Post-processed multi-purpose measurement sensor and measurement method based on the method of calibrated integral equations

Abstract

The application provides a post-processing type multipurpose measuring sensor and a measuring method based on a calibration integral equation method, wherein the sensor body is a cylindrical stainless steel heat-conducting material, one end of the stainless steel heat-conducting material is a measuring end, one end is an adiabatic end, the outer side of the stainless steel heat-conducting material is wrapped with a heat insulation material, and a thermocouple is arranged between the stainless steel heat-conducting material and the heat insulation material. The application has a slender and delicate structure, supports a probe type operation, can be inserted into the inside of a measured body through punching, avoids dependence on surface adhesion, not only maintains high precision within an error range, but also meets the requirements for flexibility and practicability of the sensor in industrial production.

Description

Technical Field

[0001] This invention belongs to the field of thermal measurement and relates to a multi-purpose measurement sensor, particularly a post-processing multi-purpose measurement sensor and measurement method based on a calibration integral equation method, for applications requiring long-term accurate measurement of the heat flux density and temperature at a point inside an object and displaying its changes based on images. Background Technology

[0002] With rapid societal development and continuous technological advancements, numerous fields, including energy efficiency, industrial process control, environmental monitoring, aerospace, and healthcare, face complex and diverse heat transfer and management challenges. Heat flux, as a core parameter describing energy transfer processes, requires precise measurement and real-time monitoring. This not only provides crucial thermal information for studying heat transfer laws but also offers a scientific basis for optimizing system design and improving operational efficiency. In the field of energy utilization, accurately understanding heat flux distribution helps improve equipment energy efficiency; in industrial production, precise heat flux monitoring is a vital means of ensuring production stability and product quality; and in environmental monitoring, heat flux measurement is one of the core technologies for studying climate change and the Earth's surface energy balance.

[0003] Meanwhile, with the development of aerospace, electronic devices, and high-end manufacturing, heat flow sensors need to achieve high-resolution measurements in smaller, more complex systems. For example, heat flow measurement inside microelectronic devices is crucial for improving their performance and stability; in the medical field, the application of heat flow sensors can help detect abnormal heat distribution in localized areas of the human body, providing a basis for early disease diagnosis.

[0004] Based on these requirements, heat flux sensors face greater challenges in terms of functionality and performance, including high sensitivity, high reliability, versatility, and adaptability to extreme environments. These technological demands have not only driven the development of materials science, micro-electro-mechanical systems (MEMS), and signal processing technologies, but also provided strong support for solving modern thermal challenges. Therefore, the continuous innovation and development of heat flux sensors are of indispensable importance for advancing scientific research and social progress.

[0005] Among the heat flux sensors currently researched and applied, thermoelectric sensors have received widespread attention and use due to their simple measurement principle and high reliability. Common types include coaxial thermocouples and thermopile-type heat flux sensors. Coaxial thermocouples offer advantages such as simple structure and rapid response, making them suitable for point measurements and internal heat flux monitoring. However, their sensitivity coefficient is relatively low, and they cannot perform continuous measurements over long periods or at varying angles of attack. Furthermore, their stability in extreme high-temperature environments is limited. Thermopile-type heat flux sensors achieve high sensitivity and a wide measurement range through multiple thermocouples connected in series. They are widely used for heat flux density measurement in harsh environments, offering advantages such as good stability and high accuracy. However, due to the complex manufacturing process, their production cost is high, and their operating temperature range still needs improvement.

[0006] Therefore, while thermoelectric sensors possess certain advantages, they still face numerous challenges in high-precision measurement, long-term continuous monitoring, and adaptability to complex environments. These issues require further solutions through improved materials, optimized structural design, and innovative processes to meet increasingly diverse application needs.

[0007] The core idea of ​​CIEM (Compound Induction Mechanism) is to reconstruct surface conditions without system parameter input through a series of ingenious mathematical processes, such as the Laplace transform. Experimenters can use CIEM to establish an integral equation relationship between calibration and reconstructed experimental data, and predict the heat flux and temperature of the reconstructed experiment by solving this integral equation. Unlike traditional inverse problem solving methods, CIEM does not require a large number of parameters before the experiment, greatly reducing experimental complexity. Simultaneously, its parameter dependence is further reduced, resulting in more stable solutions and minimizing the impact of preset parameter errors. This allows CIEM to quickly provide accurate predictive solutions when solving various types of inverse heat conduction problems. Although CIEM has been successfully applied in various working conditions, a single thermocouple heat flux density measurement sensor based on the CIEM algorithm is currently lacking, limiting its widespread adoption in practical applications. A new, ideal sensor should be able to embed itself into the host material and accurately measure heat flux density over long periods, overcoming the shortcomings of existing technologies. Summary of the Invention

[0008] To overcome the limitations of existing heat flux sensors, such as excessive size, inability to perform internal measurements, poor dynamic performance, long response time, low sensitivity, and inability to perform long-term measurements, this invention provides a post-processing multi-purpose measurement sensor and method based on a calibration integral equation method. This invention designs a sensor that simultaneously acquires heat flux and temperature while meeting the requirements of small size, internal installation, and long-term measurement. The sensor employs a calibration algorithm to optimize its measurement accuracy and dynamic response performance, achieving not only high-sensitivity and accurate response but also long-term stability. It can perform internal measurements and output temperature data, significantly improving its application range and practicality compared to traditional heat flux sensors. This invention is also suitable for short-term measurements, outputting heat flux and temperature at the measurement point.

[0009] The technical solution adopted in this invention is as follows:

[0010] A post-processing multi-purpose measurement sensor based on the calibration integral equation method, wherein the main body of the sensor is a cylindrical stainless steel thermally conductive material, one end of which is the measuring end and the other end is the insulating end. The stainless steel thermally conductive material is wrapped with a thermal insulation material, and a thermocouple is embedded in the stainless steel thermally conductive material. The thermocouple wires are led out through the thermal insulation material.

[0011] Furthermore, a temperature measuring point is provided on the axis of the stainless steel thermally conductive material, and a hole is opened radially at the temperature measuring point. The thermocouple's thermoelectrode is embedded in the hole for measuring the temperature of the temperature measuring point.

