Identification and Control of a Heating System Building Based RBF Neural Networks A. Ouaret#1, H. Lehouche#2, B. Mendil#3, L. Brikh#4, F. Yahiaoui#5 1
LTII of Bejaia university of Algeria, Email:
[email protected] LTII of Bejaia university of Algeria, Email:
[email protected] 3 LTII of Bejaia university of Algeria, Email:
[email protected] 4 LTII of Bejaia university of Algeria, Email:
[email protected] 5 LTII of Bejaia university of Algeria, Email:
[email protected] 2
Abstract— Nowadays the decrease of energy consumption is a world target and it is no longer feasible to design a system without concerning to the energy optimization. An important energy consumer is associated with building heating systems The main objective of this paper is to use a feed-forward neural network adaptive control strategy to achieve a good temperature regulation in a building zone and to insure operational safety in the presence of different types of disturbances such as neighborhood temperatures, weather data. The simulation results for different situations show the importance and the effectiveness of this identification and control methodology for unknown nonlinear dynamical processes. Keywords— Building zone, Neural network, Radial Basis Function, adaptive control, consumption index and comfort index.
I. INTRODUCTION Buildings are responsible for 40 per cent of the energy consumption in the world. Within buildings, almost half of the energy use is related to heating, ventilation and air conditioning (HVAC) systems [1]. Reducing the building energy costs has become an urgent task, due to the increasing environmental concerns and energy prices. Despite of this fact, HVAC systems at the existing buildings are not operating in the most efficient ways. Therefore, this study aims to develop a building modeling approach, which is suitable for the design of indirect adaptive control strategies in commercial buildings. The control strategy can be used to reduce the energy consumption and improve thermal comfort in the buildings. Narendra and co-authors in [2, 3] have shown that neural networks can be used as a components in dynamical systems, and that identification and control of such complex systems using neural networks should be undertaken within a unified framework of systems theory. In this paper we have continued the work of the paper [4], by using another powerful architecture called feed-forward neural networks (RBF), [5]. RBF neural network has three
layers: the input layer, the hidden layer, and the output layer. Neurons at the hidden layer are activated by a radial basis function. The hidden layer consists of an array of computing units called hidden nodes. Even if many studies were carried out in order to optimize the energy efficiency of heating systems, the control algorithms that are used for this objective remain basic or stand for local control problems, such as on/off type or PID controllers, auto-tuning methods of PID parameters [6-7], fuzzy logic controllers [8], and predictive control [9]. All these methods based on linear model, which made them unsatisfactory or limited. The main objective of this paper is to develop a strategy of identification and control based on feed-forward neural networks and adaptive control algorithm for temperature regulation in a building zone. This room is a working office in a building and can be considered as an unknown nonlinear model, which is taken from Simbad toolbox [10]. The goal is to make the indoor temperature inside the office tracks a predefined set point whatever, the climate and parameters change. The remainder of this paper is organized as follows: Section 2 describes the complete process; in the same section the main control problem is stated. Section 3 devoted to recall the methodology of identification and control using feed-forward neural networks. Section 4 presents the application of RBF for identification and control for regulating the temperature in a building zone Conclusions are drawn in the last section. II. THE BUILDING ZONE WITH ELECTRICAL HEATER CASE STUDY A. Zone model description The room model consists of a detailed envelope model, simplified radiation model and simplified convection model. It uses a central node to represent the resultant temperature in the zone. This model consists of three main parts:
Model of the envelope elements (5 separate elements including a window model), Simple radiation model using a mean radiant temperature node for the calculation of heat exchange between the different elements, Model of the room air assuming perfectly mixed conditions of the air 1) Model inputs: E_vert: Global vertical radiation [W/m²] E_vert: Global vertical illumination [Lux] Blind pos: Position of the blind taking a value between 0 and 1, where 0 corresponds to blinds completely open Text: External Temperature (vector of air and radiant temperature) [°C] Tlower: Resultant temperature of the adjacent room in contact with the floor of the treated room (vector of air and radiant temperature) [°C] Tupper: Resultant temperature of the adjacent room in contact with the ceiling of the treated room (vector of air and radiant temperature) [°C] Tadj: Resultant temperature of the adjacent room in contact with the internal walls of the treated room (vector of air and radiant temperature) [°C] Q_elec: Heat gains from electric equipment (vector containing convective and radiative part) [W] Q_occ: Heat gains from occupants (vector containing convective and radiative part) [W] Q_EM: Heat gains from convector or radiator (vector containing convective and radiative part) [W] Air in: Vector describing air flow entering the room by ventilation or infiltration [°C - g/kg - Pa - kg/s] 2) Model outputs: Tzone: Zone temperature (vector of air and radiant temperature) [°C] Tsurf: Vector of internal surface temperatures in the zone [°C] Air out: Vector of air leaving the room [°C, g/kg, Pa, kg/s] E-nat: Natural lighting into the zone [Lux] 3) Components connections: T_ext is provided by weather data files. E_vert (W/m²) and E_vert (Lux) are obtained from the weather file after being processed by the coupling module "Vertical luminance and sun altitude". Blind position comes from a model of blind or the controller of the blind. Tlower, Tupper and Tadj are either fixed or come from other zone models. Q_EM is the heat flux that is generated by any HVAC equipment in the zone, Q_elec from lighting, computers or other electrical installations. Q_occ is connected to the occupant model.
