A key parameter uncertainty analysis calibration method, storage medium and system

Abstract

The application relates to a key parameter uncertainty analysis calibration method, comprising the following steps: establishing a radioactive powder material spillage accident simulation model and solving; performing a radioactive powder spillage physical experiment to obtain aerosol distribution characteristics and diffusion rules of the released aerosol in a radioactive powder spillage accident; determining a key parameter value range and a probability distribution; establishing a Gaussian process-based proxy model; performing key parameter uncertainty analysis; and calibrating the key parameter value. The application also provides a storage medium and a key parameter uncertainty analysis calibration system. The key parameter uncertainty analysis calibration method, the storage medium and the system can improve the calculation accuracy of a numerical simulation method for simulating a radioactive powder spillage aerosol concentration field.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation of nuclear accident source terms, and specifically relates to a method, storage medium and system for uncertainty analysis and calibration of key parameters. Background Technology

[0002] During the production and operation of nuclear fuel cycle facilities, accidents involving the spillage of radioactive powder materials may occur. When this happens, aerosol particles disperse into the facility, increasing the aerosol concentration and potentially posing a radiation risk to the public and occupational workers. The diffusion conditions within the facility are relatively complex due to numerous factors, including the spatial layout of the facility, the size of the spilled material particles, gravity settling, diffusion, deposition, surface adhesion, gas flow, and the local environment.

[0003] There are currently some physical experiments conducted on the scenario of radioactive powder spillage. These experiments have preliminarily studied the differences in the aerosol release ratio after powder materials are spilled from different heights. However, the experiments have not fully considered the influence of material properties, ambient temperature, ventilation and other conditions on aerosol distribution and release ratio.

[0004] With the improvement of computer performance, numerical simulation methods, especially computational fluid dynamics (CFD), have been widely used in many fields. CFD methods can be used to simulate the spillage process of radioactive powder materials, and the simulation results can be compared and analyzed with experimental results to verify the effectiveness of the numerical model. Furthermore, it can be extended to more complex environmental conditions such as factory buildings and spillage accident scenarios of different materials, providing technical support for accident response and personnel protection, release source term estimation and consequence assessment, and accident handling.

[0005] In numerical simulations of gas-solid two-phase flows, radioactive aerosols are subjected to complex forces, and numerous parameters affect their diffusion, such as characteristic airflow velocity, turbulent dissipation rate, and drop velocity. These parameters and forces are usually difficult to obtain directly through experiments and are instead set based on empirical values. However, in reality, the values ​​of these parameters may not be completely consistent with empirical values, and may even be dynamically changing. Their actual values ​​are difficult to determine as a specific value, and can only be roughly determined as a range. In order to determine the degree of influence of these parameters and forces on aerosol diffusion in numerical simulations, there is an urgent need for an uncertainty analysis method for the parameters, and to establish a method for correcting the values ​​of these key parameters using experimental measurement data, so that their values ​​are more consistent with the real situation. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the present invention aims to provide a key parameter uncertainty analysis and calibration method, storage medium, and system to quantify the uncertainties in the output results of aerosol diffusion numerical simulations and to calibrate the parameters in the numerical simulations to make them more consistent with the true values, thereby improving the accuracy of the numerical simulations.

[0007] To achieve the above objectives, the technical solution adopted by this invention is: a key parameter uncertainty analysis and calibration method, comprising the following steps: establishing and solving a simulation model of a radioactive powder spill accident; conducting a physical experiment on radioactive powder spill to obtain the distribution characteristics and diffusion law of aerosols released during the radioactive powder spill accident; determining the value range and probability distribution of key parameters; establishing a surrogate model based on a Gaussian process; performing uncertainty analysis on key parameters; and calibrating the values ​​of key parameters.

[0008] Furthermore, the establishment and solution of a simulation model for a radioactive powder spill accident includes: establishing a geometric model, establishing a numerical model, setting parameters, and performing the solution.

[0009] Furthermore, during the physical experiment of radioactive powder spillage, the sampling port of the sampler is placed at different spatial heights to obtain the aerosol distribution at different times and in different spaces.

[0010] Furthermore, during the physical experiment of radioactive powder scattering, experiments were conducted with constant ventilation conditions but varying the material scattering height, and experiments with constant material scattering height but varying the ventilation conditions.

[0011] Furthermore, the key parameters include airflow characteristic velocity, turbulent dissipation rate, and material spill velocity; the probability distribution includes uniform distribution, normal distribution, and logarithmic distribution.