[0012] Furthermore, the temperature measuring point is 2.5cm away from the measuring end and 6.5cm away from the insulating end.

[0013] Furthermore, the thermocouple electrodes are fixed in the hole by an adhesive, which includes graphite adhesive (Graphi-Bond 669) and high-temperature two-phase adhesive (CERAMABOND 571). The graphite adhesive is poured into the hole, and the high-temperature two-phase adhesive is applied to the surface of the graphite adhesive.

[0014] Furthermore, the thermocouple is an exposed thermocouple; the insulation material is mullite.

[0015] Furthermore, the heat insulation material is wrapped with a stainless steel outer shell.

[0016] Furthermore, the insulating end is provided with a zirconia tail plug, which is embedded in the stainless steel shell.

[0017] Furthermore, the thermocouple wires are led axially from the insulation material to the insulating end of the sensor, and then turn radially to the outside of the sensor before the zirconia tail plug.

[0018] Furthermore, the sensor is connected to a signal processing module, which has a built-in calibration integral equation method.

[0019] A heat flow measurement method based on a calibration integral equation, implemented using the aforementioned sensor, includes the following steps:

[0020] The sensor is connected to a data acquisition board to acquire temperature data; the data acquisition board is connected to a computer to transmit temperature data to the computer; the computer has a built-in CIEM algorithm, and the program of the built-in CIEM algorithm can automatically determine the calibration group selection conditions, select a semi-infinite model or a back surface adiabatic model to post-process the temperature data, output the predicted values ​​of temperature and heat flux density at the measuring point, and generate an image.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0022] 1. Compared with traditional coaxial thermocouples, the post-processing multi-purpose measurement sensor designed in this invention based on the calibration integral equation algorithm can achieve long-term stable heat flow measurement, overcome the limitations of coaxial thermocouples that can only measure for short periods of time and are prone to failure, and adapt to a wider range of application scenarios.

[0023] 2. The exposed temperature sensing element of the thermocouple in this invention can fully meet the requirements of universal industrial measurement. Its fast response characteristics and good temperature measurement accuracy have irreplaceable advantages in dynamic measurement and non-harsh environments.

[0024] 3. In this invention, the measuring end of the thermocouple is embedded in the thermally conductive material using graphite adhesive and high-temperature two-phase adhesive. The structure of the embedded thermocouple not only minimizes the impact on the heat transfer layer, but also optimizes its fixation effect in the overall structure.

[0025] 4. This invention selects mullite as the heat insulation material, which is supported and wrapped by hard stainless steel layers inside and out, avoiding its physical defects. At the same time, by taking advantage of its superior thermophysical properties, it can be used as a heat insulation thin layer between the stainless steel layers, so as to reduce the overall diameter of the sensor as much as possible while ensuring heat insulation performance, which facilitates precision operation in actual production.

[0026] 5. Benefiting from the advantages of the CIEM algorithm in inverse problem processing, this invention enables the sensor to operate stably without directly installing thermocouples at the measurement point, and withstands higher temperatures than similar heat flux sensors, further enhancing its application potential in high-temperature environments. Attached Figure Description

[0027] Figure 1This is a front view of the post-processing multi-purpose measurement sensor based on the calibration integral equation method in an embodiment of the present invention.

[0028] Figure 2 This is a cross-sectional view of a post-processing multi-purpose measurement sensor based on a calibration integral equation method in an embodiment of the present invention.

[0029] Figure 3 This is a flowchart of heat flow measurement in an embodiment of the present invention.

[0030] Figure 4 This is an experimental heating element used in an embodiment of the present invention (simulating an unknown heat flow).

[0031] Figure 5 The stainless steel strip and embedded thermocouple (simulating the internal heat conduction structure) are used in the experiment of this invention.

[0032] Figure 6 This is a diagram of the overall experimental setup in an embodiment of the present invention (simulating the design of a thermal insulation layer wrapped around a thermally conductive layer).

[0033] Figure 7 The figure shows the verification results of the adiabatic model.

[0034] In the diagram, 1 is the stainless steel outer shell, 2 is the thermal insulation material, 3 is the thermocouple, 4 is the wire, 5 is the zirconia tail plug, and 6 is the stainless steel thermally conductive material. Detailed Implementation

[0035] The technical solution of the present invention will be further described clearly and in detail below with reference to the accompanying drawings and specific examples.

[0036] A post-processing multi-purpose measurement sensor based on a calibration integral equation method is disclosed. The sensor body is a cylindrical stainless steel thermally conductive material 6, with one end serving as the measuring end and the other as the insulating end. The stainless steel thermally conductive material 6 is wrapped with an insulating material 2, which in turn is wrapped with a stainless steel outer shell 1, ensuring one-dimensional heat conduction in the thermally conductive material during temperature measurement. A thermocouple 3 is embedded within the stainless steel thermally conductive material 6, with its wires passing through the insulating material 2. A temperature measuring point P is located on the axis of the stainless steel thermally conductive material 6, 2.5 cm from the measuring end and 6.5 cm from the insulating end. A radial hole is formed at the temperature measuring point, and the thermocouple's thermoelectrode is embedded within this hole for measuring the temperature at the measuring point P. A zirconia tail plug 5 is provided at the insulating end and is embedded in the stainless steel outer shell 1. The wire 4 of the thermocouple 3 is led axially from the insulation material 2 to the insulating end of the sensor, and then turns radially to the outside of the sensor before the zirconia tail plug 5.

[0037] Preferably, the thermocouple is an exposed thermocouple. Currently, commonly used thermocouples can be classified into three types according to their structure: exposed, grounded, and embedded, each with its own characteristics and applicable scenarios. Exposed thermocouples have their sensing element directly exposed to the medium, resulting in a fast response speed and suitability for instantaneous temperature measurement; however, they are susceptible to corrosion and oxidation, leading to poor durability. Grounded thermocouples have their thermoelectrodes in contact with the inner wall of the protective tube, offering both fast response speed and vibration resistance, making them suitable for high-pressure and harsh industrial environments; however, they may be affected by grounding potential differences. Embedded thermocouples have their sensing element completely embedded within the protective tube, providing better protection and a longer lifespan in high-temperature, high-pressure, and corrosive environments; however, their response speed is relatively slow, making them more suitable for steady-state temperature measurement.

