Office building energy-saving reconstruction method based on neural network optimization

Abstract

The invention discloses an office building energy-saving reconstruction method based on neural network optimization, and belongs to the field of office building energy conservation, and the method comprises the steps: carrying out the energy audit of a target building, and obtaining the field investigation data; calculating the field research data based on DeST software, and constructing a building energy consumption model; based on the building energy consumption model, performing energy consumption simulation on various external enclosure structure energy-saving reconstruction scheme combinations to obtain energy consumption data under different enclosure structure combinations; constructing an ANN neural network model, and inputting the historical data set into the ANN neural network model to obtain a prediction model; inputting the energy consumption data under different enclosure structure combinations into the prediction model to obtain an optimal energy-saving scheme; and performing technical economic analysis and environmental economic evaluation on the optimal energy-saving scheme, and generating an energy-saving transformation report.

Description

Technical Field

[0001] The invention belongs to the field of energy conservation of office buildings, and in particular relates to an energy conservation reconstruction method of office buildings based on neural network optimization. Background Art

[0002] A large number of studies have shown that renovation measures such as exterior wall insulation, replacement of energy-saving exterior windows, and whether or not to use internal and external shading can significantly reduce building operation energy consumption. Exterior wall insulation mainly depends on the type and thickness of insulation materials. A large number of studies have fully confirmed the feasibility and energy-saving effect of these measures, but for specific buildings, there are few comprehensive energy-saving renovation plans, which is because a large amount of energy consumption calculations are required during the renovation design stage. Summary of the invention

[0003] In order to solve the above technical problems, the present invention provides an office building energy-saving renovation method based on neural network optimization, comprising:

[0004] Conduct energy audits on target buildings and obtain field research data;

[0005] Calculate the field survey data based on DeST software to construct a building energy consumption model;

[0006] Based on the building energy consumption model, energy consumption simulation is performed on a combination of energy-saving transformation schemes of various external envelope structures to obtain energy consumption data under different envelope structure combinations;

[0007] Constructing an ANN neural network model, inputting the historical data set into the ANN neural network model, and obtaining a prediction model;

[0008] Inputting the energy consumption data under the different enclosure structure combinations into the prediction model to obtain the optimal energy-saving solution;

[0009] Conduct technical and economic analysis and environmental and economic evaluation on the optimal energy-saving solution and generate an energy-saving transformation report.

[0010] Preferably, the field survey data include: building envelope parameters, various internal equipment parameters, operating time and annual operating energy consumption.

[0011] Preferably, the outer wall structure of the building energy consumption model is set as a 240mm small concrete hollow porous block with a heat transfer coefficient of 2.209W / (m 2 ·K), thermal resistance is 0.295m 2 ·K / W. The window is set to ordinary 6mm single glass, and the heat transfer coefficient is 5.7W / (m 2 ·K), the solar heat gain coefficient is 0.739. The roof is set as a common insulation roof, and the heat transfer coefficient is 0.595W / (m 2·K), thermal resistance is 1.522m 2 ·K / W.

[0012] Preferably, the process of obtaining energy consumption data under different enclosure structure combinations includes:

[0013] Five exterior wall insulation materials, three roof structures and three exterior window types were selected as a combination of energy-saving renovation solutions for multiple exterior envelope structures;

[0014] Based on the building energy consumption model, energy consumption simulation is performed on a variety of external envelope structure energy-saving transformation scheme combinations to obtain energy consumption data under different envelope structure combinations.

[0015] Preferably, the process of constructing the ANN neural network model includes: taking the building cooling and heating loads as dependent variables, and taking the energy-saving transformation combination parameters and regional meteorological parameters as independent variables to construct a BP neural network model.

[0016] Preferably, the determination of the optimal energy-saving solution is based on minimization of building life cycle costs.

