- Email: [email protected]
Modelling of small scale central heating installation using artificial neural networks aiming at low electric energy consumption
Energy and Buildings 62 (2013) 126–132
Contents lists available at SciVerse ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Modelling of small scale central heating installation using artificial neural networks aiming at low electric energy consumption G.C. Bakos ∗ , A. Sismanis Democritus University of Thrace, Department of Electrical and Computer Engineering, Laboratory of Energy Economics, 67 100 Xanthi, Greece
a r t i c l e
i n f o
Article history: Received 19 December 2012 Accepted 21 December 2012 Keywords: Artificial neural networks Non-linear energy systems Central heating installation Low electric energy consumption
a b s t r a c t Artificial neural networks (ANNs) used to control the operation of energy systems is an important field of research. This paper deals with the use of ANNs as a technique of modelling real non-linear energy systems such as the flow and pressure processes related to pump and valve input voltages of a small scale central heating system aiming at low electric energy consumption. The system is located in the Energy Economics Laboratory of Democritus University of Thrace in Greece and its operational parameters were accurately captured using a backpropagation neural network. The approach described in this paper has the advantages of computational speed, low cost for feasibility and ease of design by operators. © 2013 Elsevier B.V. All rights reserved.
1. Introduction In 1995, the Greek Ministry of Environment, Urban Planning and Public Works prepared an Action Plan, entitled “Energy 2001”, aiming at promoting the application of energy-efficiency technologies, in the building sector. The Action Plan was prepared in order to define specific measures for the reduction of greenhouse gas emissions in buildings, in accordance with the “National Action Plan for the Abatement of CO2 and Other Greenhouse Gases”. Following official adoption of the Action Plan by the Greek Government, “Energy 2001” was further reinforced by the enactment of Ministerial Decree (MD) 21475/98, which incorporated the provisions of Council Directive 93/76/EC (SAVE Directive) for the stabilisation of CO2 emissions and the efficient use of energy in buildings [1]. Space air-conditioning dominates the energy consumption in residential and public building sector [2–4]. In Greece, the largest percentage of buildings (old and new) is using the classic oil-based central heating installation with water as heat transfer agent. The effective operation control of these central heating installations, based on the monitoring of different operational and performance parameters, leads to substantial energy saving reducing simultaneously the environmental pollution and the need for further capital investment in power plants construction. The use of ANNs in energy systems can be viewed as a natural step in the evolution of control methodology. This is mainly due to the fact that ANNs have good approximation capabilities and offer additional advantages such as short development and fast
∗ Corresponding author. Tel.: +30 25410 79725; fax: +30 25410 79734. E-mail address: [email protected] (G.C. Bakos). 0378-7788/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.enbuild.2012.12.018
processing times [5]. A detailed description of various applications of ANNs in energy systems is provided by Kalogirou [6]. In particular, ANN applications to building sector have attracted considerable attention from the scientific community [7–9]. Many different types of neural networks are available. Feedforward Multilayer (MLP) networks, where the inputs are fed forward through the layers to the output, have been applied in system identification problems. Normal use of an MLP network involves training the network on a set of data obtained from the installation to be controlled. The learning rule for feedforward MLP networks is called the ‘Generalised Delta rule’ or the ‘Backpropagation rule’. The backpropagation training algorithm is an iterative gradient algorithm that attempts to minimise the mean square error between the actual network output and the desired one, so that the network input–output relationship best approximates the energy system data. The model structure needs to have sufficient representation ability to enable underlying system characteristics to be approximated with an acceptable accuracy and in many cases the model needs to retain simplicity. Also the input signal to the energy system used for the generation of data must be carefully chosen so that it excites all the dynamics of the process to be modelled and generate cause and effect data which are maximally informative. Validation tests are necessary to be carried out in order to check the performance and accuracy of the developed NN model. 2. Description of the small scale central heating installation In this paper, the small scale central heating installation to be modelled is operating in the premises of the Laboratory of Energy Economics of Democritus University of Thrace in Xanthi – Northern
G.C. Bakos, A. Sismanis / Energy and Buildings 62 (2013) 126–132
127
Photo 2. View of radiator–ventilator system.
1. Controlling the flow and pressure using the control valve. 2. Controlling the flow and pressure using the pump. 3. Controlling the temperature using the heater.
Photo 1. Small scale central heating installation.
Greece. The block diagram of the experimental setup installation and its physical representation are shown in Fig. 1 and in Photo 1, respectively. The laboratory central heating system can operate as closed circuit water system. The total capacity of the system is approximately 22 l. There are 6 m of 22 mm piping and a small amount of 15 mm having a total capacity of 3 l. The pump is capable of delivering up to 45 l/min; however the system will impose restrictions on this. Water is delivered from the pump via the heater to the radiator. Forced convection through the radiator results in heat loss. Initial temperature measured by the probe will be the room temperature. When heating is started this temperature will rise and equilibrium will eventually be reached between the radiator and room temperature through heat loss, and the system temperature. This operating point can be controlled by:
The heating system is used to heat a room, situated inside the laboratory premises, constructed from compound polystyrene slates with dimensions 3.00 m × 3.00 m × 3.00 m. The radiator–ventilator system used inside the room is shown in Photo 2. The presentation of the experimental results on a PC Intel Pentium and the time interval of measurement storage can be controlled through the developed LABVIEW software. The developed data acquisition system (Photo 3) was based on two AdvanTech cards (an A/D input card PCI-1714 which can accept up to 32 analogue inputs and a D/A output card with 8 output channels). Calibration of the measurement equipment was necessary in order to capture the relationships between the two variables (flow and pressure) and the outputs of the meter circuits. 3. System representation approach The model structure needs to have sufficient representation ability to enable the underlying system characteristics to be approximated with an acceptable accuracy and in many cases the model also needs to retain simplicity.