[0038] This invention utilizes an exposed thermocouple. In precision measurement applications, especially embedded measurements, accurate measurement of instantaneous temperature changes in the medium is required, with extremely high demands on temperature response speed. This makes the exposed thermocouple the optimal choice. The temperature sensing element of an exposed thermocouple is directly exposed in the measured medium, minimizing hysteresis during heat transfer and achieving extremely fast response. This characteristic is crucial for real-time monitoring of dynamic temperature changes, such as measuring temperature fluctuations in gas flow or monitoring rapid heating / cooling processes. Grounded and embedded thermocouples, due to structural limitations, have significantly slower response speeds and cannot meet such requirements.

[0039] While grounded thermocouples offer better durability and vibration resistance in harsh environments, the grounded connection between their thermocouples and the protective tube can introduce ground potential difference interference in some applications and conditions, affecting measurement accuracy. This is unacceptable for high-precision, rapidly changing measurement tasks. Embedded thermocouples, on the other hand, offer better environmental adaptability, withstanding high temperatures, high pressures, and corrosive media. However, their sensing element is encased in a protective tube, resulting in a long heat transfer path and significantly slower response, making it impossible to capture instantaneous temperature changes in real time. Furthermore, most scenarios do not require extremely high temperatures, high pressures, or highly corrosive environments, rendering the protective advantages of embedded thermocouples unnecessary.

[0040] Taking all factors into consideration, the exposed temperature sensing element of the outcrop thermocouple can fully meet the requirements of general industrial measurement. Its fast response characteristics and good temperature measurement accuracy have irreplaceable advantages in dynamic measurement and non-harsh environments, making it the best choice for most operating conditions.

[0041] Preferably, the thermocouple electrodes are fixed in the hole by an adhesive comprising graphite adhesive and high-temperature two-phase adhesive. The graphite adhesive is poured into the hole, and the high-temperature two-phase adhesive is applied to the surface of the graphite adhesive. This invention also has technical advantages over other products using similar approaches in the operation of embedded thermocouples. During embedded thermocouple operation, to minimize measurement errors and response time between the thermocouple and the measuring point, we first wrap the connecting measuring end of the thermocouple outside the armored wire with silicone grease, which has a very high thermal conductivity. Simultaneously, we inject graphite-filled high-temperature ceramic adhesive into the gap left by drilling as a good filling adhesive. This adhesive has good thermal properties and can meet the bonding, filling, and heat conduction requirements under high-temperature conditions. After the filling adhesive layer solidifies, a high-temperature two-phase adhesive (solid and liquid components are packaged in two separate bottles, mixed uniformly at a solid-liquid ratio of 1.5:1) is applied around the outside of the drilled hole. This adhesive exhibits extremely strong adhesion under normal operating conditions. Its advantages are maximized when used to fix embedded thermocouples at low temperatures on the outer surface of the heat transfer layer, while virtually eliminating the risk of viscosity failure under overheating conditions. The embedded thermocouple structure of this invention minimizes its impact on the heat transfer layer while achieving optimal fixation within the overall structure.

[0042] Preferably, the thermal insulation material 2 is mullite. Mullite is a high-performance thermal insulation material, renowned for its excellent thermal and mechanical properties, possessing a low coefficient of thermal expansion, high thermal stability, a high melting point (approximately 1850 °C), and good thermal shock resistance and chemical stability. Mullite retains high strength and corrosion resistance even at high temperatures, making it an ideal refractory and high-temperature structural material. Mullite is widely used in metallurgy, building materials, aerospace, and ceramics industries. For example, it is often used as a lining material or structural component in high-temperature kiln linings, heat exchangers, rocket nozzles, and aero-engine parts. Furthermore, it is one of the basic raw materials for manufacturing ceramic matrix composites, often used to improve the toughness and creep resistance of ceramic materials. The main advantages of mullite include excellent high-temperature strength, low thermal expansion, and strong thermal shock resistance, enabling it to adapt to complex high-temperature environments. Although mullite is brittle and has limited resistance to mechanical impact, it is supported and encased by hard stainless steel layers inside and out, which avoids its physical defects. At the same time, taking advantage of its superior thermophysical properties, it can be used as a heat insulation thin layer between the stainless steel layers, so as to reduce the overall diameter of the sensor as much as possible while ensuring heat insulation performance, which facilitates precision operation in actual production.

[0043] Furthermore, the zirconia tail plug added to the tail of this invention greatly contributes to improving measurement accuracy and convenience. Zirconia is a dense, hard, and heat-insulating metal oxide material. Using it as the tail material further ensures the construction of the back surface insulation conditions. It can be removed after the test, preventing excessive heat insulation from affecting the sensor's heat dissipation performance during non-experimental periods, reducing the sensor's thermal cooling time, thereby reducing the necessary interval between two experiments and significantly improving the measurement efficiency of multiple experiments.

[0044] Furthermore, the wires of the thermocouple 3 extend to the outside of the sensor and connect to the signal processing module, which includes a data acquisition board and a computer. The sensor is connected to the data acquisition board to acquire temperature data, and the data acquisition board is connected to the computer to transmit the temperature data. The computer has a built-in CIEM algorithm. After post-processing the temperature data, the built-in CIEM algorithm outputs the predicted values ​​of the temperature and heat flux density at the measurement point and generates an image. For short-term measurements, heat transfer occurs in the thermally conductive material within the sensor under the assumption of semi-infinite heat transfer. The acquired data is processed using the CIEM algorithm under this heat transfer model to output the temperature and heat flux density at the measurement point and generate an image.

[0045] The program, with its built-in CIEM algorithm, can automatically determine the calibration group selection conditions, helping users efficiently choose between semi-infinite models and adiabatic conditions. After the measurement is completed, the program will automatically enter calibration mode, calibrating the effective excess temperature θ at the final measurement moment of the thermocouple via tail calibration. t Select the calibration group, where θ is defined as:

[0046]

[0047] T' is the instantaneous temperature at the measuring point at the tail, and T0 is the initial temperature at this point when t = 0. It is easy to see that θ is always non-negative during the general heating process.

