A Radiator Selection Method for Low-Temperature Heating System Based on Multiple Linear Regression

Abstract

The present invention discloses a radiator selection method for a low-temperature heating system based on multiple linear regression. The method analyzes and determines various factors affecting the indoor thermal environment of a building from three levels: building characteristics, heating system characteristics and terminal radiator characteristics, and performs uniform and orthogonal experimental design on these factors to obtain a number of typical heating rooms; the room temperature of each typical heating room under the most unfavorable working condition of outdoor meteorological conditions is obtained by means of a building thermal environment simulation method, and the design heat load of the typical heating room is calculated to characterize the influencing factors at the building characteristic level, and then a large sample database consisting of various influencing factors and the room temperature under the most unfavorable working condition is constructed; a multiple linear regression prediction model is established for the room room temperature under the most unfavorable working condition and its influencing factors; the room room temperature under the most unfavorable working condition is characterized by the heating design room temperature, and the model is deformed by taking the radiator area as the independent variable to obtain a selection model for the radiator of a low-temperature heating system.

Description

Technical Field

[0001] The invention relates to a radiator selection method for a low-temperature heating system based on multiple linear regression, and belongs to the engineering field of energy application. Background Art

[0002] In order to adapt to the development of low-temperature heating technology, the terminal equipment in the heating system also needs to be adjusted accordingly. Radiators, as traditional heating terminal equipment, are widely used in my country's centralized heating systems. Existing research has further proved the applicability of radiators in low-temperature heating systems. However, the selection of radiators in low-temperature heating systems still uses the traditional design method of high-temperature heating systems. The result is often that the radiator is too large, and the problem of indoor overheating still exists in actual operation. Instead of reducing heating energy consumption, this may lead to an increase in heating energy consumption.

[0003] Therefore, it is necessary to establish a new design and selection method for radiators in low-temperature heating systems to avoid the problem of over-sizing radiators in actual heating systems. Summary of the invention

[0004] The purpose of the present invention is to take into account the common influence and effect of building characteristics (room length, width and height dimensions, window-to-wall ratio, orientation, thermal insulation performance of enclosure structure, indoor thermal disturbance), terminal radiator characteristics (radiator thermal performance, radiator area, radiator convection radiation ratio), and heating system characteristics (water supply temperature and flow) on the indoor thermal environment of the building, and for the low-temperature heating operation system, obtain a typical heating room (calculation case) composed of the above-mentioned various influencing factors through uniform and orthogonal experimental design; then for each calculation case, apply the building thermal environment simulation software DeST to perform hourly simulation calculations, and extract the room temperature under the most unfavorable working conditions of outdoor meteorological conditions; then convert the various factors related to the building characteristics into the room design heat load, thereby obtaining a sample database of the combination of the relevant various influencing factors and the room temperature under the most unfavorable working conditions; then use the analysis method of multiple linear regression to calculate and determine the regression coefficient of each independent variable (influencing factor) in the regression model; on this basis, further carry out the analysis and verification of the multiple linear regression model; and finally construct a selection method suitable for radiators of low-temperature heating systems. The method uses statistical analysis methods and simulation calculation results of the building thermal environment to construct a large sample database, and then establishes a multivariate linear regression prediction model to reflect the impact of various influencing factors on the room temperature under the most unfavorable working conditions. From the perspective of ensuring that the room temperature under the most unfavorable working conditions meets the indoor design temperature, the radiator area that meets the design room temperature requirements is obtained for the specified building characteristics (building form and enclosure structure insulation performance), heating system characteristics (water supply temperature and flow rate) and radiator thermal performance, radiator convection radiation ratio. In order to achieve the purpose of the invention, the present invention adopts a radiator selection method for a low-temperature heating system based on multivariate linear regression, and the method comprises the following steps:

[0005] (1) Determination of factors affecting indoor thermal environment and their level

[0006] At the level of building characteristics, the room's length, width and height, window-to-wall ratio, orientation, thermal insulation performance of the enclosure structure, and indoor thermal disturbance all have an impact on the indoor thermal environment, and these impacts can ultimately be attributed to the size of the room's design heat load. At the level of heating system characteristics, the higher the water supply temperature, the higher the room temperature of the heated room; the room temperature of the heated room will first rise to a certain level as the water supply flow of the heating system increases, and then will basically remain stable. At the level of terminal radiator characteristics, the room temperature of the heated room rises as the radiator's thermal performance increases and the heat dissipation area increases, and the radiator's convection-radiation ratio has a relatively small impact on the room temperature of the heated room.

