Neural computing thermal comfort index for HVAC systems

Transcription

1 Neural computing thermal comfort index for HVAC systems S. Atthajariyakul, T. Leephakpreeda * School of Manufacturing Systems and Mechanical Engineering, Sirindhorn International Institute of Technology, Thammasat University, P.O. Box 22, Thammasat Rangsit Post Office, Patumthani 12121, Thailand Abstract The primary purpose of a heating, ventilating and air conditioning (HVAC) system within a building is to make occupants comfortable. Without real time determination of human thermal comfort, it is not feasible for the HVAC system to yield controlled conditions of the air for human comfort all the time. This paper presents a practical approach to determine human thermal comfort quantitatively via neural computing. The neural network model allows real time determination of the thermal comfort index, where it is not practical to compute the conventional predicted mean vote (PMV) index itself in real time. The feed forward neural network model is proposed as an explicit function of the relation of the PMV index to accessible variables, i.e. the air temperature, wet bulb temperature, globe temperature, air velocity, clothing insulation and human activity. An experiment in an air conditioned office room was done to demonstrate the effectiveness of the proposed methodology. The results show good agreement between the thermal comfort index calculated from the neural network model in real time and those calculated from the conventional PMV model. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Neural network; Predicted mean vote; Thermal comfort index; HVAC system 1. Introduction One of the primary purposes of heating, ventilating and air conditioning (HVAC) systems is to make occupants comfortable in terms of thermal comfort. The indicator of human thermal

2 comfort is technically called the thermal comfort index. A number of thermal comfort indices have been studied for the design of HVAC systems [1,2]. However, the most widely used thermal comfort index is the predicted mean vote (PMV) index, which was developed by Fanger [1]. This conventional PMV model predicts the mean thermal sensation vote on a standard scale of thermal feeling for a large group of persons in a given indoor climate. It is a function of two human variables and four environmental variables, i.e. clothing insulation worn by the occupants, human activity, air temperature, air relative humidity, air velocity and mean radiant temperature, respectively. The values of the PMV index have a range from 3 to +3, which corresponds to the occupantõs feeling from cold to hot, while the null value of PMV means neutral. The conventional PMV model has been an international standard since the 1980s [3,4]. It has been validated from many studies, both in climate chambers and in buildings [5 7]. In many researches related to comfort based control, the PMV index has been proposed to be maintained at the comfort level by regulating the variables affecting thermal comfort in order to provide both human comfort and low energy consumption [8 12]. Though the conventional PMV model predicts thermal sensations well, it is a nonlinear relation, and it requires iteratively computing the root of the nonlinear equation, which may take a long computation time. Therefore, Fanger [1] and ISO [4] suggest using tables to determine the PMV values of various combinations between the six thermal variables. Int-Hout [13] proposed a computer model according to FangerÕs PMV model for thermal comfort calculation. This computer model provides the convenience in thermal comfort calculations. However, the iterative step for the nonlinear equation was still included in the computer model. The use of the computer program and tables mentioned above are complicated and may not be suitable in real time control. To solve this problem, some researches were studied to avoid the iterative step by proposing simplified models of the PMV. Sherman [14] proposed a simplified model to calculate the PMV value without any iteration step by linearizing the radiation exchange term in FangerÕs model. His study indicated that the simplified model could only determine precisely when the occupants are near the comfort zone. Federspiel and Asada [15] proposed a thermal sensation index, which was modified from FangerÕs model. They supposed that the radiative exchange and the heat transfer coefficient are linear, and they also supposed that the clothing insulation and heat generation rate of human activity are constant. They then derived a thermal sensation index that is an explicit function of the four environmental variables. However, the simplification of FangerÕs PMV model results in significant error when the assumptions are not respected. Up to now, many computing applications of neural network models (NNM) in advanced research areas have confirmed that a NNM can be practically used to approximate any nonlinear relationship between input variables and output variables with a certain accuracy [16 18]. Recently, NNMs were successfully applied for both system identification and control in thermal HVAC systems [19 21]. Furthermore, NNMs have been implemented in order to predict cooling/heating load and energy consumption in buildings [22 24]. However, it has been found that there has been limited research work on thermal comfort prediction for real time control of HVAC systems [25]. Therefore, this study is to propose a practical approach to determine the PMV index of thermal comfort via neural computing in a wide range of human variables and environmental variables for an HVAC control system. The feed forward NNM is developed to capture the relations of the conventional PMV model of Fanger in a practical way.