[0048] When θ t When the temperature is less than 0.5 ℃, the temperature rise of the back surface exposed to air is extremely limited. We can assume that it meets the semi-infinite condition within the allowable error range of engineering. The program will automatically select the reasonable calibration group data under the semi-infinite condition for calculation.

[0049] When 0.5 ℃ < θ tAt temperatures below 5°C, the model no longer satisfies the semi-infinite model, but the overall heat transfer of the heat transfer layer is already sufficient. At this point, it can be assumed that the temperature rise on the back surface is not significant after sufficient heat transfer, and within the engineering error range, it can be approximately considered to meet the back surface insulation condition. In this case, the program will automatically switch to the back surface insulation model for further processing. This invention, based on a calibration integral equation method, is a post-processing multi-purpose measurement sensor capable of long-term stable heat flow measurement, overcoming the shortcomings of existing heat flow meters and adapting to a wider range of application scenarios. Existing heat flow meters can be classified into three main categories according to their working principle: temperature gradient-based, energy balance-based, and semi-infinite assumption-based. Among them, the temperature gradient type heat flow sensor (or thermal resistance heat flow meter) is the most widely used type. Its working principle is as follows: when heat flows through the heat flow sensor, a temperature difference is generated on both sides of the sensor's thermal resistance layer. According to Fourier's law, the heat flow density passing through the sensor can be calculated from the measured temperature difference as follows:

[0050]

[0051] In the formula: q″ is the heat flux density, with units of W / m³. 2 dT is the temperature difference across the thermal resistance layer, in K; dx is the thickness of the thermal resistance layer, in meters (m); λ is the thermal conductivity of the thermal resistance layer, in W / (m‧K).

[0052] These sensors can be divided into two types: those along the longitudinal temperature gradient and those along the transverse temperature gradient. The former includes thermopile heat flow meters, Schmidt-Boelter heat flow meters, etc., while the latter includes foil heat flow meters or Gordon meters, heat flow comparators, etc.

[0053] Temperature gradient-based thermal resistance heat flow meters are typically mounted by attaching to the surface being measured or suspended in the air, which can interfere with the measured temperature field. Furthermore, the heat flow meter itself experiences changes in its thermophysical parameters due to temperature variations. Therefore, the heat flow sensor should be as small as possible and calibrated under suitable operating conditions to improve measurement accuracy. In general, this type of sensor has a limited measurement method, is highly dependent on the material's thermophysical parameters, and its usage processes and environments are more demanding than other types.

[0054] Energy balance-based heat flux sensors calculate heat flux density by measuring temperature changes on the sensor surface. The sensor interior typically contains materials with good thermal conductivity, through which heat is transferred; temperature changes reflect the magnitude of the heat flux. Temperature changes on the sensor surface are monitored by temperature sensors (such as thermocouples or thermistors) to derive the heat flux density. By analyzing the material's thermal conductivity and temperature gradient, the heat flux through the surface can be calculated, enabling accurate measurement of heat flux. A typical example is the thermal isothermal heat flux meter (or absorption heat flux meter), first proposed by Ruel et al. at the 14th Space Simulation Conference in 1986. This type of heat flux meter requires calibration before use and can be used to measure radiative heat flux in spacecraft vacuum thermal experiments.

[0055] When the heat flow meter is used in a vacuum at low temperature, the heat balance equation of the sensing element is:

[0056]

[0057] In the formula: q a "" represents the absorbed heat flux on the surface of the sensing element, in W / m 2 F1, F2, and F3 are coefficients determined from calibration data; T s T h τ represents the temperature of the sensor and the heat shield, respectively, in Kelvin (K); τ represents the measurement time, in seconds (s); ε s This refers to the emissivity of the sensitive surface. Heat flow meters or calorimeters based on energy balance, represented by this, have measurement errors due to factors such as water flow rate, specific heat capacity, density, temperature difference, and dimensions. The error of water calorimeters and thin-shell calorimeters is generally around 5%; due to multi-layer heat leakage, the steady-state error of adiabatic heat flow meters is generally less than 4%; the steady-state error of isothermal heat flow meters with thermal shields, calorimeters, and double-ring thermal protection is generally less than 5%; and the measurement repeatability error of absolute radiometers is approximately 0.05%.

[0058] However, this type of heat flow sensor also has some drawbacks. First, the sensor's measurement accuracy is easily affected by external environmental factors, such as temperature fluctuations and airflow. Second, suitable environmental conditions must be ensured during installation and use to guarantee its measurement accuracy. Finally, high-precision heat flow sensors are often expensive, which limits their widespread adoption in some cost-sensitive fields.

[0059] The last type is based on semi-infinite body heat flux sensors. Their working principle assumes that the thickness of the sensor material is much greater than the distance the heat flux travels. As the heat flux passes through the sensor, a temperature gradient is generated on the sensor surface. By measuring the temperature change, the heat flux density can be calculated using a formula based on the relationship between thermal conductivity and temperature gradient. The assumption that heat flux conduction within the sensor material is stable and uniform simplifies the calculation model for heat flux transfer.

[0060]

[0061] In the formula: T is the temperature of the object, in K; T0 is the initial temperature of the object; q″ is the heat flux density, in W / m³. 2 t represents time, in seconds; K represents the thermal conductivity of the sensing element material, in W / (m²). 2 K); ρ is the material density, in kg / m³. 3 c represents the specific heat capacity of the material, in J / (kg·K).

[0062] This greatly simplifies the calculation process for heat flux measurement and is applicable to the measurement of most materials and conventional heat flux densities. Because its working principle is based on a simplified model, it has high practicality and wide applicability, especially performing well in heat flux measurement of thicker materials, providing fast and efficient heat flux estimation. However, the measurement accuracy of heat flux meters based on the semi-infinite body assumption is affected by the measurement accuracy of the thermal resistance, its size, and the calibration accuracy of the lumped thermal parameters, generally resulting in a relatively large measurement error, but less than 10%. Therefore, a major problem that this invention needs to solve is to maintain the significant advantages of this type of sensor in terms of universality and economy, while simultaneously improving measurement accuracy and reducing measurement errors, especially those caused by lumped parameter calibration.