[0012] Furthermore, in the process of establishing the surrogate model, a small number of parameters of interest, such as material release height, airflow characteristic velocity, turbulent dissipation rate, and material spillage rate, were randomly sampled to obtain 200 sets of parameter combinations. Numerical simulation was used to solve the aerosol concentration data of key monitoring points. The parameters such as material release height, airflow characteristic velocity, turbulent dissipation rate, and material spillage rate were used as inputs to the surrogate model, and the aerosol concentration data of key monitoring points were used as outputs. 180 sets of data were randomly selected as training datasets to train the Gaussian process surrogate model, and the remaining 20 sets of data were used as test datasets to evaluate the accuracy of the surrogate model output results.

[0013] Furthermore, when performing uncertainty analysis on key parameters, the Monte Carlo random sampling algorithm is used to sample the key parameters according to their probability distribution, and the sampled parameter combinations are input into the surrogate model to calculate the aerosol concentration output results of key monitoring points. After statistical processing, the range of concentration results, confidence intervals, and probabilities of different values ​​are obtained.

[0014] Furthermore, the calibration of key parameter values ​​includes: randomly obtaining an initial population from the prior distribution; calculating the likelihood of the initial population; generating candidate populations; performing candidate point crossover; calculating the likelihood of the candidate populations; calculating the acceptance probability; determining whether to accept new sample points; and repeating the steps from generating candidate populations to determining whether to accept new sample points until enough samples are generated.

[0015] The present invention also provides a storage medium storing a computer program thereon, which, when executed by a processor, implements a method for calibration of uncertainty analysis of key parameters.

[0016] This invention also provides a key parameter uncertainty analysis and calibration system, comprising: an accident simulation model module for establishing and solving a simulation model of a radioactive powder spill accident; an experimental module for conducting physical experiments on radioactive powder spillage to obtain the distribution characteristics and diffusion laws of aerosols released during a radioactive powder spill accident; a key parameter determination module for determining the value range and probability distribution of key parameters; a surrogate module for establishing a surrogate model based on a Gaussian process; an uncertainty analysis module for performing uncertainty analysis of key parameters; and a calibration module for calibrating the values ​​of key parameters.

[0017] The advantages of this invention are: using uncertainty analysis to obtain the range and confidence interval of the numerical simulation output results, using experimental data to calibrate the parameters in the numerical model, and using a surrogate model based on Gaussian process to accelerate the calculation process, ultimately improving the calculation accuracy of the concentration field simulation of radioactive powder aerosol using numerical simulation methods. Attached Figure Description

[0018] Figure 1 This is a flowchart of the steps of a key parameter uncertainty analysis and calibration method in this invention;

[0019] Figure 2 This is a schematic diagram of the module flow of a key parameter uncertainty analysis and calibration method in this invention;

[0020] Figure 3 This is a schematic diagram of the spill experiment apparatus. Detailed Implementation

[0021] The present invention will now be further described with reference to the accompanying drawings and specific embodiments.

[0022] like Figure 1-3 As shown, this invention proposes a calibration method for uncertainty analysis of key parameters, comprising the following steps:

[0023] S1. Establish and solve a simulation model of a radioactive powder spillage accident.

[0024] Specifically, for specific scenarios involving radioactive powder spillage, a similar geometric model is established, and reasonable default simulation parameters are set. The solution process mainly includes establishing the geometric model, establishing the numerical model, setting parameters, and performing the solution.

[0025] It is understandable that mature CFD simulation software such as Fluent and OpenFOAM can be used to build models and perform numerical solutions to calculate the distribution field of radionuclide concentration in the target space after a radioactive powder spill accident under default parameter values.

[0026] S2, Conduct a physical experiment on radioactive powder spillage to obtain the distribution characteristics and diffusion patterns of aerosols released during a radioactive powder spillage accident;

[0027] Specifically, taking into account material properties, environmental conditions, spill height, and ventilation factors, we will further analyze the aerosol diffusion behavior under the influence of various factors, obtain the distribution characteristics and diffusion laws of aerosols released during radioactive powder spill accidents, and provide verification data for numerical simulation.

[0028] In this embodiment, the schematic diagram of the spill experiment device is as follows: Figure 3 As shown, a collection plate is placed at the bottom of the spillage experimental apparatus to recover the spilled powder; the sampling port of the sampler is placed at different spatial heights to obtain the aerosol distribution at different times and in different spaces. Experiments were designed and conducted to measure factors affecting the spillage, such as the properties of the radioactive powder material (density and particle size) and environmental conditions (temperature and pressure). Experiments were conducted with constant ventilation conditions but varying the material spillage height, and with a constant material spillage height but varying the ventilation conditions.