3 This paper is organized as follows. Section 2 describes the field measurements of the experiment in an air conditioned office room. Section 3 briefly presents the theoretical background of the conventional model of the PMV index and the neural network model. Section 3.2 gives the explanation of the neural computing of the PMV index. In Section 4, the experimental results are discussed in detail. The conclusion is remarked in Section Field measurement Field measurements were done in an office room of size m 3. The diagram of the actual room is shown in Figs. 1 and 2. The front wall and left wall face the outside environment, while the other walls are joined to other rooms. The small circle in Figs. 1 and 2 indicates the position of the sensors where a seated person would be located, and the arrow points to the surface that a person would face. In Fig. 2, rectangles E and F of the front wall, rectangle E of the left wall and rectangles G, H and I of the back wall are glass windows as well as rectangles E, F, K and J of the back wall being doors. Field measurements of the air conditions that have effects on the PMV index were undertaken. After sensor installation, the one day measurements were recorded every 10 min from 8:00 a.m. to 5:00 p.m., and all signals of the sensors were transmitted to a data logger. The air temperature was measured by a reference temperature probe with measuring range 20 C to +70 C with an accuracy of ±0.4 C. The air humidity was measured by a humidity probe with measuring range 0 100% RH with an accuracy of ±1% RH. The air velocity was measured by a hot bulb probe with measuring range 0 10 m/s with an accuracy of ±0.03 m/s. The globe temperature was measured by a globe thermometer with a measuring range 0 C to +120 C with an accuracy of ±0.5 C. The air wet bulb temperature was measured by a thermocouple covered with a wet cotton wick under air movement of 3 4 m/s for a measuring range C with an accuracy of ±0.5 C. The surface temperature of each wall was measured by an infrared sensor with measuring range 30 C to 900 C with an accuracy of ±0.8 C. Each surface temperature was measured in order to calculate the mean radiant temperature of the room. Front wall Ceiling Right wall Floor Left wall Back wall Fig. 1. Diagram of room surface with partition divided from seated person position.

4 CEILING D C A B FRONT WALL D E F C A A B LEFT WALL D A A FLOOR 2.6 B C B C E B D C D A E D C K 0.9 F J 0.8 G H I A BACK WALL Units are in metre B Fig. 2. Room dimensions and instrument placement. 3. Theoretical background In this section, the theoretical background of the thermal comfort index and the neural network model are discussed Predicted mean vote The most widely used thermal comfort index is the predicted mean vote (PMV) of Fanger [1] which indicates the mean thermal sensation vote on a standard scale for a large group of persons. The PMV index predicts the thermal sensation as a function of two human conditions: human activity and clothing insulation and four thermal environmental variables: air temperature, air

5 humidity, air velocity and mean radiant temperature. Fig. 3 shows a combination of each thermal variable affecting the PMV level. The value of the PMV index has a range from 3 to +3, corresponding to human sensations from cold to hot, respectively, where the null value of the PMV index means neutral. The value of PMV can be determined by [1] with PMV ¼ð0:325e 0:042M þ 0:032Þ½M 0:35ð43 0:061M P v Þ 0:42ðM 50Þ 0:0023Mð44 P v Þ 0:0014Mð34 T i Þ 3:410 8 f cl ððt cl þ 273Þ 4 ðt mrt þ 273Þ 4 Þ f cl h c ðt cl T i ÞŠ T cl ¼ 35:7 0:032M 0:18I cl ½3: f cl ððt cl þ 273Þ 4 ðt mrt þ 273Þ 4 Þ f cl h c ðt cl þ T i ÞŠ ð2þ ( h c ¼ 2:05ðT cl T i Þ 0:25 for 2:38ðT cl T i Þ 0:25 p > 10:4 ffiffi v p 10:4 ffiffi v for 2:38ðT cl T i Þ 0:25 p < 10:4 ffiffi ð3þ v P v ¼ P s RH=100 where T i is the indoor air temperature ( C), T mrt is the mean radiant temperature ( C), M is the human activity (kcal/hm 2 ), v is the relative air velocity (m/s), P v is the vapor pressure in the air (mmhg), I cl is the thermal resistance of clothing (clo: 1 clo = Cm 2 h/cal), h c is the convective heat transfer coefficient (kcal/m 2 h C), f cl is the ratio of the surface area of the clothed body to the surface area of the nude body, T cl is the outer surface temperature of the clothing ( C), RH is the relative humidity in percent and P s is the saturated vapor pressure at a specific temperature. It should be noted that the value of T cl is to be computed iteratively in finding the root of the nonlinear equations in Eqs. (2) and (3). If the initial guess of T cl is far from the root, it might take a long computation time to converge to the root. It is obvious that the required amount of time can vary from case to case. The mean radiant temperature, T mrt, relating to a person in a given point in an enclosure consisting of an N surfaced room, is defined as the temperature of a uniform black enclosure in which an occupant would have the same radiant heat loss as in an actual indoor environment. The mean radiant temperature can be accurately determined from measuring the temperatures of the surrounding walls and surfaces and their positions with respect to the person using the following equation [1]. ð1þ ð4þ Air temperature Air relative humidity Air velocity Mean radiant temperature Activity level Clothing insulation PMV Calculated by Eqs.(1)-(4) PMV - 3 Hot - 2 Warm - 1 Slightly warm - 0 Neutral - -1 Slightly cool - -2 Cool - -3 Cold Six thermal variables Thermal sensation indicator Fig. 3. PMV and thermal sensation.

