A compensation method and system for continuously, rapidly and accurately measuring radon concentration in air

Abstract

A compensation method and system for continuously, quickly and accurately measuring radon concentration in air, the method taking the radionuclide quantity in the measuring cavity at the initial time of the current sampling period as the initial value, combining the model of gas exchange and radionuclide decay to obtain the function of radionuclide quantity change with time in the measuring cavity; and determining the theoretical total alpha particle count in the current measurement period, establishing the relationship between alpha particle count and radionuclide quantity; then based on the relationship and the actual measurement count, obtaining the number of environmental radon atoms, and combining the radon decay constant to calculate the radon concentration; finally, combining the number of radon atoms at the current sampling point and the model containing gas exchange and radionuclide decay to obtain the radionuclide quantity at the end of sampling, which is taken as the initial state of the next sampling period, and after switching the sampling point, the above steps are repeated to realize continuous, quick and accurate sampling. Through cyclic iteration, the method effectively saves the balance waiting time, and realizes the continuous, quick and accurate measurement of radon concentration in the environment by a single radon measuring instrument.

Description

Technical Field

[0001] This invention belongs to the field of environmental radioactivity monitoring technology, and relates to a compensation method and system for continuously, rapidly and accurately measuring radon concentration in the air. Background Technology

[0002] Radon, a radioactive rare gas, poses a serious threat to public health and dominates natural radiation exposure. Clear legal standards have been established for radon concentrations in urban environments and special areas, and regular radon concentration surveys are conducted to effectively ensure the health of residents and workers.

[0003] The determination of radon concentration in the air typically relies on detecting alpha particles released by radon and its decay products. Without compensation, reliable measurements require the air within the measurement chamber to be displaced and radioactive equilibrium established, a process that can take up to 260 minutes. Even with compensation methods, traditional techniques are primarily limited to single-point measurements under relatively stable conditions, and still require approximately 60 minutes to achieve reliable accuracy. These methods depend on static sampling and time integration, and are therefore unsuitable for survey scenarios involving rapid fluctuations in radon concentration in the environment or requiring the rapid capture of instantaneous peaks. In other words, traditional methods can only provide one-time predictions and cannot achieve continuous tracking.

[0004] The air scintillation method for radon measurement inherently possesses high sensitivity. This advantage stems from the direct detection of ultraviolet scintillation photons generated by the interaction of alpha particles with nitrogen molecules in the air. Unlike alpha particles themselves, these ultraviolet photons have strong penetrating power, capable of propagating far beyond the short-range tracks of alpha particles. This allows for a significant increase in the effective volume of the measurement cavity, thereby improving detection efficiency and further enhancing sensitivity. This characteristic enables reliable radon detection even under low concentration conditions, improving measurement accuracy and making the method particularly suitable for low-level radiation monitoring. Furthermore, high sensitivity ensures that the alpha particle signal can rapidly accumulate to a sufficient quantity within a short time, reducing statistical uncertainty and shortening response time. Therefore, the air scintillation method can support rapid and accurate radon concentration measurement and significantly improve overall monitoring efficiency. For example, Chinese patent application CN119375926A discloses a method and system for rapid determination of radioactive radon concentration in air based on scintillation in a flowing airflow. This method, based on scintillation to measure the net alpha particle count rate, requires obtaining the net alpha particle count rate within a corresponding time period during measurement. Combining the decay patterns of radon and its progeny with the ventilation conditions of the chamber, it establishes the relationship between the net alpha particle count generated from the decay of radon and its progeny in the newly drawn-in air within the measurement chamber during the corresponding measurement time period, and the volume of the measurement chamber, pump speed, and the original radioactive concentration of the air in the chamber. This yields the sensitivity coefficient for measuring the radioactive radon concentration in the target air, thus rapidly obtaining the radioactive radon concentration in the target air. While this technology overcomes the limitation of traditional methods relying on long-term equilibration and achieves rapid determination of values ​​for a single-point, single-measurement analysis, its requirement for single-measurement prediction means that it cannot continuously and promptly predict sensitivity after changes in the measurement location. This limits its application to fixed locations and cannot meet the needs of rapid, continuous monitoring over multiple time periods. Furthermore, its algorithm framework primarily relies on the net alpha particle count within a single period for estimation, resulting in insufficient adaptability to spatiotemporal changes in dynamic environments.

[0005] Chinese patent application CN118642151A discloses a long-distance, multi-point real-time online monitoring system and method for environmental radon concentration. This technology focuses on large-scale projects such as underground engineering, tunnel construction, particle accelerators, and nuclear facilities. It achieves real-time monitoring of radon concentration at different underground locations by deploying multiple radon detectors. Its operating mechanism is as follows: a data acquisition module collects data using the radon detectors, which is then transmitted wirelessly or via wired connection to a host computer control and monitoring module. The host computer monitors and analyzes the collected data, promptly alarming for exceeding limits, and can also adjust its own parameters based on real-time data and send control commands to the data acquisition module. However, this technology has certain limitations. On the one hand, the deployment of a large number of radon detectors leads to high costs, increasing project investment; on the other hand, the testing process requires a long waiting time for the testing system to reach equilibrium, resulting in low testing efficiency. Furthermore, this technology can only achieve fixed-point monitoring of multiple radon detectors, and cannot achieve continuous, rapid, and accurate testing of a single radon detector, making it difficult to meet the needs of some scenarios with high requirements for cost and testing flexibility. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a compensation method and system for continuous, rapid and accurate measurement of radon concentration in the air, thereby solving the technical problems of high cost and low efficiency when testing radon concentration at multiple points, and the inability to achieve continuous, rapid and accurate testing with a single radon meter, which makes it difficult to meet the needs of scenarios with high requirements for cost and testing flexibility.

[0007] This invention is achieved through the following technical solution: A compensation method for continuous, rapid, and accurate measurement of radon concentration in air includes the following steps: S1: Obtain the current sampling point and measure the cavity at the beginning of its sampling period. 222 The number of Rn and its daughter nuclides is used as the initial value of the nuclides. Combined with a pre-constructed forward analytical model that includes gas exchange and nuclide decay, a function is established to measure the change of the number of nuclides in the cavity over time. S2: Determine the theoretical total count of α particles at the current sampling point within its sampling period based on the function of the change in the number of nuclei in the measurement cavity over time; S3: Based on the theoretical total count of α particles at the current sampling point within its sampling period and the pre-constructed measurement equation, obtain the number of radon atoms in the environment at the current sampling point; S4: Based on the number of radon atoms in the current sampling point environment and the decay constant of radon, obtain the environmental radon concentration at the current sampling point; S5: Utilizing the number of radon atoms in the current sampling point environment, and based on a pre-constructed forward analytical model incorporating gas exchange and nuclide decay, obtain the concentration of radon atoms in the measurement chamber at the end of the current sampling point. 222The number of Rn and its daughter nuclides is used as the initial number of nuclides for the next sampling point. After switching sampling points, steps S1 to S4 are repeated. The sampling points are iterated one by one to complete the continuous measurement of environmental radon concentration.