[0017] Preferably, the calculation expression of the building life cycle cost is:

[0018]

[0019] C M =P M ×T h ×A W ;

[0020] C I =P I ×A W ;

[0021] C E =P E ×E;

[0022] ALCC is the annual life cycle cost of building heating and cooling; C M , C I are the cost of exterior wall insulation materials and installation costs, C E is the electricity cost for building heating and cooling, i is the insulation life of the exterior wall; n is the interest rate; P M is the XPS insulation price; P I is the installation price of thermal insulation materials; T h is the thickness of the exterior wall insulation; A W is the external wall insulation area; E For electricity price.

[0023] Preferably, the technical and economic analysis includes calculations of energy saving rate, cost savings, and investment payback period; and the environmental and economic evaluation includes calculations of carbon emission reduction and carbon credit income.

[0024] On the other hand, the present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the method is implemented when the processor executes the computer program.

[0025] On the other hand, the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program implements the method when executed by a processor.

[0026] Compared with the prior art, the present invention has the following advantages and technical effects:

[0027] Optimize the optimal thickness of different regions, exterior window types, roof types and exterior wall insulation materials to further reduce the heating and cooling energy consumption of public buildings, and analyze their economic, energy and carbon saving potential in China. Select museums, history museums and planning museums as case buildings, conduct energy audits, use DeST to evaluate their energy consumption, and study the impact of different envelope structures on building loads in different regions. In addition, the thickness of exterior wall insulation is optimized by combining artificial neural networks. The results show that the optimal exterior window type and roof type in city C are coated triple glass and polystyrene, respectively, and the exterior wall insulation is 30mm thick polystyrene. Compared with the original total load of the envelope structure of 67.77kWh / m2, the annual building energy saving is 9.36kWh / m2, the energy saving rate is 13.81%, and the ALLC saving percentage is 12.22%. The annual cost can be saved by 126,142.488 yuan, the payback period is 3.85 years, the annual carbon emissions can be reduced by 73.13t, and the economic benefit brought by the reduced carbon emissions is 10,237.57 yuan. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0029] Figure 1 A schematic diagram of a DeST energy consumption model according to an embodiment of the present invention;

[0030] Figure 2 Schematic diagram of the topological structure of a neural network according to an embodiment of the present invention.

[0031] Figure 3 A schematic diagram of the training process of the cold and hot load prediction model according to an embodiment of the present invention;

[0032] Figure 4 A schematic diagram of regression analysis of a full-year cumulative heat load prediction model according to an embodiment of the present invention;

[0033] Figure 5 A schematic diagram of regression analysis of the annual cumulative cooling load prediction model according to an embodiment of the present invention;

[0034] Figure 6 A schematic diagram of the optimal exterior wall insulation thickness when the exterior window type is vacuum glass according to an embodiment of the present invention;

[0035] Figure 7 This is a schematic diagram of the optimal exterior wall insulation thickness when the exterior window type is Low-plated according to an embodiment of the present invention;

[0036] Figure 8 This is a schematic diagram of the optimal exterior wall insulation thickness when the exterior window type is coated triple glass according to an embodiment of the present invention. DETAILED DESCRIPTION

[0037] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0038] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0039] Embodiment 1

[0040] This embodiment provides an office building energy-saving renovation method based on neural network optimization, including:

[0041] The museum, history museum and planning museum (referred to as the three museums) in city C have one underground floor and four above-ground floors. The building height is 20.55m and covers an area of ​​19,620m 2 The total construction area is 38946m 2 A detailed energy audit was conducted on the three museums from three aspects: lighting system, office and special equipment, air conditioning system and auxiliary equipment. Some equipment parameters and operating time were obtained as shown in Table 1:

[0042] Table 1

[0043]

[0044] According to the field survey, the exterior wall material of the target building is small hollow porous concrete blocks, and the exterior window types are mainly composed of single-glazed single-layer windows and single-glazed double-layer windows, without sunshades. The central air-conditioning system consists of four direct-fired lithium bromide absorption units, with a cooling set temperature ≥26°C and a heating temperature ≤20°C. The air-conditioning system is divided into centralized full air system, fan coil plus fresh air system, split air conditioner, and VRV local unit system. The monthly electricity and gas costs of the three museums in 2022 are summarized in Table 2:

[0045] Table 2

[0046]

