Feasibility Analysis of using Humidex as an Indoor ... - Semantic Scholar
Feasibility Analysis of using Humidex as an Indoor Thermal Comfort Predictor Rajib Ranaa,∗, Brano Kusya , Raja Jurdaka , Josh Wallb , Wen Hua a Autonomoius b CSIRO
Systems Laboratory, CSIRO, 1 Technology ct, Pullenvale, QLD - 4069, Australia. Energy Technology, 10 Murray Dwyer Circuit, Mayfield West, NSW - 2304, Australia
Abstract HVAC energy savings have been a key focus of recent building energy management efforts, but the savings typically reduce thermal comfort for building occupants. Established thermal comfort models use complex and person-specific parameters, such as clothing insulation and metabolic rate, to predict individual comfort levels, making the design of automated comfort modelling systems a highly challenging endeavour. In this paper, we investigate the use of humidex, which encapsulates both temperature and humidity, as an easily measurable and highly representative indoor thermal comfort predictor. We verify the feasibility of humidex as an indoor thermal comfort predictor by contrasting its performance to that of the best feature set (the feature set that best predicts the thermal comfort) constructed jointly by recursive sequential forward selection and support vector regression. The analysis using the global datasets, including data from seven climate zones across three continents, shows that humidex is a favourable and easily measurable indoor thermal comfort descriptor when humidity is significant. We take away the message from the analysis and design, develop, and deploy a system that couples a deployment of sensor nodes in an office environment, where each node collects the ambient temperature and humidity at each person’s desk, and an automated survey mechanism to record people’s thermal sensation votes. We use subjective response through the surveys as ground truth to validate the performance of the thermal comfort prediction using humidex. The results confirm our analysis of global datasets and show that humidex is a good predictor of indoor thermal comfort at high humidity. 1. Introduction
∗ Corresponding author. Tel.: +61 7 3327 4471; Fax: +61 7 3327 4455. E-mail address: [email protected].
Preprint submitted to Elsevier
24
45
Thermal comfort 22
−1
−0.5
0
0.5
1
1.5
40 2
Humidex
50
Humidity
Temperature
Climate change and greenhouse gas emissions are forcing society to reevaluate energy efficiency practices. Buildings consume a large portion of the total energy in industrial countries. Much of the energy consumption in buildings is due to HVAC systems, which has motivated several recent studies on making these systems more energyefficient [1][2]. Reductions in HVAC energy consumption, that limit heating in the winter or cooling in the summer, always run the risk of reducing the thermal comfort level of building occupants and of nullifying their original purpose. This has led to an increased interest in understanding and modeling thermal comfort for HVAC energy management. Modelling thermal comfort itself has been extensively studied [3] independently of energy efficiency. A major barrier to integrating thermal comfort models into HVAC control systems is the complexity of these models, as they depend on several person-specific parameters. In particular, predictive mean vote (PMV) is widely used in the literature to predict people’s thermal comfort using parameters such as metabolism rate and clothing insulation. These
26.5 26
26
25.5
25 −1
0 1 Thermal comfort
2
(a) Thermal comfort versus tem- (b) Thermal comfort versus huperature and humidity. midex.
Figure 1: Illustration of importance of humidex over temperature . parameters are very difficult to collect from each person, particularly as the scale of the problem grows. Due to difficulties of automating the thermal comfort measurement using PMV, we seek to find alternative methods to estimate thermal comfort level. In particular, we seek to identify easily and inexpensively measurable feature(s)1 and model their correlation with thermal comfort for estimating thermal comfort levels with reasonable accuracy. Recently proposed HVAC integrated thermal comfort models rely on temperature or humidity for describing 1 In this paper the term “feature” refers to various physical phenomena, e.g., temperature, air velocity etc..
May 13, 2013
thermal comfort [4, 5]. Humidex is an alternative metric that fuses temperature and humidity into a single quantity (a detailed description of humidex is provided in Section 3), but it was proposed for outdoor comfort mapping. This paper is the first to propose humidex for indoor comfort mapping. Figure 1 illustrates why considering temperature or humidity in isolation is insufficient. Using data from our campus 2 , Figure 1(a) maps the thermal comfort level to ambient temperature and humidity, showing that high humidity may distort the monotonic mapping of temperature and thermal comfort. In contrast, Figure 1(b) maps the humidex metric against thermal comfort, revealing a stronger correlation with comfort than temperature or humidity alone. The feasibility of a thermal comfort predictor needs to be verified in the global context, i.e. across different climate zones and seasons. We therefore conduct a comparative study based on publicly available data spanning 7 different climate zones across 3 continents. The data includes a large set of parameters, both easily measurable and otherwise, that are likely to determine thermal comfort. We determine the best feature set through an iterative process of sequential forward selection and support vector regression. We contrast the prediction performance of the best feature set with that of humidex and show that the humidex performs better in high humidity situations. Capitalizing on the learnings from the global datasets, we design, develop, and deploy a system for automated thermal comfort modelling. The system couples a deployment of sensor nodes in an office environment, where each node collects the ambient temperature and relative humidity at each person’s desk, and an automated survey mechanism to intake people’s subjective thermal sensation. Results from our own deployment coincide with the results of the global dataset, demonstrating the superior thermal comfort prediction performance of humidex in humid conditions. The remainder of the paper is organized as follows. In Section 2 we discuss the previous work in the area of comfort modelling. Then in the next section (Section 3) we provide background information about the conventional method of predicting thermal sensation, followed by the description of the proposed comfort modelling method in Section 4 and 5. In Section 6 we describe the simulation results, followed by the design and description and evaluation of our end-to-end system in Section 7. Finally, we conclude in Section 8.
