampling time based on the fitting curve between the average temperature at each sampling time and the overall average temperature, and for obtaining the second error based on the overall deviation of the plasma temperature values ​​measured at all measurement points at all sampling times, includes: Substituting the pressure value inside the temperature control container at each sampling time into the overall average temperature fitting curve yields the fitted average temperature at each sampling time. Subtracting the fitted average temperature at each sampling time from the average temperature at that time yields the overall deviation of the plasma temperature values ​​measured at all measurement points at that sampling time. The overall deviation of the plasma temperature values ​​measured at all measurement points at each sampling time is denoted as follows: to ;in, This indicates the number of sampling times; a least squares fitting algorithm is used, with the average temperature at each sampling time as the independent variable and the overall deviation of the plasma temperature values ​​measured at all measurement points at each sampling time as the dependent variable. to The sample points are fitted to obtain the second error; the second error is in the form of a function.

[0022] Furthermore, the method for obtaining the total error of the temperature sensor array based on the first error and the second error includes: Obtain the error value corresponding to each measurement point in the first error; obtain the second error, which is a function with average temperature as the independent variable; superimpose the error value of each measurement point in the first error with the second error to obtain the total error corresponding to each measurement point; take the set of the total errors corresponding to all measurement points as the total error of the temperature sensor array.

[0023] (3) Beneficial effects Compared with the prior art, the beneficial effects of the present invention are: The spatial residual fitting method is used to obtain the first error, which reflects the difference in deviation of each measurement point in the temperature sensor array. The joint fitting method is used to obtain the second error, which reflects the overall systematic deviation of the temperature sensor array. The error values ​​corresponding to each measurement point in the first error are superimposed with the second error to obtain the total error of the temperature sensor array, thus comprehensively characterizing the measurement error of the temperature sensor array. Attached Figure Description

[0024] Figure 1 This is a flowchart of a multi-state plasma temperature field measurement method according to Embodiment 1 of the present invention. Detailed Implementation

[0025] 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.

[0026] Before providing examples, it is necessary to describe the application scenario of this invention, which is applied to the rapid freezing process of plasma in blood banks. During the process of plasma gradually freezing from a liquid to a solid state, the error in the plasma temperature value is calculated using the measured plasma temperature value and the pressure value inside the temperature control container.

[0027] Example 1: As Figure 1 As shown, this embodiment provides a method for measuring the temperature field of multi-state plasma, the method comprising the following steps: S1, inject plasma into a temperature control container; a temperature sensor array is pre-arranged inside the temperature control container; a cooling source is installed at the bottom of the temperature control container; the temperature of the cooling source is controlled to decrease linearly from high to low; a pressure sensor is installed at the top of the temperature control container.

[0028] S2, set the sampling time according to the preset sampling time interval; at each sampling time, acquire the plasma temperature value measured by each measuring point of the temperature sensor array to obtain the plasma temperature distribution; at each sampling time, acquire the pressure value in the temperature control container through the pressure sensor and fit the container pressure value change curve; the pressure sensor is not submerged in plasma.

[0029] S3. Based on the plasma temperature distribution, a spatial residual fitting method is used to obtain the residual of the plasma temperature value measured at each measurement point at the same sampling time relative to the fitted temperature distribution surface, i.e., the spatial distribution of the residual; the average of the spatial distribution of the residual at each sampling time is used to obtain the first error; based on the plasma temperature distribution and the container pressure value change curve, a joint fitting method is used to obtain the overall deviation of the plasma temperature value measured at each measurement point as the second error.

[0030] S4. The total error of the temperature sensor array is obtained based on the first error and the second error.

[0031] For example, plasma is injected into the temperature control container through the injection port at the top of the container. After injection, the injection port is sealed with a sealant to create a closed space inside the container. The temperature control container is a rectangular sealed metal cavity with internal dimensions of 600 mm long, 600 mm wide, and 300 mm high, made of stainless steel. A cooling source, a compressor refrigeration module with a cooling power of 800 watts, is installed at the bottom of the container, exchanging heat with the plasma through a bottom cold plate. A temperature sensor array is pre-arranged inside the container, consisting of 27 platinum resistance temperature sensors in 3 layers. Each layer has 9 sensors evenly distributed in 3 rows and 3 columns. In the first and second layers from top to bottom, 8 of the 9 evenly distributed temperature sensors are located at the edges, all distributed on the inner wall of the rectangular sealed metal cavity of the container. The temperature sensor in the center is fixed inside the container by a bracket. The 9 temperature sensors in the third layer from top to bottom are evenly distributed in a matrix on the bottom surface of the container. In addition, the uppermost temperature sensor's measuring end is located on the plasma surface, with a total plasma height of 270 mm. Overall, the 27 temperature sensors are vertically divided into three layers—upper, middle, and lower—within the temperature control container, located on the plasma surface, in the middle, and at the bottom, respectively, forming a three-dimensional temperature measurement network covering the plasma area. A pressure sensor is installed at the top of the temperature control container. This pressure sensor is a piezoresistive absolute pressure sensor with a range of 0 to 0.5 MPa, installed above the highest plasma level to ensure it is not submerged. The temperature of the cooling source decreases linearly from high to low, starting at 25°C and ending at -60°C, with the entire cooling process lasting 170 minutes.