[0007] Therefore, taking the indoor thermal environment of the room as the starting point, the above-mentioned factors affecting the indoor thermal environment of the building are included in the analysis scope, including the length, width and height dimensions of the room, window-to-wall ratio, room orientation, thermal insulation performance of the enclosing structure, indoor thermal disturbance, water supply temperature, water supply flow, radiator thermal performance coefficients a and b, radiator area F, radiator convection-radiation ratio, etc., and then according to the actual variation range of each influencing factor, the respective level is analyzed and determined.

[0008] (2) Determination of typical heating rooms (calculation cases)

[0009] Based on the levels of various influencing factors such as room length, width and height, window-to-wall ratio, room orientation, thermal insulation performance of enclosing structures (walls and windows), indoor thermal disturbance, radiator thermal performance, radiator area F, radiator convection radiation ratio, heating system water supply temperature and water supply flow, SPSS statistical analysis software was used to carry out uniform and orthogonal experimental design analysis to determine the typical heating rooms (calculation cases) with different level combinations of various influencing factors.

[0010] (3) Simulation calculation and database establishment of indoor thermal environment of buildings

[0011] The building thermal environment simulation software DeST is used to simulate and calculate the indoor temperature of each typical heating room (calculation case) hourly, and the room temperature of the heating room under the most unfavorable outdoor meteorological conditions is obtained; on the other hand, according to the "Design Code for Heating, Ventilation and Air Conditioning of Civil Buildings" (GB50019-2016), the room design heat load is calculated.

[0012] Then, the room design heat load, radiator thermal performance coefficient a and b, radiator area, radiator convection radiation ratio, heating system water supply temperature and flow rate, and the heating room room temperature under the most unfavorable working conditions are used to form a large sample database.

[0013] (4) Construction of multivariate linear regression prediction model

[0014] Since each typical heating room (calculation case) is determined through uniform and orthogonal experimental design, and each influencing factor can be regarded as a continuous variable, and considering that each influencing factor is mostly linearly related to the room temperature under the most unfavorable working conditions, a multivariate linear regression prediction model is selected. Specifically, as shown in formula (1):

[0015] Y=α0+α1X1+α2X2+…+α i X i (1)

[0016] Where Y is the dependent variable of the multiple linear regression prediction model; X1, X2, …, X i is the independent variable of the multiple linear regression prediction model; α0 is the constant term of the multiple linear regression prediction model; α1, α2, …, αi is the regression coefficient of each variable in the multiple linear regression prediction model.

[0017] (5) Determination of regression coefficients of multivariate linear regression prediction model

[0018] The statistical sample database consisting of the room temperature of the heating room under the most unfavorable outdoor meteorological conditions, the room design heat load, the water supply temperature and flow rate of the heating system, the radiator thermal performance coefficients a and b, the radiator area, and the radiator convection radiation ratio is processed to eliminate abnormal data groups. Then, the multivariate linear regression method is used to fit and analyze the valid data groups to obtain the regression form as shown in formula (2).

[0019] t min =c0+c1Q+c2T g +c3G+c4F+c5a+c6b+c7R (2)

[0020] Where, t min is the room temperature of the heating room under the most unfavorable outdoor meteorological conditions, ℃; Q is the room design heat load, W / m 2 ; T g is the water supply temperature, ℃; G is the water supply flow rate, its value is a multiple of the design flow rate; F is the radiator area, m 2 ; a, b are the thermal performance coefficients of the radiator; R is the convection-radiation ratio of the radiator; c0 is a constant term; c1, c2, …, c7 are the regression coefficients of each influencing factor.

