A calculation method for determining the maximum working condition point of anti-icing heat load in a full evaporation mode

Abstract

The present application provides a kind of calculation method for determining the maximum working condition point of anti-icing thermal load under full evaporation mode, including data acquisition, proxy model construction and data optimization three parts.The present application can process under continuous maximum icing weather conditions combined with the influence of flight conditions, determine the maximum working condition point of anti-icing thermal load under full evaporation mode by the way of icing weather conditions combined with flight conditions, so as to determine the maximum working condition point of anti-icing thermal load under full evaporation mode of airfoil, which is also applicable to the anti-icing thermal load design of tail, engine lip, windshield and aircraft sensor.

Description

Technical Field

[0001] This invention relates to the field of aircraft design, and in particular to a calculation method for determining the maximum operating point of anti-icing thermal load in full evaporation mode. Background Technology

[0002] Aircraft icing can lead to decreased aerodynamic performance and deteriorated handling, jeopardizing flight safety. Therefore, aircraft require anti-icing / de-icing systems. Electrothermal or hot-gas anti-icing systems are commonly used methods. These systems utilize heat sources to evaporate supercooled water droplets collected on the surface or melt surface ice to achieve de-icing. The design of the anti-icing heat load in full evaporation mode focuses on the required heat and its distribution to evaporate supercooled water droplets impacting the surface. The calculation of the anti-icing heat load involves the following steps: first, calculating the airflow field; then, calculating the water droplet flow field to obtain the water droplet impact characteristics; finally, using a numerical calculation model of the anti-icing heat load to obtain its energy value and distribution. Anti-icing thermal loads are influenced by a variety of factors, including flight conditions such as velocity (V), altitude (H), and icing weather conditions such as altitude (H), temperature (T), median volume diameter (MVD), and liquid water content (LWC). These conditions are coupled and interdependent with each other.

[0003] In existing technology, Appendix C of Part 25 of the Federal Aviation Regulation (FAR) provides meteorological standards for the design of anti-icing and de-icing systems: continuous maximum icing conditions (icing meteorological conditions in stratus clouds) and intermittent maximum icing conditions (icing meteorological conditions in cumulus clouds). These meteorological standards provide icing envelopes for altitude, temperature, liquid water content, and average droplet diameter, and stipulate that a 99% probability of icing can be achieved within these envelopes. Taking continuous maximum icing conditions as an example, Appendix C specifies that continuous maximum icing conditions are determined by three variables: liquid water content, droplet diameter, and temperature. Figure 1 The diagram shows the continuous maximum icing meteorological conditions. Figure (a) shows the relationship between liquid water content, droplet diameter, and temperature; Figure (b) shows the relationship between altitude and temperature; and Figure (c) shows a three-dimensional surface diagram illustrating the 99% icing probability based on liquid water content, droplet diameter, and temperature. As shown in the figure, the continuous maximum icing meteorological conditions cover icing meteorological conditions with a temperature range of 0°C to -30°C, droplet size range of 15 to 40 micrometers, liquid water content range of 0.04 to 0.8 grams per cubic meter, and altitude range of 0 to 6700 meters.

[0004] Meanwhile, the design operating points of existing anti-icing thermal load systems are mainly referenced as follows:

[0005] 1) The working conditions proposed by Sogin in the literature

[0006]

[0007] 2) Working conditions mentioned by Qiu Kuigang in the literature

[0008] Civil aircraft: Temperature selection when flying at low speeds When the flight speed is high, its temperature design standard is selected. ; ; ;

[0009] U.S. Air Force: ;

[0010] US Navy: ;

[0011] However, in order to determine the anti-icing thermal load that meets the requirements of the all-evaporation mode, the reference operating point for the above-mentioned anti-icing thermal load design is too broad and only involves meteorological conditions without taking into account specific flight conditions. Therefore, it is not the maximum operating point for the anti-icing thermal load under the all-evaporation mode.