B. Electric heater model description This is a first order model of an electric heater. 1) Input: Com: Command from controller limited between 0 and 1. 2) Outputs: Heat flux: Heat dissipated to surroundings [W] P_elec: Electric consumption of heater [W] 3) Parameters: Type of heater: list of typical heater with given response time Standard = Common electric heater Quick response = Electric heaters in fan coils, air handling units... Nom_Pow: Nominal power of heater [W]. Common values of nominal power: 500, 750, 1000, 1250, 1500, 1750, 2000. The block diagram which describe the global model (zone model + electrical heater model) is given in Fig.1
Fig. 1 The simulation model of the room with different perturbations and electric heater
C. The control problem formulation The case study used in this paper is a work office room, this type of building is occupied only during the working days between certain hours relatively fixed (for example between 8H00 and 17H00). How can we define the optimality that we want to find? 1) The first objectives: The comfort objective: we want to have while the room occupancy period the ambient temperature tracks the reference temperature Tref The consumption objective: we want to minimize the energy consumed As can be seen, these two objectives are opposite and the optimal seems to be achieved if we have a constant temperature value equal to Tref during the occupancy.
In the occupation time where Tamb Tref , this index action
The coefficient of transmittance (U): formerly called K, this coefficient is the inverse of the thermal resistance R measures the amount of heat which crosses the wall. (5) U 1 / RT [ w / m 2 C ] The thermal resistance (R): The thermal resistance R is the heat flux per square meter through a wall to a difference of 1°C between the two faces. This thermal resistance is calculated from the thickness and coefficient of thermal conductivity of material [8], according to the following formula: (6) R e / [m 2 C / W ]
as penalty when the room temperature does not meet the comfort objective. In this case we are looking for a comfort index as close as possible to zero. 2. Consumption index:
D. Simulation parameters The room characteristics used in simulation for identification and control algorithms are;
2) The secondary objectives: The complexity: want a simple algorithm. Temperature stability: we want to reduce as much as possible the temperature oscillations. Command stability: we want to reduce as much as possible the command oscillations to prevent the actuator damages. To measure these performances some indices are defined: 1. Comfort index: I comfort (Tref (t ) Tamb (t ))dt
[Ch ]
(1)
Occupation
tf
I consumptio n
p(t )dt
[kWh]
(2)
TABLE I SIMULATION PARAMETERS
t0
The consumption index ( I consumptio n ), is the integral of heating power required over the simulation period and the objective is to minimize this index. 3. Temperature stability index (TSI): (3) TSI (local max (Tamb (t ) Tref (t ))) [C ]
while occupancy
This index measures the sum of the differences between the local maximums temperatures and Tref during the occupancy. This is a little bit redundant with the consumption index because if we have for two different simulations with the same comfort index if the TSI grows also the consumption index will grow and if TSI decreases, the consumption index will decrease too and obviously we want this index as close to zero as possible. 4. Command stability index (CSI):
CSI mean( u (t 1) u (t ) )
Designation and heat transfer factor Zone length Zone width Zone heigth Window length Window height Wall heat transfer coefficient
Floor heat transfer coefficient
Ceiling heat transfert coefficients
(4)
u ( t 1)u ( t )0
The index CSI measures the mean difference between two consecutive commands. It is known that if we have always a big value of u(t 1) u(t ) the actuator can be damaged and accordingly to this we are searching for a small value of CSI. 3) The third objectives: good insulation To maintain a constant temperature inside a building it is necessary to restrict the rate at which heat energy is exchanged with the surroundings. Keeping heat inside a building for as long as possible conserves energy and reduces heating costs. Thermal conductivity (λ): the effectiveness of the insulation depends on its thermal conductivity, more λ is small, more the material is insulating. A material is said insulating when the λ is less than 0.06 W/m°C. But λ is never zero.