previous work was on how to duty cycle HVAC systems aggressively when there is no occupant in the buildings and thermal comfort is irrelevant. While [1, 8] focused on office building occupancy prediction, [6, 9] focused residential home occupancy. In this paper, we focus on the automatic thermal comfort prediction in commercial buildings when there are occupants inside. Note that there are occupants in most of the commercial buildings during the critical “peak load” periods when the price of electricity is most expensive. American Society of Heating, Refrigerating and Airconditional Engineers (ASHRAE) defines Thermal comfort as “the state of mind in humans that expresses satisfaction with the surrounding environment” [10]. This implies that the thermal satisfaction depends on both physiological and psychological factors, which makes it difficult to measure. The most popular comfort measurement is Fanger’s PMV model which is standardised in ISO 7730 [11, 12]. PMV model requires significant number of parameters (see Section 3.1 for the details), and some of them such as metabolic rate and clothing insulation are too complex to be measured by inexpensive sensors automatically. One of the conventional ways to collect these parameters is via expensive and labour intensive survey. De Dear collected 22,000 sets of PMV records in 160 buildings across four continents and the datasets are available to the public online [13], which is also being used for evaluation in this paper (see Section 6 for the details). Due to the complexity of PMV measurements, a number of researchers proposed methods to estimate PMV by assuming values for some parameters (e.g., clothing insulation is 1.0 m2 K/W during winter and 0.5 m2 K/W during summer) and modelling the other parameters using easily measurable parameters (e.g. model mean radiant temperature using room temperature). For example, Naive Bayes model [4] proposed by Ahmed et al. and Artificial Neural Networks(ANN) based learning approach proposed by Ploennings et al. follow the above principle to estimate PMV values. However, we do not follow this pathway, as realistically people form diverse cultural and country background inhabiting in the office buildings are very likely to have non-uniform clothing insulation, metabolism etc. Furthermore, some of the above work assume constant air velocity in the calculation of PMV, which may also be unachieveable. There has been work done in the literature where people tend to model the thermal sensation directly from indoor temperature. For example, Bermejo et. al. proposed a fuzzy logic based [7] on-line learning system to predict the user’s thermal sensation. Users are required to provide binary input of “too cold” or “too warm” during training phase. Then, a comfort model is built for each user based on the individual input and the thermal parameters. Another example is ThermoNet[5], which uses indoor temperature as a proxy of the thermal comfort in open plan office buildings. However, for both of the methods it is not clear how the authors identified temperature as an impor-
2. Related Work Smart HVAC control to reduce building energy consumption and carbon footprint has been an active research area in the past few years [6, 1, 7]. A major theme of the 2 The
dataset will be discussed in Section 7.1.
2
tant parameter to proxy for thermal sensation. Note that we conduct a comprehensive study on the global climate data to demonstrate the feasibility of humidex an indoor thermal comfort predictor. Anika et al. in [14] developed algorithms to model thermal comfort from tempearture and validated their method by conducting study on the global climate dataset (same dataset as used in this paper). However, our focus is different to them as we seek to understand the feasibility of humidex as a thermal comfort predictor. Furthermore, we develop and deploy a sensor network system for automatically modelling thermal comfort, which was not of interest to the authors in [14].
we use a variant (see Eqn. (1) [16] ) which uses relative humidity and temperature ([T = Temperatureo C, H = Relative humidity] ). Humidex = T + 5/9(e − 10)
e = 6.112 × 10
(7.5T /(237.7+T ))
(1)
× H/100.
Humidex is mainly used in outdoor environments, however, in this paper we investigate its feasibility as an indoor thermal comfort predictor. In order to contrast the performance of humidex as an indoor comfort predictor, we consider additional features subject to their ease and affordability of acquisition. We consider indoor air temperature, relative humidity, air velocity, mean radiant temperature and outdoor temperature and relative humidity. In addition, we consider a simple feature: climate, which is however not a physical phenomenon. It is a unique identifier assigned to each season and climate zone pair. We select the best set out of these features to contrast the performance of humidex as an indoor comfort predictor.
3. Background In this section we describe the classical method of computing thermal sensation using PMV. We report the features required to compute PMV, outlining their measurement complexity. We then define humidex and describe its scope for comfort modelling. 3.1. Thermal Comfort and Predictive Mean Vote(PMV)
4. Feature Selection for Comfort Modelling
Thermal comfort (or sensation) is often measured using the predicted mean vote (PMV) [11], which predicts the mean vote of a large group of people according to the ASHRAE thermal sensation scale [10]. The ASHRAE thermal sensation scale spans over the range -3 to +3 and has the following definition: +3 = hot; +2 = warm; +1 = slightly warm; 0 = neutral; -1 = slightly cool; -2 = cool; -3 = cold. PMV depends on six features, amongst them two are personal dependent variables: metabolic rate and clothing insulation and the remaining four are environmental variables: indoor air temperature, mean radiant temperature, air velocity and relative humidity. A room is said to have optimal thermal conditions if its PMV value is zero. Note that PMV is sensitive to estimates of features such as metabolic rate and clothing insulation, which are difficult to estimate, and in practical situations often vary. Therefore, it is very difficult to measure thermal sensation using PMV in dynamic office environments [3, 15]. Moreover, two of the environmental features: mean radiant temperature and air velocity require expensive sensors to measure accurately.
In order to study the feasibility of humidex as a thermal comfort predictor, we contrast its performance with the best possible feature set. In this section we describe the process of determining the best feature set form a set of features. 4.1. Feature Selection Practical machine learning algorithms are known to degrade prediction accuracy when provided with many features which are not necessary to predict the desired output [17]. We therefore use a feature selection algorithm to select the best set of features to accurately predict thermal comfort. We adopt the wrapper based feature selection algorithm proposed by Ron Kohavi et al. in [17]. In particular, we use their sequential forward selection (SFS) approach. In the literature “Filter based feature selection” algorithms are also used for sequential feature selection. However, we prefer a wrapper based approach due to better accuracy. Sequential forward selection is a simple “greedy” search algorithm. Starting from an empty feature set, the SFS algorithm creates candidate feature subsets by sequentially adding each of the features not yet selected. For each candidate feature subset, the algorithm performs n-fold (typically 10-fold) cross-validation by repeatedly calling an “evaluation” function with different training and test subsets. Each time the evaluation function is called, it returns a “criterion value”. Typically, the evaluation function uses the train subsets to train or fit a model, then predicts values for test subsets using that model, and finally returns the distortion, of those predicted values from real observations as the criterion value.