6 T 4 mrt ¼ T 4 1 F P 1 þ T 4 2 F P 2 þ...þ T 4 N F P N where T 1, T 2,..., T N are the temperatures of the N surfaces and F P 1, F P 2,..., F P N are the angle factors between the person and the surrounding N surfaces. In calculating the angle factors for all the surfaces in a room where a person is directly facing one wall, each surface must be divided into four rectangles using the center and position of the seated person as the dividing point. The angle factor of each rectangle with respect to the person is then determined according to the diagrams shown in Fig. 2 where the details of calculation can be found in the study of Fanger [1]. However, an example of the calculation in this study is provided in Section 4. At this point, it is obviously seen that the measurement of all wall temperatures may not be possible to obtain in a practical way for determining the mean radiant temperature in Eq. (5). In turn, the PMV index can not be calculated accordingly as introduced in Section Neural network model The multilayer feed forward neural network is widely used for the input/output pair mapping of qualitative relationships due to its capability of approximating nonlinear model functions. It can approximate any continuous nonlinear functions provided there are sufficient numbers of nonlinear processing nodes, or neurons, in the hidden layers. The basic structural architecture of the neural network is the sequence of an input layer, a single hidden layer and an output layer is shown in Fig. 4. However, more than one hidden layer can be added to the neural network. Fig. 4 shows the K outputs (y 1,..., y k,..., y K ) that are transformed from the I inputs (x 1,..., x i,..., x I ) through the hidden layer with J neurons (z 1,..., z j,..., z J ). The output of the neural network model (NNM), y k, can be determined as follows [26]:! X J y k ¼ f y w kj z j þ c k ð6þ with z j ¼ f z j¼1 X I i¼1 w ji x i þ b j! ð5þ ð7þ x 1 z 1 y 1 x i z j y k x I z J y K Input layer Hidden layer Output layer Fig. 4. Multilayer feed forward neural network.

7 where w kj is the weight from neuron z j to neuron y k, c k is the bias for the neurons y k, w ji is the weight from neuron x i to neuron z j, b j is the bias for neurons z j, f y and f z are the activation functions, which are normally nonlinear functions. Sigmoid shape activation functions are normally used and defined as 1 f ðfþ ¼ ð8þ ð1 þ e f Þ In order to yield the quantitative relationship between the inputs and outputs, a training set of data inputs and desired outputs must be available for training the NNM. There are K desired outputs y d with the I inputs x. During training the NNM model, the input data is used to produce the outputs according to the NNM from Eqs. (6) (8). Now, there are K outputs y produced by the NNM. The outputs from the NNM are then compared with the desired outputs. The errors between the outputs from the NNM and the desired outputs are typically defined as the error function for minimization as Eq. (9) [26]. Jðu * Þ¼ 1 2 X K k¼1 ðy k y dk Þ 2 where u * is the vector containing all the weights or/and biases of the NNM. Here, it should be noted that the desired output is the PMV value from the FangerÕs model, while the output from the NNM is forced to mimic the desired output. The inputs of the NNM correspond to the inputs of FangerÕs model, which are the human variables and environmental variables. If the error is greater than the desired tolerance, the connection weights and biases of the NNM are adjusted in the direction that decreases the error. In order to yield the minimum error, a gradient descent based algorithm is usually implemented to adapt all the weights and biases. This method is typically called the back propagation method. The weights and biases of the NNM are to be adjusted by applying Eq. (10). * * * u ðt þ 1Þ ¼u ðtþ kðtþr uðtþ ð10þ where k is the magnitude of the learning rate of the step size and t is the iteration index. r * u is the gradient of the cost function with respect to the weights and/or the biases, which is defined as Eq. (11). r * u ¼ oj ou * ð11þ When the new weights and biases are obtained according to Eqs. (10) and (11), the outputs are recalculated according to the NNM from Eqs. (6) (8). If the error is still greater than the desired tolerance, calculation of the weights and biases of the NNM is repeated until the error is within the required tolerance. ð9þ 4. Neural computing PMV index Although the thermal comfort index developed by Fanger [1], PMV, is widely used and can be calculated according to Eqs. (1) (4), it is noticed that the T cl is to be determined by iteratively