[0021] For a specific building, its building characteristics, water supply temperature and water supply flow, radiator type and radiator convection-radiation ratio are all known parameters. The radiator area is used as the dependent variable and other factors are used as independent variables to transform formula (2) to obtain the radiator selection model, as shown in formula (3):

[0022] F=(t min -c0-c1Q-c2T g -c3G-c5a-c6b-c7R) / c4 (3)

[0023] In actual engineering applications, in order to ensure the comfort of the indoor thermal environment of the heated room in winter, the actual room temperature must not be lower than the heating design room temperature. Therefore, the room heating design room temperature (t d ) is used to replace the room temperature of the heating room under the most unfavorable outdoor meteorological conditions (t min ), thus obtaining the radiator area that meets the room design room temperature requirements, as shown in formula (4):

[0024] F=(t d -c0-c1Q-c2T g-c3G-c5a-c6b-c7R) / c4 (4)

[0025] (6) Analysis and verification of the multivariate linear regression prediction model

[0026] Further, according to the level of each influencing factor, several verification calculation cases that meet the statistical quantity requirements are randomly formed. For these verification calculation cases, the DeST software is used to simulate and calculate the room temperature of the heating room under the most unfavorable outdoor meteorological conditions, and it is regarded as the true value of the room temperature; on the other hand, the established multivariate linear regression model is used to predict the room temperature of the heating room under the most unfavorable outdoor meteorological conditions. The room temperature results obtained by the above two methods are compared. If the number of calculation cases with an absolute error within the range of ±2.0℃ can reach 80% of the total, it means that the obtained multivariate linear regression prediction model has good accuracy.

[0027] The beneficial effects of the radiator selection method for a low-temperature heating system based on multivariate linear regression described in the present invention are mainly reflected as follows:

[0028] Compared with the traditional design method applied to high-temperature heating systems, the invented method takes the indoor thermal environment of the building as the starting point, constructs a large sample database based on the simulation results of the building thermal environment, truly reflects the influence of various factors on the room temperature of the room under the most unfavorable outdoor meteorological conditions, and uses the statistical analysis of big data to reasonably determine the correlation between the room temperature and various influencing factors including the radiator area. The physical meaning of the method is clear, the mathematical reasoning is appropriate, and the test steps can be simplified to the maximum extent, reducing the test cost. At the same time, the method described in the invention is highly operable, and the application process and steps are clear, which ensures the feasibility of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a flow chart of the radiator selection method for low temperature heating system based on multiple linear regression;

[0030] Figure 2 It is a graph showing the changes of indoor occupants’ daily routines and other indoor thermal disturbances over time;

[0031] Figure 3 It is a graph showing the changes in the number of ventilation changes between the room and the outside world hour by hour.

[0032] Figure 4 This is the absolute error diagram of the room temperature calculated by multivariate linear regression prediction and the DeST simulated room temperature when the room temperature is 16℃-22℃ under the most unfavorable outdoor meteorological conditions. DETAILED DESCRIPTION

[0033] A method for selecting radiators for low-temperature heating systems based on multivariate linear regression. The residential bedrooms in a certain area were taken as the research object. The thermal insulation performance and structure of the enclosure structure were determined according to the energy-saving standards of the area. The relevant parameters are shown in Table 1. Through the actual investigation of the residential bedrooms in a certain area, the changes in the heat disturbance of indoor personnel, lighting and equipment over time and the number of indoor and outdoor ventilation in the room were obtained, as shown in the attached figure. Figure 2 and attached Figure 3 For this research object, combined with the attached Figure 1 , the specific application ideas and application steps of the present invention are described as follows:

[0034] Table 1 Enclosure structure and heat transfer coefficient

[0035]

[0036] 1. Determination of factors affecting indoor thermal environment and their level

[0037] For residential bedrooms that use radiator low-temperature heating systems, the factors that affect the room temperature under the most unfavorable outdoor meteorological conditions mainly come from three aspects: building characteristics (room length, width and height dimensions, window-to-wall ratio, room orientation, and indoor thermal disturbance), heating system characteristics (water supply temperature, water supply flow) and terminal radiator characteristics (radiator thermal performance coefficient a, radiator thermal performance coefficient b, radiator area F and radiator convection radiation ratio), a total of 12 influencing factors, among which the factors related to building characteristics can ultimately be attributed to the size of the room design heat load.