[0008] Preferably, in step S1, the pre-constructed forward analytical model that includes gas exchange and nuclide decay is specifically as follows:

[0009]

[0010] In the formula, To measure the chamber 222 The number of atoms in Rn at time t; This refers to the sampling pump speed; To measure the cavity volume; This represents the number of radon atoms in the environment being tested at the current sampling point. for 222 The effective proportion of Rn carried away from the cavity during gas exchange; for 222 The decay constant of Rn; To measure the first in the chamber The number of atoms of a single nuclide at time t; for 222 The decay constant of the daughter nuclide of Rn; for 222 The effective proportion of Rn daughter nuclides that are carried out of the cavity during gas exchange.

[0011] It is worth noting that the key parameters in this method that depend on the specific settings of the detector include: , and the initial measurement chamber 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The number of atoms in Po, i.e. , , , , At the initial moment, the number of radon atoms and their daughter atoms in the chamber was measured to be 0, i.e. = = = = =0, and 222 Rn、 218 Po、 214 Pb, 214 Bi、 214The effective proportion of Po carried away from the cavity during gas exchange, i.e. It was obtained through a pre-set experimental condition calibration.

[0012] Preferably, in step S1, in the process of establishing the function of the number of kernels in the measurement cavity changing with time, it is assumed that the radon concentration of the environment under test remains constant within a single sampling period.

[0013] Preferably, in step S1, the pre-constructed forward analytical model containing gas exchange and nuclide decay is converted into matrix form and solved to establish a function of the change in the number of nuclides in the measurement cavity over time.

[0014] Preferably, in step S1, the pre-constructed forward analytical model including gas exchange and nuclide decay is transformed into matrix form for solution, specifically as follows:

[0015] in, It is a coefficient matrix; It is a state vector; The source term vector;

[0016] In the formula, , , , , They are respectively 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The decay constant of Po; , , , , They are respectively 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The effective proportion of Po that is carried away from the cavity during gas exchange; , , , , In the measuring chamber 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The number of atoms Po at time t; This refers to the sampling pump speed; To measure the cavity volume; This indicates transpose.

[0017] Preferably, in step S2, the theoretical total count of α particles at the current sampling point within its sampling period is determined based on the function of the change in the number of nuclei in the measurement cavity over time, specifically as follows:

[0018]

[0019] in, This represents the theoretical total count of α particles at the current sampling point within its sampling period. The sampling period; The instantaneous α emissivity; , as well as They are respectively 222 Rn、 218 Po、 214 The number of atoms Po at time t; , , They are respectively 222 Rn、 218 Po、 214 The decay constant of Po; , , They are respectively 222 Rn、 218 Po、 214 The detection efficiency of Po is obtained by calibration under preset experimental conditions.

[0020] Preferably, in step S3, the pre-constructed measurement equation is:

[0021] in, This represents the number of radon atoms in the environment being tested at the current sampling point. The total number of α particles at the current sampling point within its sampling period, as measured in the experiment; The residual decay contribution of existing nuclides in the test cavity at the beginning of the current sampling point's sampling period; This represents the linear contribution of radon in the environment directly input into the test chamber during the sampling period at the current sampling point.

[0022] A compensation system for continuous, rapid, and accurate measurement of radon concentration in air, used to implement the aforementioned compensation method for continuous, rapid, and accurate measurement of radon concentration in air, includes: The first data acquisition module is used to acquire the current sampling point's measurement cavity at the beginning of its sampling period. 222The number of Rn and its daughter nuclides is used as the initial value of the nuclides. Combined with a pre-constructed forward analytical model that includes gas exchange and nuclide decay, a function is established to measure the change of the number of nuclides in the cavity over time. The second data acquisition module is used to determine the theoretical total count of α particles at the current sampling point within its sampling period based on the function of the change of the number of nuclei in the measurement cavity over time. The third data acquisition module is used to obtain the number of radon atoms in the environment at the current sampling point based on the theoretical total count of α particles at the current sampling point within its sampling period and the pre-constructed measurement equation. The fourth data acquisition module is used to obtain the environmental radon concentration at the current sampling point based on the number of radon atoms in the environment at the current sampling point and the decay constant of radon. The fifth data acquisition module is used to utilize the number of radon atoms in the environment at the current sampling point and, based on a pre-built forward analytical model that includes gas exchange and nuclide decay, to obtain the data in the measurement chamber at the end of the sampling at the current sampling point. 222 The number of Rn and its daughter nuclides is used as the initial number of nuclides for the next sampling point. After switching sampling points, steps S1 to S4 are repeated. The sampling points are iterated one by one to complete the continuous measurement of environmental radon concentration.

[0023] A computer system includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described method.

[0024] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described method.

[0025] Compared with the prior art, the present invention has the following beneficial technical effects: A compensation method for continuous, rapid, and accurate measurement of radon concentration in air, wherein in step S1, the concentration of radon in the measurement chamber at the current sampling point at the beginning of its sampling period is obtained. 222The number of Rn and its daughter nuclides is used as the initial nuclide value to provide basic data for subsequent calculations. Then, combined with a pre-constructed forward analytical model that includes gas exchange and nuclide decay, a function of the change of nuclide number in the measurement chamber over time is established. Step S2 determines the theoretical total alpha particle count based on the function of the change of nuclide number in the measurement chamber over time, establishing the relationship between the total alpha particle count and the number of nuclides. Step S3 obtains the number of radon atoms in the current sampling point environment based on the theoretical total alpha particle count and the pre-constructed measurement equation. Step S4 obtains the environmental radon concentration at the current sampling point based on the number of radon atoms in the current sampling point environment and the decay constant of radon, achieving accurate calculation of the radon concentration at the current sampling point. The most crucial step is S5, which uses the number of environmental radon atoms at the current sampling point, based on the pre-constructed forward analytical model that includes gas exchange and nuclide decay, to obtain the concentration of radon in the measurement chamber at the end of the current sampling point. 222 The method calculates the number of Rn and its daughter nuclides, using this as the initial nuclide count for the next sampling point. By switching sampling points and repeating steps S1-S4, it iterates based on the sampling points. This method, through parameter iteration, allows a single radon meter to sample multiple points sequentially. Each measurement is based on the latest cavity state, eliminating the need for multiple devices to operate simultaneously, significantly reducing equipment costs. Furthermore, the iterative approach avoids the cumbersome balancing waiting process of traditional methods, significantly improving measurement efficiency. Moreover, this method is highly flexible, allowing for flexible switching of sampling points according to actual needs, meeting the requirements of scenarios with high cost and testing flexibility, and providing an effective solution for continuous, efficient, and accurate measurement of environmental radon concentration. Attached Figure Description