8 computing the root of the nonlinear functions in Eqs. (2) and (3). This step of calculation may take a long computation time, and this is not practical for determining PMV in real time applications. Moreover, in real time control, although the method to determine the mean radiant temperature by measuring all the surrounding surface temperatures and then calculating according to Eq. (5) may be possible, but this method requires a considerable amount of calculation burden. In measuring the relative humidity, the sensors mostly used are hygrometers, which are complex and costly. To avoid these problems, this study proposes to use a feed forward NNM in order to determine the value of PMV instead of applying Eqs. (1) (4) which here is called the neural PMV. This neural PMV is to be the function of the variables that can be measured by commonly available instruments in HVAC systems. The globe temperature, T g, is used for the mean radiant temperature due to its simple measurement. The globe temperature can be measured by the globe thermometer. The globe thermometer consists of a black spherical shell, usually 15.2 cm in diameter, and a thermocouple or thermometer bulk placed at its center [27]. The air relative humidity can be calculated directly from the indoor air temperature and wet bulb temperature of the air. The wet bulb temperature can be easily measured by a thermocouple that is wrapped with a piece of wet cotton wick and placed in an airflow of 3 5 m/s [27]. In this work, the proposed neural PMV model is developed for capturing the quantitative relation of FangerÕs PMV model. It relates the thermal comfort index to six easily accessible variables: air temperature, air wet bulb temperature, globe temperature, air velocity, clothing insulation and human activity in HVAC systems as summarized in Eq. (12). PMV neural ¼ f ðt wb ; M; T i ; T g ; v; I cl Þ ð12þ The globe temperature is used to determine the mean radiant temperature in FangerÕs PMV model, which is embedded in the neural-pmv model according to the following equation [27]. T mrt ¼ 1 1:8 ð1:8t i þ 492Þ 4 þ 1: v 0:6 1=4 ðt g T i Þ 492 ð13þ ed 0:4 1:8 where T g is the globe temperature ( C), D is the globe diameter (m) and e is the emissivity of the globe (0.95 for black globe). The relative humidity in FangerÕs model, related to the wet bulb temperature can be determined according to the following equation [28]. with 100Px RH ¼ ðx þ 0:622ÞP s P s ¼ 1000 expðat 2 i þ BT i þ C þ DT 1 i Þ ð15þ x ¼ ð2501 2:381T wbþx s ðt i T wb Þ 25:1 þ 1:805T i 4:186T wb ð16þ ð14þ x s ¼ 0:622P s wb P P s wb P s wb ¼ 1000 expðat 2 wb þ BT wb þ C þ DT 1 wb Þ ð17þ ð18þ