[0012] The maximum continuous icing weather conditions in Appendix C of FAR Part 25 were obtained from data obtained by the United States through icing flight experiments in the 1940s-1950s and statistical analysis. Figure 2 The diagram above illustrates the reference operating point for anti-icing thermal load design. Data at any point within the range shown in the diagram has the same probability of exceeding the limit, and the probability of simultaneously exceeding the specified MVD, LWC, and T during an icing event is 1%. Furthermore, T, MVD, and LWC are mutually constrained; any deviation from the corresponding point will prevent the design of the anti-icing system with the same probability of exceeding the limit, resulting in an increase or decrease in the probability of exceeding the limit. This could cause the anti-icing system to fail to meet anti-icing requirements or waste energy under certain conditions. Figure 2 The red curve is The curve at that time, according to both US Air Force and civilian aircraft standards, Under the condition of MVD=20um, its corresponding LWC is significantly higher than that of the corresponding point in Appendix C. MVD=20um At this point, the design results in redundancy and wasted energy; and for the US Navy standard, its LWC is significantly lower than the corresponding point under the same probability in Appendix C, indicating a design deficiency at this point. Furthermore, none of these reference standards consider areas where the LWC exceeds the standard-specified value, as shown by the shaded area in the figure. Additionally, these standards do not consider the impact of velocity on anti-icing thermal loads during design. Therefore, how to comprehensively consider the impact of icing weather envelope and flight speed on anti-icing thermal loads, and identify the most severe icing condition, is one of the urgent problems to be solved in the design of anti-icing systems. Summary of the Invention

[0013] To address the problems existing in the prior art, this application proposes a method based on the POD-Kriging method and genetic algorithm to determine the maximum operating point of anti-icing thermal load under the all-evaporation mode. At the same time, it also proposes a numerical simulation method for determining the maximum operating point of anti-icing thermal load under the all-evaporation mode for the airfoil surface under continuous maximum icing weather conditions.

[0014] The technical solution of this invention is as follows:

[0015] A calculation method for determining the maximum operating point of anti-icing thermal load under full evaporation mode includes the following steps:

[0016] Step 1: The optimized Latin hypercube sampling method is used to sample the parameters affecting the icing of aircraft components to obtain the sample point conditions. The sample point conditions include flight speed V, altitude H, temperature T, average droplet volume diameter MVD, and liquid water content LWC.

[0017] Step 2: Obtain the anti-icing thermal load on the surface of aircraft components under sample point conditions through numerical simulation;

[0018] Step 3: Based on the sample point operating conditions and the anti-icing thermal load on the surface of aircraft components at the sampling points, construct the POD-Kriging predictive surrogate model. This allows the POD method to obtain the functional relationship between the sample point operating conditions and the anti-icing thermal load, and enables the Kriging model to predict the anti-icing thermal load at non-sample point operating conditions.

[0019] Step 4: Using Max(max(anti-icing thermal load (T,MVD,LWC,H,V))) as the objective function, the maximum working condition point is obtained by global optimization under the set constraints through optimization algorithm; during the optimization process, the POD-Kriging predictive surrogate model obtained in Step 3 is used to obtain the distribution of anti-icing thermal load under different working conditions.

[0020] Furthermore, in step 1, data on altitude, temperature, and average droplet volume diameter are sampled from Appendix C of FAR25, and the sampling range for speed is determined based on the aircraft's mission parameters.

[0021] Furthermore, the temperature range is within The water droplet size ranges from 15 to 40 micrometers, the height ranges from 0 to 6700 meters, and the speed ranges from 50 to 100 meters per second.

[0022] Furthermore, the numerical simulation in step 2 includes the following steps:

[0023] Step 2.1: The CFD method is used to numerically calculate the flow field around the aircraft components, and the continuity equation, momentum equation and energy equation of the air are solved to obtain the velocity distribution and pressure distribution of the flow field;

[0024] Step 2.2: Based on the aircraft flow field calculation results in Step 2.1, the motion equation of the supercooled water droplets is numerically solved to obtain the distribution of water droplets in the flow field and to determine the collision situation between water droplets and the surface of aircraft components.

[0025] Step 2.3: Based on the collision between the water droplets and the surface of the aircraft components obtained in Step 2.2, the anti-icing thermal load on the surface of the aircraft components is obtained using the mass and heat transfer model of icing.

[0026] A computer-readable storage medium storing a computer-executable program, which, when executed, is used to implement the above-described method.

[0027] A computer system includes: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the above-described method.