Initial temperature Reference temperature while occupancy Electric heater nominal power Number of occupants Occupancy interval Weather data Simulation time Equipment heat emission per m2 Fresh air supply Mean outside temperature
Dimension 4m 3m 3m 2m 1m 0.25 W/m2/k ( Plasterboard - Expanded Polystyrene - Parpaings ) 0.0000001 W/m2/k ( Plastic - hollow concrete slabs - Polystyrene foam Polyurethane - Sable ) 0.25 W/m2/k ( Plasterboard - Expanded Polystyrene - hollow concrete slabs - Polyurethane - Neoprene ) 8 ºC 19 ºC 1000W 2 persons 8H00 : 17H00 ( Monday to Friday) Rennes (region in France) 1 day 5 days 1 W/m2 40 m3/h 24/24h 6.5 °C
III. RADIAL BASIS FUNCTION (RBF) ARCHITECTURE In 1990, artificial neural networks were first proposed for the adaptive control of nonlinear dynamical systems [11]. Since that time, both multilayer neural networks (MNN) and
radial basis function (RBF) networks have been used in numerous applications for the identification and control [12]. RBF neural networks were addressed in 1988 [13], which have recently drawn much attention due to their good generalization ability and a simple network structure that avoids unnecessary and lengthy calculation as compared to the multilayer feed-forward network (MFN). Past research of universal approximation theorems on RBF has shown that any nonlinear function over a compact set with arbitrary accuracy can be approximated by RBF neural network [14, 15]. There have been significant research efforts on RBF neural control for nonlinear systems [5, 16]. RBF neural network has three layers: the input layer, the hidden layer, and the output layer. Neurons at the hidden layer are activated by a radial basis function. The hidden layer consists of an array of computing units called hidden nodes. Each hidden node contains a center c vector that is a parameter vector of the same dimension as the input vector x; the Euclidean distance between the center and the network input vector x is defined x(t ) c j (t ) . The output of hidden layer can be produced through a nonlinear activation function h j (t ) as follows:
x(t ) c (t ) 2 j (7) h j (t ) exp j 1,...,m 2 , 2b j where b j notes a positive scalar called a width and m notes the number of hidden nodes. The output layer is a linear weighted combination as follows: m
y j (t ) wij h j (t ) ,
i 1, ...,n
(8)
j 1
where w are the output layer weights, n notes the number of outputs, and y notes the network output.
RBF Neural Network Design and Simulation RBF Algorithm
For the vector b [b1 , ...,bm ]T , b j represents the width value of Gaussian function for neural net j.
Fig. 2 RBF neural network structure
The weight value of RBF is
w [ w1 , ..., wm ]T .
(10)
The output of RBF neural network is
y (t ) wT h w1h1 w2 h2 ... wm hm .
(11)
IV. APPLICATION OF RBF NEURAL NETWORKS FOR IDENTIFICATION AND CONTROL OF HEATING BUILDING ZONE PROCESS The control of temperature in the room is to minimize the energy consumption maintaining a certain thermal comfort for the occupation. Assuming that the comfort in this case is defined by reference temperature, therefore, we need to use a nonlinear algorithm for identification and control which is the feed-forward neural networks. A. Identification of the process in open loop To realize the identification of the process described in section 2, we have chosen the structure of feed-forward neural network used as identifier, the number of network in each layer and the activation function used for each layer. The difference between the output of the system and the one of network is the estimation error used to train the network weights. The series-parallel identification architecture is preferred (fig. 3).
The structure of a typical three-layer RBF neural network is shown as Fig. 2. In RBF neural network, x [ xi ]T is input vector. Assuming there are mth neural nets, and radial-basis function vector in hidden layer of RBF is h [h j ]T , h j is Gaussian function value for neural net j in hidden layer, and 2 x c j h j exp 2b 2j where
c11 c1m c cij cn1 cnm
Fig. 3 Identification of the process in open loop
(9)
The parameters of this network are illustrated in the following table
represents the coordinate TABLE II IDENTIFIER FEED-FORWARD NEURAL NETWORK
value of center point of the Gaussian function of neural net j for the ith input, i 1, ...,n, j 1, ...,m. Number of network neurons Activation functions
Input layer 2 ----------
Hidden layer 3 Gaussian
Output layer 1 Linear
After, the choice of the RBF neural network structure, the identification procedure is done according to these steps: - Initialization of weight: the weights are initialized randomly between 0 and 1 in the form of a matrix, W2 (3×1) between the hidden layer and the output layer. - Initialization of centers of Gaussians: centers are initialized randomly as a matrix C (2×3). - The adaptation step: the step of adapting our case is equal to 0.1. - Learning algorithm: in our case we worked with the system implemented by the CSTB, so it makes sense that we did an online learning. Which we used the K-means algorithm (learning in layer 1) and LMS (Learning in layer 2), where we took the input vector as: [u (k), y (k-1)], was chosen since the series-parallel structure. - Training sequence is 100 samples. To evaluate the performance and the capacity of this feedforward neural network as identifier, we have simulated the process for one case during a period of time of one day the parameters and different inputs are given in table III.