[0032] Sampling times were set according to a pre-set sampling interval of 30 seconds, starting from second 0, with a sampling time set every 30 seconds, for a total of 341 sampling times during the 170-minute cooling process. At each sampling time, the plasma temperature value measured by 27 measurement points of the temperature sensor array was acquired, resulting in a plasma temperature distribution. The plasma temperature distribution is a 341-row, 27-column data matrix, with each row corresponding to a sampling time and each column corresponding to a measurement point. Each element in the matrix is ​​the plasma temperature value measured at the corresponding measurement point at the corresponding sampling time. At each sampling time, the pressure value inside the temperature control container was acquired via a pressure sensor, resulting in 341 pressure values. Cubic spline interpolation was used to fit the pressure values ​​at the 341 sampling times to obtain a container pressure change curve. The container pressure change curve is a continuous curve, with the horizontal axis representing the sampling time and the vertical axis representing the container pressure value.

[0033] Based on the plasma temperature distribution, a spatial residual fitting method was used. At the same sampling time, a three-dimensional spatial coordinate system was established with the center of the bottom of the temperature control container as the origin. The spatial coordinates of 27 measurement points were obtained. A ternary quadratic polynomial surface fitting method was used to perform least-squares fitting between the spatial coordinates of the 27 measurement points and the plasma temperature values, resulting in the fitted temperature distribution surface for that sampling time. The fitted temperature values ​​of the spatial coordinates of the 27 measurement points on the fitted temperature distribution surface were calculated. The plasma temperature value measured at each measurement point was subtracted from the corresponding fitted temperature value to obtain 27 temperature residuals. These 27 temperature residuals constituted the spatial distribution of the residuals at that sampling time. The spatial distribution of the residuals reflects the differences in deviation between measurement points at the same time. After traversing 341 sampling times, the spatial distribution of the residuals at each sampling time was averaged according to the measurement point positions to obtain the first error. The first error contains 27 error values, each corresponding to one of the 27 measurement points, representing the average deviation of each measurement point across all sampling times. Based on the plasma temperature distribution and container pressure change curves, a joint fitting method was used. First, the average plasma temperature measured at 27 points at each sampling time was obtained as the average temperature for that sampling time, resulting in 341 average temperatures. Then, based on the container pressure change curve, a pressure change rate abrupt change point identification method was used. A sliding time window of 5 sampling intervals (150 seconds) was set, and the pressure change rate curve was obtained by sliding derivative calculation. The sampling time when the absolute value of the pressure change rate first exceeded a first threshold of 25 Pa / s was designated as the first abrupt change point. From the first abrupt change point, the sampling time when the absolute value of the pressure change rate last exceeded the first threshold was designated as the second abrupt change point. The average temperature corresponding to the first abrupt change point was obtained as the average temperature at the start of coagulation, and the average temperature corresponding to the second abrupt change point was obtained as the average temperature at the end of coagulation. The calculated average temperature at the start of coagulation was -0.5213℃, and the average temperature at the end of coagulation was -4.8715℃. The intervals with average temperatures greater than the initial average temperature of solidification are divided into the liquid interval, the intervals with average temperatures less than or equal to the initial average temperature of solidification but greater than or equal to the final average temperature of solidification are divided into the phase transition interval, and the intervals with average temperatures less than the final average temperature of solidification are divided into the solid interval. Piecewise fitting relationships between average temperature and pressure are established within the liquid, phase transition, and solid intervals, respectively. In each fitting segment, the fitted curve is forced to pass through the solidification initiation and solidification termination points; that is, the residual of the first fitting function at the solidification initiation point is zero, the residuals of the second fitting function at both the solidification initiation and solidification termination points are zero, and the residual of the third fitting function at the solidification termination point is zero. This yields the average temperature fitting curves for the liquid, phase transition, and solid intervals. Connecting these three fitting curves sequentially yields the overall average temperature fitting curve.Substituting the container pressure value corresponding to each of the 341 sampling times into the overall average temperature fitting curve yields the fitted average temperature for each sampling time. Subtracting the corresponding fitted average temperature from the average temperature at each sampling time gives the overall deviation of the plasma temperature values ​​measured at all measurement points at that sampling time, resulting in 341 overall deviation values. A least-squares fitting algorithm is used, with the average temperature at each sampling time as the independent variable and the overall deviation of the plasma temperature values ​​measured at all measurement points at each sampling time as the dependent variable, to fit the 341 collected sample points, yielding a second error. This second error is a function reflecting the overall deviation of the temperature sensor array from the pressure-derived temperature under different average temperature environments, i.e., the systematic deviation.