[0028] Beneficial effects

[0029] This invention can comprehensively consider icing meteorological conditions and flight conditions to determine the maximum operating point of anti-icing thermal load in the full evaporation mode, and can be applied in the design of anti-icing and de-icing systems such as wings, tail fins, engine lips, windshields, and aircraft sensors.

[0030] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0031] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0032] Figure 1 The diagram shows the meteorological conditions for continuous maximum icing; (a) the relationship between liquid water content, droplet diameter, and temperature; (b) the relationship between altitude and temperature; and (c) a schematic diagram of the equiprobability surface of liquid water content, droplet diameter, and temperature.

[0033] Figure 2 The design reference points for anti-icing thermal load are shown; (a) a two-dimensional schematic diagram of the design reference points for anti-icing thermal load, (b) a three-dimensional schematic diagram of the design reference points for anti-icing thermal load, and (c) areas not considered in each design condition.

[0034] Figure 3 The method flowchart is shown;

[0035] Figure 4 The comparison diagrams of the Latin hypercube sampling method are shown; (a) Latin hypercube sampling, (b) optimized Latin hypercube sampling;

[0036] Figure 5 Schematic diagram of water droplet impact on the wing surface;

[0037] Figure 6 This diagram illustrates the construction of the POD-Kriging predictive agent model.

[0038] Figure 7 A schematic diagram of the steps in the embodiment is shown;

[0039] Figure 8 This diagram illustrates the sampling distribution of icing meteorological conditions in FAA Appendix C.

[0040] Figure 9 The numerical simulation algorithm verification comparison chart is shown; (a) ice shape comparison in case 1, (b) ice shape comparison in case 2;

[0041] Figure 10 The following charts show the comparison of the validation results of the prediction models: (a) case 1, (b) case 2, and (c) case 3.

[0042] Figure 11 The isosurface plots of anti-icing thermal loads at some sample points are shown; (a) case 1, (b) case 2; (c) case 3; (d) case 4, (e) case 5;

[0043] Figure 12 The distribution of anti-icing thermal loads on the airfoil at some sample points is shown.

[0044] Figure 13 The iterative computation graph of the genetic algorithm is shown. Detailed Implementation

[0045] Aircraft anti-icing system design requires the system to meet the anti-icing thermal load requirements under the most severe icing conditions, with the maximum operating point being the most severe operating point. Currently, the most severe operating point is generally based on standards for civil aircraft, the US Navy, and the Air Force. However, as described in the background section, these standards are either too low, too high, or do not take all factors into account. They do not consider flight conditions when determining the maximum operating point of the anti-icing thermal load under the full evaporation mode. Therefore, the icing meteorological conditions in Appendix C with the same probability of exceeding the limit should be fully considered. To this end, this invention provides a calculation method for determining the maximum operating point of the anti-icing thermal load under the full evaporation mode. In application, it can handle the influence of flight conditions combined with continuous maximum icing meteorological conditions, so as to determine the maximum operating point of the anti-icing thermal load that meets the requirements of the full evaporation mode by combining icing meteorological conditions with flight conditions. It can determine the maximum operating point of the anti-icing thermal load under the full evaporation mode of the wing surface, and is also applicable to the anti-icing thermal load design of the tail, engine lip, windshield, and aircraft sensors.

[0046] This invention mainly consists of three parts: data acquisition, proxy model construction, and data optimization. Figure 3 A flowchart of the method of the present invention is shown.

[0047] (a) Data Acquisition

[0048] Data acquisition is divided into the following parts: by optimizing the Latin hypercube sampling of several factors affecting icing, a sampling point design matrix is ​​constructed, and the distribution of anti-icing thermal load on the airfoil under each sample point state is obtained by performing icing numerical simulation on the design matrix.