Fig. 1. Block diagram of the small scale central heating system.
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G.C. Bakos, A. Sismanis / Energy and Buildings 62 (2013) 126–132
the pump input voltage and the mean value of output voltage was calculated for the following three valve positions (Figs. 2 and 3): (a) valve fully open (Vin = 10 V), (b) valve half open (Vin = 5 V) and (c) valve almost closed (Vin = 1 V). The way the position of the control valve affects the flow and pressure in the system was found by carrying out the following experiments. Keeping the pump operating at a fixed speed by applying constant input voltages to the pump interface circuit, the input voltage to the control valve was varied from 1 V (valve almost closed) up to 10 V (valve fully open) in steps of 1 V. The corresponding output voltage readings from the interface circuits were recorded. The procedure was repeated two times, once for increasing and once for decreasing the control valve input voltage and the mean value of output voltage was calculated for the following three pump operating voltages (Figs. 4 and 5):
Photo 3. View of developed Data Acquisition Interface.
3.1. Dynamic response analysis In order to find out how the input voltage to the pump affects the flow and pressure in the system, the following experiments were carried out. Keeping the valve at a fixed position by applying constant voltages to the E/P transducer, the input voltage to the pump was varied from 0 V (pump at standstill) up to 5 V (pump operating at max speed) in steps of 0.5 V. The corresponding output voltage readings from the interface circuits were recorded. The procedure was repeated two times, once for increasing and once for decreasing
(a) pump Vin = 1 V, (b) pump Vin = 2.5 V and (c) pump Vin = 5 V. Step response testing of the flow and pressure in the laboratory central heating system was obtained using a set of step voltage inputs to the pump and the valve in order to obtain a general idea of the genetic dynamic characteristics of the two processes and also the type of non-linearity of the system. Simple observation of
30 VALVE Vin=10V
25
VALVE Vin=5V
Flow (Lit/min).
VALVE Vin=0V
20 15 10 5 0 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Pump input voltage (Volts).
Fig. 2. Variations of flow due to different power inputs to the pump for fixed control valve positions.
20 Valve Vin=1V Valve 1/2 open
Pressure (lb/sq.in).
15
Valve Vin=10V
10
5
0 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Pump input voltage (Volts). Fig. 3. Variations of pressure due to different power inputs to the pump for fixed control valve positions.
5
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Fig. 4. Variations of flow due to different control valve positions for fixed pump speeds.
20 PUMP Vin=5V
18
PUMP Vin=2.5V
Pressure (lb/sq.in).
16
PUMP Vin=1V
14 12 10 8 6 4 2 0 0
1
2
3
4
5
6
7
8
9
10
11
Valve input voltages (Volts). Fig. 5. Variations of pressure due to different control valve positions for fixed pump speeds.
Figs. 2–5 showed that the system was not oscillatory. By simple measurements the order of magnitude of the dominant time constant and the dead-time were obtained (Table 1). As it was expected these values were not constant due to the non-linearities present in the laboratory system. 3.2. System identification Pseudo Random Binary Sequence (PRBS) is a commonly used and easily generated input signal that is frequently the preferred choice of test input signal in identification experiments. These are signals which can take on only two possible states (+˛ and −˛). The state can change only at discrete intervals of time t. The change occurs in a deterministic pseudo random manner and the sequence is periodic with period T = Nt, where N is an integer. A PRBS input is a persistently exciting signal which excites all dynamics of the process which a constant input signal fails to do, and generates far more cause and effect data which provide information about the true dynamics of the system to be modelled.
The interval of PRBS must be carefully selected for good identification. Not too long, because transient dynamic information will be lost as process dynamics will reach steady state values between PRBS changes and the output will be seen to change from one operating level to the next. Not too short, otherwise the process output will not have had sufficient chance to change in response and the resulting small output changes will be masked by noise resolution effects on ADC [10]. A rule of thumb for the choice of the PRBS interval is about ¼ of the dominant system time constant. In this work the update interval of the PRBS was set to 0.75 s since the dominant time constants of both the flow and pressure responses to pump step inputs was found to be 2.3 s. 3.3. Noise effects In order to verify that injecting artificial noise (Jitter) into the inputs during training is one of several ways to improve generalisation, the following experiment was carried out in MATLAB. A simple second order system was simulated in SIMULINK to generate
Table 1 Time constant and dead time measurements. Step inputs
Pump step 0–5 V when valve ¼ open Pump step 0–5 V when valve ½ open Pump step 0–5 V when valve ¾ open Pump step 0–5 V when valve fully open Pump step 0–2.5 V when valve ¼ open Pump step 0–2.5 V when valve ½ open Pump step 0–2.5 V when valve ¾ open Pump step 0–2.5 V when valve fully open
Flow
Pressure
Time constant (s)
Dead time (s)
Time constant (s)
Dead time (s)
0.8 1.8 1.8 1.0 2.1 1.5 1.3 1.4
0.9 0.8 0.8 0.8 0.5 0.7 0.4 0.7
2.2 2.2 2.1 2.3 1.3 1.3 1.1 1.5
1 1.4 1.3 1.1 1.0 1.1 1.0 0.9
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Fig. 6. The two-input–two-output model.