3.2. Thermal Comfort and Humidex The humidex [16] is an index number used by Canadian meteorologists to describe the perceived thermal feeling of a person, by combining the effect of heat and humidity. The humidex is a unitless number, however, it roughly refers to the temperature in degree centigrade. For example, if the temperature is 30 o C, but the calculated humidex is 35, the perceived temperature by any average person will be close to 35 o C. The typical formula to calculate Humidex involves dewpoint and temperature, however 3
In the cross-validation calculation for a given candidate feature set, the criterion values are averaged and the mean criterion value is then used to evaluate each candidate feature subset. If the criterion value is an error metric, SFS chooses the candidate feature subset that minimizes the mean criterion value. The forward feature selection steps are summarized in Algorithm 4.1. This process continues until adding more features does not decrease the criterion.
shows the SVR line given by f (x) = ωx + b. The cylinderical area between the dotted lines shows the region without penalty. Points lying outside the cylinder are penalized by -intensive loss function (2) [18] given by |ξ| . ( 0 if |ξ| ≤ |ξ| := (2) |ξ| − otherwise. In the extreme case when ω = 0 (as in Figure 2(a)), is not big enough to give zero loss for all points, therefore the overall error becomes very high. Next Figure 2(b)) represents the case where the training data fits the solid line quite well. The solid line represents the classical regression analysis, where the loss function is measured as the squared estimation error. Note that although the solid line fits the data well, the cylindrical area between dotted line has shrunk, which shows less generalization capacity. SVR seeks to find a balance between amount of flatness (represented by the cylindrical area between dotted lines) and amount of training mistakes i.e., fit (see Figure 2(c)). Mathematically, SVR minimizes the following optimization problem ([18, 19]) to compute the decision surface:
Algorithm 4.1: SFS() 1. Start with the empty set X0 = {∅} 2. Select the next best feature x+ = arg minx6∈Xk PredictionError(Xk + x) 3. Update Xk+1 = Xk + x+ ; k = k + 1 4. If criterion(Xk+1 ) < criterion(Xk ), Go to 2; otherwise return Xk+1 .
In this paper we use root-mean-square (RMS) to compute the difference between predicted and real thermal sensation. We observe that for a given dataset the selected feature sets sometimes vary. We therefore, run the feature selection algorithm multiple times and choose the set of features that was selected the maximum number of times. 5. Support Vector Regression for Predicting Thermal Comfort
`
arg min
Given a feature set computed by the sequential forward selection algorithm, we use support vector regression (SVR) for modelling thermal comfort from features. This section will briefly describe how the SVR algorithm predicts the thermal sensation vote from the input features. Given a training set {(x1 , y1 ), (x2 , y2 ), ..., (x` , y` )}, support vector regression computes the function f (x) that has at most deviation from the actual observed yi for the complete training set. In our setting xi ’s are the values of a given feature and yi ’s are the corresponding thermal sensation votes. Note that x can be a vector representing one feature or a matrix representing multiple features. However, for simplicity let us first assume that x is a vector; later on we will revert back to matrix. Let us assume
ǫ
C|y − f(x)|
y
ǫ
s.t.
x
x
The optimization problem in (3) is convex quadratic with linear constraints, therefore, a unique solution exists. The first term of the objective function, 21 ω 2 , represents the degree of complexity, which is represented by the insensitive region between lines y = ωx + b + and y = ωx + b − . The slack variables ξi and ξi? , i = 1, 2, ..., l, are constrained to be nonnegative. All points i inside the insensitive region have both ξi = 0 and ξi? = 0. If a point i lies outside the -insensitive region, then either ξi > 0 and ξi? = 0 or ξi = 0 and ξi? => 0. The adjustable constant C determines the trade-off between functions complexity, 1 2 2 ω and the overall loss associated with it. Since loss occurs only if a point lies outside the -insensitive region, P` the second term of the objective function, C i=1 (ξi +ξi? ), stands for the actual amount of loss associated P` with the estimated function, if ω = 0, then the loss C i=1 (ξi + ξi? ) would be extremely big, as depicted in Figure 2a. Likewise, P` if the sum C i=1 (ξi +ξi? ) is relatively small, then ω would be extremely big, and consequently 21 ω 2 too. Therefore, at the minimum of the objective function in (3) a balance is P` found between 12 ω 2 and C i=1 (ξi + ξi? ), ensuring neither the resulting function f (x) = ωx+b fits the data perfectly, nor that it is too flat. Gnerally a dual representation of the optimization problem (3) is used to solve for the SVR. We now abuse x to represent multiple independent variable. If there are n
C|y − f(x)|
x regres-
(3)
ξi?
ξi ξi? ≥ 0 for i = 1.2.3..., `
ǫ (a) No relation be- (b) Linear tween x and y. sion.
yi − (ωi xi` ) − b ≤ + ξi
(ωi xi` ) + b − yi ≤ +
y
y
X 1 2 (ξi + ξi? ) ω +C 2 i=1
(c) Linear SVR.
Figure 2: Support vector regression explained. the relationship between the variables is linear of the form y = ωx + b, where ω and b are parameters need to be estimated. Figure 2 shows a few possible linear relationships between the points x and y. The solid line in Figure 2(b) 4
independent variables, then we are looking for the opti0 mal regression function f (x) = (ω x) + b, with a vector of 0 independent variables x = (x1 , x2 , ..., xn ), weight vector ω = (ω1 , ω2 , ..., ωn ), and flatness is defined in terms of the Euclidean p norm of the weight vector: ||ω|| = ω12 + ω22 , ..., ωn2 . The unknown parameters of the linear SVR ω, b, i and , i = 1, 2, ..., l, can be found as the unique solution of the dual of the primal problem of (3) ([20, 21]):
arg max − +
` 1 X (αi − αi? )(αj − αj? )(xi .xj ) 2 i,j=1 ` X i=1
s.t.
884 database [13]. This database contains 52 studies with more than 20,000 user comfort votes from office buildings across 10 different climate zones. We use data from seven different climate zones which spans three continents. We did not consider the climate zones which had: (1) less than 200 records; or (2) excluded any of the features that we consider in this paper. We also consider the full range of seasonal data whenever available within each climate zone. Considering that a climate zone across different continents has similar weather conditions, we include each climate zone only once in our analysis. To avoid cluttering the image, in some illustrations, we use short names of climate zones which are mapped to their full names in Table 1. In total, we use 6, 837 records from the entire dataset.
0≤ ` X i=1
(αi − αi? )yi −
αi , αi?
` X (αi − αi? )
(4) 6.2. Simulation Setting
i=1
≤ C, i = 1, 2, ..., `
6.2.1. Performance Metric Thermal sensation votes are taken in the ASHARE scale which spans a range of −3 to 3 with an interval 1. However, the predicted votes can be fractions, therefore, an exact match of predicted and true thermal sensation vote is not viable. Followed by Anika et. al. in [14], if the difference between true and predicted thermal sensation is upto 0.5, we consider the prediction as correct.