[0049] (1) Optimize Latin hypercube sampling

[0050] Latin hypercube sampling is a stratified sampling method. Its principle is to divide each coordinate interval in an n-dimensional space... (k is [1, n]) Divide the interval into m equal parts, and denote each interval as . Let i be [1, m]. Randomly select m points to ensure that each level of a factor is studied only once, thus forming a Latin hypercube design with an n-dimensional space and m samples. Therefore, Latin hypercube sampling has good space-filling properties in any single dimension. However, when randomly selected, it may have poor space-filling properties across the entire sampling space. Optimized Latin hypercube sampling is a method that introduces an optimal criterion into the Latin hypercube sampling process, selects the optimal Latin hypercube design based on this criterion, and then randomly samples based on this Latin hypercube design. In the optimal Latin hypercube technique, the design space for each factor is uniformly divided (all factors have the same number of divisions, n). Random combinations are used to generate a Latin hypercube as the initial design matrix with n points (each level of the factor is studied only once). The optimization process is applied to the initial Latin hypercube design matrix. By swapping the order of two factors in the matrix columns, a new matrix is ​​generated, and the new overall spacing of the points is evaluated. The goal of this optimization process is to design a matrix such that each sampling point is distributed as uniformly as possible within the design space. Figure 4 The comparison chart of Latin hypercube sampling and optimized Latin hypercube sampling shows that the sampling points of optimized hypercube sampling are more evenly distributed.

[0051] Aircraft icing is influenced by multiple factors, namely altitude (H), velocity (V), temperature (T), mean volume diameter (MVD) of water droplets, and liquid water content (LWC). Appendix C of FAR25 provides the maximum possible icing conditions for continuous maximum (stratus cloud), giving the icing envelopes for altitude, temperature, liquid water content, and mean volume diameter of water droplets. After determining altitude (H), temperature (T), and mean volume diameter of water droplets (MVD), the liquid water content (LWC) is a constant. Therefore, there are four independent conditions affecting aircraft icing: flight speed (V), altitude (H), temperature (T), and mean volume diameter of water droplets (MVD). This invention employs an optimized Latin hypercube sampling method to sample these four parameters. In the data sampling, the data for altitude, temperature, and mean volume diameter of water droplets are obtained from Appendix C, while the sampling range for velocity is determined based on the aircraft's mission parameters.

[0052] In this embodiment, optimized Latin hypercube sampling is performed on the continuous maximum icing meteorological conditions and flight speed in Appendix C. The sampled data range is: temperature range within... The water droplet size ranges from 15 to 40 micrometers, the height ranges from 0 to 6700 meters, and the speed ranges from 50 to 100 meters per second. Figure 8 The diagram below shows the sampling points under continuous maximum meteorological conditions; the table below shows the operating conditions of some sampling points.

[0053]

[0054] (2) Numerical simulation of anti-icing thermal load

[0055] After obtaining the operating conditions at the sampling points, the anti-icing thermal load at these points needs to be determined through numerical simulation. The numerical simulation process can be divided into the following steps: first, solving for the airflow field; then, solving for the water droplet flow field to obtain the water droplet impact characteristics; and finally, determining the anti-icing thermal load using a mass and heat transfer model of icing. The specific steps of the numerical calculation method can be summarized as follows:

[0056] (a) Flow field calculation. Computational fluid dynamics (CFD) is used to numerically calculate the flow field around the object, and solve the continuity equation, momentum equation and energy equation of the air to obtain the distribution of parameters such as velocity and pressure in the flow field.

[0057] (b) Calculation of the motion of supercooled water droplets and their impact characteristics with the airfoil surface. Based on the results of the airfoil flow field calculation, the motion equation of the supercooled water droplets is solved numerically to obtain the distribution of water droplets in the flow field and to determine the collision situation between the water droplets and the airfoil surface. Figure 5 The diagram illustrates a water droplet collision. As shown, the area between the water droplet's trajectory and the tangents on the upper and lower surfaces of the airfoil is the water droplet impact zone, where the water droplet is collected.

[0058] (c) The surface anti-icing thermal load can be obtained using the mass and heat transfer model of icing.

[0059] (II) Constructing the POD-Kriging Predictive Proxy Model

[0060] The Proper Orthogonal Decomposition (POD) method orthogonally transforms sample data and extracts the optimal orthogonal basis, using this basis to represent the physical field represented by the original data. In this invention, a functional relationship is established between sample operating points and their anti-icing thermal loads. After obtaining this relationship using the POD method, the Kriging model is used to predict the anti-icing thermal loads at non-sample operating points. Figure 6 This is a schematic diagram of the POD-Kriging predictive surrogate model.