[0063] After a heat flow meter is manufactured, due to inconsistencies in manufacturing processes and material properties, the output parameters of the sensor are difficult to be completely consistent. Therefore, each sensor needs to be individually calibrated before use. Currently, the commonly used calibration methods in engineering are the absolute method and the relative method.

[0064] The absolute method uses standard heat flux for calibration. Commonly used standard heat fluxes are electric heaters and blackbody furnaces. Electric heaters are generally used to calibrate resistance heat flux meters, such as thermopile heat flux meters; blackbody furnaces are generally used to calibrate radiation heat flux meters, such as Gordon's meters, Schmidt-Boelter heat flux meters, and heat flux comparators. This calibration method determines the sensor's response by directly measuring and comparing the heat flux of a standard source, typically without relying on any other sensor or calibration object. Its advantage lies in providing very high accuracy and reliability because it is calibrated based on a known standard source and is unaffected by errors in other equipment. This makes absolute method calibration suitable for measurement applications requiring high precision, such as scientific research experiments and the calibration of high-precision equipment.

[0065] However, the drawback of absolute calibration lies in its complexity and expense, primarily due to the need for high-precision standard sources and specialized equipment. These standard sources typically require extremely rigorous accuracy verification, and in many cases, their purchase and maintenance costs are very high. For many laboratory and industrial environments, this translates to significant financial investment and resource consumption. Furthermore, the calibration process usually requires strict environmental control conditions, including precise adjustments to factors such as temperature, humidity, and airflow, which greatly increases operational complexity. The calibration time is also typically long, limiting its flexible application in demanding environments. Due to these factors, absolute calibration is uneconomical and inefficient in some routine applications, especially for equipment requiring frequent calibration and in large-scale production environments, where its high cost and time consumption may be unacceptable.

[0066] Another method, the relative method, also known as the standard heat flux method, is generally used to calibrate radiative heat flux meters. Its basic principle is to place the heat flux meter to be calibrated and a standard heat flux meter simultaneously under a stable radiation source. The standard heat flux meter is used to determine the magnitude of the radiative heat flux, and the relationship between the output signal and the input heat flux density is determined based on the output of the heat flux sensor to be calibrated. Typically, a quartz lamp assembly combined with a silicon controlled rectifier (SCR) is used to control the radiative heat flux.

[0067] Relative calibration, which compares the sensor under test (SUT) with a known standard sensor, is simple to operate, low in cost, and can be completed quickly, making it suitable for large-scale applications. However, its drawback lies in its over-reliance on the accuracy and stability of the standard sensor. If the standard sensor itself has deviations or is aging, the calibration results may be inaccurate. Furthermore, environmental changes (such as temperature and humidity fluctuations) affect the SUT and standard sensors differently, introducing systematic errors and reducing measurement accuracy. Since the absolute accuracy of the sensor cannot be independently verified, errors may accumulate over long-term use, especially in applications requiring high precision, potentially amplifying measurement errors and affecting equipment performance and reliability.

[0068] It is easy to see that the advantages and disadvantages of both methods are too obvious, and they are too extreme in practical engineering applications. Therefore, there is an urgent need in production for a high-performance algorithm that can balance the advantages and disadvantages of both methods. The calibration integral equation method (CIEM) in this invention perfectly meets this requirement.

[0069] CIEM has lower requirements for calibration accuracy and is not strongly dependent on the parameters of the material itself. It only requires one set of easily obtainable calibration data under normal operating conditions. It combines the advantages of both methods, balancing their extreme disadvantages, making it a more suitable method for large-scale applications while meeting basic efficiency and accuracy requirements. Furthermore, this invention meets the trend of miniaturization and shortened transient response time in heat flow measurement technology, reduces interference with the test specimen, is suitable for heat flow measurement in small areas, and possesses excellent transient response capabilities. Given the increasing demand for precise and transient measurements in the future, it has great development potential.

[0070] Compared to traditional coaxial thermocouples, this invention's sensor can transmit the acquired signals to a computer, where they are processed and displayed in real time as curves showing the changes in heat flow and temperature over time, facilitating digital data processing and subsequent analysis. Unlike foil-type heat flow meters and other sensors that can only be attached to surfaces for measurement, this sensor features a slender and compact structure, supporting probe-type operation. It can be inserted into the measured object through drilling, avoiding dependence on surface adhesion. This not only maintains high accuracy within the error range but also better meets the needs of industrial production for sensor flexibility and practicality. Thanks to the advantages of the CIEM algorithm in inverse problem handling, this sensor can operate stably without directly installing a thermocouple at the measurement point, and can withstand higher temperatures than similar heat flow sensors, further enhancing its application potential in high-temperature environments. Unlike the single algorithm model and function implementation of general heat flow sensors, this patent embeds two calibration algorithms: a semi-infinite heat transfer model and a back surface adiabatic model, used to handle short-term and long-term heat transfer scenarios respectively. Furthermore, it simultaneously visualizes temperature changes and heat flow, making it more convenient and versatile.

[0071] The following is a specific example of the present invention: a post-processing multi-purpose measurement sensor based on the calibration integral equation method. It has a slender cylindrical shape and consists of three symmetrical layers from the inside out: the innermost layer is a 2.5 mm diameter stainless steel thermally conductive material; the middle layer is a 1.5 mm thick mullite powder thermal insulation material; the outermost layer is a stainless steel shell with a thickness controlled within 0.5 mm, used to compact and fix the mullite powder thermal insulation material; the tail is a zirconia tail plug: used for thermal insulation and fixing the mullite powder. After the experiment, the zirconia tail plug can be pulled out to accelerate heat dissipation and cooling, facilitating the next test as soon as possible.