[0038] The actual range of each factor is determined according to relevant design specifications and engineering experience. The ranges of length, width and height of the room are 2.4-4.8m, 2.4-4.8m and 2.6-3.4m respectively; the ranges of window-to-wall ratio, room orientation and indoor thermal disturbance are 0.1-0.9, 0-270° and 0.5-1 times respectively; the ranges of water supply temperature and water supply flow are 45-75℃ and 0.5-3 times respectively; the ranges of radiator area, radiator thermal performance coefficient a, radiator thermal performance coefficient b and radiator convection radiation ratio are 1-5m 2 , 1~4, 0.1~0.4 and 0.2~0.8.

[0039] For the length, width and height of the room, the floor height is divided into 9 levels at intervals of 0.1m, and the length and width of the room are divided into 9 levels at intervals of 0.3m respectively, to ensure that the number of levels between factors is the same and the intervals between different levels within each factor are uniform, laying the foundation for the subsequent uniform experimental design. The specific levels are shown in Table 2.

[0040] Table 2 Room size factor level table

[0041]

[0042] In addition, for the window-to-wall ratio, radiator area, radiator thermal performance coefficient a, radiator thermal performance coefficient b, and radiator convection radiation ratio, their values ​​are continuous within their range of variation, so their respective levels are determined at intervals of 0.2, 1, 1, 0.1, and 0.2 respectively according to their range of variation; in actual projects, the room orientation is mostly positive, so four levels of due north (0°), due east (90°), due south (180°), and due west (270°) are selected; since this method is mainly aimed at low-temperature heating systems, the water supply temperature range that needs to be focused on is 45-65°C, and the level is determined at intervals of 5°C in this range, and in the range of 65-75°C, the level is determined at intervals of 10°C; for water supply flow, its impact on the room temperature under the most unfavorable outdoor meteorological conditions gradually decreases after reaching a certain level, so the interval between adjacent levels of water supply flow gradually increases with the increase of water supply flow. The specific level of each factor is shown in Table 3.

[0043] Table 3 Levels of other factors except room size

[0044]

[0045] 2. Determination of typical heating rooms (calculation cases)

[0046] The number of levels of the above factors is large, and the number of levels of different factors varies. In order to obtain an experimental scheme that can reflect the influence characteristics of each factor and has a reasonable number, a scientific experimental design is required. First, the level of each factor determined in Table 2 is input into the SPSS software, and the typical size room (typical room) of a certain area is obtained through the uniform experimental design method, as shown in Table 4.

[0047] Table 4 Uniformity Test Table

[0048]

[0049] Through the above uniform test design, 9 typical rooms of different sizes can be obtained to fully reflect the room size characteristics of residential bedrooms in a certain area. Based on these 9 typical rooms, the level of each factor determined in Table 3 is input into the SPSS statistical analysis software, and the typical heating conditions of each typical room in a certain area are obtained through the orthogonal test design method, also known as the typical heating room (calculation case), as shown in Table 5.

[0050] Table 5 Orthogonal test table

[0051]

[0052]

[0053] In summary, 9 typical rooms were identified through experimental design (see Table 4), each of which contains 64 typical heating conditions (see Table 5), so a total of 9×64=576 typical heating rooms (calculation cases) were finally obtained.