[0026] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a schematic flowchart of a compensation method for continuous, rapid and accurate measurement of radon concentration in the air according to the present invention. Figure 2 This is a compensation method for continuously, rapidly and accurately measuring radon concentration in the air, as described in Embodiment 2 of the present invention. Figure 3 for 222 decay framework diagram of Rn and its daughters; Figure 4 To describe the evolution of radon and its progeny within the cavity; Figure 5The figure shows the experimental results of the algorithm under multiple cycles of 10 minutes in a gas-flow circulation system (in the figure: the radon concentration in the test environment is...). The RAD7-5830 serves as a standard instrument for monitoring radon concentration in the environment under test. Its radon concentration curve reflects the rapid radon concentration during the measurement process. The real-time radon concentration measured by the air scintillation radon meter is: Radon concentration value under compensation algorithm Furthermore, the 0th moment of the measurement in the diagram is the moment the pump starts working, and the stages are continuous. Figure 6 This is a schematic diagram of the structure of a compensation system for continuous, rapid and accurate measurement of radon concentration in air according to the present invention; Figure 7 This is a schematic diagram of a rapid compensation system for continuously measuring radon concentration in air, according to another specific embodiment of the present invention. Detailed Implementation

[0028] The present invention will now be described in further detail with reference to the accompanying drawings: Example 1 like Figure 1 As shown, this invention discloses a compensation method for continuously, rapidly, and accurately measuring radon concentration in the air. The key parameters in this method, depending on the specific settings of the detector, include... , and the initial measurement chamber 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The number of atoms in Po, i.e. , , , , At the initial moment, the number of radon atoms and their daughter atoms in the chamber was measured to be 0, i.e. = = = = =0, and 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The effective proportion of Po carried away from the cavity during gas exchange and the corresponding detection efficiency for alpha particles, i.e. and It is obtained through calibration using preset experimental conditions. Specifically, the method includes the following steps: S1: Obtain the current sampling point and measure the cavity at the beginning of its sampling period. 222The number of Rn and its daughter nuclides is used as the initial value of the nuclides. Combined with a pre-constructed forward analytical model that includes gas exchange and nuclide decay, a function is established to measure the change of the number of nuclides in the cavity over time. The aforementioned pre-constructed forward analytical model, which incorporates gas exchange and nuclide decay, is as follows:

[0029]

[0030] In the formula, To measure the chamber 222 The number of atoms in Rn at time t; This refers to the sampling pump speed; To measure the cavity volume; This represents the number of radon atoms in the environment being tested at the current sampling point. for 222 The effective proportion of Rn carried away from the cavity during gas exchange; for 222 The decay constant of Rn; To measure the first in the chamber The number of atoms of a single nuclide at time t; for 222 The decay constant of the daughter nuclide of Rn; for 222 The effective proportion of Rn daughter nuclides that are carried out of the cavity during gas exchange.

[0031] In step S1, during the process of establishing the function of the number of nuclides in the measurement cavity changing with time, it is assumed that the radon concentration of the environment under test remains constant within a single sampling period. Furthermore, the pre-constructed forward analytical model, which includes gas exchange and nuclide decay, is transformed into matrix form and solved to establish the function of the number of nuclides in the measurement cavity changing with time.

[0032] In step S1 above, the pre-constructed forward analytical model, which includes gas exchange and nuclide decay, is transformed into matrix form for solution, specifically as follows:

[0033] in, It is a coefficient matrix; It is a state vector; The source term vector;

[0034] In the formula, , , , , They are respectively222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The decay constant of Po; , , , , They are respectively 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The effective proportion of Po that is carried away from the cavity during gas exchange; , , , , In the measuring chamber 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The number of atoms Po at time t, which is a function of the change in the number of nuclei in the measurement cavity over time. This refers to the sampling pump speed; To measure the cavity volume; This indicates transpose.

[0035] S2: Determine the theoretical total count of α particles at the current sampling point within its sampling period based on the function of the change in the number of nuclei in the measurement cavity over time; In step S2, the current sampling point is measured at the beginning of its sampling period in the chamber. 222 The quantity distribution of Rn and its daughter nuclides determines the theoretical total count of α particles at the current sampling point, specifically:

[0036]

[0037] in, This represents the theoretical total count of α particles at the current sampling point within its sampling period. The sampling period; The instantaneous α emissivity; , as well as They are respectively 222 Rn、 218 Po、 214 The number of atoms Po at time t; , , They are respectively 222 Rn、 218Po、 214 The decay constant of Po; , , They are respectively 222 Rn、 218 Po、 214 Po's detection efficiency.

[0038] S3: Based on the theoretical total count of α particles at the current sampling point within its sampling period and the pre-constructed measurement equation, obtain the number of radon atoms in the environment at the current sampling point; In step S3, the pre-constructed measurement equation is:

[0039] in, This represents the number of radon atoms in the environment being tested at the current sampling point. The total number of α particles at the current sampling point within its sampling period, as measured in the experiment; The residual decay contribution of the existing nuclides in the test cavity at the beginning of the current sampling point's sampling period; This represents the linear contribution of radon in the environment directly input into the test chamber during the sampling period at the current sampling point. S4: Based on the number of radon atoms in the current sampling point environment and the decay constant of radon, obtain the environmental radon concentration at the current sampling point;

[0040] In the formula, for 222 decay constant of Rn ； For environmental radon concentration, This represents the number of radon atoms in the environment being tested at the current sampling point.

[0041] S5: Utilizing the number of radon atoms in the current sampling point environment, and based on a pre-constructed forward analytical model incorporating gas exchange and nuclide decay, obtain the concentration of radon atoms in the measurement chamber at the end of the current sampling point. 222 The number of Rn and its daughter nuclides is used as the initial number of nuclides for the next sampling point. After switching sampling points, steps S1 to S4 are repeated. The sampling points are iterated one by one to complete the continuous measurement of environmental radon concentration.

[0042] Specifically, in constructing the aforementioned forward analytical model encompassing gas exchange and nuclide decay, firstly, based on clearly defining the geometric parameters of the measurement cavity, gas flow parameters, and the physical constants of each nuclide, a forward analytical model capable of characterizing the dynamic behavior of radon and its progeny within the cavity is established. This model, through a coupled set of ordinary differential equations, uniformly describes the radioactive decay chain and the gas replacement process, thus comprehensively reflecting the change in the number of nuclides within the cavity over time. Furthermore, considering the volume of the measurement cavity... Gas exchange flow rate and the decay constants of each nuclide. Ratio of carry-out The following basic relationship can be established for: 222 Rn, its quantity change is driven by both the environmental radon concentration input and its own radioactive decay and gas exchange consumption; for its daughter nuclides ( 218 Po、 214 Pb, 214 Bi、 214 The quantity variation of nuclides (such as Po) is determined by the decay supply of precursor nuclides, their own decay consumption, and gas exchange losses. Therefore, the dynamic processes of nuclides within the measurement chamber can be represented by the following set of coupled equations:

[0043]

[0044] In the formula, To measure the chamber 222 The number of atoms in Rn at time t; For sampling pump speed, m 3 / s; To measure the cavity volume, m 3 ; The radon atom number density in the environment to be tested at the current sampling point is [number] atoms. for 222 Rn is the effective proportion of gas that is carried away from the cavity during gas exchange; it is dimensionless. for 222 The decay constant of Rn, s -1 ; To measure the first in the chamber The number of atoms of a daughter nuclide at time t; for 222 The decay constant of the daughter nuclide of Rn, s -1 ; for 222 The effective proportion of Rn daughter nuclides that are carried away from the cavity during gas exchange, without units.