[0061] POD reduces the order of the anti-icing thermal load distribution matrix at the sampling points, obtaining a series of coefficients and eigenvector products. Since the sum of the coefficients and eigenvector products of the previous terms can already describe the anti-icing thermal load distribution under different anti-icing conditions, the remaining coefficients and eigenvector products are discarded. This transforms the complex numerical simulation process into a simple solution of the sum of coefficients and vector products, greatly reducing computational costs. At this point, the coefficients and eigenvectors can describe the anti-icing thermal load distribution at the sampling points. For the thermal load distribution at non-sampling points, the kriging method is used to perform multidimensional interpolation on the coefficients to obtain a series of coefficients at non-sampling points. The sum of the interpolated coefficients and eigenvector products can be considered as the anti-icing thermal load distribution at non-sampling points.

[0062] According to POD theory, the required physical field In a certain region, it can be represented as an infinite series as shown below:

[0063] (1)

[0064] In the above formula It can represent different variable states, such as angle of attack, Mach number, Reynolds number, and time variables, etc. This is called the empirical coefficient. These are called characteristic basis functions. The purpose of the POD method is to obtain the characteristic basis functions and empirical coefficients in the above equation, and to express the infinite series in the above equation in the following form:

[0065] (2)

[0066] In the above formula, M is a positive integer less than N. The specific solution process is as follows:

[0067] (a) Obtain the sample matrix

[0068] Suppose that the physical field to be solved can be expressed as Forms, different parameters The physical field under the given conditions can be represented as The physical field values ​​at a constant t are arranged into an L-row column vector, and the physical field values ​​at all N different parameters are arranged into a single vector. matrix This is called the sample matrix.

[0069] (b) Construct the eigenvalue matrix and solve for the eigenvalues ​​and eigenvectors.

[0070] The matrix elements are obtained from equation (3), resulting in the eigenvalue matrix A:

[0071] (3)

[0072] in, Solving the above equation yields the eigenvalues ​​of matrix A. and eigenvectors The obtained eigenvalues ​​are arranged in order of their size, i.e. Meanwhile, the feature vectors are arranged according to the order of their corresponding feature values.

[0073] (c) Construct the characteristic function, as shown in formula (4); solve for the empirical coefficients, as shown in formula (5).

[0074] (4)

[0075] (5)

[0076] The empirical coefficients sought at this point are all known. The result is obtained under the given conditions; if the requirement is to be obtained under the unknown... The empirical coefficients can be obtained by interpolation based on the calculated data.

[0077] (d) Reconstructing the physical field

[0078] The sum of the first M eigenvalues ​​accounts for the majority of the sum of all eigenvalues, exceeding 99.99%. Therefore, the physical field can be represented as the sum of the products of the first M characteristic basis functions and empirical coefficients. Thus, the physical field to be determined can be expressed as...

[0079] (6)

[0080] The Kriging model has a good ability to approximate nonlinear functions. It is an interpolation model, and its interpolation result is defined as a linear weighted sum of known sample function response values.

[0081] (7)

[0082] Therefore, all we need to do is provide the weighting coefficients. The expression can be used to obtain the performance evaluation of any design scheme in the design space.

[0083] The CFD numerical simulation method and predictive surrogate model are validated here:

[0084] CFD numerical method verification condition

[0085]

[0086] Predictive agent model validation working condition

[0087]

[0088] The CFD numerical simulation method was validated by comparing the performance of different ice formation types, such as... Figure 9 As shown in the figure, the ice type obtained from the numerical simulation and the experimental ice type exhibit consistent characteristics in terms of ice angle and ice thickness.

[0089] The anti-icing thermal load results from the predictive surrogate model and the anti-icing thermal load results from the numerical simulation are as follows: Figure 10 As shown in the figure, the calculation results of the two methods agree well, indicating that the accuracy of the predictive agent model is reliable.

[0090] Numerical simulations were performed on the operating conditions at the sampling points to obtain the anti-icing thermal load data at the sampling points, and then a surrogate model was established based on POD-Kriging for prediction. Figure 11 The above provides isosurface plots of the anti-icing thermal load for some sample points. Figure 12 The image shows the airfoil distribution of anti-icing thermal loads at some of the sample points mentioned above. This result was obtained through numerical simulation.