[0034] The error value corresponding to each measurement point in the first error is obtained; each of the 27 error values ​​in the first error is different. The second error is obtained, which is a function of the average temperature as the independent variable. The error values ​​of each measurement point in the first error are superimposed with the second error to obtain the total error corresponding to the 27 measurement points. The total error corresponding to the 27 measurement points is a function of 27 values ​​of average temperature as the independent variable, denoted as the total error of the temperature sensor array. The total error of the temperature sensor array includes both the differential deviations between measurement points and the systematic deviation of the temperature sensor array as a whole.

[0035] Furthermore, the method of injecting plasma into a temperature-controlled container includes: Plasma is injected into the temperature control container through an injection port located at the top of the container; after the plasma is injected into the temperature control container, the injection port is sealed with a sealing element to form a closed space inside the temperature control container.

[0036] Furthermore, the method for obtaining the residuals of the plasma temperature values ​​measured at each measurement point at the same sampling time relative to the fitted temperature distribution surface, i.e., the spatial distribution of the residuals, based on the plasma temperature distribution, using a spatial residual fitting method, includes: A three-dimensional spatial coordinate system is established with the center of the bottom of the temperature control container as the origin; the spatial position coordinates of each measurement point of the temperature sensor array in the three-dimensional spatial coordinate system are obtained; the plasma temperature values ​​measured at each measurement point at the same sampling time are extracted from the plasma temperature distribution; a polynomial surface fitting method is used to perform least squares fitting on the spatial position coordinates of all measurement points at the same sampling time and the plasma temperature values ​​to obtain a fitted temperature distribution surface; based on the fitted temperature distribution surface, the fitted temperature value corresponding to the spatial position coordinates of each measurement point is calculated; the fitted temperature value corresponding to the spatial position coordinates is subtracted from the plasma temperature value measured at each measurement point to obtain the temperature residual of each measurement point, i.e., the residual spatial distribution.

[0037] For example, according to the established three-dimensional spatial coordinate system, the spatial coordinates of the nine measurement points in the first layer from top to bottom are (-300, -300, 270), (-300, 0, 270), (-300, 300, 270), (0, -300, 270), (0, 0, 270), (0, 300, 270), (300, -300, 270), (300, 0, 270), (300, 300, 270). The coordinates of the nine measurement points on the second layer are (-300, -300, 135), (-300, 0, 135), (-300, 300, 135), (0, -300, 135), (0, 0, 135), (0, 300, 135), (300, -300, 135), (300, 0, 135), (300, 300, 135). The coordinates of the nine measurement points on the third layer are (-300, -300, 0), (-300, 0, 0), (-300, 300, 0), (0, -300, 0), (0, 0, 0), (0, 300, 0), (300, -300, 0), (300, 0, 0), (300, 300, 0). Taking the second sampling time, i.e., 30 seconds, as an example, the ternary quadratic polynomial surface fitting method is used to perform least-squares fitting of the spatial coordinates of the 27 measurement points with the plasma temperature value corresponding to the second sampling time. The fitted temperature distribution surface at this sampling time is as follows: ; in, This represents the fitted temperature distribution surface. , , These represent the coordinates of the X, Y, and Z axes in a three-dimensional spatial coordinate system, respectively, in millimeters. to These are the fitting variables for the first to ninth surfaces, respectively. The fitted variables obtained are... to The values ​​are 24.72, 0, 0, and 6.5 × 10. -4 1.8×10 -7 1.8×10 -7 -1.0×10 -7The values ​​were 0, 0, 0. Substituting the spatial coordinates of the 27 measurement points into the fitted temperature distribution surface, the corresponding fitted temperature values ​​were: 24.9206℃, 24.9044℃, 24.9206℃, 24.9044℃, 24.8882℃, 24.9044℃, 24.9206℃, 24.9044℃, 24.8206℃, 24.8383℃, 24.8221℃, 24. 8383℃, 24.8221℃, 24.8059℃, 24.8221℃, 24.8383℃, 24.8221℃, 24.8383℃, 24.7524℃, 24.7362℃, 24.7524℃, 24.7362℃, 24.7200℃, 24.7362℃, 24.7524℃, 24.7362℃, 24.7524℃. The plasma temperature values ​​measured at 27 points were subtracted from the fitted temperature values ​​corresponding to their spatial coordinates to obtain the temperature residuals for each measurement point, i.e., the spatial distribution of the residuals, which were: +0.1894℃, +0.0556℃, -0.0806℃, +0.0556℃, -0.1982℃, +0.0056℃, +0.0994℃, +0.1556℃, -0.1206℃, and -0.0683℃. The residual spatial distribution shows temperatures of -0.0121℃, -0.1883℃, +0.0179℃, -0.1759℃, +0.0279℃, -0.1383℃, +0.1779℃, -0.1383℃, +0.0476℃, -0.0562℃, -0.0624℃, -0.1362℃, -0.0400℃, -0.0562℃, -0.0724℃, +0.0538℃, and -0.0724℃. The residuals at each measurement point in this spatial distribution are both positive and negative, reflecting the deviation between the measured temperature values ​​and the fitted spatial trend at the same time point due to inherent differences in the sensors. It is noteworthy that a residual spatial distribution can be obtained for each sampling time.

