Use of neural networks and expert systems to control a gas/solidsorption chilling machine

A. Palau, E. Velo, L. Puigjaner

Department of Chemical Engineering, Universitat PoliteÁcnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain

Abstract

This works focuses on using neural networks and expert systems to control a gas/solid sorption chilling machine. In such

systems, the cold production changes cyclically with time due to the batchwise operation of the gas/solid reactors. The accurate

simulation of the dynamic performance of the chilling machine has proven to be dif®cult for standard computers when using

deterministic models. Additionally, some model parameters dynamically change with the reaction advancement. A new

modelling approach is presented here to simulate the performance of such systems using neural networks. The backpropagation

learning rule and the sigmoid transfer function have been applied in feedforward, full connected, single hidden layer neural

networks. Overall control of this system is divided in three blocks: control of the machine stages, prediction of the machine

performance and fault diagnosis. q 1998 Published by Elsevier Science Ltd and IIR. All rights reserved.

Keywords: Absorption; Refrigeration; Chemical reaction; Expert systems

Utilisation des reÂseaux neuronaux et des systeÁmes experts pourreÂguler une machine frigori®que aÁ sorption gaz/solide

ResumeÂ

Ce travail traite de l'usage des reÂseaux neuronaux et des systeÁmes experts pour reÂguler une machine frigori®que aÁ sorption

gaz/solide. Dans ce type de systeÁme, la production de froid varie dans le temps de facËon cyclique, du fait du fonctionnement

discontinu des reÂacteurs gaz/solide. La simulation preÂcise de la performance dynamique de la machine frigori®que s'est reÂveÂleÂe

dif®cile pour un ordinateur normal en cas d'utilisation de modeÁles deÂterministes. De plus, certains parameÁtres du modeÁle

varient au fur et aÁ mesure de la reÂaction. On preÂsente ici une nouvelle approche de modeÂlisation pour simuler la performance

de tels systeÁmes utilisant les reÂseaux neuronaux. On applique la reÂgle d'apprentissage par reÂtropropagation et la fonction de

transfert sigmoõÈde dans des reÂseaux neuronaux aÁ commande preÂdictive, entieÁrement connecteÂs aÁ couche cacheÂe simple. Le

systeÁme est divise en trois parties: reÂgulation des eÂtages des machines, preÂvision de la performance de la machine et diagnostic

des deÂfauts. q 1998 Published by Elsevier Science Ltd and IIR. All rights reserved.

Mots cleÂs: Absorption; ReÂfrigeÂration; ReÂaction chimique; SysteÁme expert

Nomenclature

u j Bias for neurone j

wij Weight between neurone i and neurone j

xi Output for neurone i

Sj Weighted sum othe input for neurone j

E Overall network error

Ep Neural net output error for input pattern p

dj Desired neural net output for neurone j

aj Neural net output for neurone j

International Journal of Refrigeration 22 (1999) 59±66

0140-7007/99/$ - see front matter q 1998 Published by Elsevier Science Ltd and IIR. All rights reserved.

PII: S0140-7007(97)00046-7

1. Introduction

Refrigeration and air conditioning is one of the industrial

applications ®elds forced to introduce technology improve-

ments due to environmental requirements. Chemical chil-

ling machines and chemical heat pumps offer an attractive

alternative to classical compression±expansion engines that

use refrigerants depleting the ozone layer. These processes

also allow the recovery of energy from residual heat

streams. Liquid/gas absorption processes for industrial and

domestic uses are generating increasing interest throughout

the world. Such systems are well understood and are widely

applied in some industrial sectors. As they give a constant

chilling power for a given set of operating conditions the

system control is focused towards maximising the system

ef®ciency. Some studies focus on such kind of control [1].

Other alternatives to the classical refrigeration machines

are the gas/solid systems. Reversible solid/gas reactions are

well suited to processes such as chemical heat pumps and

energy storage systems. These kinds of processes have now

reached a stage where it is possible to manufacture pre-

industrial prototypes [2±6]. A large number of solid/gas

couples [3,5] can be used, making it possible to produce

energy over a wide range of temperatures and thus ensure

the extensive use of such processes. Unreacted-core models

have been formulated [7±9] in the case of reversible solid±

gas reactions and applied to the interpretation of experimen-

tal results obtained by microcalorimetry for the MnCl2±NH3

couple. The solution of heat and mass balance equations

applied to a reactive mixture used in a chemical heat

pump has been widely used to simulate the transient beha-

viour of such systems. This approach has given good results

for speci®c reactor geometries and reacting-bed thicknesses

where heat and mass transfer limitations are negligible

compared to the reaction rate [7,10].

Neural networks [11] are one of the arti®cial intelligence

concepts that have proved to be useful for dynamic model-

ling and control of chemical processes [12] due to their

ability to handle non-linear relationships. They can solve

problems much faster than other approaches. Additionally,

neural nets have the ability to `learn'. Rather than program-

ming these nets, one presents them with a series of exam-

ples. From these examples the net learns the governing

relationships involved in the training database. The system

is considered as a black box, and it is unnecessary to know

the internal behaviour, so the nets may offer a cost-effective

approach for modelling chemical process systems.