[0045] By establishing the above model, the dynamic behavior of radon and its progeny within the measurement cavity is clearly characterized, achieving a precise mathematical characterization of the behavior of radon and its progeny within the measurement cavity, and laying a theoretical foundation for the calculation of nuclide numbers.

[0046] Further, the above-mentioned coupled equations, namely the forward analytical model that includes gas exchange and nuclide decay, are as follows:

[0047] In the formula, , , , , They are respectively 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The number of Po atoms changes with time t, i.e. the distribution of the number of different nuclides in the current sampling period; For sampling pump speed, m 3 / s; To measure the cavity volume, m 3 ; The radon atom number density in the environment to be measured at the current sampling point is the radon atom number density in the environment to be measured at the current sampling point within its sampling period ΔT. , , , , They are respectively 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 Po is the effective proportion of gas that is carried away from the cavity during gas exchange; it has no unit. , , , , They are respectively 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The decay constant of Po, s -1 .

[0048] Furthermore, the pre-constructed forward analytical model incorporating gas exchange and nuclide decay is solved to obtain the current nuclide distribution state. Additionally, during the solution process, it is assumed that the environmental radon atom number density is [value missing] within a single sampling period ΔT. Keep it constant.

[0049] Furthermore, in solving the pre-constructed forward analytical model incorporating gas exchange and nuclide decay, the model is transformed into a matrix form for solution. Specifically, after establishing the forward analytical model incorporating gas exchange and nuclide decay, it is necessary to further obtain the quantity variation law of radon and its progeny within the measurement chamber in the short-time sampling interval [0, ΔT]. To this end, this step performs analytical solution on the above differential equation system to obtain the explicit expression of each nuclide over time. First, it is assumed that the radon concentration in the measured environment remains approximately constant within a single sampling period ΔT. Under this premise, the equation system can be regarded as a linear differential equation system with constant coefficients. Combining the given initial conditions, the nuclide concentrations can be solved sequentially, with the solution process starting from the parent nuclide. 222 Rn begins; its daughter bodies 218 Po、 214 Pb, 214 Bi、 214 The evolution of Po quantity is driven by the decay of precursor nuclides, passing down step by step. To improve analytical and computational efficiency, this invention reorganizes the equations into a compact matrix form, that is, transforms the pre-constructed forward analytical model involving gas exchange and nuclide decay into a matrix form for solution, specifically:

[0050] in, It is a coefficient matrix that comprehensively includes parameters such as the decay constant of each nuclide, the proportion carried out by gas exchange, pump speed, and cavity volume; This is a state vector representing the quantity of radon and its progeny within the measurement cavity; The source term vector is used to characterize the input effect of environmental radon into the cavity. The specific forms of the three are as follows.

[0051] Specifically,

[0052] By solving the above matrix equations, analytical solutions for each nuclide were obtained, and the distribution state of each nuclide was acquired, i.e., the distribution state of the nuclide within the measurement chamber. 222 The number of atoms of Rn and its daughters at time t. This analytical solution fully characterizes the dynamic behavior of nuclide accumulation (driven by environmental radon input), decay (determined by the decay constant), and efflux (determined by gas exchange). It provides the nuclide number distribution at any given time, facilitating the calculation of the theoretical total α count.

[0053] For the above iterative testing process, the environmental radon atom number density under the current sampling period was obtained by solving the measurement equation. ,Right now To represent a cyclic process, Change to That is, the current period is period k. To ensure that the model can continuously and accurately reflect the true physical state of the measurement cavity, the number of nuclides in the cavity needs to be updated at the end of each period and used as the initial condition for the next period, thus forming a recursive iterative process. Specifically, let the number of nuclides be k at the end of the current period. At the start of each sampling period, the quantities of each nuclide within the cavity are respectively for The environmental radon concentration obtained in the previous cycle was... In the sampling interval [ , Within this period, using the forward analytical model established in step 1, iterative calculations are performed on the generation, decay, and efflux processes of nuclides to obtain the updated state at the end of the period:

[0054] in As an analytical function, it comprehensively characterizes the effects of environmental radon input, radioactive decay, and gas exchange carryover. The resulting... This serves as the initial condition for the next sampling period, used to recalculate the theoretical total alpha particle count. In this way, the environmental radon concentration is obtained. This establishes a seamless connection with the updated internal state of the cavity: the estimated environmental radon concentration provides input for nuclide evolution, while the updated nuclide evolution, in turn, serves as the initial condition for the measurement equations of the next period. The resulting closed-loop recursive process can be expressed as:

[0055] This closed-loop mechanism ensures that the model can continuously track the actual physical evolution within the cavity, thus maintaining accurate and rapid estimation of environmental radon concentration even under non-equilibrium conditions. Compared with traditional methods that rely on radioactive equilibrium and require long-term stabilization, this method can obtain reliable results within a short sampling period, achieving rapid determination in dynamic environments. Furthermore, because the model employs a fully analytical approach, the computation is efficient and suitable for embedded implementation, meeting the rapid application requirements of long-term online monitoring systems. This method measures the contents of the chamber at the beginning of its sampling period using the current sampling point. 222 The theoretical total alpha particle count at the current sampling point is obtained by determining the number distribution of Rn and its daughter nuclides. Then, combined with the measured total alpha particle count, the radon concentration in the test environment at the current sampling point can be obtained by solving the measurement equation. Subsequently, iterative updates are performed, and the radon concentration in the test chamber at the end of the sampling period at the current sampling point is obtained from the radon concentration in the test environment at the current sampling point. 222The quantity distribution of Rn and its daughter nuclides is used as the initial state for the next sampling point. This is then iteratively updated according to steps S1-S5 to continuously obtain the environmental radon concentration at multiple sampling points. Key parameters in this method, dependent on the specific detector settings, include... , and the initial measurement chamber 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The number of atoms in Po, i.e. , , , , At the initial moment, the number of radon atoms and their daughter atoms in the chamber was measured to be 0, i.e. = = = = =0, and 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The effective proportion of Po carried away from the cavity during gas exchange and the corresponding detection efficiency for alpha particles, i.e. and The radon concentration is obtained through a pre-set experimental calibration. This method can continuously, rapidly, and accurately measure radon concentration in the air at different locations, effectively addressing the shortcomings of existing technologies, such as limited monitoring range and inability to track radon concentration trends. Therefore, this compensation method helps to protect workers and the public from radon exposure in a timely manner.