[0038] Furthermore, the method for averaging the spatial distribution of the residuals at each sampling time to obtain the first error includes: By iterating through all sampling times, the average of the spatial distribution of the residuals corresponding to each sampling time is taken to obtain the first error.

[0039] For example, the first error is obtained by averaging the spatial distribution of the residuals corresponding to 341 sampling times. The first error is: +0.1754℃, +0.0489℃, -0.0753℃, +0.0521℃, -0.1876℃, +0.0012℃, +0.0921℃, +0.1498℃, -0.1153℃, -0.0628℃, -0.0094℃, -0.1798℃, +0.0213℃, -0.1684℃, +0.0315℃, -0.1321℃, +0.1692℃, -0.1289℃, +0.0437℃, -0.0513℃, -0.0581℃, -0.1287℃, -0.0365℃, -0.0498℃, -0.0679℃, +0.0576℃, -0.0658℃.

[0040] Furthermore, the method of obtaining the overall deviation of the plasma temperature values ​​measured at each measurement point as the second error by using a joint fitting method based on the plasma temperature distribution and container pressure value change curves includes: The average value of the plasma temperature measured by all measurement points of the temperature sensor array at each sampling time is obtained as the average temperature at that sampling time. Based on the container pressure change curve, a method for identifying abrupt changes in pressure rate is used to obtain the average temperature at the start of plasma coagulation and the average temperature at the end of plasma coagulation, respectively, as the average temperature at the start of coagulation and the average temperature at the end of coagulation. Based on the average temperature at the start of coagulation and the average temperature at the end of coagulation, the average temperature is divided into a liquid zone, a phase transition zone, and a solid zone. Within each of the liquid, phase transition, and solid zones, a fitting relationship between the average temperature and the pressure value is established to obtain the average temperature fitting curves for the liquid zone, phase transition, and solid zones. These curves are then sequentially connected to obtain the overall average temperature fitting curve. The overall deviation of the plasma temperature measured by all measurement points at each sampling time is calculated based on the average temperature at each sampling time and the overall average temperature fitting curve. A second error is obtained based on the overall deviation of the plasma temperature measured by all measurement points at all sampling times.

[0041] For example, the average value of the plasma temperature measured by all measuring points of the temperature sensor array at each sampling time is obtained as the average temperature at that sampling time. Taking the sampling time of second 0 as an example, the average value of the plasma temperature measured by 27 measuring points at that sampling time is calculated to be 24.9986℃, which is taken as the average temperature at the sampling time of second 0. Taking the sampling time of second 30 as another example, the average value of the plasma temperature measured by 27 measuring points at that sampling time is calculated to be 24.7619℃, which is taken as the average temperature at the sampling time of second 30. And so on, to obtain the average temperature of 341 sampling times. The average temperature of the 341 sampling times is then combined with the container pressure value change curve to obtain the second error.

[0042] Furthermore, the method of obtaining the average temperature corresponding to the start of plasma coagulation and the average temperature corresponding to the complete coagulation of plasma based on the pressure change curve of the container using a pressure change rate abrupt change point identification method, and using these as the average temperature at the start of coagulation and the average temperature at the end of coagulation, respectively, includes: The pressure change curve of the container is differentiated according to a pre-set sliding time window to obtain a pressure change rate curve. The sampling time when the absolute value of the pressure change rate on the pressure change rate curve first exceeds a pre-set first threshold is identified in the order of sampling time from front to back and recorded as the first abrupt change time. From the first abrupt change time, the sampling time when the absolute value of the pressure change rate on the pressure change rate curve last exceeds the first threshold is recorded as the second abrupt change time. The average temperature corresponding to the first abrupt change time is obtained as the solidification start average temperature, and the average temperature corresponding to the second abrupt change time is obtained as the solidification end average temperature.