training and validation data for a neural network. Two training sets were obtained using two different input signals: a Square input and a Square input with White Noise added to it. The square inputs had an amplitude of 5 V and a frequency of 0.015 Hz and the standard deviation of the White noise was 0.1. After the training, validation tests were carried out to check the quality of each of the two models obtained, using a sinusoidal and a random input of amplitude 5 V and frequency of 0.015 Hz, and the sum squared error was calculated in each case. The network that was used had the typical two-layer architecture used for function approximation. It had a hidden layer of 5 sigmoidal neurons (in this case tan-sigmoid) neurons, which receive directly and then broadcast their outputs to a layer of 1 linear neuron that computes the network output. As it was expected the network gave a far better model when it was trained using the data obtained from the simulation using a square input together with white noise. In this work the White noise standard deviation used was 0.05. The filter was of type lowpass of order 10 and with low cutoff frequency of 2.5 Hz in order to satisfy the requirement 0 ≤ low cutoff frequency ≤ 0.5 sampling frequency (10 Hz). 4. Neural network model The objective was to develop a neural network and train it using data from the central heating system in order to obtain the model of the process. This model had two outputs, the flow and pressure voltage readings in the system. The reason temperature was not used as an output in the model was that its time constant was approximately = 15 min and that would result in a very large sampling period and thus the data collection experiment would become a very time consuming process. The model outputs were the valve and pump input voltages. The heater input variable was not used as an input to the neural model since it was proven that flow and pressure were unaffected by the temperature of the system. The input–output dynamics of the real system processes can be characterised in the continuous-time domain by the general NARX (Non-linear, Auto-Regressive, eXogenous) model defined by:
vector valued non-linear function the neural network was used to implement. The values of both na and nb were set to be 2. Thus the two first columns of the input and output vector to the neural network have the following matrix form in the discrete-time domain:
⎡
y1(k−1) y1(k−2) y2(k−1) y2(k−2)
⎢ ⎢ ⎢ ⎢ Yk = ⎢ ⎢ u1(k−L/Ts −1) ⎢ ⎢ u1(k−L/Ts −2) ⎣u 2(k−L/Ts −1)
u2(k−L/Ts −2)
⎤
y1(k) y1(k−1) ⎥ ⎥ y2(k) ⎥ y2(k−1) ⎥ ⎥ u1(k−L/Ts ) ⎥ ⎥ u1(k−L/Ts −1) ⎥ u2(k−L/Ts ) ⎦ u2(k−L/Ts −1)
Uk =
u1(k) u2(k)
u1(k+1) u2(k+1)
If Ts is the sampling period and N is the number of input–output data pairs then the total number of columns of these vectors will be N − L/Ts − 2. The two-input–two-output model to be developed is given in Fig. 6. The sampling interval set in the LABVIEW program developed for the collection of data from central heating system was 0.1 s. It was not necessary to sample more quickly since the process will not respond to high frequency control signals. Also rapid sampling increases quantisation noise effects and numerical problems with the accuracy of calculations may occur. The neural network can learn significant information concerning the plant dynamics and provide an accurate model by mapping a particular set of inputs to a set of desired outputs. The delay of the system is of no importance when selecting data to form the input and target vector for the NN since the relationship between the input and the output is contained in all set of input–output pairs. The value of delay used in the MATLAB program developed to form the input and target vectors for the NN was set to 1. In the development of this model, there were a number of issues that needed consideration, such as the network topology, network training and validation. 4.1. Neural network topology
Y (t) = F[(Y (t − 1), . . . , Y (t − na ), U(t − L), . . . , U(t − L − nb )] + E(t) where Y(t) is the output vector; U(t) is the input vector; E(t) is the noise exogenous input vector; L is the process deadtime; na and nb are the number of past output and input data used; F(·) is the
Since two past inputs and two past outputs of the process were used as inputs to the neural network, the back-propagation network had to have 8 input nodes and 2 output nodes. One hidden layer was used which had 4 hidden neurons with tansigmoid
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Training data set. 10 9
- PRBS input to valve
Amplitude (Volts)
8 7
- PRBS input to pump
6 5
- Flow response
4 3
- Pressure response
2 1 0
0
20
40
60
80
100
Time (sec) Fig. 7. The training data set.
10
Amplitude (Volts)
9
- PRBS input to valve
8 7
- PRBS input to pump
6 5 4
- Flow response
3 2
- Pressure response
1 0
0
20
40
60
80
100
Time (sec) Fig. 8. The validation data set.
activation function. In the output layer the linear activation function was used.