(αi − αi? ) = 0
In the dual formulation (5) the unknowns are the multipliers αi and αi? , i = 1, 2, ..., `. They are weight associated with each data point i. If both αi and αi? are zero for a point i, then the point lies inside the -insensitive region, therefore, plays no role for final formulation of SVR function. The SVR regression now takes the form of f (x) =
` X (αi? − αi )(x.xi ) + b,
6.2.2. Local and Global Features In this paper “local features” correspond to the feature set constructed by the SFS method for individual climate zone and season. On the other hand “global features” are the feature set constructed by the SFS over all the seven climate zones. We study and compare the performance of global and local features in predicting the thermal sensation. If the prediction performance of the global feature set is similar to that of local feature sets, it would be sufficient to compare the prediction performance of humidex with only the global feature set. The SFS algorithm selects indoor relative humidity, air velocity, temperature and outdoor temperature as the global features. Local features were constructed by applying SFS for each individual climate zone and season. The features selected for the local datasets are summarized in Table 2.
(5)
i=1
where x is a vector containing the values of independent variables for a new test point. There are a number of popular implementations of SVR in the literature, among them ν-SVR [22] and -SVR [23] are two worth mentioning. However, -SVR or ν-SVR just use different versions of the penalty parameter, the same optimization problem is solved in either case. We use SVR in our experiments. We use the matlab library LIBSVM [24] to implement -SVR. There are two functions: svmtrain and svmpredict for training and testing, respectively. Recall from Section 6 that we incorporate indoor air temperature, relative humidity, air velocity, mean radiant temperature and outdoor temperature, climate and relative humidity as candi0 date features. We construct input feature x using values of these independent variables. Using the input features mapped to corresponding thermal comfort votes, svmtrain then outputs α? − α and b. The prediction method, svmpredict, then use these values and some other parameters (for details please review [24]) to predict the thermal comfort given the new value of input features.
6.2.3. Experiments The prediction experiments were conducted in two steps: feature selection and prediction. In the feature selection step the SFS method used 10-fold cross validation to construct the feature set. The evaluation function computed the root mean square error between the predicted and actual thermal sensation. Features were added to the set until the RMS error decreased. We used the built-in implementation of SFS in Matlab [25]. In the prediction step we divided any given dataset into training and test sets with no overlaps. In particular, in order to produce the results we permutated the dataset 100 times and used the first half as training set and the
6. Simulation 6.1. Dataset We test the feasibility of humidex as an indoor comfort predictor using the publicly available ASHRAE RP5
Table 1: Summary of climate zones and seasons (with short form representation) used in this paper. Climate Zone semi arid high altitude wet equatorial tropical savanna hot arid humid subtropical west coast marine mediterranean
City-country
Seasons
Short form
Saidu Pakistan Singapore Townsville Australia Kalgoorlie-Boulder Australia Brisbane Australia Merseyside UK Athens, Greece
Summer, Winter Summer Dry, Wet Winter, Summer Summer Summer Summer
SH-s WE-s TS-d,TS-wt HA-w,HA-s HS-s WCM-s M-s
Building Type NV HVAC HVAC HVAC HVAC HVAC NV
Mean indoor humidity % 45.96 55.40 50.83,56.30 41.44,41.44 53.22 33.47 33.47
Table 2: Local feature sets. “1” means corresponding feature is included and “0” means otherwise.
SH-s WE-s TS-wt TS-d HA-s HA-w HS-s WCM-s M-s
mean radiant temperature 1 1 1 1 0 0 1 1 1
relative humidity 1 0 0 0 1 1 1 0 0
air velocity 1 1 0 0 1 1 1 1 1
room temperature 1 1 1 1 1 1 1 0 0
second half as test set and averaged the prediction results over these 100 iterations. We used the implementation of -support vector regression from the LIBSVM [24] web portal. Both training and test data were scaled within range [−1, 1]. The data was then sparsified to meet the LIBSVM input format. We used Linear Kernel since the number of features was sufficiently large. The other popular alternative of linear kernel is the Radial basis function (RBF), which is however used when the number of features (attributes) is relatively small and the relationship between the attributes and labels (thermal sensation vote) is nonlinear. We used the linear kernel after empirically verifying that it performs better than RBF for our datasets.
outdoor temperature 0 0 1 1 0 1 0 0 0
outdoor relative humidity 0 0 1 1 1 1 0 1 0
climate
humidex
0 0 0 0 1 0 0 0 0
1 1 1 1 1 1 1 0 0
6.3.2. Global Features versus Humidex The comparison of humidex with global features across seven climate zones of three different continents is illustrated in Figure 4 . Except for three climate zones: wet equatorial summer, humid subtropical summer and tropical savana wet, humidex performs similarly to the global features. For the above three climate zones, humidex performs 5-10% better compared to the global feature set. Mean indoor humidity of various climate zones reported in Table 1 shows that the humidity in the above three climate zones is quite high, which forms the basis for humidex to obtain higher accuracy (recall that the global feature set does not include humidex). 6.3.3. Humidex versus Humidity and Tempearature Compared to humidity, humidex performs significantly better (approx. 10 − 25%) in five (tropical savan wet, humid subtropical summer, semi arid high altitude summer, west coast marian summer and mediterranean summer) out of nine climate zones and seasons. For the rest of the climate zones and seasons the performance of humidex is similar to humidity. The comparison of humidex and temperature is similar to the comparison of humidex with global features. For the three climates with high humidity (see Table 1): wet equatorial summer, humid subtropical summer and tropical savana wet, the performance of humidex is significantly (approximately 10%) better compared to temperature. In the rest of the climate zone and seasons, temperature and humidex perform quite similarly (less than 5% difference). Prediction accuracy offered by radiant temperature is almost similar to that of operative temperature (Temperature in the plot). Therefore, the comparison of humidex with two different temperatures reveal three facts: (1) humidex is preferable to temperature in high humid situation; (2) temperature (operative) could also be a strong
6.3. Results In this section we contrast the performance of the global features with that of the local features to find the best performing feature set. We then compare the performance of humidex with that of the best feature set. In addition, we compare the prediction performance of humidex with individual features: indoor temperature and humidity, since these two features were used in the past for automatic thermal comfort modelling in the indoor setting. 6.3.1. Global versus Local Features Local features are expected to perform better than the global features, and this has been observed in Figure 3. Encouragingly, the difference between global and local features is quite insignificant for most of the climates. Therefore, we conclude that the global features sufficiently represent thermal comfort. We now compare the performance of humidex with that of the global feature set as a common benchmark.
6
80% Prediction accuracy
70% 60% 50% 40% SFS features − Local SFS features − Global
30% 20% 10% semi arid high altitude summer
wet equatorial summer
tropical savanna dry
tropical savana wet
hot arid summer
hot arid winter
humid subtropical west coast marine summer summer
mediterranean summer
Figure 3: Local versus Global SFS features. !"#$%&'()*"$+),-'.")