[0043] For example, the sliding time window is set to 150 seconds. The method for differentiating the container pressure change curve according to the preset sliding time window is as follows: starting from second 0, the sliding time window is shifted forward by a sampling time interval of 30 seconds with each slide, until the end time of the sliding time window covers the last sampling time. All values ​​of the container pressure change curve at the sampling time are obtained within the sliding time window to obtain the sampled pressure value sequence. to .in, This represents the number of sampling moments within the sliding time window. The sliding derivative value within this sliding time window is calculated using the discrete derivative formula. The discrete differentiation formula is as follows: ; in, This represents the sampling time interval, in seconds. For each sampling moment, the arithmetic mean of the sliding derivative values ​​corresponding to all sliding time windows covering that sampling moment is obtained as the pressure change rate value for that sampling moment. For example, if a sampling moment falls within 6 sliding time windows, then the pressure change rate value corresponding to that sampling moment is the average of the sliding derivative values ​​calculated within those 6 sliding time windows. All pressure change rate values ​​are connected sequentially according to the sampling moments to obtain the pressure change rate curve. The sampling moment on the pressure change rate curve where the absolute value of the pressure change rate first exceeds a pre-set first threshold is identified in the order of sampling moments from beginning to end and is recorded as the first abrupt change moment. From the first abrupt change moment, the sampling moment where the absolute value of the pressure change rate on the pressure change rate curve last exceeds the first threshold is recorded as the second abrupt change moment. The average temperature corresponding to the first abrupt change moment is obtained as the average temperature at the start of solidification, and the average temperature corresponding to the second abrupt change moment is obtained as the average temperature at the end of solidification. In this embodiment, the first threshold is 25 Pascals per second, the first abrupt change time is the 103rd sampling time, the second abrupt change time is the 120th sampling time, the average temperature at the start of solidification is -0.5213℃, and the average temperature at the end of solidification is -4.8715℃.

[0044] In this embodiment, a sliding time window is used for differentiation to suppress the interference of random noise in the pressure measurement data on the differentiation results. The average rate of change within the window is calculated by the difference between the pressure values ​​at the beginning and end of the window, avoiding the problem of noise amplification caused by point-by-point differentiation. Using the average value of all sliding windows covering a certain sampling time as the pressure change rate value at that time can further smooth the calculation fluctuations caused by different window positions, making the pressure change rate curve more stable and continuous in the overall trend, which is conducive to the reliable identification of subsequent abrupt change points. Plasma temperature goes through three stages during coagulation: liquid, phase transition, and solid. In the liquid region, the pressure decreases slowly with the temperature, and the absolute value of the pressure change rate remains at a low level. After entering the phase transition region, the water in the plasma begins to freeze, expands in volume, and compresses the gas space above in the sealed container, resulting in a significant increase in pressure and a large increase in the absolute value of the pressure change rate. After the phase transition ends, the plasma enters the solid region, and the pressure returns to the state of slowly changing with the temperature. By identifying the abrupt change time of the pressure change rate, the start and end times of the phase transition can be determined, and the corresponding average temperature at the start and end of coagulation can be obtained, realizing the automatic division of the plasma solid-liquid state based on pressure change information. The principle for selecting the first threshold is to distinguish between normal pressure fluctuations in the liquid and solid states and significant pressure changes caused by volume expansion in the phase transition state, so as to avoid misjudgment due to random fluctuations.

[0045] Furthermore, the method for dividing the average temperature into a liquid state range, a phase transition range, and a solid state range based on the average solidification initiation temperature and the average solidification end temperature includes: The average temperature above the average temperature at the start of solidification is divided into the liquid phase range; the average temperature below or equal to the average temperature at the start of solidification and above or equal to the average temperature at the end of solidification is divided into the phase transition range; and the average temperature below the average temperature at the end of solidification is divided into the solid phase range.

[0046] Further, the method of establishing fitting relationships between average temperature and pressure values ​​in the liquid region, phase transition region, and solid region respectively, to obtain average temperature fitting curves for the liquid region, phase transition region, and solid region, and then sequentially connecting these average temperature fitting curves to obtain the overall average temperature fitting curve includes: Within the liquid region, a first fitting function is constructed; the first fitting function is expressed as: ; in, Denotes the first fitted function. Indicates the container pressure value. Indicates the first variable to be fitted. This indicates the average temperature at which solidification begins. This represents the container pressure value corresponding to the first abrupt change in the container pressure value change curve.

[0047] Within the phase transition range, a second fitting function is constructed; the second fitting function is expressed as: ; in, This represents the second fitting function. Indicates the second variable to be fitted. This represents the third variable to be fitted.

[0048] Within the solid-state region, a third fitting function is constructed; the third fitting function is expressed as: ; in, This represents the third fitting function. This represents the fourth variable to be fitted. This indicates the average temperature at which solidification ends. This represents the container pressure value corresponding to the second abrupt change moment on the container pressure value change curve.