[0056] Example 2 To further explain the solution of the present invention, this embodiment will be used as an example: like Figure 2 As shown, this invention discloses a compensation method for continuously, rapidly, and accurately measuring radon concentration in the air. The key parameters in this method, depending on the specific settings of the detector, include... , and the initial measurement chamber 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The number of atoms in Po, i.e. , , , , At the initial moment, the number of radon atoms and their daughter atoms in the chamber was measured to be 0, i.e. = = = = =0, and 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The effective proportion of Po carried away from the cavity during gas exchange and the corresponding detection efficiency for alpha particles, i.e. and It is obtained through calibration using preset experimental conditions. Specifically, the method includes the following steps: Step 1: Set initial conditions and establish a forward analytical model that includes gas exchange and nuclide decay; In this step, the geometric volume of the measuring cavity, the flow parameters of the sampling pump, and... 222 Based on the decay constants of Rn and its progeny and the proportion carried out by the flow, a forward analytical model capable of characterizing the dynamic behavior of radon and its progeny within the measurement cavity was established. The modeling process referenced… 222 decay outline of Rn and its daughters (e.g., decay outline of Rn and its daughters) Figure 3 As shown), this outline diagram illustrates 222 Rn is generated via α decay. 218 Po、 214 Pb, 214 Bi、 214 Po, eventually forming a stable 210 The chain evolution of Pb. The decay constant of each nuclide. Both half-life and radioactive decay are introduced as key physical parameters in the model to ensure an accurate description of the radioactive decay process.

[0057] On the other hand, it also incorporates "the description of the evolution of radon and its progeny within the cavity" (such as...). Figure 4 As shown in the figure, this diagram visually illustrates the migration and evolution of radon and its progeny within the cavity under flowing air conditions from a physical process perspective: 222 Rn enters the measurement chamber with the sampling gas flow, where it undergoes radioactive decay to continuously generate daughter nuclides. These daughter nuclides undergo three types of processes within the chamber: first, a stepwise transformation driven by the radioactive decay chain; second, loss due to being carried out of the chamber by the gas flow; and third, deposition on the chamber walls or aerosols. All three types of effects influence the instantaneous quantity of each nuclide within the chamber and must be considered uniformly in the kinetic model.

[0058] Regarding initial conditions, this embodiment assumes that the cavity is empty and the number of each nuclide is zero when the system starts up; while during continuous multi-cycle operation, the initial state of each cycle is directly inherited from the nuclide state at the end of the previous cycle to ensure the continuity of the physical process. In mathematical description, a set of coupled ordinary differential equations is used to uniformly express the above process.

[0059]

[0060] In the formula, , , , , In the measuring chamber 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The number of atoms Po at time t; For sampling pump speed, m 3 / s; To measure the cavity volume, m 3 ; This represents the radon atom number density in the environment to be tested at the current sampling point. , , , , They are respectively 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 Po is the effective proportion of gas that is carried away from the cavity during gas exchange; it has no unit. , , , , They are respectively 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The decay constant of Po, s -1 .

[0061] Step 2: Solve for the time evolution of the number of nuclides; After establishing a forward analytical model incorporating gas exchange and radioactive decay, it is necessary to further obtain the quantity variation law of radon and its progeny within the measurement chamber in the short-time sampling interval [0, ΔT]. This embodiment refers to " 222Based on the decay pattern of Rn and its progeny and the description of the evolution law of radon and its progeny in the measurement cavity, the coupled differential equations in step 1 are solved analytically to obtain the explicit expression of the evolution of each nuclide over time.

[0062] For ease of solution, assume that the radon concentration in the environment to be measured is within a single sampling period ΔT. Keeping the equations constant, the system can now be considered a linear system with constant coefficients. This is in conjunction with the given initial conditions (i.e., the quantity and state of each nuclide within the cavity at the beginning of the period, as mentioned in step 1). This allows us to solve for the concentrations of each nuclide sequentially. The order of solutions is determined by the parent nuclide. 222 Starting with Rn, it is passed down level by level to 218 Po、 214 Pb, 214 Bi、 214 Po. First, write the system of equations in matrix form:

[0063] in, It is a coefficient matrix that comprehensively includes parameters such as the decay constant of each nuclide, the proportion carried out by gas exchange, pump speed, and cavity volume; This is a state vector representing the quantity of radon and its progeny within the measurement cavity; The source term vector is used to characterize the input effect of environmental radon into the cavity. The specific forms of the three are as follows.

[0064]

[0065] For this type of linear differential equation system with constant coefficients, its analytical solution can be expanded step-by-step. Parent body 222 The solution to Rn is:

[0066] in , , , For daughter body 218 Po, whose quantity over time is the analytical solution:

[0067]

[0068] in .

[0069] Similarly, we can obtain 214 Pb, 214 Bihe 214 Analytical solution for Po:

[0070] The recursive parameters are as follows: , , , , , ,

[0071] , , ,

[0072] ,

[0073] In the above formula , = , = , = , = ; ;

[0074] In summary, the analytical solution fully characterizes the accumulation, consumption, and evolution of radon and its progeny within the measurement cavity under the combined effects of environmental input, radioactive decay, and gas exchange. It can provide the nuclide quantity distribution at any given time. This analytical solution is a function of the change in the number of nuclides within the measurement cavity over time, laying the foundation for subsequent theoretical α total count calculations and the construction of measurement equations.

[0075] Step 3: Obtain the theoretical total count of alpha particles; Based on the analytical solutions obtained in step 2 for N0(t), N1(t), and N4(t), the instantaneous α-emission rate is first written to calculate the theoretical total count of α particles within a single sampling interval [0, ΔT]. Given that the α-emitting nuclides detectable in this system in the radon decay chain are... 222 Rn (where i=0), 218 Po (denoted as i=1) and 214 Po (denoted as i=4), the instantaneous α emission rate is:

[0076] in: The solution is given by the analytical solution in step 2; Let s be the decay constant. -1 ; The detection efficiency is for different nuclides. The theoretical total α count for the sampling interval is given by integration:

[0077] To obtain an explicitly computable closed-form expression, this embodiment adopts the engineering-standard assumption of "constant external source within the period" (consistent with the constant coefficient framework in step 2) within a single period [0, ΔT]. It remains constant within this interval. (Introduced in step 2) as well as and define

[0078] Then (16) can be written as the sum of the contributions of the three components:

[0079] The explicit expression of each component is as follows, corresponding to 222 The contribution of Rn to the total count of α. Its mathematical form is as follows:

[0080] correspond 218 Po's contribution to the total count of α. Its mathematical form is as follows:

[0081] correspond 214 Po's contribution to the total count of α. Its mathematical form is as follows:

[0082] In the formula, For the recursive parameter, see formula (14) above; For the recursive parameters, see formulas (11) to (14) above.

[0083] Equations (19)–(21) give , , The total α count is explicitly decomposed into a linear combination of two effects: external radon input-driven and hysteretic decay of residual progeny within the cavity. The terms reflect the direct contributions of external sources within and during the test period ΔT; including The terms reflect the continuation and compensation of the state during the cycle. The above closed-form results directly serve to establish the next step of the measurement equation: [The following is a continuation of the previous continuation, but the context is unclear: "will..."] Total count with experiment α Alignment allows the current environmental radon concentration to be determined within each cycle, and the nuclide state at the end of the cycle can be used for continuous compensation in subsequent cycles, thus forming a fast and accurate closed-loop measurement process.