[0072] This example uses an SCAXL-020E-6 thermocouple. The measuring and calibration thermocouples are embedded at designated locations along the cylindrical axis. First, the thermocouple electrodes are wrapped with silicone grease. Then, high-temperature resistant graphite adhesive is used to fill the perforated gaps. After solidification, a high-viscosity two-phase adhesive is applied to the outer surface of the hole. This process provides both strong adhesion and high-temperature resistance. Simultaneously, the thermocouple wire is pulled from the perforated area and led out along the mullite insulation layer. When the wire reaches its end, insulating plastic is wrapped around the metal wire, which is then led out from the side, wrapped with the outer metal layer. The perforated area is then secured with glue.

[0073] After the thermocouple wire is led out, it is connected to a K-type thermocouple temperature acquisition module, such as PT100. The acquired data is then connected to a computer. The computer program stores commonly used calibration data, but users can also add their own experimental calibration groups to improve accuracy. The computer program uses a built-in CIEM calibration method to calculate the heat flow and temperature changes at the sensor measurement points over a given period, and then performs image visualization processing. Users can also extract specific data for further processing.

[0074] like Figure 3 As shown, the steps for measuring heat flow using the sensor of this invention are as follows:

[0075] When conducting the experiment, first refer to Figure 1 The main view structure shown indicates the completeness of the experimental instrument assembly: for example, whether the tail plug is strictly inserted into the sensor tail to ensure proper insulation of the back surface; and whether the wires inside the mullite interlayer are pulled out from the designated position. After confirming that everything is correct, connect the thermocouple wires to the data acquisition module, with each wire connected to a different data acquisition port. Record the corresponding interface numbers of different thermocouple wires at this stage, and avoid tangling the wires at the data acquisition board connectors as much as possible. Also, ensure that this stage is performed without power to fully guarantee the personal safety of the experimental personnel. After arranging the thermocouples and data acquisition module, connect the other end of the data acquisition board to the computer.

[0076] After connecting the thermocouple leads to the data acquisition board and computer, the experimenter opens the experimental testing platform on the computer, selects the "pre-calibration" mode, and checks whether the measuring point sensor and the calibration sensor are powered on and working properly. Before starting the formal experiment, both should be at the same normal operating temperature, close to room temperature. If the calibration status on the screen shows that the two thermocouple temperatures are inconsistent, or if there are invalid thermocouple readings (displayed as NaN), the pre-calibration mode should be ended in advance. After disconnecting the computer from the data acquisition module, return to the inspection module mentioned above and focus on checking whether the thermocouple leads are connected properly and whether the input and output ports of the data acquisition module are matched, etc., which may affect data transmission.

[0077] After completing the pre-calibration steps and verifying that everything is correct, the experimenter can begin the formal measurement steps. First, the specific installation method of the sensor should be determined: If it is necessary to measure the surface heat flow and temperature of the experimental object, the zirconia tail plug at the end of the sensor can be held directly, and the measuring surface on the other side can be brought into close contact with the experimental surface to be measured, maintaining a stable fit as much as possible. If the surface to be measured is not a completely smooth plane, the central stainless steel thermally conductive layer should be kept in stable contact with the measuring point. If it is necessary to measure the internal heat flow and temperature of the experimental object, attention should be paid to the length corresponding to the specific model of the product. Taking the 100 mm sensor (here, 100 mm refers to the effective length L0 of this product, which is the total length of the product excluding the 1 mm thickness of the zirconia tail plug base) as an example, the theoretical measurement depth range is 0-100 mm, and the actual optimal measurement depth without assistance is 30-95 mm. If the depth is less than 30 mm, the exposed portion of the sensor is too large, which is not conducive to establishing the stability of fixed measurements. Manual fixation may be required, reducing the experimental efficiency of embedded, unassisted measurement designs. If the measurement depth exceeds 95 mm, approaching the 100 mm limit measurement length, the fit of the embedded measurement surface cannot be guaranteed to be stable and compacted. Furthermore, it is difficult to inspect the internal measurement portion from the inside out, potentially causing subsequent measurement data failure and increasing the risk of data processing errors. Similarly, the lengths of other sensor models vary, but the optimal measurement depth can be estimated for all of them: Regarding the confidence interval within the engineering error range, the lower threshold L... d = L * 30%, upper limit of threshold L u = L - 5 mm.

[0078] Before performing embedded measurements, necessary pretreatment of the experimental materials is required. In this example, the sensors are all slender cylindrical shapes with a diameter of 5 mm. The optimal drilling diameter is slightly larger than 5 mm. To minimize the impact on internal heat transfer of the material, the pretreatment drilling diameter should ideally not exceed 7 mm; otherwise, the reliability of the data source within the allowable error range cannot be guaranteed. Generally, a small excess gap will remain after embedding the sensor. This gap can be manually filled and compacted using the additional mullite powder provided. Furthermore, the spare mullite powder pack can be used during the inspection phase to replenish the wear of the mullite interlayer at the measurement surface, address wear from repeated measurements, and extend the product's lifespan. After completing the above pretreatment steps, gently rotate the sensor to check the fit of the embedded outer surface: if the sensor remains stable under manually applied slight disturbance torque, it can be considered to have a good embedded fit; otherwise, more mullite powder needs to be added to further compact the gaps left during the drilling stage.

