A method for modeling thermal dissatisfaction rate based on negative feedback thermal adaptation

Abstract

A thermal dissatisfaction rate modeling method based on negative feedback thermal adaptation, based on thermal environment data collected in the field, and based on a Fanger predicted thermal dissatisfaction percentage PPD model, a thermal dissatisfaction rate model arPPD is constructed through the following formula: Wherein, PMV i is PMV of the ith data set collected in the field research, VPD i is the proportion of people dissatisfied with the thermal environment in the ith data set collected in the field research, T i is the environmental temperature of the ith data set collected in the field research; n PMV, VPD and environmental temperature T data sets are collected. The thermal dissatisfaction rate model arPPD constructed in the application improves the original PPD model's explanation ability for thermal adaptation, thereby realizing more accurate and reliable thermal dissatisfaction rate prediction.

Description

Technical Field

[0001] This invention relates to the field of indoor thermal comfort prediction, and more specifically to a method for modeling thermal dissatisfaction rate based on negative feedback thermal adaptation. Background Technology

[0002] Thermal comfort is a key indicator for measuring the quality of the built environment and energy efficiency, directly impacting human health, work efficiency, and resident satisfaction. In thermal comfort research, PPD (Positive Pressure Displacement), as a core indicator for measuring group satisfaction, has become an important basis for building design and operational optimization. The currently mainstream international PPD assessment system is based on Fanger's PMV-PPD theoretical framework. PMV comprehensively considers environmental parameters such as air temperature, wind speed, and radiant temperature, as well as individual parameters such as clothing thermal resistance and metabolic rate to estimate thermal sensation values, while PPD estimates the proportion of dissatisfied individuals based on PMV values. However, this model fails to fully consider the dynamic thermal adaptation capabilities of the human body in real-world environments.

[0003] Recent studies have shown that thermal adaptation is a crucial factor influencing human thermal sensation and thermal satisfaction. While some studies have incorporated thermal adaptation into the correction of PMV prediction models, research on the role of thermal adaptation in PPD calculation is lacking. Currently, the common practice is to input thermally adapted PMV values ​​into Fanger's PMV-PPD theoretical framework for calculation. However, PPD exhibits a non-linear amplification characteristic of PMV; slight deviations in PMV can be magnified, leading to PPD predictions that deviate from reality. If the model fails to effectively integrate the impact of thermal adaptation on PPD, it will be difficult to accurately reflect the thermal comfort level of a group under dynamic conditions. Therefore, improving the accuracy of PPD prediction of thermal dissatisfaction rate is an urgent problem to be solved. Summary of the Invention

[0004] To address the aforementioned issues, this invention provides a thermal dissatisfaction rate modeling method based on negative feedback thermal adaptation. This method integrates adaptive and inference methods, introduces an adaptive factor λ and a offset calibration coefficient c, and can comprehensively explain thermal adaptation, thereby improving the accuracy of thermal dissatisfaction rate prediction.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for modeling thermal dissatisfaction rate based on negative feedback thermal adaptation is proposed. Based on field-collected thermal environment data, a new thermal dissatisfaction rate model is established using Fanger's Predicted Percentage of Thermal Dissatisfaction (PPD) model. The method is characterized by introducing an adaptation factor λ and a offset calibration coefficient c based on Fanger's PPD model, and constructing a new thermal dissatisfaction rate model arPPD using the following formula:

[0007]

[0008] Where PMV is the predicted average vote value, c is the offset calibration coefficient, and λ is the adaptation factor;

[0009] The adaptability factor λ changes linearly with the reciprocal of the ambient temperature T, specifically expressed as:

[0010]

[0011] Where T is the ambient temperature, which represents a key environmental parameter affecting human thermal adaptability. Indoor or outdoor ambient temperature is typically chosen as the indicator. p and q are constant parameters, calculated using the following formulas:

[0012]

[0013] PPD i =100-95exp(-0.03353(PMV) i +c) 4 -0.2179 (PMV) i +c) 2 (3)

[0014] In the formula, PMV i It is the PMV and VPD of the i-th data set collected in the field research. i T represents the proportion of people dissatisfied with the thermal environment in the i-th data set collected during the on-site study. i It is the ambient temperature of the i-th data set collected in the field study; a total of n data sets of PMV, VPD and ambient temperature T were collected.

[0015] The optimization methods for the offset calibration coefficient c and the constant parameters p and q are as follows:

[0016] Step 1: Set the search range of the offset calibration coefficient c to [m, n], and the search step size to Δc, generating a set of candidate values ​​c. (j) The range of [m,n] should not exceed the range of PMV values;

[0017] Step 2: For each candidate value c (j) Perform the following calculations:

[0018] Step 2.1, Calculation

[0019]

[0020] Step 2.2: Calculate p according to formula (1) and formula (2). (j) and q (j) ;

[0021] Step 2.3: Calculate the predicted value of the thermal dissatisfaction rate model.