1. A random binary signal with levels 2–3 V, when applied to the pump, and 2–8 V, when applied to the valve. 2. A random signal with an amplitude varying within the operating levels of the pump and the valve.
4.2. Neural network training The neural network was trained using the Levenberg–Marquardt back-propagation algorithm. The training data set (Fig. 7), containing 1000 pairs of input–output values, was generated by the application of a random binary signal in the both inputs with Gaussian white noise added to each one of them and filtering of the data obtained from the output. The lower and upper levels of the input signals applied to the pump and valve were 2–3 V and 2–8 V, respectively, at an update interval of 0.75 s.
The update interval of each of the input signal was 1 s. Each of the signals was applied to:
1. The pump whilst the valve was ½ open. 2. The valve whilst the pump was operating with Vin = 2.5 V. 3. Both the pump and the valve.
Thus six validation data sets were generated which were applied to the trained neural network. The sum squared errors, which were calculated in each case, are given in Table 2. Fig. 8 shows the third validation test and Figs. 9 and 10 present the corresponding sum squared errors.
4.3. Model validation tests The neural network model was validated using two test signals that had not been used in training. These were: 10
Amplitude (Lit/min)
9
- Heating system
8 7 6
- NN model
5 4 3 2 1 0
0
200
400
600
800
1000
Data points per sec Fig. 9. The neural network response compared to the system’s actual response concerning the flow process (sum squared error = 47 × 10−3 ).
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Amplitude (lb/sq.in)
18
- Heating system
16 14 12
- NN model
10 8 6 4 2 0
0
200
400
600
800
1000
Data points per sec Fig. 10. The neural networks response compared to the system’s actual response concerning the pressure process (sum squared error = 62 × 10−3 ). Table 2 Sum squared errors corresponding to six validation data sets applied to the NN. Test
Sum squared Flow response
Errors Pressure response
1 2 3 4 5 6
0.8 × 10−3 0.3237 × 10−3 47 × 10−3 0.6312 × 10−3 1.2 × 10−3 0.66 × 10−3
14.6 × 10−3 0.2389 × 10−3 62 × 10−3 0.5209 × 10−3 16.7 × 10−3 0.629 × 10−3
It can be seen that the neural network was successful in approximating the flow and pressure processes in the laboratory central heating system related to the pump and valve input voltages. 5. Summary and conclusions The purpose of this project was to investigate the use of neural networks as a technique of modelling non-linear energy systems and to apply this technique in a real laboratory system (small scale central heating system). The main objective was to develop a neural network and train it in order to approximate the flow and pressure processes related to the pump and valve input voltages. Critical issues were:
back-propagation network with 4 tansigmoid neurons in the hidden layer and a linear output layer was a successful network design. The network was trained using the Levenberg–Marquardt backpropagation algorithm. Three different methods for generating data were tested. The method that produced the best training sets for the neural network was the one that caused reduction of the effects of noise in generalisation and excitation of all the dynamics of the system. This involved the application of random binary signals to the system inputs with white noise added to them and filtering of the target values. To avoid the effects of noise in generalisation, the input and output data from the real system were generated by applying random binary signals with Gaussian white noise added to them to both the pump and the valve, and the target values where filtered. The sampling interval was 0.1 s. Six validation tests were carried out to check the performance of the neural network model, i.e. the network was simulated with input–output data other than those used for training. The sum squared error between the network output and the plant actual response was calculated each time. The results were very satisfactory and proved that neural networks can approximate non-linear dynamic systems and that can be a valuable tool in control applications, especially in modelling of complex non-linear energy systems. References
(a) the selection of the architecture of the neural network, (b) the implementation of the Levenberg–Marquardt backpropagation in MATLAB, (c) the development of virtual instruments in LABVIEW for data collection and monitoring of the heating system and (d) the choice of the excitation method for the generation of maximally informative data for the network. Analysis of the dynamic response was performed and the step response characteristics of flow and pressure of the heating system were obtained in order to understand its operation and to obtain the genetic dynamic characteristics and the type of non-linearity of the processes involved. By applying a set of different steps into the system, the values of the time constant and the dead-time were found to vary because of the non-linearities present in the system which were mainly due to the flow of water trough the pipes and the differential pressures this was causing. Calibration tests were also performed for the pressure and flow meter circuits. In the development of the neural model, there were a number of issues that needed consideration such as the network topology, training strategy and validation. It was found that a two-layer
[1] G.C. Bakos, Technical Report WP1 “Review of current policy strategies and promotion schemes for RUE & RES in various countries and regions”. ALTENER2002-094, May–December 2003. [2] G.C. Bakos, A. Spirou, N.F. Tsagas, Energy management method for fuel saving in central heating installations, Energy and Buildings 29 (1999) 135–139. [3] G.C. Bakos, Insulation protection studies for energy saving in residential and tertiary section, Energy and Buildings 31 (2000) 251–259. [4] European Commission, Directorate XVII, Retrofitting of Metering and Control Technology for Heating Systems in Residential Buildings, Programme THERMIE, 1998. [5] S.A. Kalogirou, S. Panteliou, A. Dentsoras, Artificial neural networks used for the performance prediction of a thermosyphon solar water-heater, Renewable Energy 18 (1999) 87–99. [6] S.A. Kalogirou, Applications of artificial neural networks in energy systems – a review, Energy Conversion & Management 40 (1999) 1073–1087. [7] S. Kalogirou, M. Eftekhari, D. Pinnock, Artificial neural networks used for the prediction of air flow in a single-sided naturally ventilated test room, Building Services Engineering Research and Technology Journal 22 (2) (2001) 83–93. [8] S. Kalogirou, M. Eftekhari, L. Marjanovic, Predicting the pressure coefficients in a naturally ventilated test room using artificial neural networks, Building and Environment 38 (2003) 399–407. [9] S. Kalogirou, M. Bojic, Artificial neural networks for the prediction of the energy consumption of a passive solar building, Energy 25 (2000) 479–491. [10] G. Schwarzenbach, K.F. Gill, System Modelling and Control, 3rd ed., Edward Arnold, 1995, ISBN 0-340-54379-5.