Discussion of the results: We have remarked from the figure 4, that the outputs of the process track perfectly the outputs of the feed-forward neural network identifier. The identification error is of the order 10-4 (see the figures 5).
TABLE III
The feed-forward neural network architecture used for identification is the same given in the table II, but the characteristics of the one used as controller is shown in table IV. This approach is illustrated for the case cited before. The control signal is bounded between 0 and 0.5.
THE INPUTS USED IN OUR CASE
Inputs E_vert [W/m²] E_vert [luxe] Blind_pos Text [°C] (Tlower, Tupper, Tadj) [°C] Q_elec [W] Q_occ [W] Air in Q_EM [W] Control input signal
parameters Connected to weather data (Rennes, France) Connected to weather data (Rennes, France) 0 opened in the night Connected Connected Connected Connected Connected Connected In the interval [0,1]
B. Indirect neural adaptive control of heating zone regulation in a building The structure of indirect adaptive control based on feedforward neural networks is shown below.
Fig. 6 The structure of neural indirect adaptive control applied to heating regulation of building zone
TABLE IV CONTROLLER FEED-FORWARD NEURAL NETWORK
Number of network neurons Activation functions
Output layer
6 Gaussian
1 Linear
20
System Identifier 20
Occupation period
15 Temperature [°C]
25
Temperature [°C]
Hidden layer
1) Case (1day): all the inputs are connected and the simulation results are:
All the inputs are connected as shown in the figure 1 and table III, the simulation results are:
10
5
15
0
10
-5
System Reference model External temperature 0
5
Input layer 4 --------
1
2
3
4
5
6
7
8
Time [s] 0
1
2
3
4
5
6
7
8
Time [s]
9
9 4
x 10
Fig. 7 The output of the process and the reference (1 day)
4
x 10
Fig. 4 The outputs of the process and identifier
10
-4
x 10
8
Control error
5
Identification error
4
3
2
6
4
2
1
0 0
3
3.5
4
4.5 Time [s]
5
5.5
Fig. 5 The identification error (occupation period)
6 4
x 10
3
3.5
4
4.5 Time [s]
5
5.5
Fig. 8 The control error (occupation period)
6 4
x 10
The simulation for 5 days (Figure 13) show that the temperature remains close to the desired temperature during the period of occupation from which we conclude that comfort is maintained.
0.5
Control input
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
V. CONCLUSION In this paper, we proposed an identification and control methodology based on feed-forward neural network RBF for regulating the temperature in a building zone. The main objective addressed herein is the application of indirect adaptive control based on this RBF neural network to a process of heating a building zone in the presence of a climate and environmental constraints. From the simulation results the stability and the performances are eventually achieved and satisfied in view of the capability of this type of neural networks. The future work will focus on the application of other control strategies and to consider a multi zones heating processes.
9
Time [s]
4
x 10
Fig. 9 The control input 20 System Identifier
18
Temperature [°C]
16 14 12 10 8 6
0
1
2
3
4
5
6
7
8
9
Time [s]
4
x 10
Fig. 10 The outputs of the process and identifier -4
5.5
x 10
Identification error
5
4.5
REFERENCES
4
[1]
3.5
3
3.5
4
4.5 Time [s]
5
5.5
6
[2]
4
x 10
Fig. 11 The identification error (occupation period) 9
[3]
8 7 6
[4]
5 4 3 2
[5]
Consumption index [kWh] Comfort index [°Ch]
1 0
3
3.5
4
4.5 Time [s]
5
5.5
6 4
x 10
Fig.12 Indices of comfort and consumer (occupation period)
[6]
Case (5 days): The simulations results for five days is given by:
[7] [8]
20
Temperature [°C]
15
[9]
10
5
[10] 0 System Reference model External temperature
-5 0
0.5
1
1.5
2
2.5
3
3.5
4
Time [s]
[11] 4.5 5
x 10
[12]
Fig.13 The output of the process and the reference (5 days)
Discussion of the results: We have seen from the figures (7, 8 and 9) in the beginning of the occupation period the output of the process tracks the reference signal, the control error is very small and the control input stays in his operational interval (good input signal). The online identification of the process in the same time with the controller shows that the identifier network N i is a perfect approximation to the system (see figures 10). The identification error is of the order 10-4(see the figures11).
[13] [14]
[15] [16]
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