[0029] S3, determine the range and probability distribution of key parameter values;

[0030] Specifically, in the case of radioactive powder spill accidents, the diffusion conditions within the plant are relatively complex due to numerous factors such as gas flow and local environment. Turbulence parameters also have a significant impact on the diffusion behavior and distribution characteristics of aerosols. Based on the established numerical model, this study investigates key parameters such as airflow characteristic velocity, turbulent dissipation rate, and material spill velocity to obtain their reasonable value ranges and probability distributions under actual conditions.

[0031] It is understandable that probability distributions can include uniform distribution, normal distribution, logarithmic distribution, etc.

[0032] S4, Establish a proxy model based on Gaussian processes;

[0033] Specifically, in the process of parameter numerical simulation uncertainty analysis and parameter calibration, tens of thousands of parameter sampling processes are involved. Solving for the aerosol concentration at the key monitoring point using numerical simulation methods after each sampling would incur a huge time cost. Using Gaussian processes as surrogate models to replace numerical simulation processes can reduce the time cost of analysis.

[0034] The distribution of a Gaussian process is the joint distribution of all infinitely many random variables, which is the function distribution over a continuous domain.

[0035] To illustrate with a specific example, given the training dataset D = (X, y) = {(X...} i ,y i Let |i = 1, ..., N, where Xi is the input vector and yi is the output vector. Given a new input x*, predict the corresponding target data. (The actual output is y) * ).

[0036] First, make prior assumptions (f(x) and y) * (Joint probability distribution):

[0037]

[0038] Where: K ff =k(x,x),K fy =k(x,x * ),k yy =k(x * ,x * According to the conditional distribution properties of the multidimensional Gaussian distribution, we can obtain:

[0039]

[0040] The probability distribution can be obtained from a Gaussian distribution. The probability is highest for that.

[0041] k is the kernel function (or covariance function), used to capture the relationship between random variables at different times. The most widely used is the radial basis function kernel.

[0042]

[0043] By randomly sampling a small number of parameters of interest, such as material release height, airflow characteristic velocity, turbulent dissipation rate, and material spill velocity, 200 sets of parameter combinations were obtained. Numerical simulation was used to solve for the aerosol concentration data at key monitoring points. The parameters of material release height, airflow characteristic velocity, turbulent dissipation rate, and material spill velocity were used as inputs to the surrogate model, and the aerosol concentration data at key monitoring points were used as the output of the surrogate model. 180 sets of data were randomly selected as the training dataset to train the Gaussian process surrogate model, and the remaining 20 sets of data were used as the test dataset to evaluate the accuracy of the surrogate model's output results.

[0044] It is understood that in this embodiment, the surrogate model is constructed using a Gaussian process that is simple and easy to use and does not require complex parameter adjustment. In some embodiments, the surrogate model can also be established using neural network methods, random forest methods, support vector machine methods, etc.

[0045] S5, perform uncertainty analysis on key parameters;

[0046] Specifically, the Monte Carlo random sampling algorithm is used to sample key parameters in the numerical model, such as airflow characteristic velocity, turbulent dissipation rate, and material spill velocity, according to their probability distribution. The sampled parameters are then combined and input into the surrogate model to calculate the aerosol concentration output at key monitoring points. After statistical processing, the possible range of concentration values, confidence intervals, and probabilities of different values ​​are obtained.

[0047] S6, perform calibration of key parameter values;

[0048] Specifically, the DREAM algorithm is used to sample the parameters so that their values ​​satisfy both the original prior probability distribution and the output concentration results of the surrogate model are as close as possible to the monitored values ​​obtained in the experiment. After a large number of samples, the posterior distribution of the parameters in the numerical model under real conditions can be obtained, that is, more reasonable values ​​that are closer to the real situation. The calibration results of the parameters are obtained to improve the accuracy of numerical simulation.

[0049] It is understandable that the DREAM algorithm, as an improved MCMC algorithm, has higher computational efficiency and accuracy. In some embodiments, the Monte Carlo Markov Chain (MCMC) method can also be used to sample the parameters.