Contents lists available at SciVerse ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Modelling of small scale central heating installation using artificial neural networks aiming at low electric energy consumption G.C. Bakos ∗ , A. Sismanis Democritus University of Thrace, Department of Electrical and Computer Engineering, Laboratory of Energy Economics, 67 100 Xanthi, Greece
a r t i c l e
i n f o
Article history: Received 19 December 2012 Accepted 21 December 2012 Keywords: Artificial neural networks Non-linear energy systems Central heating installation Low electric energy consumption
a b s t r a c t Artificial neural networks (ANNs) used to control the operation of energy systems is an important field of research. This paper deals with the use of ANNs as a technique of modelling real non-linear energy systems such as the flow and pressure processes related to pump and valve input voltages of a small scale central heating system aiming at low electric energy consumption. The system is located in the Energy Economics Laboratory of Democritus University of Thrace in Greece and its operational parameters were accurately captured using a backpropagation neural network. The approach described in this paper has the advantages of computational speed, low cost for feasibility and ease of design by operators. © 2013 Elsevier B.V. All rights reserved.
1. Introduction In 1995, the Greek Ministry of Environment, Urban Planning and Public Works prepared an Action Plan, entitled “Energy 2001”, aiming at promoting the application of energy-efficiency technologies, in the building sector. The Action Plan was prepared in order to define specific measures for the reduction of greenhouse gas emissions in buildings, in accordance with the “National Action Plan for the Abatement of CO2 and Other Greenhouse Gases”. Following official adoption of the Action Plan by the Greek Government, “Energy 2001” was further reinforced by the enactment of Ministerial Decree (MD) 21475/98, which incorporated the provisions of Council Directive 93/76/EC (SAVE Directive) for the stabilisation of CO2 emissions and the efficient use of energy in buildings [1]. Space air-conditioning dominates the energy consumption in residential and public building sector [2–4]. In Greece, the largest percentage of buildings (old and new) is using the classic oil-based central heating installation with water as heat transfer agent. The effective operation control of these central heating installations, based on the monitoring of different operational and performance parameters, leads to substantial energy saving reducing simultaneously the environmental pollution and the need for further capital investment in power plants construction. The use of ANNs in energy systems can be viewed as a natural step in the evolution of control methodology. This is mainly due to the fact that ANNs have good approximation capabilities and offer additional advantages such as short development and fast
∗ Corresponding author. Tel.: +30 25410 79725; fax: +30 25410 79734. E-mail address: [email protected] (G.C. Bakos). 0378-7788/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.enbuild.2012.12.018
processing times [5]. A detailed description of various applications of ANNs in energy systems is provided by Kalogirou [6]. In particular, ANN applications to building sector have attracted considerable attention from the scientific community [7–9]. Many different types of neural networks are available. Feedforward Multilayer (MLP) networks, where the inputs are fed forward through the layers to the output, have been applied in system identification problems. Normal use of an MLP network involves training the network on a set of data obtained from the installation to be controlled. The learning rule for feedforward MLP networks is called the ‘Generalised Delta rule’ or the ‘Backpropagation rule’. The backpropagation training algorithm is an iterative gradient algorithm that attempts to minimise the mean square error between the actual network output and the desired one, so that the network input–output relationship best approximates the energy system data. The model structure needs to have sufficient representation ability to enable underlying system characteristics to be approximated with an acceptable accuracy and in many cases the model needs to retain simplicity. Also the input signal to the energy system used for the generation of data must be carefully chosen so that it excites all the dynamics of the process to be modelled and generate cause and effect data which are maximally informative. Validation tests are necessary to be carried out in order to check the performance and accuracy of the developed NN model. 2. Description of the small scale central heating installation In this paper, the small scale central heating installation to be modelled is operating in the premises of the Laboratory of Energy Economics of Democritus University of Thrace in Xanthi – Northern
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Photo 2. View of radiator–ventilator system.
1. Controlling the flow and pressure using the control valve. 2. Controlling the flow and pressure using the pump. 3. Controlling the temperature using the heater.
Photo 1. Small scale central heating installation.