[0049] Based on the average temperature and pressure data at all sampling times within the liquid region, the first fitting function is applied at point... The residual at point 0 is taken as the first constraint condition. Using the first constraint condition as a constraint, the least squares fitting method is used to obtain the result. The optimal value is denoted as Based on the average temperature and pressure data at all sampling times within the phase transition interval, the second fitting function is used at point... place and point The residuals at each point are all zero, which serves as the second constraint. Using this second constraint as a constraint, the least squares fitting method is employed to obtain the desired result. , The optimal values ​​are denoted as follows: , Based on the average temperature and pressure data at all sampling times within the solid-state region, the third fitting function is used at point... Using the constraint that the residual at point 0 is zero, a constrained least squares fitting method is employed to obtain the result. The optimal value is denoted as ;according to , , , The average temperature fitting curves for the liquid phase, phase transition, and solid phases are obtained, and then sequentially connected to obtain the overall average temperature fitting curve, which is expressed as follows: ; in, This represents the fitted curve of the overall average temperature.

[0050] For example, in the liquid phase, the plasma is entirely liquid, and temperature changes mainly cause thermal expansion and contraction of the plasma and the gas inside the container. Since the coefficient of thermal expansion of liquid plasma is small and the container is sealed, the gas pressure and temperature have an approximately linear relationship. Therefore, a linear function is used to construct the first fitting function, which accurately describes the physical process of the average temperature decreasing linearly with pressure in the liquid phase. In the phase transition phase, the water in the plasma gradually freezes into ice, expanding in volume and compressing the gas space above, causing a sharp increase in pressure. Simultaneously, the latent heat of solidification released during the phase transition slows the rate of temperature decrease, resulting in a non-linear relationship between pressure and temperature. A quadratic function is used to construct the second fitting function, which captures the non-linear characteristic of pressure change during the phase transition—first slow, then fast, then slow again—and the quadratic function smoothly connects with the linear functions on both sides at its endpoints. In the solid phase, the plasma is completely solidified, and the coefficient of thermal expansion of solid ice is small, restoring an approximately linear relationship between temperature and pressure. Therefore, a linear function is used to construct the third fitting function. The final overall average temperature fitting curve is as follows: .

[0051] in, The unit is Celsius. The unit is Pascal.

[0052] Further, the method for calculating the overall deviation of the plasma temperature values ​​measured at all measurement points at each sampling time based on the fitting curve between the average temperature at each sampling time and the overall average temperature, and for obtaining the second error based on the overall deviation of the plasma temperature values ​​measured at all measurement points at all sampling times, includes: Substituting the pressure value inside the temperature control container at each sampling time into the overall average temperature fitting curve yields the fitted average temperature at each sampling time. Subtracting the fitted average temperature at each sampling time from the average temperature at that time yields the overall deviation of the plasma temperature values ​​measured at all measurement points at that sampling time. The overall deviation of the plasma temperature values ​​measured at all measurement points at each sampling time is denoted as follows: to ;in, This indicates the number of sampling times; a least squares fitting algorithm is used, with the average temperature at each sampling time as the independent variable and the overall deviation of the plasma temperature values ​​measured at all measurement points at each sampling time as the dependent variable. to The sample points are fitted to obtain the second error; the second error is in the form of a function.

[0053] For example, the second error reflects the overall systematic deviation of the temperature sensor array during measurement. This systematic deviation originates from the possibility that temperature sensors from the same batch may deviate from the true temperature value under low-temperature conditions, and cannot be obtained through simple spatial fitting methods. To obtain this systematic deviation, utilizing the physical correlation between pressure change and average plasma temperature, a piecewise fitting curve for the overall average temperature is first established. This curve describes the baseline relationship between the average temperature of plasma and pressure changes in the liquid, phase transition, and solid states. Substituting the container pressure value at each sampling moment into the overall average temperature fitting curve yields a fitted average temperature based on pressure inversion. This fitted average temperature represents the theoretically calculated value of the average plasma temperature under the current pressure conditions. Subtracting the fitted average temperature from the average temperature calculated from the measured temperature values ​​of 27 measurement points at each sampling moment yields the overall deviation of the plasma temperature values ​​measured at all measurement points at that sampling moment, resulting in 341 overall deviation values. These 341 overall deviation values ​​reflect the degree of deviation between the actual measured average value of the temperature sensor array and the theoretical value obtained through pressure inversion under different temperature conditions. Using the average temperature at each sampling moment as the independent variable and the corresponding overall deviation as the dependent variable, a least-squares fitting algorithm was used to fit 341 sample points to obtain the second error. The second error is a function with the average temperature as the independent variable; inputting any average temperature yields the overall systematic deviation value of the temperature sensor array at that temperature. Unlike the first error, which contains fixed deviation values ​​for each of the 27 measurement points, the second error is a function that varies with temperature and is uniformly applied to all measurement points, reflecting the dynamic changes in the systematic deviation of the temperature sensor array under different temperature environments.