[0047] Since the only equipment consuming gas in the building is the air conditioning unit, the unit performance parameters in Table 1 show that the cumulative cooling capacity of the refrigeration unit in summer is 861669.8705 kWh, and the cumulative heating capacity in winter is 720655.1681 kWh. When auditing the target building, the central air conditioning system was not turned on in the office area of ​​the Planning Museum in summer, but split air conditioners were used for cooling (a total of 120 units, each with a power of 1.5 kW and a cop of 3.36, assuming that each unit works 8 hours a day). Therefore, the actual cumulative cooling capacity in summer needs to be added to the calculation result of the gas consumption bill by 716083.2 kWh, totaling 1577753.071 kWh.

[0048] like Figure 1 As shown in the figure, the energy consumption model of the three museums was constructed using DeST software based on the field survey data. The exterior wall structure is set as a 240mm concrete small hollow porous block with a heat transfer coefficient of 2.209W / (m 2 ·K), thermal resistance is 0.295m 2 ·K / W. The window is set to ordinary 6mm single glass, and the heat transfer coefficient is 5.7W / (m 2 ·K), the solar heat gain coefficient is 0.739. The roof is set as a common insulation roof, and the heat transfer coefficient is 0.595W / (m 2 ·K), thermal resistance is 1.522m 2 ·K / W. Room types include offices, exhibition halls, corridors, lobbies, lounges, etc. The internal lighting and equipment are set according to the survey data in Table 1 using square meter indicators.

[0049] The software calculation shows that the total energy consumption for the simulated heating season is 838591.41 kWh, which is 14.06% lower than the total energy consumption for the heating season calculated from the actual gas consumption bill of 720655.1681 kWh. The total energy consumption for the simulated cooling season is 1809715.39 kWh, which is 12.82% lower than the calculated 1577753.071 kWh. It can be seen from the above that the model can effectively simulate the overall energy consumption of the target building.

[0050] In this embodiment, five cities in five different climate zones (City A, City B, City C, City D, and City E) were selected, five types of exterior wall insulation materials (rock wool, glass wool, extruded polystyrene board, polystyrene foam, and polyurethane rigid foam) were selected, from 0mm-200mm, every 20mm was a group, three roof structures (aerated concrete roof, lightweight polystyrene insulation roof, lightweight glass wool insulation roof), and three types of exterior windows (ordinary hollow glass, vacuum glass, and low-e film-coated vacuum glass) were selected. A total of 2250 sets of simulation data were used as the database for subsequent prediction model training. The detailed setting parameters are shown in Tables 3, 4, and 5.

[0051] Table 3

[0052]

[0053] Table 4

[0054]

[0055] Table 5

[0056]

[0057] ANN is a network composed of multiple neurons, each of which is connected to other neurons to form a complex network structure. Each neuron receives an input signal and outputs a result after processing it through an activation function. BP neural network is a specific implementation of ANN, which consists of an input layer, a hidden layer, and an output layer. The connection weights between the hidden layer and the output layer are trained and adjusted through the back propagation algorithm. In this study, the type and thickness of exterior wall insulation materials (exterior wall heat transfer coefficient, thermal conductivity, density, constant pressure specific heat, vapor permeability, heat storage coefficient), exterior window type (exterior window heat transfer coefficient, exterior window SHGC), roof insulation heat transfer coefficient, meteorological parameters (average ambient temperature, maximum temperature, minimum temperature, annual total radiation, average radiation) are used as input parameters (Tables 3-6), and the energy consumption (cooling, heating) simulated and calculated by DeST software is used as the output parameter. Through the MATLAB neural network tool, a model that can quickly predict the energy consumption of the target building is established (such as Figure 2When establishing an ANN model, it is necessary to specify the percentage of sample points used for training, testing, and validation, which are 70%, 15%, and 15% respectively in this study. In addition, the number of hidden layers in the ANN model is 1, and the number of neurons in the hidden layer is 10, as shown in Figure 2 After training, validating and testing the sample points, the regression value R is calculated in the neural network model. R represents the correlation between the actual result and the predicted result, and the closer R is to 1, the more accurate the result is.