Greece. The block diagram of the experimental setup installation and its physical representation are shown in Fig. 1 and in Photo 1, respectively. The laboratory central heating system can operate as closed circuit water system. The total capacity of the system is approximately 22 l. There are 6 m of 22 mm piping and a small amount of 15 mm having a total capacity of 3 l. The pump is capable of delivering up to 45 l/min; however the system will impose restrictions on this. Water is delivered from the pump via the heater to the radiator. Forced convection through the radiator results in heat loss. Initial temperature measured by the probe will be the room temperature. When heating is started this temperature will rise and equilibrium will eventually be reached between the radiator and room temperature through heat loss, and the system temperature. This operating point can be controlled by:
The heating system is used to heat a room, situated inside the laboratory premises, constructed from compound polystyrene slates with dimensions 3.00 m × 3.00 m × 3.00 m. The radiator–ventilator system used inside the room is shown in Photo 2. The presentation of the experimental results on a PC Intel Pentium and the time interval of measurement storage can be controlled through the developed LABVIEW software. The developed data acquisition system (Photo 3) was based on two AdvanTech cards (an A/D input card PCI-1714 which can accept up to 32 analogue inputs and a D/A output card with 8 output channels). Calibration of the measurement equipment was necessary in order to capture the relationships between the two variables (flow and pressure) and the outputs of the meter circuits. 3. System representation approach The model structure needs to have sufficient representation ability to enable the underlying system characteristics to be approximated with an acceptable accuracy and in many cases the model also needs to retain simplicity.
Fig. 1. Block diagram of the small scale central heating system.
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G.C. Bakos, A. Sismanis / Energy and Buildings 62 (2013) 126–132
the pump input voltage and the mean value of output voltage was calculated for the following three valve positions (Figs. 2 and 3): (a) valve fully open (Vin = 10 V), (b) valve half open (Vin = 5 V) and (c) valve almost closed (Vin = 1 V). The way the position of the control valve affects the flow and pressure in the system was found by carrying out the following experiments. Keeping the pump operating at a fixed speed by applying constant input voltages to the pump interface circuit, the input voltage to the control valve was varied from 1 V (valve almost closed) up to 10 V (valve fully open) in steps of 1 V. The corresponding output voltage readings from the interface circuits were recorded. The procedure was repeated two times, once for increasing and once for decreasing the control valve input voltage and the mean value of output voltage was calculated for the following three pump operating voltages (Figs. 4 and 5):
Photo 3. View of developed Data Acquisition Interface.
3.1. Dynamic response analysis In order to find out how the input voltage to the pump affects the flow and pressure in the system, the following experiments were carried out. Keeping the valve at a fixed position by applying constant voltages to the E/P transducer, the input voltage to the pump was varied from 0 V (pump at standstill) up to 5 V (pump operating at max speed) in steps of 0.5 V. The corresponding output voltage readings from the interface circuits were recorded. The procedure was repeated two times, once for increasing and once for decreasing
(a) pump Vin = 1 V, (b) pump Vin = 2.5 V and (c) pump Vin = 5 V. Step response testing of the flow and pressure in the laboratory central heating system was obtained using a set of step voltage inputs to the pump and the valve in order to obtain a general idea of the genetic dynamic characteristics of the two processes and also the type of non-linearity of the system. Simple observation of
30 VALVE Vin=10V
25
VALVE Vin=5V
Flow (Lit/min).
VALVE Vin=0V
20 15 10 5 0 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Pump input voltage (Volts).
Fig. 2. Variations of flow due to different power inputs to the pump for fixed control valve positions.
20 Valve Vin=1V Valve 1/2 open
Pressure (lb/sq.in).
15
Valve Vin=10V
10
5
0 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Pump input voltage (Volts). Fig. 3. Variations of pressure due to different power inputs to the pump for fixed control valve positions.
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Fig. 4. Variations of flow due to different control valve positions for fixed pump speeds.
20 PUMP Vin=5V
18
PUMP Vin=2.5V
Pressure (lb/sq.in).
16
PUMP Vin=1V
14 12 10 8 6 4 2 0 0
1
2
3
4
5
6
7
8
9
10
11
Valve input voltages (Volts). Fig. 5. Variations of pressure due to different control valve positions for fixed pump speeds.
Figs. 2–5 showed that the system was not oscillatory. By simple measurements the order of magnitude of the dominant time constant and the dead-time were obtained (Table 1). As it was expected these values were not constant due to the non-linearities present in the laboratory system. 3.2. System identification Pseudo Random Binary Sequence (PRBS) is a commonly used and easily generated input signal that is frequently the preferred choice of test input signal in identification experiments. These are signals which can take on only two possible states (+˛ and −˛). The state can change only at discrete intervals of time t. The change occurs in a deterministic pseudo random manner and the sequence is periodic with period T = Nt, where N is an integer. A PRBS input is a persistently exciting signal which excites all dynamics of the process which a constant input signal fails to do, and generates far more cause and effect data which provide information about the true dynamics of the system to be modelled.