/%01%#2),"&$") !/)3--(4.'5%&)
/(40'2") *%0")
,:;)
Systems Laboratory, CSIRO, 1 Technology ct, Pullenvale, QLD - 4069, Australia. Energy Technology, 10 Murray Dwyer Circuit, Mayfield West, NSW - 2304, Australia
Abstract HVAC energy savings have been a key focus of recent building energy management efforts, but the savings typically reduce thermal comfort for building occupants. Established thermal comfort models use complex and person-specific parameters, such as clothing insulation and metabolic rate, to predict individual comfort levels, making the design of automated comfort modelling systems a highly challenging endeavour. In this paper, we investigate the use of humidex, which encapsulates both temperature and humidity, as an easily measurable and highly representative indoor thermal comfort predictor. We verify the feasibility of humidex as an indoor thermal comfort predictor by contrasting its performance to that of the best feature set (the feature set that best predicts the thermal comfort) constructed jointly by recursive sequential forward selection and support vector regression. The analysis using the global datasets, including data from seven climate zones across three continents, shows that humidex is a favourable and easily measurable indoor thermal comfort descriptor when humidity is significant. We take away the message from the analysis and design, develop, and deploy a system that couples a deployment of sensor nodes in an office environment, where each node collects the ambient temperature and humidity at each person’s desk, and an automated survey mechanism to record people’s thermal sensation votes. We use subjective response through the surveys as ground truth to validate the performance of the thermal comfort prediction using humidex. The results confirm our analysis of global datasets and show that humidex is a good predictor of indoor thermal comfort at high humidity. 1. Introduction
∗ Corresponding author. Tel.: +61 7 3327 4471; Fax: +61 7 3327 4455. E-mail address: [email protected].
Preprint submitted to Elsevier
24
45
Thermal comfort 22
−1
−0.5
0
0.5
1
1.5
40 2
Humidex
50
Humidity
Temperature
Climate change and greenhouse gas emissions are forcing society to reevaluate energy efficiency practices. Buildings consume a large portion of the total energy in industrial countries. Much of the energy consumption in buildings is due to HVAC systems, which has motivated several recent studies on making these systems more energyefficient [1][2]. Reductions in HVAC energy consumption, that limit heating in the winter or cooling in the summer, always run the risk of reducing the thermal comfort level of building occupants and of nullifying their original purpose. This has led to an increased interest in understanding and modeling thermal comfort for HVAC energy management. Modelling thermal comfort itself has been extensively studied [3] independently of energy efficiency. A major barrier to integrating thermal comfort models into HVAC control systems is the complexity of these models, as they depend on several person-specific parameters. In particular, predictive mean vote (PMV) is widely used in the literature to predict people’s thermal comfort using parameters such as metabolism rate and clothing insulation. These
26.5 26
26
25.5
25 −1
0 1 Thermal comfort
2
(a) Thermal comfort versus tem- (b) Thermal comfort versus huperature and humidity. midex.
Figure 1: Illustration of importance of humidex over temperature . parameters are very difficult to collect from each person, particularly as the scale of the problem grows. Due to difficulties of automating the thermal comfort measurement using PMV, we seek to find alternative methods to estimate thermal comfort level. In particular, we seek to identify easily and inexpensively measurable feature(s)1 and model their correlation with thermal comfort for estimating thermal comfort levels with reasonable accuracy. Recently proposed HVAC integrated thermal comfort models rely on temperature or humidity for describing 1 In this paper the term “feature” refers to various physical phenomena, e.g., temperature, air velocity etc..
May 13, 2013
thermal comfort [4, 5]. Humidex is an alternative metric that fuses temperature and humidity into a single quantity (a detailed description of humidex is provided in Section 3), but it was proposed for outdoor comfort mapping. This paper is the first to propose humidex for indoor comfort mapping. Figure 1 illustrates why considering temperature or humidity in isolation is insufficient. Using data from our campus 2 , Figure 1(a) maps the thermal comfort level to ambient temperature and humidity, showing that high humidity may distort the monotonic mapping of temperature and thermal comfort. In contrast, Figure 1(b) maps the humidex metric against thermal comfort, revealing a stronger correlation with comfort than temperature or humidity alone. The feasibility of a thermal comfort predictor needs to be verified in the global context, i.e. across different climate zones and seasons. We therefore conduct a comparative study based on publicly available data spanning 7 different climate zones across 3 continents. The data includes a large set of parameters, both easily measurable and otherwise, that are likely to determine thermal comfort. We determine the best feature set through an iterative process of sequential forward selection and support vector regression. We contrast the prediction performance of the best feature set with that of humidex and show that the humidex performs better in high humidity situations. Capitalizing on the learnings from the global datasets, we design, develop, and deploy a system for automated thermal comfort modelling. The system couples a deployment of sensor nodes in an office environment, where each node collects the ambient temperature and relative humidity at each person’s desk, and an automated survey mechanism to intake people’s subjective thermal sensation. Results from our own deployment coincide with the results of the global dataset, demonstrating the superior thermal comfort prediction performance of humidex in humid conditions. The remainder of the paper is organized as follows. In Section 2 we discuss the previous work in the area of comfort modelling. Then in the next section (Section 3) we provide background information about the conventional method of predicting thermal sensation, followed by the description of the proposed comfort modelling method in Section 4 and 5. In Section 6 we describe the simulation results, followed by the design and description and evaluation of our end-to-end system in Section 7. Finally, we conclude in Section 8.