[0058] from Figure 3-5 It can be seen that for the training of the annual cumulative heat load of the building, the mean square error of the training set and the test set has been decreasing from the beginning to the 9th epoch. After the 27th step, the MSE remained relatively stable, with a minimum value of 0.12249. For the training of the annual cumulative cooling load, the best epoch was the 30th, with an MSE of 0.0082911. The goodness of fit (R) of the training, validation and testing of the heat load prediction model 2 ) were 0.9999, 0.99982 and 0.99988, respectively, and the MSE values ​​were 0.076, 0.1225 and 0.0951, respectively. The goodness of fit (R 2 ) were 0.99996, 0.99999 and 0.99992, and the MSE values ​​were 0.0308, 0.0083 and 0.0553, respectively. 2 The values ​​are all above 90%, indicating that the neural network training has achieved good results. In general, the predicted values ​​of the cumulative heating load and the cumulative cooling load of the building are within the range of the simulation values ​​and show up and down fluctuations. The change trends of the two predicted values ​​are consistent, indicating that the overall prediction error is small. This shows that the established neural network model can accurately predict the energy consumption of the target building.

[0059] This embodiment uses ALLC for optimization to obtain the optimal exterior wall insulation materials and their thicknesses for each typical region under different exterior window and roof insulation combinations, and studies the energy saving rate and carbon emissions.

[0060]

[0061] C M =P M ×T h ×A W ;

[0062] C I =P I ×A W ;

[0063] C E =P E ×E;

[0064] ALCC is the annual life cycle cost of building heating and cooling, RMB / (m 2 CM and CI are the cost of external wall insulation materials and installation fees, respectively; CE is the electricity cost for building heating and cooling, i is the life of external wall insulation, years; n is the interest rate, %; PM is the price of XPS insulation, RMB / m 3 PI is the installation price of thermal insulation materials, RMB / m 2 ; Th is the thickness of the exterior wall insulation (mm); AW is the exterior wall insulation area (m) 2 ; PE is the electricity price, RMB yuan / kWh.

[0065] Adding exterior wall insulation to buildings is a common energy-saving renovation solution. Generally speaking, as the thickness of the insulation increases, the energy consumption of the building will gradually decrease. However, when the thickness of the insulation is too large, the energy-saving effect will begin to decrease if the thickness is further increased. At the same time, as the thickness of the insulation increases, the renovation cost also continues to increase. This embodiment selects meteorological parameters in typical cities in five climate zones as an example, and studies five types of exterior wall insulation materials under nine combinations of external envelope structures through the trained energy consumption prediction model. At the same time, ALCC is used to determine the optimal thickness of different materials, and their energy-saving benefits are analyzed.

[0066] Compared with the cold / heat loads of different cities, the change in heat load is more obvious than that in cold load as the thickness of exterior wall insulation increases. Especially in areas with cold winters, the range of heat load changes is larger. For example, as the thickness of insulation increases, the heat load of target buildings located in colder areas in winter is reduced far more than the increase in cold load. The total building load decreases with the increase in insulation thickness, which shows that exterior wall insulation is still an effective energy-saving measure in extremely cold areas. The building load of city B increases throughout the year with the increase in the thickness of exterior wall insulation. This is because the reduction in the heat load of the building in city B is less than the increase in the cold load. Therefore, for cities in mild areas, exterior wall insulation does not necessarily save energy and may even increase the overall building operating energy consumption. Generally, by designing a reasonable orientation and using natural ventilation, the indoor environment can be guaranteed without using exterior wall insulation.