[0084] Step 4: Solve the measurement equation based on the total alpha particle count obtained from the experiment to obtain the current period's environmental radon concentration; Building upon the explicit expression of the theoretical total alpha particle count obtained in step 3, this step combines the theoretical results with experimental observations to construct a measurement equation to solve for the environmental radon concentration during the current sampling period [0, ΔT]. Analytical derivation allows the theoretical total count to be decomposed into the sum of exogenous driving forces and residual terms:

[0085] in The linear contribution of direct external radon input within the current cycle is characterized by relying solely on system parameters and integration duration. This reflects the residual decay contribution of existing nuclides in the cavity at the beginning of the period. , , , , , , , , , , , ,

[0086]

[0087] , , , , , , , , , , , ,

[0088]

[0089] The total number of α particles measured in the sampling interval is denoted as . The measurement equation is obtained by comparing the theory with the experiment.

[0090] Therefore, the environmental radon atom number density for the current period can be directly calculated.

[0091] And can be converted into the corresponding activity concentration.

[0092] Thus, a one-to-one closed mapping is established between experimental observations and environmental radon concentration; Equation (24) clearly distinguishes the dual contribution of external radon input and internal progeny residue, so even under short sampling or non-equilibrium conditions, the environmental radon concentration to be measured can still be reliably obtained, providing input for the state update and continuous compensation of the next cycle.

[0093] Step 5: Update environmental radon concentration based on iterative loop In step 4, the environmental radon atom number density for the current sampling period has been obtained by solving the measurement equation. In this invention, this parameter can also be expressed as This refers to the number of radon atoms in the environment at the current sampling point. To characterize the continuous sampling process, it is denoted as the environmental radon concentration in the k-th sampling period. To ensure the model accurately reflects the true physical state of the measurement cavity, the number of nuclides within the cavity needs to be updated at the end of each cycle, and this update is used as the initial condition for the next cycle, thus constructing a recursive iterative process. Specifically, let the number of each nuclide within the cavity at the beginning of the k-th sampling cycle be... for The environmental radon concentration obtained in the previous cycle was... In the sampling interval [t] k ,t k+1 Within this process, using the forward analytical model established in step 1, iterative calculations are performed on the generation, decay, and gas exchange processes of nuclides to obtain the updated state at the end of the cycle:

[0094] in This is an analytic function that comprehensively characterizes the combined effects of environmental radon input, radioactive decay, and gas exchange losses. The resulting... This serves as the initial condition for the next cycle and can be used to recalculate the theoretical total alpha particle count. Thus, the environmental radon concentration obtained in step 4... The update of the cavity's internal state in step 5 is closely linked: on the one hand, the estimated environmental radon concentration provides input for nuclide evolution; on the other hand, the updated nuclide evolution results, in turn, serve as the initial conditions for the measurement equations in the next cycle. This closed-loop iterative process can be formally represented as:

[0095] Through this recursive update mechanism, the model can continuously track the actual physical evolution of the measurement cavity, thus maintaining an accurate and rapid estimate of environmental radon concentration even under non-equilibrium conditions. Compared with traditional methods that rely on radioactive equilibrium and require long-term stabilization, this method can obtain reliable results within a short sampling period, achieving rapid determination in dynamic environments. Furthermore, because the model employs a fully analytical approach, the computation process is efficient and stable, facilitating real-time applications in embedded processors or long-term online monitoring systems, and possessing significant engineering application value.

[0096] Furthermore, to ensure the accuracy of the model, this embodiment incorporates the calibration results from cavity experiments to perform experimental calibration of key system parameters. The calibration results for the proportional vector carried over by the flow are as follows:

[0097] Simultaneously, detection experiments were conducted on various alpha-emitting nuclides. By fitting relevant parameters through experiments, the following results were obtained:

[0098] The introduction of these parameters makes the forward analytical model and iterative update mechanism more consistent with the actual detector performance, ensuring the reliability of the algorithm in engineering applications. Through this calibration process, the system can stably output fast and accurate environmental radon concentration results in multi-cycle continuous measurements, realizing real-time compensation and continuous monitoring of radon concentration changes under dynamic non-equilibrium conditions.

[0099] It should be noted that due to the coupling between the governing equations and the simplification assumptions of the model, the set of parameter values ​​may not be unique in a mathematical sense. The parameter values ​​obtained here are only the results that meet the relatively optimal measured values ​​under the current model framework and experimental conditions.

[0100] After completing the modeling, measurement, and iterative updates in steps 1–5, this embodiment designed and conducted an independent experiment to further verify the performance of the fast compensation algorithm under dynamic radon exposure conditions. The experiment used calibrated system parameters to switch between different radon chambers and different stages of exposure, constructing a dynamically changing radon concentration environment to comprehensively evaluate the algorithm's prediction accuracy and robustness.

[0101] The specific experimental procedure was as follows: In the initial stage of the experiment, the sampling gas path was sequentially switched to radon chamber 3 (Phase I: 0–210 minutes), radon chamber 2 (Phase II: 210–510 minutes), radon chamber 1 (Phase III: 510–810 minutes), and finally switched to the outdoor atmospheric environment (Phase IV: 810–1450 minutes). The concentration levels and exposure durations of the radon chambers in each phase differed from those in the modeling phase to test the algorithm's adaptability under varying radon source sequences and extended exposure durations. During the experiment, an air scintillation detector collected alpha particle count data in real time, which was then processed using a fast compensation algorithm to obtain the reconstructed environmental radon concentration.

[0102] Figure 5 A comparison is presented between the calculation results of the fast compensation algorithm and the measurement results of the reference instrument (RAD7-5830). It can be seen that in all four stages, the radon concentration reconstructed by the algorithm is highly consistent with the reference value, and can accurately reproduce the fluctuations of the experimental radon concentration. In particular, it shows excellent response speed at the beginning and end points of concentration abrupt changes, while the reference instrument has a significant hysteresis effect in the rapid change stage.

[0103] Quantitative analysis shows that the average relative error of this method throughout the entire experimental sequence is only 0.57%, and the maximum deviation at each stage does not exceed 3.29%. This not only proves that the algorithm can accurately reproduce steady-state concentration levels, but also enables high-precision tracking of abrupt changes under short-term sampling. In contrast, traditional instruments require a long stabilization time to output reliable results, while the fast compensation algorithm can complete the settling within minutes, highlighting its advantages in dynamic environments.

[0104] Furthermore, experiments show that even with short-term airflow disturbances and pressure fluctuations during manual switching of sampling points, the radon concentration reconstructed by the algorithm remains consistent with the reference value, without any systematic deviation. This demonstrates that the proposed analytical modeling and iterative update framework has good anti-interference capabilities and can effectively suppress unavoidable transient noise in experiments.