[0079] In addition, we need to consider the placement and orientation of the sensor when it is embedded. The optimal placement method for this invention is top-down measurement, that is, opening a hole on the top surface and inserting the sensor downwards from the opening. This placement method can maximize the use of the downward pressure of the tail plug, thereby ensuring the fit of the measurement point and the overall stable operation, while also making it the easiest to fill the gaps. A reasonable measurement orientation only needs to ensure that the center of the tail plug is higher than the plane of the overall center of gravity of the device in the vertical plane, that is, from the angle from top to bottom to the angle of horizontal placement: in actual measurement, we take the measurement point as the fixed point of the circle, the direction of gravity is the negative z-axis, and the effective placement plane of the tail plug is the upper half of the spherical surface of the z-axis. Under a reasonable measurement orientation, the tail plug can still play a part in counterweight compaction, although the effect is reduced compared to the optimal measurement method, it is still an effective placement orientation. Apart from the above two cases, when the center of gravity of the tail plug is lower than the overall center of gravity of the sensor, that is, when the relative position of the tail plug is on the hemisphere in the negative z-axis direction, we call it the theoretical measurement orientation. This situation is not the measurement method recommended by this invention and usually requires an additional fixing method. For near the upper limit of the optimal measurement depth threshold L u For certain operating conditions, tape can be used to connect the back surface of the tail plug, forming a three-point fixation between the measuring material, the zirconia back surface, and the measuring material. For other measurements, a method similar to that used for embedded thermocouples can be employed, using silicone sealant at the contact points, filling the gaps with high-temperature resistant adhesive, and securing the outer edge with room-temperature high-viscosity adhesive to ensure the overall stability of the measuring device. It is important to note that using adhesive-assisted fixation carries significant risks and may cause irreversible damage to the experimental materials; experimenters should use this method with extreme caution. To avoid potential material loss, manual fixation can also be used, with all installation methods prioritizing the actual measurement environment conditions.

[0080] After securing the entire measuring device, the experimenter should return to the test platform, select "Start," fill in the "Measurement Time" in the pop-up window, and click "After-Checked Start." The maximum measurement temperature of this invention is 1000℃. If a transient exceeding the measurement limit is detected during the measurement process, the sensor's fuse mechanism will be automatically triggered: data acquisition will automatically stop, and the test platform will display a "WARNING: EXCESSIVELY HIGH TEMPERATURE!" window, along with the measurement results up to the point before the fuse trigger. At this time, the experimenter should take protective measures as quickly as possible, such as wearing heat-resistant gloves, removing the sensor from the measurement point, and removing the tail plug for heat dissipation to prevent damage to the sensor components from prolonged overheating. Under normal circumstances, after the preset measurement time is reached, a window will automatically pop up with the message "Successfully completed the measurement within the set time frame!" Clicking "View Results" will allow you to view the specific images and corresponding data.

[0081] The above section describes how the test platform automatically selects data from the default calibration database for processing. If the experimenter needs to manually add calibration groups, they can click "Advanced Options" - "Customized Calibration Data" below after setting the measurement time, select their own calibration data file, apply it, and then return to the normal measurement steps.

[0082] After completing all measurements, select "Files" in the upper left corner and then "Export". You can choose the type of data to export, such as a heat flux over time image (default format is .png, but can be adjusted to other image formats) or a heat flux over time data table (default format is .csv, but can be manually adjusted to .dat or .txt, with a default minimum time interval of 200ms).

[0083] After completing an experimental measurement, it is recommended to immediately remove the zirconia tail plug to cool the device (this step also requires the use of heat-resistant gloves). Allow the device to cool sufficiently before proceeding to the next experiment. To end the experiment, first disconnect the computer from the data acquisition module output, then disconnect the thermocouple wires from the data acquisition module input, following the reverse installation steps. Finally, slowly remove the sensor from the measurement point.

[0084] The following provides a specific implementation idea for the CIEM method in this invention:

[0085] Let the heat transfer length under one-dimensional conditions be L, α be the thermal diffusivity of the thermally conductive material, T be the temperature at the measuring point, t be the diffusion time, and x represent the coordinate along the direction of heat conduction. Then, x ∈ (0, L), and the initial ambient temperature is T0.

[0086] The heat conduction equation in the one-dimensional model is:

[0087] (1)

[0088] Under the thermal deformation of the back surface, the boundary conditions are:

[0089] (2)

[0090] The initial conditions are:

[0091] (3)

[0092] Define θ as the excess temperature, representing the difference between the transient temperature and the initial conditions:

[0093] (4)

[0094] Replacing T0 with the excess temperature θ from (3) and substituting it into (1) and (2), we can simplify to get:

[0095] (5)

[0096] (6)

[0097] And as can be seen from the previous definition:

[0098] (7)

[0099] After processing, we obtained both homogeneous boundary conditions and simpler initial conditions.

[0100] Defined by heat flux density:

[0101] (8)

[0102] After applying the Laplace transform to (5), we get:

[0103] (9)

[0104] Substituting condition (7) and simplifying, we get:

[0105] (10)

[0106] Another option is:

[0107] (11)

[0108] The equation can be simplified to its frequency domain form as follows:

[0109] (12)

[0110] Its analytical solution is:

[0111] (13)

[0112] Here, A(s) and B(s) are both functions of s.

[0113] Substituting the boundary condition (6) into the equation and further solving for the two coefficients, we get:

[0114] (14)

[0115] Substituting back into (13) and simplifying, we get:

[0116] (15)

[0117] At this point, we still lack a solution condition, and q" is the result we need to invert, so we cannot start from here. Therefore, we introduce a calibration set: Suppose a thermocouple is buried at x = t, which in the mathematical model is represented by T(b,t), which can be regarded as known. Simply substituting it back into (15) yields:

[0118] (16)

[0119] From (8) and (15), we can also know that:

[0120] (17)

[0121] Dividing the two equations above, we can eliminate B(s):

[0122] (18)

[0123] For the same homogeneous material, k and ∝ can be considered constant during heat conduction, as can length L and b. Therefore, the denominator in (18) is a constant, which simplifies to:

[0124]

[0125] Therefore, it is not difficult to conclude that, under the condition that all the above remain unchanged, an identity exists between experiments using different heat fluxes:

[0126] (19)

[0127] Assuming the second set of experiments is a reconstruction experiment and the first set of experiments is a calibration experiment, during calibration, as long as q from the calibration experiment can be obtained... c "with θ c Theoretically, q of the reconstruction group can be obtained. r Cross-multiplication, simplified using the properties of convolution, yields:

[0128] (20)

[0129] Normally, since the other three conditions in the time domain are known, we can obtain q. r However, this equation is actually ill-posed, and we can still process it further to obtain a more accurate solution, which we call the regularization method.

[0130] The regularization method used in CIEM is the future time method, which requires determining the regularization parameter, i.e., the future time γ. As γ gradually increases, the solution data will gradually experience a process of divergence-fitting-overfitting. Therefore, we need to select the optimal regularization parameter, but this is a more complex, mathematical, and theoretical problem, which will not be elaborated here.