[0067] like Figure 6-8As shown, the heat transfer coefficient of the exterior window reflects the heat transfer capacity of the window. When the heat transfer coefficient becomes larger, it indicates that the rate of heat transfer from the exterior window to the indoor space per unit time has increased. The SHGC of the exterior window reflects the ability of the window to allow radiation to pass through. When the SHGC increases, it indicates that the exterior window will allow more solar radiation to enter the room, thereby increasing the indoor temperature. This embodiment compares the effects of three types of exterior windows on the cold and hot loads: vacuum glass, Low-e film-coated hollow (high-transmittance type), and coated triple glass (coated + hollow + single glass). The heat transfer coefficients and SHGC of the three types of glass are 3.0, 2.4, 2.3 and 0.713, 0.487, 0.426, respectively. When the heat transfer coefficient and SHGC of the exterior window increase, the cold load of buildings in all cities will increase, because the exterior window transfers more heat to the indoor space. In winter, the higher heat transfer coefficient will cause more cold air to enter the room, resulting in an increase in the heat load. However, due to the increase in SHGC, the room receives more solar radiation, resulting in a decrease in the heat load. Therefore, among the three types of exterior windows, the cumulative heat load of the Low-e film-coated hollow window (high transmittance type) is the smallest.

[0068] The meteorological parameters of the research site have the greatest impact on the optimal thickness of exterior wall insulation of different materials. City B belongs to a mild area with suitable temperature all year round, and the thickness of exterior wall insulation is the smallest. In most cases, the thickness of all materials is only 5mm. Even when the external window type is vacuum glass, the roof is a lightweight insulation roof-glass wool and a lightweight insulation roof-polystyrene, the thickness of all exterior wall insulation materials is 0mm. Obviously, cold areas in winter need to increase the thickness of exterior wall insulation to improve the insulation effect. At the same time, exterior wall insulation can also better play a heat insulation effect in summer. This embodiment compares the optimal thickness of five exterior wall insulation materials: rock wool, glass wool, polystyrene foam, extruded polystyrene board, and polyurethane hard foam. The thermal conductivity of the five materials is 0.093, 0.058, 0.047, 0.037, and 0.034, respectively. As the thermal conductivity of the insulation material decreases, the optimal thickness of the insulation material also begins to increase. Among them, the optimal thickness of polyurethane is the smallest of all materials, and the optimal thickness of rock wool is the largest.

[0069] This embodiment uses ALLC for optimization to obtain the optimal exterior wall insulation materials and their thicknesses for each typical region under different exterior window and roof insulation combinations and analyzes their energy-saving benefits. As the thickness of the insulation material increases, the renovation cost increases linearly, and although the building energy saving is increasing, the rate of increase begins to slow down, so ALLC shows a trend of first decreasing and then increasing. In city B, when the exterior window type is coated triple glass, the roof type is gas-filled, and the exterior wall insulation is 5mm thick rock wool, the building life cycle cost is the lowest. Compared with the original total load of the envelope structure of 21.78kWh / m 2 , the annual building energy saving is 2.65kWh / m 2The energy saving rate is 12.15%, and the ALLC saving percentage is 7.05%. The central air-conditioning system of the target building adopts a lithium bromide system, and the carbon emission coefficient and cost of the gas are 0.2t CO2 / MWh and 2.65 yuan / m 3 Therefore, the annual cost can be saved by 32,976.25 yuan, the recovery period is 1.82 years, the annual carbon emissions can be reduced by 20.69 tons, and the economic benefit brought by the reduced carbon emissions is 2,896.05 yuan.

[0070] The exterior window types and roof types with the lowest life cycle in all other cities are coated triple glass and polystyrene. The best exterior wall insulation in city A is 20mm thick polystyrene foam, which has a total load of 68.04kWh / m compared to the original enclosure structure. 2 The annual building energy saving is 6.94kWh / m2, the energy saving rate is 10.20%, and the ALLC saving percentage is 8.60%. The annual cost saving is 81,748.67 yuan, the payback period is 8.60 years, the annual carbon emissions can be reduced by 54.27t, and the economic benefits brought by the reduced carbon emissions are 7,597.53 yuan.