[0054] Furthermore, the method for obtaining the total error of the temperature sensor array based on the first error and the second error includes: Obtain the error value corresponding to each measurement point in the first error; obtain the second error, which is a function with average temperature as the independent variable; superimpose the error value of each measurement point in the first error with the second error to obtain the total error corresponding to each measurement point; take the set of the total errors corresponding to all measurement points as the total error of the temperature sensor array.

[0055] Finally, it should be noted that although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for measuring the temperature field of multi-state plasma, characterized in that, The method Includes the following steps: S1, inject plasma into a temperature control container; a temperature sensor array is pre-arranged inside the temperature control container; a cooling source is installed at the bottom of the temperature control container; the temperature of the cooling source is controlled to decrease linearly from high to low; a pressure sensor is installed at the top of the temperature control container. S2, set the sampling time according to the preset sampling time interval; at each sampling time, acquire the plasma temperature value measured at each measurement point of the temperature sensor array to obtain the plasma temperature distribution; at each sampling time, acquire the pressure value inside the temperature control container through the pressure sensor and fit the container pressure value change curve; the pressure sensor is not submerged in plasma. S3. Based on the plasma temperature distribution, a spatial residual fitting method is used to obtain the residual of the plasma temperature value measured at each measurement point at the same sampling time relative to the fitted temperature distribution surface, i.e., the spatial distribution of the residual; the average of the spatial distribution of the residual at each sampling time is used to obtain the first error; based on the plasma temperature distribution and the container pressure value change curve, a joint fitting method is used to obtain the overall deviation of the plasma temperature value measured at each measurement point as the second error. S4. The total error of the temperature sensor array is obtained based on the first error and the second error.

2. The multi-state plasma temperature field measurement method as described in claim 1, characterized in that, The method of injecting plasma into a temperature-controlled container includes: Plasma is injected into the temperature control container through an injection port located at the top of the container; after the plasma is injected into the temperature control container, the injection port is sealed with a sealing element to form a closed space inside the temperature control container.

3. The multi-state plasma temperature field measurement method as described in claim 2, characterized in that, The method for obtaining the residuals of the plasma temperature values ​​measured at each measurement point at the same sampling time relative to the fitted temperature distribution surface, i.e., the spatial distribution of the residuals, based on the plasma temperature distribution, using a spatial residual fitting method includes: A three-dimensional spatial coordinate system is established with the center of the bottom of the temperature control container as the origin; the spatial position coordinates of each measurement point of the temperature sensor array in the three-dimensional spatial coordinate system are obtained; the plasma temperature values ​​measured at each measurement point at the same sampling time are extracted from the plasma temperature distribution; a polynomial surface fitting method is used to perform least squares fitting on the spatial position coordinates of all measurement points at the same sampling time and the plasma temperature values ​​to obtain a fitted temperature distribution surface; based on the fitted temperature distribution surface, the fitted temperature value corresponding to the spatial position coordinates of each measurement point is calculated; the fitted temperature value corresponding to the spatial position coordinates is subtracted from the plasma temperature value measured at each measurement point to obtain the temperature residual of each measurement point, i.e., the residual spatial distribution.

4. The multi-state plasma temperature field measurement method as described in claim 3, characterized in that, The method for averaging the spatial distribution of the residuals at each sampling time to obtain the first error includes: By iterating through all sampling times, the average of the spatial distribution of the residuals corresponding to each sampling time is taken to obtain the first error.

5. The multi-state plasma temperature field measurement method as described in claim 4, characterized in that, The method of obtaining the overall deviation of the plasma temperature values ​​measured at each measurement point as the second error by using a joint fitting method based on the plasma temperature distribution and container pressure value change curves includes: The average value of the plasma temperature measured by all measurement points of the temperature sensor array at each sampling time is obtained as the average temperature at that sampling time. Based on the container pressure change curve, a method for identifying abrupt changes in pressure rate is used to obtain the average temperature at the start of plasma coagulation and the average temperature at the end of plasma coagulation, respectively, as the average temperature at the start of coagulation and the average temperature at the end of coagulation. Based on the average temperature at the start of coagulation and the average temperature at the end of coagulation, the average temperature is divided into a liquid zone, a phase transition zone, and a solid zone. Within each of the liquid, phase transition, and solid zones, a fitting relationship between the average temperature and the pressure value is established to obtain the average temperature fitting curves for the liquid zone, phase transition, and solid zones. These curves are then sequentially connected to obtain the overall average temperature fitting curve. The overall deviation of the plasma temperature measured by all measurement points at each sampling time is calculated based on the average temperature at each sampling time and the overall average temperature fitting curve. A second error is obtained based on the overall deviation of the plasma temperature measured by all measurement points at all sampling times.