[0054] 3. Simulation calculation and database establishment of indoor thermal environment of buildings

[0055] According to the level parameters of each factor in the above calculation cases, the building thermal environment simulation software DeST was used to build a model, and the indoor temperature of these 576 calculation cases was simulated and calculated hourly, and the room temperature of each calculation case under the most unfavorable outdoor meteorological conditions was extracted. On the other hand, according to the level parameters of each factor in the above calculation cases and the "Design Code for Heating, Ventilation and Air Conditioning of Civil Buildings" (GB50019-2016), the design heat load of each of the 576 calculation cases was calculated, and the influence of the length, width and height of the room, the window-to-wall ratio, the room orientation, and the indoor thermal disturbance on the room temperature under the most unfavorable outdoor meteorological conditions was equivalently replaced. The calculation results were processed to eliminate the abnormal results caused by insufficient heat exchange, and then the room design heat load, radiator thermal performance coefficient a and b, radiator area, radiator convection radiation ratio, heating system water supply temperature and flow, and the heating room room temperature under the most unfavorable outdoor meteorological conditions were combined into a large sample database.

[0056] 4. Determination of regression coefficients of multivariate linear regression prediction model

[0057] The room temperature of the heating room under the most unfavorable working conditions is taken as the dependent variable, and the seven factors of room design heat load, heating system water supply temperature, water supply flow, radiator thermal performance coefficient a and b, radiator area F, and radiator convection radiation ratio are taken as independent variables. A multivariate linear regression prediction model is constructed, and the SPSS statistical analysis software is used to fit the established sample database to obtain the regression coefficient of each independent variable. The fitting analysis results are shown in formula (5):

[0058] t min =-12.908-0.012Q+0.314T g +1.473G+2.567F+2.933a+18.017b+2.849R (5)

[0059] Where, t min is the room temperature of the heating room under the most unfavorable outdoor meteorological conditions, ℃; Q is the room design heat load, W / m 2 ; T g is the water supply temperature, ℃; G is the water supply flow rate, its value is a multiple of the design flow rate; F is the radiator area, m 2 ; a and b are the thermal performance coefficients of the radiator; R is the convection-radiation ratio of the radiator.

[0060] Therefore, according to the specified building characteristics (building form and thermal insulation performance of the envelope structure), heating system characteristics (water supply temperature and flow rate) and radiator type (radiator thermal performance, radiator convection radiation ratio), the radiator area F is used as the dependent variable to transform formula (5), and then the radiator design selection model is obtained, as shown in formula (6):

[0061] F=(t min +12.908+0.012Q-0.314T g -1.473G-2.933a-18.017b-2.849R) / 2.567 (6)

[0062] To ensure the comfort of the indoor thermal environment of the heating room, the room design room temperature (t d ) replaces the room temperature (t min ), and thus the radiator area F that meets the room design temperature requirements is obtained, as shown in formula (7):

[0063] F=(t d +12.908+0.012Q-0.314T g -1.473G-2.933a-18.017b-2.849R) / 2.567 (7)

[0064] 5. Analysis and verification of the multivariate linear regression prediction model

[0065] Two rooms with length, width and height of 2.8m, 3.8m, 2.6m and 3.3m, 4.2m, 2.6m were randomly selected to analyze and verify the prediction model, and then an orthogonal experimental design was performed on the two rooms, and a total of 2*64=128 calculation cases were obtained. According to the DeST simulation calculation results of the room temperature of the 128 calculation cases under the most unfavorable outdoor meteorological conditions, the multivariate linear regression prediction model was verified. That is, for the case where the DeST simulation calculation results of the room temperature under the most unfavorable outdoor meteorological conditions are 16℃-22℃, the multivariate linear regression prediction calculation value is compared with the corresponding DeST simulation value to obtain the absolute error diagram, as shown in the attached figure. Figure 4 As shown in the figure, it can be seen that the absolute error of 80% of the calculation cases is within ±2□, and the calculation cases with absolute errors outside ±2□ almost all have the problem that the calculated area of ​​the radiator is too small (<1m 2 ) situation.

[0066] Therefore, the verification results show that the radiator selection method for low-temperature heating system based on multivariate linear regression proposed in this invention eliminates the problem of radiator calculation area being too small (<1m 2) can basically meet the accuracy requirements of actual engineering radiator design and selection.