[0050] The DREAM algorithm uses random subspace sampling to generate candidate points. For a d-dimensional parameter space, where x is a d-dimensional parameter vector, a total of N chains are used, and the steps are as follows:

[0051] First, obtain the initial population:

[0052] The initial population is randomly selected from the prior distribution and used as the initial value {x} for each chain. i i = 1, ..., N;

[0053] For i = 1, ..., N, calculate the likelihood π(x) of the initial population (i.e., the initial value of each chain). i Next is the evolutionary process of the MCMC chain, which includes the following steps:

[0054] Generate candidate population: For the j-th chain, the following formula is used:

[0055]

[0056] In the formula: δ represents the number of pairs used to generate candidate points; r1(j), r2(n) ∈ {1,…,N}; for j=1,…,δ and n=1,…,δ, r1(j)≠r2(n)≠i. The value of e is randomly distributed from a d-dimensional uniform distribution U. d The values ​​of ε are sampled from (-b, b), where b is a positive number less than 1. The values ​​of ε are obtained from a d-dimensional normal distribution N. d (0,b * Obtained from ), where b * γ is a positive number that is very small relative to the width of the target distribution. γ is the jump rate, which depends on δ and d.

[0057] The jump rate is generally calculated using the following formula:

[0058]

[0059] Candidate point crossover: The following formula is used to determine whether each individual in the candidate population should replace the initial population:

[0060]

[0061] Where U is a random number generated based on the uniform distribution U(0,1), and CR is defined as the crossover probability ∈ [0,1].

[0062] For i = 1, ..., N, calculate the likelihood π(z) of the candidate population. i )

[0063] Calculate the probability of acceptance:

[0064]

[0065] Determine whether to accept new sample points. If new sample points are accepted, then... If not accepted, then maintain the current position, that is...

[0066] Repeat the steps above, from generating candidate populations to determining whether to accept new sample points, until enough samples are generated.

[0067] The DREAM algorithm inputs the model parameter values ​​obtained from each sampling into the surrogate model, stores the corresponding model output results, and judges how close the values ​​are to the actual measured aerosol concentration, until the set total number of samples is reached.

[0068] By selecting the parameter sampling results after the DREAM algorithm converges, we can obtain the posterior distribution of the parameters. The maximum probability value in the posterior distribution will be closer to the true value of the parameters, thus obtaining the calibration result of the parameters.

[0069] The present invention also provides a storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of a calibration method for uncertainty analysis of key parameters.

[0070] It should be noted that the storage medium shown in this application can be a computer-readable signal medium or a storage medium, or any combination of the two. The storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or any combination thereof. More specific examples of the storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this application, the storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, system, or device. In this application, the storage medium can include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The storage medium may also be any computer-readable medium other than a storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, system, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0071] The present invention also provides a calibration system for uncertainty analysis of key parameters, comprising:

[0072] The accident simulation model module is used to build and solve simulation models of radioactive powder spillage accidents.

[0073] The experimental module is used to conduct physical experiments on radioactive powder spills to obtain the distribution characteristics and diffusion patterns of aerosols released during radioactive powder spill accidents.

[0074] The key parameter determination module is used to determine the range and probability distribution of key parameter values;

[0075] The proxy module is used to create a proxy model based on Gaussian processes.

[0076] The uncertainty analysis module is used to perform uncertainty analysis on key parameters;

[0077] The calibration module is used to calibrate the values ​​of key parameters.

[0078] As can be seen from the above embodiments, the beneficial effects of the present invention are as follows: the uncertainty analysis method is used to obtain the value range and confidence interval of the numerical simulation output results, and the experimental data is used to calibrate the parameters in the numerical model based on the DREAM algorithm. At the same time, the calculation process is accelerated based on the surrogate model of Gaussian process, which can ultimately improve the calculation accuracy of the concentration field simulation of radioactive powder aerosol using numerical simulation method.

[0079] The system described in this invention is not limited to the embodiments described in the specific implementation. Other implementation methods derived by those skilled in the art based on the technical solution of this invention also fall within the scope of technical innovation of this invention.