[0131] Another case, namely the semi-infinite condition, differs mainly in the boundary conditions. Unlike (6), the boundary conditions in this case should be replaced with:

[0132] (twenty one)

[0133] Subsequently, the boundary conditions are substituted into q"(0,t), and after Laplace transform, mathematical processing is performed in the frequency domain. Finally, the result is restored to the time domain through convolution properties.

[0134] To verify the feasibility of the algorithm and structure mentioned in this invention, a simplified structure was designed for easy experimentation:

[0135] A stainless steel strip and a mullite shell were used to simulate the encapsulation layer structure. An electric heating device and heating elements were used as the simulated heat source. Data collected by thermocouples was processed by a computer to obtain visualized comparison results, demonstrating the accuracy of the inversion verification of this invention. The experimental sample is roughly as follows: Figures 4-6 As shown:

[0136] In the experiment, voltage and current change data can be directly obtained through the DC power supply output device. Combined with the known heating element area, the instantaneous heat flux density of the heating element for the stainless steel material can be calculated. Three thermocouples (only two are actually needed, with the third as a backup) are connected to the data acquisition board and then input into the computer. Real-time temperature changes can be displayed in the computer's visualization interface. Finally, the data can be exported as a table, showing the temperature measurement data of different thermocouples over time. The above is the preliminary data required for the experiment. The specific steps of the algorithm processing have been derived above and will not be repeated here.

[0137] After processing with an adiabatic model algorithm and then in MATLAB, the comparison images are as follows: Figure 7 As shown, the solid red line represents the actual heat flow input of the heating element to the stainless steel material, used to simulate the complex thermal environment that the sensor may need to detect in a real-world scenario; the dashed blue line represents the predicted external input heat flow result reconstructed from thermocouple temperature measurement data, which is the sensor output content after the chart visualization process.

[0138] As can be seen, under this simulation condition, when the regularization parameter γ is selected as 9.8438 s, the reconstructed heat flow is basically consistent with the actual heat flow, which proves that the experimental device can make relatively accurate predictions for complex input heat flow models.

[0139] Since the adiabatic model is a more complex condition than the semi-infinite model in heat transfer theory, if the adiabatic experiment is proven to be feasible, then the more idealized semi-infinite model must also be feasible. Therefore, the semi-infinite model verification experiment will not be carried out here.

[0140] The above verification results prove that this patent is practically feasible.

[0141] This invention presents a post-processing multi-purpose measurement sensor based on the calibration integral equation method. It features a slender and compact structure, supports probe-type operation, and can be inserted into the measured object through drilling, avoiding reliance on surface adhesion. This not only maintains high accuracy within the error range but also better meets the flexibility and practicality requirements of sensors in industrial production. Benefiting from the advantages of the CIEM algorithm in inverse problem handling, this sensor can operate stably without directly installing thermocouples at the measurement point, and can withstand higher temperatures than similar heat flux sensors, further enhancing its application potential in high-temperature environments. Unlike the single algorithm model and function implementation of general heat flux sensors, this invention's CIEM algorithm embeds two calibration algorithms: a semi-infinite heat transfer model and a back surface adiabatic model. These are used to handle short-term and long-term heat transfer scenarios respectively, and temperature changes and heat flux are visualized simultaneously, making it more convenient and versatile.

[0142] The above specific embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A measurement method for a post-processing multi-purpose measurement sensor based on a calibration integral equation method, characterized in that, The sensor body is a cylindrical stainless steel thermal conductive material (6). One end of the stainless steel thermal conductive material (6) is the measuring end and the other end is the insulating end. The stainless steel thermal conductive material (6) is wrapped with a heat insulation material (2). A thermocouple (3) is embedded in the stainless steel thermal conductive material (6). The wire of the thermocouple (3) passes through the heat insulation material (2) and is led out. The measurement method includes the following steps: The sensor is connected to a data acquisition board to acquire temperature data; the data acquisition board is connected to a computer to transmit temperature data to the computer; the computer has a built-in CIEM algorithm, and the program of the built-in CIEM algorithm performs post-processing on the temperature data, outputs the predicted values ​​of temperature and heat flux density at the measuring point, and generates an image. The principle of the CIEM algorithm is as follows: The sensor exhibits an identity across experiments with different heat flows: ， By using cross-multiplication and the properties of convolution to simplify, we have: ， in, θ The excess temperature represents the difference between the transient temperature and the initial conditions. , This indicates the heat flux density of the calibration group. , This represents the heat flux density of the reconstruction group. , Indicates the excess temperature of the calibration group. , The excess temperature of the reconstruction group is represented by , and s is the parameter of the Laplace transform. u For integration variables, b These are the coordinates of the thermocouple's placement.

2. The measurement method according to claim 1, characterized in that, A temperature measuring point is provided on the axis of the stainless steel thermally conductive material (6), and a hole is opened radially at the temperature measuring point. The thermocouple's thermoelectrode is embedded in the hole for measuring the temperature of the temperature measuring point.

3. The measurement method according to claim 2, characterized in that, The temperature measuring point is 2.5cm away from the measuring end and 6.5cm away from the insulating end.

4. The measurement method according to claim 2, characterized in that, The thermocouple's thermoelectrodes are fixed in the hole by an adhesive, which includes a graphite adhesive and a high-temperature two-phase adhesive. The graphite adhesive is poured into the hole, and the high-temperature two-phase adhesive is applied to the surface of the graphite adhesive.

5. The measurement method according to claim 1, characterized in that, The thermocouple is an exposed thermocouple; the insulation material is mullite.

6. The measurement method according to claim 1, characterized in that, The heat insulation material (2) is wrapped with a stainless steel shell (1).

7. The measurement method according to claim 6, characterized in that, The insulating end is provided with a zirconia tail plug (5), which is embedded in the stainless steel shell (1).

8. The measurement method according to claim 7, characterized in that, The wires of the thermocouple (3) are led axially from the insulating material (2) to the insulating end of the sensor, and then turn radially to the outside of the sensor before the zirconia tail plug (5).

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