[0091] (III) Optimization

[0092] In this invention, the distribution of anti-icing thermal load under different operating conditions is obtained through POD-kriging, and the maximum value of the anti-icing thermal load under different operating conditions is obtained. A genetic algorithm is used to globally optimize the results to maximize the maximum value of the anti-icing thermal load. After finding the maximum value of the anti-icing thermal load, the maximum operating point is also determined. The objective function for optimization is:

[0093] Max(max(anti-icing thermal load (T,MVD,LWC,H,V)))

[0094] The constraints are:

[0095]

[0096] Here, MVD represents the average volume diameter of a water droplet, in μm, and T represents temperature, in μm. LWC represents liquid water content, in units of: H is the height, in meters (m), and V is the velocity, in meters per second (m / s).

[0097] Figure 13 This is the iteration diagram of the genetic algorithm. Based on the surrogate model constructed in this invention, a genetic algorithm is used to globally optimize the surrogate model. The maximum heat load for anti-icing under full evaporation mode is obtained after 141 generations of genetic algorithm iterations. The corresponding maximum operating point and the calculation results of anti-icing thermal load are shown in the table below.

[0098] Maximum operating point and maximum anti-icing thermal load results

[0099]

[0100] The table above also shows the maximum total evaporative anti-icing thermal loads of civil aircraft, the US Air Force, and the US Navy under icing weather conditions, under the same flight conditions as the optimal operating condition. It can be observed that the total evaporative anti-icing thermal load at the optimal operating point proposed by this method is the largest, meaning that the design operating points of civil aircraft, the US Air Force, and the US Navy are at the maximum evaporative anti-icing thermal loads. Figure 2 The area shown in c cannot meet the anti-icing requirements.

[0101] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A calculation method for determining the maximum operating point of anti-icing thermal load under full evaporation mode, characterized in that: Includes the following steps: Step 1: The optimized Latin hypercube sampling method is used to sample the parameters affecting the icing of aircraft components to obtain the sample point conditions. The sample point conditions include flight speed V, altitude H, temperature T, average droplet volume diameter MVD, and liquid water content LWC. Step 2: Obtain the anti-icing thermal load on the surface of aircraft components under sample point conditions through numerical simulation; Step 3: Based on the sample point operating conditions and the anti-icing thermal load on the surface of aircraft components at the sampling points, construct the POD-Kriging predictive surrogate model. This allows the POD method to obtain the functional relationship between the sample point operating conditions and the anti-icing thermal load, and enables the Kriging model to predict the anti-icing thermal load at non-sample point operating conditions. Step 4: Using Max(max(anti-icing thermal load (T,MVD,LWC,H,V))) as the objective function, perform global optimization under the set constraints to obtain the maximum working point; During the optimization process, the POD-Kriging predictive surrogate model obtained in step 3 is used to obtain the anti-icing thermal load distribution under different working conditions. The constraints are: Here, MVD represents the average volume diameter of a water droplet, in μm, and T represents temperature, in μm. LWC represents liquid water content, in units of: H is the height, in meters (m), and V is the velocity, in meters per second (m / s).

2. The calculation method for determining the maximum operating point of anti-icing thermal load under full evaporation mode according to claim 1, characterized in that: The numerical simulation in step 2 includes the following steps: Step 2.1: The CFD method is used to numerically calculate the flow field around the aircraft components, and the continuity equation, momentum equation and energy equation of the air are solved to obtain the velocity distribution and pressure distribution of the flow field; Step 2.2: Based on the aircraft flow field calculation results in Step 2.1, the motion equation of the supercooled water droplets is numerically solved to obtain the distribution of water droplets in the flow field and to determine the collision situation between water droplets and the surface of aircraft components. Step 2.3: Based on the collision between the water droplets and the surface of the aircraft components obtained in Step 2.2, the anti-icing thermal load on the surface of the aircraft components is obtained using the mass and heat transfer model of icing.

3. A computer-readable storage medium, characterized in that: The device contains a computer-executable program, which, when executed, is used to implement the method described in any one of claims 1 to 2.

4. A computer system, characterized in that: include: One or more processors, the computer-readable storage medium of claim 3, for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of any one of claims 1 to 2.

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