9 where T wb is the wet bulb temperature (K), P is the barometric pressure at sea level (101,325 Pa), P s_wb is the saturated vapor pressure (Pa) at T wb, x and x s are the humidity ratios at T i and T wb, respectively. A = , B = , C = and D = Result and discussion The operating ranges of each input variable for training the neural PMV are (16, 34) for air temperature, (8, 31) for wet bulb temperature, (14, 36) for globe temperature, (0.1, 1) for air velocity, (50, 80) for activity level and (0.5, 1) for clothing insulation. The training data points covering the above range are 23,040, and the sum of the square errors between the values of PMV calculated from Eq. (1) and the values obtained from the neural-pmv was 0.11 with a NNM structure where there are one input layer with six nodes, two hidden layers with eight nodes and five nodes, respectively, and one output layer with one node in the NNM. The weight and bias of each neuron are obtained as shown in Table 1. It should be noted from Table 1 that w l,k is the weight connecting a neuron from the second hidden layer to the output layer and d l is the bias of the neuron in the output layer. In calculating FangerÕs PMV, the mean radiant temperatures were calculated according to Eq. (5). The angle factor was a function of the two length relationships b/c and a/c, where a and b are the side lengths in the rectangle and c is the normal distance between the person (center) and the rectangle. The relationship between the angle factor and the two length relationships, b/c and a/c can be found in Ref. [1]. The obtained angle factors were obtained and shown in Table 2. In the real time experiment in the air conditioned room, the PMV obtained from the neural PMV model and FangerÕs PMV model were compared and shown in Fig. 5 where the clothing insulation was 0.6 for a cotton work shirt and the human activity was 60 kcal/hm 2 for Table 1 Weight and bias of each neuron in neural-pmv j w j,i= w j,i= w j,i= w j,i= w j,i= w j,i= w k=1,j w k=2,j w k=3,j w k=4,j b j k w l=1,k c k l 1 d l

10 Table 2 Angle factor calculation of each surface (b/c, a/c) Front wall Whole wall F P A (0.9/2.6, 2.4/2.6) F P B (0.9/2.6, 53/2.6) F P C (2.7/2.6, 5.3/2.6) F P D (27/2.6, 2.4/2.6) Angle factor Window (E F) F P E (2.6/2.6, 1.9/2.6) F P F (2.6/2.6, 3.1/2.6) The rest wall (whole wall-window) Back wall Whole wall F P A (2.7/1, 2.4/1) F P B (27/1, 5.3/1) F P C (0.9/1, 5.3/1) F P D (0.9/1, 2.4/1) Door (E F J K) F P E (0.9/1, 0.8/1) F P F (1.1/1, 0.8/1) F P J (1.1/1, 0.8/1) F P K (0.9/1, 0.8/1) Window(G H I) F P G (1.1/1, 0.5/1) F P H (1.1/1, 1.3/1) F P I (1.1/1, 1.8/1) The rest wall (whole wall-window-door) Left wall Whole wall F P A (0.9/2.4, 2.6/2.4) F P B (0.9/2.4, 1/2.4) F P C (2.7/2.4, 1/2.4) F P D (2.7/2.4, 2.6/2/4) Window F P E (2.1/2.4, 0.8/2.4) The rest wall (whole wall-window) Right wall Whole wall F P A (2.7/53, 1/5.3) F P B (2.7/53, 2.6/5.3) F P C (0.9/5.3, 2.6/5.3) F P D (0.9/5.3, 1/5.3)

11 Table 2 (continued) Floor Ceiling (b/c, a/c) Angle factor Whole wall F P A (2.6/0.9, 2.4/0.9) F P B (2.6/0.9, 5.3/0.9) F P C (1/0.9, 5.3/0.9) F P D (1/0.9, 2.4/0.9) Whole wall F P A (1/2.7, 2.4/2.7) F P B (1/2.7, 5.3/2.7) F P C (2.6/2.7, 5.3/2.7) F P D (2.6/2.7, 2.4/2.7) PMV Fanger's model Neural-PMV model :00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 Time Fig. 5. Comparison of PMV between neural-pmv and FangerÕs model. office work. At 8.00 h, the air conditioning system is usually turned on. The value of the PMV index started at 0.8, which indicates slight warm to occupants. After that, the value of PMV decreased to 0.3 close to the neutral zone. It shifted up to 0.7 again in the afternoon. It can be seen that the results showed good agreement of both models in determination of the PMV values during the day time. 6. Conclusion In this paper, a neural PMV model to calculate a humanõs thermal comfort index from practical measurements is proposed where the wet bulb temperature and globe temperature are measured instead of the relative humidity and mean radiant temperature, respectively. The feed forward neural network model is used as an explicit function of the relation of the air temperature, wet bulb temperature, globe temperature, air velocity, clothing insulation and human activity to the PMV value. An experiment in an air conditioned room was done to demonstrate the effectiveness of the proposed neural network model in computing the values of PMV in real time for a

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