Claims

1. A radiator selection method for a low-temperature heating system based on multivariate linear regression, characterized in that: Based on the building thermal environment simulation method and the multivariate regression analysis method, a linear regression model with the room temperature under the most unfavorable outdoor meteorological conditions as the dependent variable is established. From the perspective of ensuring that the room temperature under the most unfavorable conditions meets the indoor design temperature under the most unfavorable conditions, the radiator area that meets the design room temperature requirements is obtained from three levels: building characteristics, heating system characteristics, and terminal radiator characteristics. The model specifically includes the following steps: (1) Determination of factors affecting indoor thermal environment and their level: Taking the indoor thermal environment of the room as the starting point, the factors affecting the indoor thermal environment of the building are included in the analysis scope, and the respective level is determined according to the actual variation range of each influencing factor; the factors affecting the indoor thermal environment of the building include three categories: building characteristics, heating system characteristics and terminal radiator characteristics, among which the building characteristics include room size factors; (2) Determination of typical heating rooms: Statistical analysis software is used to carry out uniform and orthogonal test design to analyze the level of room size factors and determine several rooms of typical sizes; then statistical analysis software is used to carry out uniform and orthogonal test design to analyze the level of other factors except room size factors and determine the corresponding typical heating conditions for each room of typical size, also known as typical heating rooms; (3) Simulation calculation and database establishment of indoor thermal environment of buildings: Using the building thermal environment simulation software, the room temperature of each typical heating room is simulated and calculated hourly, and the room temperature of each typical heating room under the most unfavorable outdoor meteorological conditions is extracted; on the other hand, according to the design specifications for heating, ventilation and air conditioning of civil buildings, the design heat load of each typical heating room is calculated, and then the design heat load of each typical heating room, the characteristics of the heating system, the characteristics of the terminal radiator and the room temperature of the heating room under the most unfavorable conditions are formed into a large sample database; (4) A radiator selection model for low-temperature heating systems based on multivariate linear regression is established. The model is used to calculate the required radiator area F when the building characteristics, heating system characteristics, and terminal radiator characteristics are known: Using a large sample database and multiple linear regression method, a regression model is established between the room temperature of a typical heating room under the most unfavorable outdoor meteorological conditions and the room design heat load, heating system characteristics, and terminal radiator characteristics. The terminal radiator characteristics include the radiator area F. The regression model takes the room temperature of a typical heating room under the most unfavorable conditions as the dependent variable, and the rest as independent variables. Then, the radiator selection model for low-temperature heating system is derived, which is the functional relationship between the radiator area F and other characteristics; Building characteristics include room length, width and height, window-to-wall ratio, room orientation, and indoor thermal disturbance; heating system characteristics include water supply temperature and water supply flow; terminal radiator characteristics include radiator thermal performance coefficient a and b, radiator area F, and radiator convection-radiation ratio; The regression model is as follows: t min =-12.908-0.012Q+0.314T g +1.473G+2.567F+2.933a+18.017b+2.849R Where, t min is the room temperature of the heating room under the most unfavorable outdoor meteorological conditions, ℃; Q is the room design heat load, W / m 2 ; T g is the water supply temperature, ℃; G is the water supply flow rate, its value is a multiple of the design flow rate; F is the radiator area, m 2 ; a, b are the thermal performance coefficients of the radiator; R is the convection-radiation ratio of the radiator; Design room temperature with heating room t d Replace the room temperature t under the most unfavorable outdoor meteorological conditions min , thus obtaining the radiator selection model that meets the design room temperature requirements of the heating room as follows: F=(t d +12.908+0.012Q-0.314T g -1.473G-2.933a-18.017b-2.849R) / 2.567。 2. The method for selecting a radiator for a low-temperature heating system based on multiple linear regression according to claim 1, characterized in that: Building characteristics include room length, width and height, window-to-wall ratio, room orientation, and indoor thermal disturbance. Heating system characteristics include water supply temperature and water supply flow. Terminal radiator characteristics include radiator thermal performance coefficients a and b, radiator area F, and radiator convection-radiation ratio.

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