[0022] Step 2.4: Calculate the root mean square error:

[0023]

[0024] Step 3: Calculate the optimal solution for c, which is c that minimizes RMSE. opt :

[0025]

[0026] Step 4, c opt The corresponding p (j) and q (j) The optimal solution for p and q is p. opt and q opt .

[0027] The derivation process of formulas (1) and (2) is as follows:

[0028] Determining the constant parameters p and q is to minimize the deviation between the new thermal dissatisfaction rate model arPPD and the actual thermal dissatisfaction rate VPD. The terms in the following formula (4) are... When the proposed arPPD can accurately predict VPD, it is close to 1. Therefore, determining the constant parameters p and q is to minimize the objective function, as shown in formula (4). Formula (4) is then transformed into formula (5). In order to minimize the objective function, the derivatives of formula (5) with respect to p and q should both be 0, i.e. formulas (6) and (7). By solving these formulas, the calculation formulas (1) and (2) for p and q can be obtained.

[0029]

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] This invention builds upon Fanger's Predictive Percentage of Thermal Dissatisfaction (PPD) model by introducing a dual dynamic compensation mechanism of a dynamically changing adaptation factor and a offset calibration coefficient. This new model, arPPD, not only retains the parameter system of the standard PPD model but also incorporates the adaptation factor λ and the offset calibration coefficient c, enabling it to account for human thermal adaptation. Compared to the standard PPD model, which cannot consider thermal adaptation, the thermal dissatisfaction rate model constructed in this invention can predict thermal dissatisfaction rates more accurately. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the process for constructing the thermal dissatisfaction rate model of this invention.

[0033] Figure 2 This is a comparison chart of the prediction effects of the newly developed thermal dissatisfaction rate model arPPD, Fanger's thermal dissatisfaction rate model PPDo1, and arPMV-based thermal dissatisfaction rate model PPDo2 in Example 1.

[0034] Figure 3 This is a comparison chart of the prediction effects of the newly developed thermal dissatisfaction rate model arPPD, Fanger's thermal dissatisfaction rate model PPDo1, and arPMV-based thermal dissatisfaction rate model PPDo2 in Example 2. Detailed Implementation

[0035] The present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments of the present invention include, but are not limited to, the following embodiments.

[0036] This invention provides a novel thermal dissatisfaction rate model based on negative feedback thermal adaptation. By introducing an adaptation factor and a offset calibration coefficient, the model can account for human thermal adaptation, thereby improving the accuracy of thermal dissatisfaction rate prediction. Figure 1 As shown, the method for constructing this thermal dissatisfaction rate model in this invention is as follows: Based on the thermal environment data collected on-site, a new thermal dissatisfaction rate model is established based on Fanger's predicted thermal dissatisfaction percentage (PPD) model. An adaptation factor λ and a offset calibration coefficient c are introduced, and a new thermal dissatisfaction rate model arPPD based on negative feedback thermal adaptation is constructed using the following formula:

[0037]

[0038] Where PMV is the predicted average vote value, c is the offset calibration coefficient, and λ is the adaptation factor.

[0039] The adaptability factor λ changes linearly with the reciprocal of the ambient temperature T, specifically expressed as:

[0040]

[0041] Where T is the ambient temperature, a key environmental parameter affecting human thermal adaptability, typically selected as either indoor or outdoor ambient temperature. In practical applications, correlation analysis and other methods can be used to determine the environmental parameter that best reflects human thermal adaptability. In this embodiment, indoor air temperature is chosen as T. p and q are constant parameters, calculated using the following formulas:

[0042]

[0043] PPD i =100-95exp(-0.03353(PMV) i +c) 4-0.2179 (PMV) i +c) 2 (3)

[0044] In the formula, PMV i It is the PMV of the i-th data set collected in the field research; VPD i T represents the proportion of people dissatisfied with the thermal environment in the i-th data set collected during the on-site study; i It is the ambient temperature of the i-th data set collected in the field study; a total of n data sets of PMV, VPD and ambient temperature T were collected.

[0045] The optimization methods for the parameters c, p, and q are as follows:

[0046] like Figure 1 As shown, in step 1, the search range of the offset calibration coefficient c is set to [m,n], the search step size is set to Δc, and a set of candidate values ​​c is generated. (j) The range of [m,n] should not exceed the range of PMV values ​​[-3,3]. A smaller Δc results in higher search accuracy but longer computation time. In this embodiment, the search space for c is chosen to be [-3,3], and the search step size Δc is chosen to be 0.01.