previous work was on how to duty cycle HVAC systems aggressively when there is no occupant in the buildings and thermal comfort is irrelevant. While [1, 8] focused on office building occupancy prediction, [6, 9] focused residential home occupancy. In this paper, we focus on the automatic thermal comfort prediction in commercial buildings when there are occupants inside. Note that there are occupants in most of the commercial buildings during the critical “peak load” periods when the price of electricity is most expensive. American Society of Heating, Refrigerating and Airconditional Engineers (ASHRAE) defines Thermal comfort as “the state of mind in humans that expresses satisfaction with the surrounding environment” [10]. This implies that the thermal satisfaction depends on both physiological and psychological factors, which makes it difficult to measure. The most popular comfort measurement is Fanger’s PMV model which is standardised in ISO 7730 [11, 12]. PMV model requires significant number of parameters (see Section 3.1 for the details), and some of them such as metabolic rate and clothing insulation are too complex to be measured by inexpensive sensors automatically. One of the conventional ways to collect these parameters is via expensive and labour intensive survey. De Dear collected 22,000 sets of PMV records in 160 buildings across four continents and the datasets are available to the public online [13], which is also being used for evaluation in this paper (see Section 6 for the details). Due to the complexity of PMV measurements, a number of researchers proposed methods to estimate PMV by assuming values for some parameters (e.g., clothing insulation is 1.0 m2 K/W during winter and 0.5 m2 K/W during summer) and modelling the other parameters using easily measurable parameters (e.g. model mean radiant temperature using room temperature). For example, Naive Bayes model [4] proposed by Ahmed et al. and Artificial Neural Networks(ANN) based learning approach proposed by Ploennings et al. follow the above principle to estimate PMV values. However, we do not follow this pathway, as realistically people form diverse cultural and country background inhabiting in the office buildings are very likely to have non-uniform clothing insulation, metabolism etc. Furthermore, some of the above work assume constant air velocity in the calculation of PMV, which may also be unachieveable. There has been work done in the literature where people tend to model the thermal sensation directly from indoor temperature. For example, Bermejo et. al. proposed a fuzzy logic based [7] on-line learning system to predict the user’s thermal sensation. Users are required to provide binary input of “too cold” or “too warm” during training phase. Then, a comfort model is built for each user based on the individual input and the thermal parameters. Another example is ThermoNet[5], which uses indoor temperature as a proxy of the thermal comfort in open plan office buildings. However, for both of the methods it is not clear how the authors identified temperature as an impor-
2. Related Work Smart HVAC control to reduce building energy consumption and carbon footprint has been an active research area in the past few years [6, 1, 7]. A major theme of the 2 The
dataset will be discussed in Section 7.1.
2
tant parameter to proxy for thermal sensation. Note that we conduct a comprehensive study on the global climate data to demonstrate the feasibility of humidex an indoor thermal comfort predictor. Anika et al. in [14] developed algorithms to model thermal comfort from tempearture and validated their method by conducting study on the global climate dataset (same dataset as used in this paper). However, our focus is different to them as we seek to understand the feasibility of humidex as a thermal comfort predictor. Furthermore, we develop and deploy a sensor network system for automatically modelling thermal comfort, which was not of interest to the authors in [14].
we use a variant (see Eqn. (1) [16] ) which uses relative humidity and temperature ([T = Temperatureo C, H = Relative humidity] ). Humidex = T + 5/9(e − 10)
e = 6.112 × 10
(7.5T /(237.7+T ))
(1)
× H/100.
Humidex is mainly used in outdoor environments, however, in this paper we investigate its feasibility as an indoor thermal comfort predictor. In order to contrast the performance of humidex as an indoor comfort predictor, we consider additional features subject to their ease and affordability of acquisition. We consider indoor air temperature, relative humidity, air velocity, mean radiant temperature and outdoor temperature and relative humidity. In addition, we consider a simple feature: climate, which is however not a physical phenomenon. It is a unique identifier assigned to each season and climate zone pair. We select the best set out of these features to contrast the performance of humidex as an indoor comfort predictor.
3. Background In this section we describe the classical method of computing thermal sensation using PMV. We report the features required to compute PMV, outlining their measurement complexity. We then define humidex and describe its scope for comfort modelling. 3.1. Thermal Comfort and Predictive Mean Vote(PMV)
4. Feature Selection for Comfort Modelling
Thermal comfort (or sensation) is often measured using the predicted mean vote (PMV) [11], which predicts the mean vote of a large group of people according to the ASHRAE thermal sensation scale [10]. The ASHRAE thermal sensation scale spans over the range -3 to +3 and has the following definition: +3 = hot; +2 = warm; +1 = slightly warm; 0 = neutral; -1 = slightly cool; -2 = cool; -3 = cold. PMV depends on six features, amongst them two are personal dependent variables: metabolic rate and clothing insulation and the remaining four are environmental variables: indoor air temperature, mean radiant temperature, air velocity and relative humidity. A room is said to have optimal thermal conditions if its PMV value is zero. Note that PMV is sensitive to estimates of features such as metabolic rate and clothing insulation, which are difficult to estimate, and in practical situations often vary. Therefore, it is very difficult to measure thermal sensation using PMV in dynamic office environments [3, 15]. Moreover, two of the environmental features: mean radiant temperature and air velocity require expensive sensors to measure accurately.
In order to study the feasibility of humidex as a thermal comfort predictor, we contrast its performance with the best possible feature set. In this section we describe the process of determining the best feature set form a set of features. 4.1. Feature Selection Practical machine learning algorithms are known to degrade prediction accuracy when provided with many features which are not necessary to predict the desired output [17]. We therefore use a feature selection algorithm to select the best set of features to accurately predict thermal comfort. We adopt the wrapper based feature selection algorithm proposed by Ron Kohavi et al. in [17]. In particular, we use their sequential forward selection (SFS) approach. In the literature “Filter based feature selection” algorithms are also used for sequential feature selection. However, we prefer a wrapper based approach due to better accuracy. Sequential forward selection is a simple “greedy” search algorithm. Starting from an empty feature set, the SFS algorithm creates candidate feature subsets by sequentially adding each of the features not yet selected. For each candidate feature subset, the algorithm performs n-fold (typically 10-fold) cross-validation by repeatedly calling an “evaluation” function with different training and test subsets. Each time the evaluation function is called, it returns a “criterion value”. Typically, the evaluation function uses the train subsets to train or fit a model, then predicts values for test subsets using that model, and finally returns the distortion, of those predicted values from real observations as the criterion value.
3.2. Thermal Comfort and Humidex The humidex [16] is an index number used by Canadian meteorologists to describe the perceived thermal feeling of a person, by combining the effect of heat and humidity. The humidex is a unitless number, however, it roughly refers to the temperature in degree centigrade. For example, if the temperature is 30 o C, but the calculated humidex is 35, the perceived temperature by any average person will be close to 35 o C. The typical formula to calculate Humidex involves dewpoint and temperature, however 3
In the cross-validation calculation for a given candidate feature set, the criterion values are averaged and the mean criterion value is then used to evaluate each candidate feature subset. If the criterion value is an error metric, SFS chooses the candidate feature subset that minimizes the mean criterion value. The forward feature selection steps are summarized in Algorithm 4.1. This process continues until adding more features does not decrease the criterion.