[0071] It can be seen that the optimal external wall insulation thickness is 30mm, which is 67.77kWh / m 2 , the annual building energy saving is 9.36kWh / m 2 , the energy saving rate is 13.81%, and the ALLC saving percentage is 12.22%. The annual cost can be saved by 126142.488 yuan, the recovery period is 3.85 years, the annual carbon emissions can be reduced by 73.13t, and the economic benefits brought by the reduced carbon emissions are 10237.57 yuan. The optimal exterior wall insulation thickness in city D is 50mm, compared with the original total load of the enclosure structure of 71.51kWh / m 2 , the annual building energy saving is 18.78kWh / m 2 , the energy saving rate is 18.78%, and the ALLC saving percentage is 22.98%. The annual cost can be saved by 260,869.05 yuan, the recovery period is 3.10 years, the annual carbon emissions can be reduced by 146.81 tons, and the economic benefits brought by the reduced carbon emissions are 20,552.83 yuan. The optimal exterior wall insulation thickness in E City is 75mm, compared with the original total load of the enclosure structure of 90.82kWh / m 2 The annual building energy saving is 27.71kWh / m2, the energy saving rate is 30.51%, and the ALLC saving percentage is 27.34%. The annual cost saving is 413,254.59 yuan, the payback period is 2.94 years, the annual carbon emissions can be reduced by 216.56t, and the economic benefits brought by the reduced carbon emissions are 30,318.81 yuan.

[0072] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for energy-saving renovation of office buildings based on neural network optimization, characterized in that: include: Conduct energy audits on target buildings and obtain field research data; Calculate the field survey data based on DeST software to construct a building energy consumption model; Based on the building energy consumption model, energy consumption simulation is performed on a combination of energy-saving transformation schemes of various external envelope structures to obtain energy consumption data under different envelope structure combinations; Constructing an ANN neural network model, inputting the historical data set into the ANN neural network model, and obtaining a prediction model; Inputting the energy consumption data under the different enclosure structure combinations into the prediction model to obtain the optimal energy-saving solution; Conduct technical and economic analysis and environmental and economic evaluation on the optimal energy-saving solution and generate an energy-saving transformation report.

2. The method according to claim 1, characterized in that The field survey data include: building envelope structure parameters, various internal equipment parameters, operating time and annual operating energy consumption.

3. The method according to claim 1, characterized in that The exterior wall structure of the building energy consumption model is set as a 240mm small concrete hollow porous block, and the heat transfer coefficient is 2.209W / (m 2 ·K), thermal resistance is 0.295m 2 ·K / W. The window is set to ordinary 6mm single glass, and the heat transfer coefficient is 5.7W / (m 2 ·K), the solar heat gain coefficient is 0.

739. The roof is set as a common insulation roof, and the heat transfer coefficient is 0.595W / (m 2 ·K), thermal resistance is 1.522m 2 ·K / W.

4. The method according to claim 1, characterized in that: The process of obtaining energy consumption data for different envelope structure combinations includes: Five exterior wall insulation materials, three roof structures and three exterior window types were selected as a combination of energy-saving renovation solutions for multiple exterior envelope structures; Based on the building energy consumption model, energy consumption simulation is performed on a variety of external envelope structure energy-saving transformation scheme combinations to obtain energy consumption data under different envelope structure combinations.

5. The method according to claim 1, characterized in that The process of constructing the ANN neural network model includes: taking the building cooling and heating load as the dependent variable, and taking the energy-saving transformation combination parameter and the regional meteorological parameter as the independent variables to construct the BP neural network model.

6. The method according to claim 1, characterized in that The determination of the optimal energy-saving solution is based on minimization of the building life cycle cost.

7. The method according to claim 1, characterized in that The calculation expression of the building life cycle cost is: C M =P M ×T h ×A W ; C I =P I ×A W ; C E =P E ×E; ALCC is the annual life cycle cost of building heating and cooling; C M , C I are the cost of exterior wall insulation materials and installation costs, C E is the electricity cost for building heating and cooling, i is the insulation life of the exterior wall; n is the interest rate; P M Price for XPS insulation; P I Installation price for insulation materials; T h is the thickness of the exterior wall insulation; A W is the external wall insulation area; E For electricity price.

8. The method according to claim 1, characterized in that The technical and economic analysis includes the calculation of energy saving rate, cost saving and investment payback period; the environmental and economic evaluation includes the calculation of carbon emission reduction and carbon credit income.

9. An electronic device comprising a memory, a processor, and a computing program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the method described in any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method described in any one of claims 1 to 8 is implemented.

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