The interval of PRBS must be carefully selected for good identification. Not too long, because transient dynamic information will be lost as process dynamics will reach steady state values between PRBS changes and the output will be seen to change from one operating level to the next. Not too short, otherwise the process output will not have had sufficient chance to change in response and the resulting small output changes will be masked by noise resolution effects on ADC [10]. A rule of thumb for the choice of the PRBS interval is about ¼ of the dominant system time constant. In this work the update interval of the PRBS was set to 0.75 s since the dominant time constants of both the flow and pressure responses to pump step inputs was found to be 2.3 s. 3.3. Noise effects In order to verify that injecting artificial noise (Jitter) into the inputs during training is one of several ways to improve generalisation, the following experiment was carried out in MATLAB. A simple second order system was simulated in SIMULINK to generate
Table 1 Time constant and dead time measurements. Step inputs
Pump step 0–5 V when valve ¼ open Pump step 0–5 V when valve ½ open Pump step 0–5 V when valve ¾ open Pump step 0–5 V when valve fully open Pump step 0–2.5 V when valve ¼ open Pump step 0–2.5 V when valve ½ open Pump step 0–2.5 V when valve ¾ open Pump step 0–2.5 V when valve fully open
Flow
Pressure
Time constant (s)
Dead time (s)
Time constant (s)
Dead time (s)
0.8 1.8 1.8 1.0 2.1 1.5 1.3 1.4
0.9 0.8 0.8 0.8 0.5 0.7 0.4 0.7
2.2 2.2 2.1 2.3 1.3 1.3 1.1 1.5
1 1.4 1.3 1.1 1.0 1.1 1.0 0.9
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Fig. 6. The two-input–two-output model.
training and validation data for a neural network. Two training sets were obtained using two different input signals: a Square input and a Square input with White Noise added to it. The square inputs had an amplitude of 5 V and a frequency of 0.015 Hz and the standard deviation of the White noise was 0.1. After the training, validation tests were carried out to check the quality of each of the two models obtained, using a sinusoidal and a random input of amplitude 5 V and frequency of 0.015 Hz, and the sum squared error was calculated in each case. The network that was used had the typical two-layer architecture used for function approximation. It had a hidden layer of 5 sigmoidal neurons (in this case tan-sigmoid) neurons, which receive directly and then broadcast their outputs to a layer of 1 linear neuron that computes the network output. As it was expected the network gave a far better model when it was trained using the data obtained from the simulation using a square input together with white noise. In this work the White noise standard deviation used was 0.05. The filter was of type lowpass of order 10 and with low cutoff frequency of 2.5 Hz in order to satisfy the requirement 0 ≤ low cutoff frequency ≤ 0.5 sampling frequency (10 Hz). 4. Neural network model The objective was to develop a neural network and train it using data from the central heating system in order to obtain the model of the process. This model had two outputs, the flow and pressure voltage readings in the system. The reason temperature was not used as an output in the model was that its time constant was approximately = 15 min and that would result in a very large sampling period and thus the data collection experiment would become a very time consuming process. The model outputs were the valve and pump input voltages. The heater input variable was not used as an input to the neural model since it was proven that flow and pressure were unaffected by the temperature of the system. The input–output dynamics of the real system processes can be characterised in the continuous-time domain by the general NARX (Non-linear, Auto-Regressive, eXogenous) model defined by:
vector valued non-linear function the neural network was used to implement. The values of both na and nb were set to be 2. Thus the two first columns of the input and output vector to the neural network have the following matrix form in the discrete-time domain:
⎡
y1(k−1) y1(k−2) y2(k−1) y2(k−2)
⎢ ⎢ ⎢ ⎢ Yk = ⎢ ⎢ u1(k−L/Ts −1) ⎢ ⎢ u1(k−L/Ts −2) ⎣u 2(k−L/Ts −1)
u2(k−L/Ts −2)
⎤
y1(k) y1(k−1) ⎥ ⎥ y2(k) ⎥ y2(k−1) ⎥ ⎥ u1(k−L/Ts ) ⎥ ⎥ u1(k−L/Ts −1) ⎥ u2(k−L/Ts ) ⎦ u2(k−L/Ts −1)
Uk =
u1(k) u2(k)
u1(k+1) u2(k+1)
If Ts is the sampling period and N is the number of input–output data pairs then the total number of columns of these vectors will be N − L/Ts − 2. The two-input–two-output model to be developed is given in Fig. 6. The sampling interval set in the LABVIEW program developed for the collection of data from central heating system was 0.1 s. It was not necessary to sample more quickly since the process will not respond to high frequency control signals. Also rapid sampling increases quantisation noise effects and numerical problems with the accuracy of calculations may occur. The neural network can learn significant information concerning the plant dynamics and provide an accurate model by mapping a particular set of inputs to a set of desired outputs. The delay of the system is of no importance when selecting data to form the input and target vector for the NN since the relationship between the input and the output is contained in all set of input–output pairs. The value of delay used in the MATLAB program developed to form the input and target vectors for the NN was set to 1. In the development of this model, there were a number of issues that needed consideration, such as the network topology, network training and validation. 4.1. Neural network topology
Y (t) = F[(Y (t − 1), . . . , Y (t − na ), U(t − L), . . . , U(t − L − nb )] + E(t) where Y(t) is the output vector; U(t) is the input vector; E(t) is the noise exogenous input vector; L is the process deadtime; na and nb are the number of past output and input data used; F(·) is the
Since two past inputs and two past outputs of the process were used as inputs to the neural network, the back-propagation network had to have 8 input nodes and 2 output nodes. One hidden layer was used which had 4 hidden neurons with tansigmoid
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Training data set. 10 9
- PRBS input to valve
Amplitude (Volts)
8 7
- PRBS input to pump
6 5
- Flow response
4 3
- Pressure response
2 1 0
0
20
40
60
80
100
Time (sec) Fig. 7. The training data set.