[0047] Step 2: For each candidate value c (j) Perform the following calculations:

[0048] Step 2.1, Calculation

[0049]

[0050] Step 2.2: Calculate p according to formulas (1) and (2). (j) and q (j) ;

[0051] Step 2.3: Calculate the predicted value of the thermal dissatisfaction rate model.

[0052] Step 2.4: Calculate the root mean square error:

[0053]

[0054] Step 3: Calculate the optimal solution for c, which is c that minimizes RMSE. opt :

[0055]

[0056] Step 4, c opt The corresponding p (j) and q (j) The optimal solution for p and q is p.opt and q opt .

[0057] The error calculation methods in steps 2.4 and 3 above can be replaced by the root mean square error, or by the standard deviation of the error, and still fall within the scope of protection of this invention.

[0058] The derivation process of formulas (1) and (2) is as follows:

[0059] Determining the constant parameters p and q is to minimize the deviation between the new thermal dissatisfaction rate model arPPD and the actual thermal dissatisfaction rate VPD. The terms in formula (4) When the proposed arPPD can accurately predict VPD, it approaches 1. Therefore, determining the constant parameters p and q is to minimize the objective function, as shown in formula (4). Formula (4) can be transformed into formula (5). In order to minimize the objective function, the derivatives of formula (5) with respect to p and q should both be 0, i.e., formulas (6) and (7). By solving these formulas, the calculation formulas (1) and (2) for p and q can be obtained.

[0060]

[0061] The method for determining c and the derived formulas 1 and 2 for calculating p and q are concise and clear, facilitating practical engineering applications. Modifying the above algorithm to other optimization algorithms (such as gradient descent) still falls within the scope of this invention.

[0062] The advantages of this invention are illustrated below with two implementation examples. The implementation examples use the root mean square error (RMSE) to compare the thermal dissatisfaction rate model arPPD of this invention, Fanger's thermal dissatisfaction rate model PPDo1, and the thermal dissatisfaction rate model PPDo2 based on arPMV. PPDo2 is calculated as follows: First, according to the literature [Zhang S, Lin Z. Adaptive-rational thermal comfort model: Adaptive predicted mean vote with variable adaptive coefficient[J]. Indoor Air, 2020, 30(6):1052-1062.], arPMV is calculated using PMV. Then, arPMV is used to replace PMV in Fanger's thermal dissatisfaction rate model to calculate PPDo2. A smaller RMSE indicates a smaller model error.

[0063] Example 1

[0064] The PMV, VPD, and ambient temperature T data used in the thermal dissatisfaction rate model established in Example 1 were obtained from measured data of air-conditioned office buildings in temperate climate zones (Köppen climate classification C) in the ASHRAE Global Thermal Comfort Database II. After equal-width binning based on ambient temperature T (0.5℃), 22 valid samples were obtained. PMV was calculated based on physical measurements and Fanger's formula; VPD was obtained by statistically analyzing the proportion of dissatisfaction based on the subjects' subjective votes on thermal acceptability; ambient temperature T refers to the indoor air temperature.

[0065] Figure 2 The results show that the root mean square error (RMSE) of PPDo1 in predicting VPD is 23.61%, while that of PPDo2 is 14.52%. Based on PMV, VPD, and ambient temperature T, the constant parameters c, p, and q, calculated using the optimization method proposed in this invention, are 1.64, 1.376, and -0.04, respectively. Using the obtained a, p, and q, the newly developed thermal dissatisfaction rate model arPPD is calculated. The RMSE of arPPD in predicting VPD is 7.76%. Compared to PPDo1 and PPDo2, the prediction accuracy of arPPD is improved by 67.13% and 46.56%, respectively.

[0066] Therefore, in air-conditioned buildings, the arPPD model for thermal dissatisfaction rate constructed according to the method of this invention effectively improves the accuracy and stability of thermal dissatisfaction rate prediction.

[0067] Example 2

[0068] The PMV, VPD, and ambient temperature T data used to establish the thermal dissatisfaction rate in Example 2 were obtained from measured data of mixed-mode office buildings (simultaneous or alternating use of natural ventilation and mechanical refrigeration systems) in arid climate zones (Köppen climate classification B) in the ASHRAE Global Thermal Comfort Database II. In mixed-mode buildings, thermal adaptation has a more significant impact on the thermal dissatisfaction rate; therefore, this case study can be used to test the model's predictive ability for thermal adaptability. After equal-width binning with a 0.5°C increment based on ambient temperature T, 22 valid samples were obtained. PMV was calculated based on physical measurements and Fanger's formula; VPD was obtained by statistically analyzing the proportion of dissatisfaction based on the subjects' subjective votes on thermal acceptability; ambient temperature T refers to the indoor air temperature.