[0105] In summary, experimental verification fully demonstrates that the fast compensation algorithm proposed in this invention can achieve reliable real-time continuous monitoring in dynamic radon exposure environments without relying on radioactive equilibrium conditions. Through the organic combination of analytical solutions and iterative updates, this method possesses both high accuracy and strong robustness, making it particularly suitable for long-term online monitoring in rapidly changing and unpredictable field environments with varying radon concentrations. It has significant application value and promotional significance.

[0106] Example 3 like Figure 6 As shown, this invention discloses a compensation system for continuous, rapid, and accurate measurement of radon concentration in the air, used to implement the compensation method for continuous, rapid, and accurate measurement of radon concentration in the air described in this invention, comprising: The first data acquisition module is used to acquire the current sampling point's measurement cavity at the beginning of its sampling period. 222 The number of Rn and its daughter nuclides is used as the initial value of the nuclides. Combined with a pre-constructed forward analytical model that includes gas exchange and nuclide decay, a function is established to measure the change of the number of nuclides in the cavity over time. The second data acquisition module is used to determine the theoretical total count of α particles at the current sampling point within its sampling period based on the function of the change of the number of nuclei in the measurement cavity over time. The third data acquisition module is used to obtain the number of radon atoms in the environment at the current sampling point based on the theoretical total count of α particles at the current sampling point within its sampling period and the pre-constructed measurement equation. The fourth data acquisition module is used to obtain the environmental radon concentration at the current sampling point based on the number of radon atoms in the environment at the current sampling point and the decay constant of radon. The fifth data acquisition module is used to utilize the number of radon atoms in the environment at the current sampling point and, based on a pre-built forward analytical model that includes gas exchange and nuclide decay, to obtain the data in the measurement chamber at the end of the sampling at the current sampling point. 222 The number of Rn and its daughter nuclides is used as the initial number of nuclides for the next sampling point. After switching sampling points, steps S1 to S4 are repeated. The sampling points are iterated one by one to complete the continuous measurement of environmental radon concentration.

[0107] Additionally, a schematic diagram of a terminal device according to an embodiment of the present invention is provided. This terminal device includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the various method embodiments described above. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the various device embodiments described above.

[0108] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention.

[0109] The terminal device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0110] The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0111] The memory can be used to store the computer program and / or module. The processor implements various functions of the terminal device by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory.

[0112] If the modules / units integrated into the terminal device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0113] Example 4 To further explain the radon measurement system in this invention, this embodiment will be used as an example: like Figure 7As shown, this invention discloses a compensation system for continuous, rapid, and accurate measurement of radon concentration in air. This system, based on a rapid compensation algorithm, aims to achieve sequential acquisition, dynamic correction, and rapid value determination of air samples from multiple measurement points under non-equilibrium conditions, making it particularly suitable for short sampling cycles and continuous monitoring scenarios. The system comprises a gas path switching and flow control unit, a measurement chamber and air scintillation detection unit, a data acquisition and counting unit, a centralized data processing unit, and a result output and storage unit. These units work closely together, organically integrating the hardware platform with the rapid compensation algorithm to form a complete solution. Compared to traditional methods relying on radioactive equilibrium and long-term stabilization, this system can rapidly output reliable radon concentration values ​​within a short sampling cycle of several minutes, maintaining continuous compensation and real-time tracking in dynamic environments. This significantly improves the timeliness and accuracy of measurements. It is suitable for radon chamber calibration under laboratory conditions, as well as for nuclear facility safety monitoring, underground engineering environmental protection, and long-term online monitoring networks, demonstrating significant engineering application value and broad prospects for promotion.

[0114] During system operation, the gas path switching and flow control unit plays a crucial role. Through pre-defined timing logic, it utilizes the coordinated action of switching valves, flow meters, and pressure regulators to sequentially switch between multiple sampling points while maintaining a stable and uniform airflow. Ambient air, driven by the sampling pump, enters the sampling branch at the selected point and is ultimately introduced into the measurement chamber. The system allows for the setting of sampling timing and flow calibration programs to ensure that cross-contamination or measurement lag does not occur during point switching, guaranteeing the representativeness and accuracy of air samples collected at each point.

[0115] Radon and its decay products entering the measurement chamber excite air molecules during radioactive decay, generating ultraviolet scintillation signals. At this point, the measurement chamber and the air scintillation detection unit begin operation. This unit employs a high-sensitivity photomultiplier tube (PMT), combined with reflective materials and optical coupling devices to improve photon collection efficiency. The generated weak light signal is converted into electrical pulses by the PMT, and then transmitted to the data acquisition and counting unit. In this unit, the electrical pulses are amplified, filtered, and shaped by front-end electronic circuitry before being transmitted to the coincidence logic and counting circuitry. To ensure counting accuracy, the system incorporates background subtraction, dead-time correction, and noise filtering mechanisms in the data acquisition stage, ultimately obtaining a reliable net alpha particle count, providing input for subsequent calculations.

[0116] The centralized data processing unit, embedded with a fast compensation algorithm, is the core of the system. Based on analytical modeling, this algorithm first establishes a forward analytical model that simultaneously considers gas exchange and nuclide decay after setting initial conditions. By solving a matrix-based system of constant-coefficient differential equations, the theoretical analytical solution for the change in the quantity of radon and its progeny within the cavity over time is obtained, and the theoretical total alpha particle count is further calculated. Key parameters of the analytical model are obtained through preset experimental conditions and cavity calibration, including pump speed, cavity volume, decay constants of each nuclide, carry-over ratio, and detection efficiency, ensuring that the calculation results accurately reflect the physical state within the measurement cavity. Subsequently, the algorithm compares the theoretical value with the measured total alpha particle count obtained by the detector during the sampling period, constructs and solves the measurement equation, thereby obtaining the environmental radon concentration for the current period. To achieve continuous measurement, the algorithm utilizes an iterative update mechanism to correct the nuclide state within the cavity. At the end of each cycle, the nuclide state is corrected based on the predicted radon concentration, and the corrected result is used as the initial condition for the next cycle, allowing the result at the end of the cycle to naturally transition to the initial condition for the next cycle. The entire closed-loop process of "modeling-measurement-solving-updating" is directly embedded in the algorithm itself, ensuring that the system can compensate for lag effects in real time and closely track dynamic changes during continuous multi-cycle measurements. This guarantees both computational accuracy and real-time performance, making it suitable for efficient operation in embedded devices and long-term online monitoring systems. The centralized data processing unit here includes the first, second, third, and fourth data acquisition modules mentioned above.

[0117] The results output and storage unit is used to organize and present radon concentration values ​​from different locations and over different periods. This unit supports the intuitive display of radon concentration changes at different locations on a local terminal in numerical, curve, or chart form, facilitating operators' quick understanding of the monitoring situation. Furthermore, it can store measurement data long-term or upload it to a remote server via a communication interface, enabling centralized management, trend analysis, and early warning of exceedances for multi-location data. The system supports continuous measurement at a single location over multiple periods, and also supports sequential switching between multiple locations, ultimately forming a radon concentration dataset covering multiple spatial locations with time-series characteristics. This dataset reflects both the dynamic evolution of a single location and the overall distribution across different spatial locations.