10
Amplitude (Volts)
9
- PRBS input to valve
8 7
- PRBS input to pump
6 5 4
- Flow response
3 2
- Pressure response
1 0
0
20
40
60
80
100
Time (sec) Fig. 8. The validation data set.
activation function. In the output layer the linear activation function was used.
1. A random binary signal with levels 2–3 V, when applied to the pump, and 2–8 V, when applied to the valve. 2. A random signal with an amplitude varying within the operating levels of the pump and the valve.
4.2. Neural network training The neural network was trained using the Levenberg–Marquardt back-propagation algorithm. The training data set (Fig. 7), containing 1000 pairs of input–output values, was generated by the application of a random binary signal in the both inputs with Gaussian white noise added to each one of them and filtering of the data obtained from the output. The lower and upper levels of the input signals applied to the pump and valve were 2–3 V and 2–8 V, respectively, at an update interval of 0.75 s.
The update interval of each of the input signal was 1 s. Each of the signals was applied to:
1. The pump whilst the valve was ½ open. 2. The valve whilst the pump was operating with Vin = 2.5 V. 3. Both the pump and the valve.
Thus six validation data sets were generated which were applied to the trained neural network. The sum squared errors, which were calculated in each case, are given in Table 2. Fig. 8 shows the third validation test and Figs. 9 and 10 present the corresponding sum squared errors.
4.3. Model validation tests The neural network model was validated using two test signals that had not been used in training. These were: 10
Amplitude (Lit/min)
9
- Heating system
8 7 6
- NN model
5 4 3 2 1 0
0
200
400
600
800
1000
Data points per sec Fig. 9. The neural network response compared to the system’s actual response concerning the flow process (sum squared error = 47 × 10−3 ).
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Amplitude (lb/sq.in)
18
- Heating system
16 14 12
- NN model
10 8 6 4 2 0
0
200
400
600
800
1000
Data points per sec Fig. 10. The neural networks response compared to the system’s actual response concerning the pressure process (sum squared error = 62 × 10−3 ). Table 2 Sum squared errors corresponding to six validation data sets applied to the NN. Test
Sum squared Flow response
Errors Pressure response
1 2 3 4 5 6
0.8 × 10−3 0.3237 × 10−3 47 × 10−3 0.6312 × 10−3 1.2 × 10−3 0.66 × 10−3
14.6 × 10−3 0.2389 × 10−3 62 × 10−3 0.5209 × 10−3 16.7 × 10−3 0.629 × 10−3
It can be seen that the neural network was successful in approximating the flow and pressure processes in the laboratory central heating system related to the pump and valve input voltages. 5. Summary and conclusions The purpose of this project was to investigate the use of neural networks as a technique of modelling non-linear energy systems and to apply this technique in a real laboratory system (small scale central heating system). The main objective was to develop a neural network and train it in order to approximate the flow and pressure processes related to the pump and valve input voltages. Critical issues were:
back-propagation network with 4 tansigmoid neurons in the hidden layer and a linear output layer was a successful network design. The network was trained using the Levenberg–Marquardt backpropagation algorithm. Three different methods for generating data were tested. The method that produced the best training sets for the neural network was the one that caused reduction of the effects of noise in generalisation and excitation of all the dynamics of the system. This involved the application of random binary signals to the system inputs with white noise added to them and filtering of the target values. To avoid the effects of noise in generalisation, the input and output data from the real system were generated by applying random binary signals with Gaussian white noise added to them to both the pump and the valve, and the target values where filtered. The sampling interval was 0.1 s. Six validation tests were carried out to check the performance of the neural network model, i.e. the network was simulated with input–output data other than those used for training. The sum squared error between the network output and the plant actual response was calculated each time. The results were very satisfactory and proved that neural networks can approximate non-linear dynamic systems and that can be a valuable tool in control applications, especially in modelling of complex non-linear energy systems. References
(a) the selection of the architecture of the neural network, (b) the implementation of the Levenberg–Marquardt backpropagation in MATLAB, (c) the development of virtual instruments in LABVIEW for data collection and monitoring of the heating system and (d) the choice of the excitation method for the generation of maximally informative data for the network. Analysis of the dynamic response was performed and the step response characteristics of flow and pressure of the heating system were obtained in order to understand its operation and to obtain the genetic dynamic characteristics and the type of non-linearity of the processes involved. By applying a set of different steps into the system, the values of the time constant and the dead-time were found to vary because of the non-linearities present in the system which were mainly due to the flow of water trough the pipes and the differential pressures this was causing. Calibration tests were also performed for the pressure and flow meter circuits. In the development of the neural model, there were a number of issues that needed consideration such as the network topology, training strategy and validation. It was found that a two-layer
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