[0069] Figure 3The results show that the root mean square error (RMSE) of PPDo1 in predicting VPD is 14.22%, while that of PPDo2 is 16.70%. Based on PMV, VPD, and ambient temperature T, the constant parameters c, p, and q, calculated using the optimization method proposed in this invention, are 2.26, 3.813, and -0.107, respectively. Using the obtained a, p, and q, the newly developed thermal dissatisfaction rate model arPPD is calculated. The RMSE of arPPD in predicting VPD is 6.28%. Compared to PPDo1 and PPDo2, the prediction accuracy of arPPD is improved by 55.84% and 62.40%, respectively.

[0070] Therefore, in hybrid buildings, the arPPD model for thermal dissatisfaction rate constructed according to the method of this invention effectively improves the accuracy and stability of thermal dissatisfaction rate prediction.

[0071] In summary, this invention constructs a new thermal dissatisfaction rate model, arPPD, by introducing an adaptation factor and an offset calibration coefficient. This thermal dissatisfaction rate model can comprehensively explain thermal adaptation in both air-conditioned and mixed-mode buildings, thereby more accurately predicting thermal dissatisfaction rates.

[0072] The above embodiments are merely one of the preferred embodiments of the present invention and should not be used to limit the scope of protection of the present invention. Any modifications or refinements made to the main design concept and spirit of the present invention that are not of substantial significance, but solve the same technical problem as the present invention, should be included within the scope of protection of the present invention.

Claims

1. A method for modeling thermal dissatisfaction rate based on negative feedback thermal adaptation, which establishes a new thermal dissatisfaction rate model based on Fanger's Predicted Percentage of Thermal Dissatisfaction (PPD) model, using field-collected thermal environment data. The method is characterized by... Based on Fanger's predictive thermal dissatisfaction percentage (PPD) model, an adaptive factor is introduced. And the offset calibration coefficient c, a new thermal dissatisfaction rate model arPPD based on negative feedback thermal adaptation is constructed using the following formula: Where PMV is the predicted average vote value, and c is the offset calibration coefficient. It is an adaptive factor; Adaptive factors It changes linearly with the reciprocal of the ambient temperature T, specifically expressed as: Where T is the ambient temperature, which is a key environmental parameter affecting human thermal adaptability. Indoor or outdoor ambient temperature is selected as the indicator, and p and q are constant parameters, which are calculated according to the following formulas: (1) (2) (3) In the formula, PMV i It is the PMV and VPD of the i-th data set collected on-site. i T represents the proportion of people dissatisfied with the thermal environment in the i-th data set collected on-site. i This is the ambient temperature of the i-th data set collected on-site; a total of n PMV data sets were collected. i VPD i And ambient temperature T data set.

2. The thermal dissatisfaction rate modeling method based on negative feedback thermal adaptation according to claim 1, characterized in that, The optimization methods for the offset calibration coefficient c and the constant parameters p and q are as follows: Step 1: Set the search range of the offset calibration coefficient c to [m, n], and the search step size to Δc, generating a set of candidate values ​​c. (j) The range of [m,n] does not exceed the range of PMV values; Step 2: For each candidate value c (j) Perform the following calculations: Step 2.1, Calculation : Step 2.2: Calculate p according to formula (1) and formula (2). (j) and q (j) ; Step 2.3: Calculate the predicted value of the thermal dissatisfaction rate model. : Step 2.4: Calculate the root mean square error: Step 3: Calculate the optimal solution for c, which is c that minimizes RMSE. opt : Step 4, c opt The corresponding p (j) and q (j) The optimal solution for p and q is p. opt and q opt .

3. The thermal dissatisfaction rate modeling method based on negative feedback thermal adaptation according to claim 2, characterized in that, The derivation process of formulas (1) and (2) is as follows: Determining the constant parameters p and q is to minimize the deviation between the new thermal dissatisfaction rate model arPPD and the actual thermal dissatisfaction rate VPD. The terms in the following formula (4) are... When the proposed arPPD can accurately predict VPD, it is close to 1. Therefore, determining the constant parameters p and q is to minimize the objective function, as shown in formula (4). Formula (4) is then transformed into formula (5). In order to minimize the objective function, the derivatives of formula (5) with respect to p and q should both be 0, i.e. formulas (6) and (7). By solving these formulas, we can obtain the calculation formulas (1) and (2) for p and q. (4) (5) (6) (7)。

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