shows the SVR line given by f (x) = ωx + b. The cylinderical area between the dotted lines shows the region without penalty. Points lying outside the cylinder are penalized by -intensive loss function (2) [18] given by |ξ| . ( 0 if |ξ| ≤ |ξ| := (2) |ξ| − otherwise. In the extreme case when ω = 0 (as in Figure 2(a)), is not big enough to give zero loss for all points, therefore the overall error becomes very high. Next Figure 2(b)) represents the case where the training data fits the solid line quite well. The solid line represents the classical regression analysis, where the loss function is measured as the squared estimation error. Note that although the solid line fits the data well, the cylindrical area between dotted line has shrunk, which shows less generalization capacity. SVR seeks to find a balance between amount of flatness (represented by the cylindrical area between dotted lines) and amount of training mistakes i.e., fit (see Figure 2(c)). Mathematically, SVR minimizes the following optimization problem ([18, 19]) to compute the decision surface:
Algorithm 4.1: SFS() 1. Start with the empty set X0 = {∅} 2. Select the next best feature x+ = arg minx6∈Xk PredictionError(Xk + x) 3. Update Xk+1 = Xk + x+ ; k = k + 1 4. If criterion(Xk+1 ) < criterion(Xk ), Go to 2; otherwise return Xk+1 .
In this paper we use root-mean-square (RMS) to compute the difference between predicted and real thermal sensation. We observe that for a given dataset the selected feature sets sometimes vary. We therefore, run the feature selection algorithm multiple times and choose the set of features that was selected the maximum number of times. 5. Support Vector Regression for Predicting Thermal Comfort
`
arg min
Given a feature set computed by the sequential forward selection algorithm, we use support vector regression (SVR) for modelling thermal comfort from features. This section will briefly describe how the SVR algorithm predicts the thermal sensation vote from the input features. Given a training set {(x1 , y1 ), (x2 , y2 ), ..., (x` , y` )}, support vector regression computes the function f (x) that has at most deviation from the actual observed yi for the complete training set. In our setting xi ’s are the values of a given feature and yi ’s are the corresponding thermal sensation votes. Note that x can be a vector representing one feature or a matrix representing multiple features. However, for simplicity let us first assume that x is a vector; later on we will revert back to matrix. Let us assume
ǫ
C|y − f(x)|
y
ǫ
s.t.
x
x
The optimization problem in (3) is convex quadratic with linear constraints, therefore, a unique solution exists. The first term of the objective function, 21 ω 2 , represents the degree of complexity, which is represented by the insensitive region between lines y = ωx + b + and y = ωx + b − . The slack variables ξi and ξi? , i = 1, 2, ..., l, are constrained to be nonnegative. All points i inside the insensitive region have both ξi = 0 and ξi? = 0. If a point i lies outside the -insensitive region, then either ξi > 0 and ξi? = 0 or ξi = 0 and ξi? => 0. The adjustable constant C determines the trade-off between functions complexity, 1 2 2 ω and the overall loss associated with it. Since loss occurs only if a point lies outside the -insensitive region, P` the second term of the objective function, C i=1 (ξi +ξi? ), stands for the actual amount of loss associated P` with the estimated function, if ω = 0, then the loss C i=1 (ξi + ξi? ) would be extremely big, as depicted in Figure 2a. Likewise, P` if the sum C i=1 (ξi +ξi? ) is relatively small, then ω would be extremely big, and consequently 21 ω 2 too. Therefore, at the minimum of the objective function in (3) a balance is P` found between 12 ω 2 and C i=1 (ξi + ξi? ), ensuring neither the resulting function f (x) = ωx+b fits the data perfectly, nor that it is too flat. Gnerally a dual representation of the optimization problem (3) is used to solve for the SVR. We now abuse x to represent multiple independent variable. If there are n
C|y − f(x)|
x regres-
(3)
ξi?
ξi ξi? ≥ 0 for i = 1.2.3..., `
ǫ (a) No relation be- (b) Linear tween x and y. sion.
yi − (ωi xi` ) − b ≤ + ξi
(ωi xi` ) + b − yi ≤ +
y
y
X 1 2 (ξi + ξi? ) ω +C 2 i=1
(c) Linear SVR.
Figure 2: Support vector regression explained. the relationship between the variables is linear of the form y = ωx + b, where ω and b are parameters need to be estimated. Figure 2 shows a few possible linear relationships between the points x and y. The solid line in Figure 2(b) 4
independent variables, then we are looking for the opti0 mal regression function f (x) = (ω x) + b, with a vector of 0 independent variables x = (x1 , x2 , ..., xn ), weight vector ω = (ω1 , ω2 , ..., ωn ), and flatness is defined in terms of the Euclidean p norm of the weight vector: ||ω|| = ω12 + ω22 , ..., ωn2 . The unknown parameters of the linear SVR ω, b, i and , i = 1, 2, ..., l, can be found as the unique solution of the dual of the primal problem of (3) ([20, 21]):
arg max − +
` 1 X (αi − αi? )(αj − αj? )(xi .xj ) 2 i,j=1 ` X i=1
s.t.
884 database [13]. This database contains 52 studies with more than 20,000 user comfort votes from office buildings across 10 different climate zones. We use data from seven different climate zones which spans three continents. We did not consider the climate zones which had: (1) less than 200 records; or (2) excluded any of the features that we consider in this paper. We also consider the full range of seasonal data whenever available within each climate zone. Considering that a climate zone across different continents has similar weather conditions, we include each climate zone only once in our analysis. To avoid cluttering the image, in some illustrations, we use short names of climate zones which are mapped to their full names in Table 1. In total, we use 6, 837 records from the entire dataset.
0≤ ` X i=1
(αi − αi? )yi −
αi , αi?
` X (αi − αi? )
(4) 6.2. Simulation Setting
i=1
≤ C, i = 1, 2, ..., `
6.2.1. Performance Metric Thermal sensation votes are taken in the ASHARE scale which spans a range of −3 to 3 with an interval 1. However, the predicted votes can be fractions, therefore, an exact match of predicted and true thermal sensation vote is not viable. Followed by Anika et. al. in [14], if the difference between true and predicted thermal sensation is upto 0.5, we consider the prediction as correct.
(αi − αi? ) = 0
In the dual formulation (5) the unknowns are the multipliers αi and αi? , i = 1, 2, ..., `. They are weight associated with each data point i. If both αi and αi? are zero for a point i, then the point lies inside the -insensitive region, therefore, plays no role for final formulation of SVR function. The SVR regression now takes the form of f (x) =
` X (αi? − αi )(x.xi ) + b,
6.2.2. Local and Global Features In this paper “local features” correspond to the feature set constructed by the SFS method for individual climate zone and season. On the other hand “global features” are the feature set constructed by the SFS over all the seven climate zones. We study and compare the performance of global and local features in predicting the thermal sensation. If the prediction performance of the global feature set is similar to that of local feature sets, it would be sufficient to compare the prediction performance of humidex with only the global feature set. The SFS algorithm selects indoor relative humidity, air velocity, temperature and outdoor temperature as the global features. Local features were constructed by applying SFS for each individual climate zone and season. The features selected for the local datasets are summarized in Table 2.