[0118] The method and system described in this invention effectively address the shortcomings of existing technologies, such as limited monitoring range and inability to capture dynamic changes in radon concentration. The closed-loop analytical framework established through a fast compensation algorithm improves measurement efficiency and enhances the reliability of results, providing scientific and real-time radon monitoring data in complex scenarios such as nuclear facility operation, underground engineering construction, and public health protection. Furthermore, the system is compact, stable, and equipped with a computer-readable storage medium containing a computer program. When executed by a processor, the program implements all steps of the aforementioned fast compensation method. With this computer program, the system can operate efficiently on embedded platforms, industrial computers, or centralized servers, ensuring low power consumption, high stability, and real-time performance during long-term operation, demonstrating significant application value and promising prospects. However, it is worth noting that the scope of computer-readable storage media may vary depending on the legislation and patent practices of different jurisdictions. In some regions, electrical carrier signals and telecommunication signals may not be considered part of computer-readable storage media. Appropriate adjustments must be made according to local laws and regulations in specific applications.

[0119] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A compensation method for continuous, rapid, and accurate measurement of radon concentration in air, characterized in that, Includes the following steps: S1: Obtain the current sampling point and measure the cavity at the beginning of its sampling period. 222 The number of Rn and its daughter nuclides is used as the initial value of the nuclides. Combined with a pre-constructed forward analytical model that includes gas exchange and nuclide decay, a function is established to measure the change of the number of nuclides in the cavity over time. S2: Determine the theoretical total count of α particles at the current sampling point within its sampling period based on the function of the change in the number of nuclei in the measurement cavity over time; S3: Based on the theoretical total count of α particles at the current sampling point within its sampling period and the pre-constructed measurement equation, obtain the number of radon atoms in the environment at the current sampling point; S4: Based on the number of radon atoms in the current sampling point environment and the decay constant of radon, obtain the environmental radon concentration at the current sampling point; S5: Utilizing the number of radon atoms in the current sampling point environment, and based on a pre-constructed forward analytical model incorporating gas exchange and nuclide decay, obtain the concentration of radon atoms in the measurement chamber at the end of sampling at the current sampling point. 222 The number of Rn and its daughter nuclides is used as the initial number of nuclides for the next sampling point. After switching sampling points, steps S1 to S4 are repeated. The sampling points are iterated one by one to complete the continuous measurement of environmental radon concentration. In step S1, the pre-constructed forward analytical model, which includes gas exchange and nuclide decay, is as follows: In the formula, To measure the number of 222Rn atoms in the chamber at time t; This refers to the sampling pump speed; To measure the cavity volume; This represents the number of radon atoms in the environment being tested at the current sampling point. This refers to the effective proportion of 222Rn that is carried away from the cavity during gas exchange; The decay constant is 222Rn; To measure the first in the chamber The number of atoms of a single nuclide at time t; The decay constant of the daughter nuclide of 222Rn; The effective proportion of 222Rn daughter nuclides carried away from the cavity during gas exchange; In step S3, the pre-constructed measurement equation is: in, This represents the number of radon atoms in the environment being tested at the current sampling point. The total number of α particles at the current sampling point within its sampling period, as measured in the experiment; The residual decay contribution of the existing nuclides in the test cavity at the beginning of the current sampling point's sampling period; This represents the linear contribution of radon in the environment directly input into the test chamber during the sampling period at the current sampling point.

2. The compensation method for continuous, rapid, and accurate measurement of radon concentration in air according to claim 1, characterized in that, In step S1, during the process of establishing the function of the number of kernels in the measurement cavity changing with time, it is assumed that the radon concentration of the environment under test remains constant within a single sampling period.

3. The compensation method for continuous, rapid, and accurate measurement of radon concentration in air according to claim 1, characterized in that, In step S1, the pre-constructed forward analytical model, which includes gas exchange and nuclide decay, is transformed into matrix form and solved to establish a function of the change in the number of nuclides in the measurement cavity over time.

4. The compensation method for continuous, rapid, and accurate measurement of radon concentration in air according to claim 3, characterized in that, In step S1, the pre-constructed forward analytical model, which includes gas exchange and nuclide decay, is transformed into matrix form for solution, specifically as follows: in, It is a coefficient matrix; It is a state vector; The source term vector; In the formula, , , , , They are respectively 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The decay constant of Po; , , , , They are respectively 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The effective proportion of Po that is carried away from the cavity during gas exchange; , , , , In the measuring chamber 222 Rn、 218 Po、 214 Pb, 214 Bi、 214 The number of atoms Po at time t; This refers to the sampling pump speed; To measure the cavity volume; This indicates transpose.

5. The compensation method for continuous, rapid, and accurate measurement of radon concentration in air according to claim 1, characterized in that, In step S2, the theoretical total count of α particles at the current sampling point within its sampling period is determined based on the function of the change in the number of nuclei in the measurement cavity over time. Specifically: in, This represents the theoretical total count of α particles at the current sampling point within its sampling period. The sampling period; The instantaneous α emissivity; , as well as They are respectively 222 Rn、 218 Po、 214 The number of atoms Po at time t; , , They are respectively 222 Rn、 218 Po、 214 The decay constant of Po; , , They are respectively 222 Rn、 218 Po、 214 Po's detection efficiency.

6. A compensation system for continuous, rapid, and accurate measurement of radon concentration in air, characterized in that, A compensation method for implementing the continuous, rapid, and accurate measurement of radon concentration in air as described in any one of claims 1 to 5, comprising: The first data acquisition module is used to acquire the current sampling point's measurement cavity at the beginning of its sampling period. 222 The number of Rn and its daughter nuclides is used as the initial value of the nuclides. Combined with a pre-constructed forward analytical model that includes gas exchange and nuclide decay, a function is established to measure the change of the number of nuclides in the cavity over time. The second data acquisition module is used to determine the theoretical total count of α particles at the current sampling point within its sampling period based on the function of the change of the number of nuclei in the measurement cavity over time. The third data acquisition module is used to obtain the number of radon atoms in the environment at the current sampling point based on the theoretical total count of α particles at the current sampling point within its sampling period and the pre-constructed measurement equation. The fourth data acquisition module is used to obtain the environmental radon concentration at the current sampling point based on the number of radon atoms in the environment at the current sampling point and the decay constant of radon. The fifth data acquisition module is used to utilize the number of radon atoms in the environment at the current sampling point and, based on a pre-built forward analytical model that includes gas exchange and nuclide decay, to obtain the data in the measurement chamber at the end of the sampling at the current sampling point. 222 The number of Rn and its daughter nuclides is used as the initial number of nuclides for the next sampling point. After switching sampling points, steps S1 to S4 are repeated. The sampling points are iterated one by one to complete the continuous measurement of environmental radon concentration.

7. A computer system comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method as described in any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method as described in any one of claims 1 to 5.

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