Claims

1. A calibration method for uncertainty analysis of key parameters, characterized in that, include: Establish and solve a simulation model of a radioactive powder spillage accident. Conduct physical experiments on radioactive powder spillage to obtain the distribution characteristics and diffusion patterns of aerosols released during radioactive powder spillage accidents; Determine the value range and probability distribution of key parameters; Establish a proxy model based on Gaussian processes; Perform uncertainty analysis on key parameters; Perform calibration of key parameter values; The key parameters include airflow characteristic velocity, turbulent dissipation rate, and material drop velocity; the probability distribution includes uniform distribution, normal distribution, and logarithmic distribution. In the process of establishing the surrogate model, a small number of parameters of interest, such as material release height, airflow characteristic velocity, turbulent dissipation rate, and material spill velocity, were randomly sampled to obtain 200 sets of parameter combinations. Numerical simulation was used to solve the aerosol concentration data of key monitoring points. The parameters of material release height, airflow characteristic velocity, turbulent dissipation rate, and material spill velocity were used as inputs to the surrogate model, and the aerosol concentration data of key monitoring points were used as outputs to the surrogate model. 180 sets of data were randomly selected as training datasets to train the Gaussian process surrogate model, and the remaining 20 sets of data were used as test datasets to evaluate the accuracy of the surrogate model output results. When performing uncertainty analysis on key parameters, the Monte Carlo random sampling algorithm is used to sample the key parameters according to their probability distribution, and the sampled parameter combinations are input into the surrogate model to calculate the aerosol concentration output results of key monitoring points. After statistical processing, the range of concentration results, confidence interval, and probability of different values ​​are obtained. The calibration of key parameter values ​​includes: The initial population is randomly obtained from the prior distribution; Calculate the likelihood of the initial population; Generate a candidate population; Perform candidate point crossover; Calculate the likelihood of the candidate population; Calculate the probability of acceptance; Determine whether to accept new sample points; Repeat the steps from generating candidate populations to deciding whether to accept new sample points until enough samples are generated.

2. The method for uncertainty analysis and calibration of key parameters as described in claim 1, characterized in that, The establishment and solution of a simulation model for a radioactive powder spill accident includes: Establish a geometric model, establish a numerical model, set parameters, and perform the solution.

3. The key parameter uncertainty analysis and calibration method as described in claim 1, characterized in that: During the physical experiment of radioactive powder spillage, the sampling port of the sampler was placed at different spatial heights to obtain the aerosol distribution at different times and in different spaces.

4. The method for uncertainty analysis and calibration of key parameters as described in claim 1, characterized in that: When conducting the physical experiment of radioactive powder scattering, experiments were carried out with constant ventilation conditions and varying material scattering height, and experiments with constant material scattering height and varying ventilation conditions were also conducted.

5. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the key parameter uncertainty analysis and calibration method according to any one of claims 1 to 4.

6. A calibration system for uncertainty analysis of key parameters, characterized in that, include: The accident simulation model module is used to build and solve simulation models of radioactive powder spillage accidents. The experimental module is used to conduct physical experiments on radioactive powder spills to obtain the distribution characteristics and diffusion patterns of aerosols released during radioactive powder spill accidents. The key parameter determination module is used to determine the range and probability distribution of key parameter values; The proxy module is used to create a proxy model based on Gaussian processes. The uncertainty analysis module is used to perform uncertainty analysis on key parameters; The calibration module is used to calibrate the values ​​of key parameters. The key parameters include airflow characteristic velocity, turbulent dissipation rate, and material drop velocity; the probability distribution includes uniform distribution, normal distribution, and logarithmic distribution. In the process of establishing the surrogate model, a small number of parameters of interest, such as material release height, airflow characteristic velocity, turbulent dissipation rate, and material spill velocity, were randomly sampled to obtain 200 sets of parameter combinations. Numerical simulation was used to solve the aerosol concentration data of key monitoring points. The parameters of material release height, airflow characteristic velocity, turbulent dissipation rate, and material spill velocity were used as inputs to the surrogate model, and the aerosol concentration data of key monitoring points were used as outputs to the surrogate model. 180 sets of data were randomly selected as training datasets to train the Gaussian process surrogate model, and the remaining 20 sets of data were used as test datasets to evaluate the accuracy of the surrogate model output results. When performing uncertainty analysis on key parameters, the Monte Carlo random sampling algorithm is used to sample the key parameters according to their probability distribution, and the sampled parameter combinations are input into the surrogate model to calculate the aerosol concentration output results of key monitoring points. After statistical processing, the range of concentration results, confidence interval, and probability of different values ​​are obtained. The calibration of key parameter values ​​includes: The initial population is randomly obtained from the prior distribution; Calculate the likelihood of the initial population; Generate a candidate population; Perform candidate point crossover; Calculate the likelihood of the candidate population; Calculate the probability of acceptance; Determine whether to accept new sample points; Repeat the steps from generating candidate populations to deciding whether to accept new sample points until enough samples are generated.

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