(5)
i=1
where x is a vector containing the values of independent variables for a new test point. There are a number of popular implementations of SVR in the literature, among them ν-SVR [22] and -SVR [23] are two worth mentioning. However, -SVR or ν-SVR just use different versions of the penalty parameter, the same optimization problem is solved in either case. We use SVR in our experiments. We use the matlab library LIBSVM [24] to implement -SVR. There are two functions: svmtrain and svmpredict for training and testing, respectively. Recall from Section 6 that we incorporate indoor air temperature, relative humidity, air velocity, mean radiant temperature and outdoor temperature, climate and relative humidity as candi0 date features. We construct input feature x using values of these independent variables. Using the input features mapped to corresponding thermal comfort votes, svmtrain then outputs α? − α and b. The prediction method, svmpredict, then use these values and some other parameters (for details please review [24]) to predict the thermal comfort given the new value of input features.
6.2.3. Experiments The prediction experiments were conducted in two steps: feature selection and prediction. In the feature selection step the SFS method used 10-fold cross validation to construct the feature set. The evaluation function computed the root mean square error between the predicted and actual thermal sensation. Features were added to the set until the RMS error decreased. We used the built-in implementation of SFS in Matlab [25]. In the prediction step we divided any given dataset into training and test sets with no overlaps. In particular, in order to produce the results we permutated the dataset 100 times and used the first half as training set and the
6. Simulation 6.1. Dataset We test the feasibility of humidex as an indoor comfort predictor using the publicly available ASHRAE RP5
Table 1: Summary of climate zones and seasons (with short form representation) used in this paper. Climate Zone semi arid high altitude wet equatorial tropical savanna hot arid humid subtropical west coast marine mediterranean
City-country
Seasons
Short form
Saidu Pakistan Singapore Townsville Australia Kalgoorlie-Boulder Australia Brisbane Australia Merseyside UK Athens, Greece
Summer, Winter Summer Dry, Wet Winter, Summer Summer Summer Summer
SH-s WE-s TS-d,TS-wt HA-w,HA-s HS-s WCM-s M-s
Building Type NV HVAC HVAC HVAC HVAC HVAC NV
Mean indoor humidity % 45.96 55.40 50.83,56.30 41.44,41.44 53.22 33.47 33.47
Table 2: Local feature sets. “1” means corresponding feature is included and “0” means otherwise.
SH-s WE-s TS-wt TS-d HA-s HA-w HS-s WCM-s M-s
mean radiant temperature 1 1 1 1 0 0 1 1 1
relative humidity 1 0 0 0 1 1 1 0 0
air velocity 1 1 0 0 1 1 1 1 1
room temperature 1 1 1 1 1 1 1 0 0
second half as test set and averaged the prediction results over these 100 iterations. We used the implementation of -support vector regression from the LIBSVM [24] web portal. Both training and test data were scaled within range [−1, 1]. The data was then sparsified to meet the LIBSVM input format. We used Linear Kernel since the number of features was sufficiently large. The other popular alternative of linear kernel is the Radial basis function (RBF), which is however used when the number of features (attributes) is relatively small and the relationship between the attributes and labels (thermal sensation vote) is nonlinear. We used the linear kernel after empirically verifying that it performs better than RBF for our datasets.
outdoor temperature 0 0 1 1 0 1 0 0 0
outdoor relative humidity 0 0 1 1 1 1 0 1 0
climate
humidex
0 0 0 0 1 0 0 0 0
1 1 1 1 1 1 1 0 0
6.3.2. Global Features versus Humidex The comparison of humidex with global features across seven climate zones of three different continents is illustrated in Figure 4 . Except for three climate zones: wet equatorial summer, humid subtropical summer and tropical savana wet, humidex performs similarly to the global features. For the above three climate zones, humidex performs 5-10% better compared to the global feature set. Mean indoor humidity of various climate zones reported in Table 1 shows that the humidity in the above three climate zones is quite high, which forms the basis for humidex to obtain higher accuracy (recall that the global feature set does not include humidex). 6.3.3. Humidex versus Humidity and Tempearature Compared to humidity, humidex performs significantly better (approx. 10 − 25%) in five (tropical savan wet, humid subtropical summer, semi arid high altitude summer, west coast marian summer and mediterranean summer) out of nine climate zones and seasons. For the rest of the climate zones and seasons the performance of humidex is similar to humidity. The comparison of humidex and temperature is similar to the comparison of humidex with global features. For the three climates with high humidity (see Table 1): wet equatorial summer, humid subtropical summer and tropical savana wet, the performance of humidex is significantly (approximately 10%) better compared to temperature. In the rest of the climate zone and seasons, temperature and humidex perform quite similarly (less than 5% difference). Prediction accuracy offered by radiant temperature is almost similar to that of operative temperature (Temperature in the plot). Therefore, the comparison of humidex with two different temperatures reveal three facts: (1) humidex is preferable to temperature in high humid situation; (2) temperature (operative) could also be a strong
6.3. Results In this section we contrast the performance of the global features with that of the local features to find the best performing feature set. We then compare the performance of humidex with that of the best feature set. In addition, we compare the prediction performance of humidex with individual features: indoor temperature and humidity, since these two features were used in the past for automatic thermal comfort modelling in the indoor setting. 6.3.1. Global versus Local Features Local features are expected to perform better than the global features, and this has been observed in Figure 3. Encouragingly, the difference between global and local features is quite insignificant for most of the climates. Therefore, we conclude that the global features sufficiently represent thermal comfort. We now compare the performance of humidex with that of the global feature set as a common benchmark.
6
80% Prediction accuracy
70% 60% 50% 40% SFS features − Local SFS features − Global
30% 20% 10% semi arid high altitude summer
wet equatorial summer
tropical savanna dry
tropical savana wet
hot arid summer
hot arid winter
humid subtropical west coast marine summer summer
mediterranean summer
Figure 3: Local versus Global SFS features. !"#$%&'()*"$+),-'.")
/%01%#2),"&$") !/)3--(4.'5%&)
/(40'2") *%0")
,:;)