6. The multi-state plasma temperature field measurement method as described in claim 5, characterized in that, The method for obtaining the average temperature at the start of coagulation and the average temperature at the end of coagulation, based on the pressure change curve of the container and using a pressure change rate abrupt change point identification method, and using these as the average temperature at the start of coagulation and the average temperature at the end of coagulation, respectively, includes: The pressure change curve of the container is differentiated according to a pre-set sliding time window to obtain a pressure change rate curve. The sampling time when the absolute value of the pressure change rate on the pressure change rate curve first exceeds a pre-set first threshold is identified in the order of sampling time from front to back and recorded as the first abrupt change time. From the first abrupt change time, the sampling time when the absolute value of the pressure change rate on the pressure change rate curve last exceeds the first threshold is recorded as the second abrupt change time. The average temperature corresponding to the first abrupt change time is obtained as the solidification start average temperature, and the average temperature corresponding to the second abrupt change time is obtained as the solidification end average temperature.

7. The multi-state plasma temperature field measurement method as described in claim 6, characterized in that, The method for dividing the average temperature into a liquid zone, a phase transition zone, and a solid zone based on the average temperature at the start of solidification and the average temperature at the end of solidification includes: The average temperature above the average temperature at the start of solidification is divided into the liquid phase range; the average temperature below or equal to the average temperature at the start of solidification and above or equal to the average temperature at the end of solidification is divided into the phase transition range; and the average temperature below the average temperature at the end of solidification is divided into the solid phase range.

8. The multi-state plasma temperature field measurement method as described in claim 7, characterized in that, The method of establishing fitting relationships between average temperature and pressure values ​​in the liquid, phase transition, and solid regions respectively, to obtain average temperature fitting curves for the liquid, phase transition, and solid regions, and then sequentially connecting these curves to obtain the overall average temperature fitting curve includes: Within the liquid region, a first fitting function is constructed; the first fitting function is expressed as: ； in, Denotes the first fitted function. Indicates the container pressure value. Indicates the first variable to be fitted. This indicates the average temperature at which solidification begins. This represents the container pressure value corresponding to the first abrupt change in the container pressure change curve. Within the phase transition range, a second fitting function is constructed; the second fitting function is expressed as: ； in, This represents the second fitting function. Indicates the second variable to be fitted. Indicates the third variable to be fitted; Within the solid-state region, a third fitting function is constructed; the third fitting function is expressed as: ； in, This represents the third fitting function. This represents the fourth variable to be fitted. This indicates the average temperature at which solidification ends. This represents the container pressure value corresponding to the second abrupt change moment on the container pressure change curve. Based on the average temperature and pressure data at all sampling times within the liquid region, the first fitting function is applied at point... The residual at point 0 is taken as the first constraint condition. Using the first constraint condition as a constraint, the least squares fitting method is used to obtain the result. The optimal value is denoted as Based on the average temperature and pressure data at all sampling times within the phase transition interval, the second fitting function is used at point... place and point The residuals at each point are all zero, which serves as the second constraint. Using this second constraint as a constraint, the least squares fitting method is employed to obtain the desired result. , The optimal values ​​are denoted as follows: , Based on the average temperature and pressure data at all sampling times within the solid-state region, the third fitting function is used at point... Using the constraint that the residual at point 0 is zero, a constrained least squares fitting method is employed to obtain the result. The optimal value is denoted as ;according to , , , The average temperature fitting curves for the liquid phase, phase transition, and solid phases are obtained, and then sequentially connected to obtain the overall average temperature fitting curve, which is expressed as follows: ； in, This represents the fitted curve of the overall average temperature.

9. The multi-state plasma temperature field measurement method as described in claim 8, characterized in that, The method for calculating the overall deviation of the plasma temperature values ​​measured at all measurement points at each sampling time based on the fitting curve between the average temperature at each sampling time and the overall average temperature, and for obtaining the second error based on the overall deviation of the plasma temperature values ​​measured at all measurement points at all sampling times, includes: Substituting the pressure value inside the temperature control container at each sampling time into the overall average temperature fitting curve yields the fitted average temperature at each sampling time. Subtracting the fitted average temperature at each sampling time from the average temperature at that time yields the overall deviation of the plasma temperature values ​​measured at all measurement points at that sampling time. The overall deviation of the plasma temperature values ​​measured at all measurement points at each sampling time is denoted as follows: to ;in, This indicates the number of sampling times; a least squares fitting algorithm is used, with the average temperature at each sampling time as the independent variable and the overall deviation of the plasma temperature values ​​measured at all measurement points at each sampling time as the dependent variable. to The sample points are fitted to obtain the second error; the second error is in the form of a function.

10. The multi-state plasma temperature field measurement method as described in claim 9, characterized in that, The method for obtaining the total error of the temperature sensor array based on the first error and the second error includes: Obtain the error value corresponding to each measurement point in the first error; obtain the second error, which is a function with average temperature as the independent variable; superimpose the error value of each measurement point in the first error with the second error to obtain the total error corresponding to each measurement point; take the set of the total errors corresponding to all measurement points as the total error of the temperature sensor array.

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