Control concepts applied to gas/solid chilling machines

must be different from those used in compression±

expansion units of gas/liquid systems. The main difference

is due to the batchwise operation of the gas/solid reactors.

Existing prototypes generally are not automatically oper-

ated, so more advancement on the controllability of these

systems is needed to implement for further industrial appli-

cations. This work aims to present the application of

concepts related to arti®cial intelligence, like neural

networks and expert systems, for the control of a gas/solid

chilling machine.

An expert system is regarded as the embodiment within a

computer of a knowledge-based component, from an expert

skill, in such form that the system can offer intelligent

advice or take an intelligent decision about processing func-

tion. Detailed information about expert systems can be

found widely on arti®cial intelligence literature.

Another important issue for the industrial application of

gas/solid chilling machines is to detect malfunction of the

system. Additionally, because of its complexity, it is impor-

tant to let computers continuously trace the overall system

searching the malfunctions better than leave this task to

human operators. Usually expert systems have been devel-

oped to do this job, with a previous work in acquiring all the

system knowledge from an expert. In this work we will

study the use of neural nets as an alternative of the expert

systems for the fault diagnosis.

As it has been previously said, global control for this

machine has been divided in three blocks. Stage control

has been implemented with an expert system that uses

neural networks to take stage change decisions. An expert

system has been chosen as a stage control tool to demon-

strate its capabilities when control actions must be taken

over the system. In fact, this is a ®rst step to implement

expert systems in more complex situations involving several

chilling machines producing cold with scheduling decision

tasks. Neural networks were, also, used as an alternative

approach to fault diagnosis of gas/solid chilling machines.

Their main advantage is that once we have created them we

need very few amount of memory in the computer to store

the information. Also this approach allows to have a parallel

processing of the faults of our system, instead of checking

the faults one by one as does an expert system. The main

disadvantage is that if we change some of the single symp-

toms, faults or their relationships we have to train again the

neural networks.

2. The gas/solid chilling machine

This work focuses on gas±solid sorption machines based

on the absorption of ammonia by a solid matrix [7,13]. A

®xed bed reactor containing a chlorine salt absorbs ammo-

nia at low pressure from an evaporator, which takes up heat

at low temperature from a given environment. Once the

reactor is exhausted, it must be regenerated by desorbing

the chemically linked gas. This step consumes heat at high

temperature from an external source. A thermodynamic

cycle can be completed by condensing the gas in a conden-

ser at high pressure and moderate temperature and then

passing it through an expansion valve into the evaporator.

For a single reactor, alternatively connected to an evaporator

and a condenser, the cold production, which is related to the

reaction rate is not uniform and discontinuous over a

complete cycle.

A. Palau et al. / International Journal of Refrigeration 22 (1999) 59±6660

In our case, two different reactors containing different

salts are used in order to allow simultaneously a more

continuous cold production and internal heat recovery [5].

Since these reactors operate at different temperature levels,

the released heat from the absorption step inside the high-

temperature reactor (R2) can be used to regenerate the

reactor that runs at the medium temperature level (R1)

(see Fig. 1). For a known amount of salt and at a given

conversion, the heat absorbed in the evaporator may be

easily calculated.

3. Neural networks

The net consists of processing neurons (circles) and infor-

mation ¯ow channels between the neurons, called intercon-

nects. These interconnects have speci®c weights that re-

enforces or inhibits the connections. If the information

¯ows from one layer to the next layer it is called feedfor-

ward neural network. The boxes are input layer neurons that

simply store inputs to the net. Each processing neurone

typically has a small amount of local memory and it carries

out a local computation which converts inputs to the

neurone to outputs. This computation is called the transfer

function of the neuron. The transfer function can be linear or

non linear and consists of algebraic or differential equations.

Fig. 2 presents an example of a typical neural net.

The backpropagation training algorithm has been used

successfully in training the neural nets with one input

layer, one hidden layer and one output layer, for wide appli-

cations. The backpropagation algorithm adjusts the weights

in feedforward neural nets consisting of several layers, and

an output layer. The goal is to reach the network to associate

speci®c output states, called target states, to each of several

input states. Having learnt the fundamental relationships

between inputs and outputs, the neural nets can produce

the correct output for a new previously unseen input.

The governing equations for a backpropagation net are

brie¯y reviewed here. The inputs and outputs to the net have

to be scaled into the range 0±1. The neurons in the input

layer simply store the scaled input values. The hidden and

the output layer neurons each carry out two calculations. To

explain these calculations consider the general jth element

shown in Fig. 3 and assume that this neurone is in the hidden

A. Palau et al. / International Journal of Refrigeration 22 (1999) 59±66 61

Fig. 1. Gas-solid chilling machine with internal heat recovery. (a)

stage 1: R1 in absorption, R2 in desorption. (b) stage 2: R1 in

desorption, R2 in absorption.

Fig. 1. Machine frigori®que gaz±solide aÁ reÂcupeÂration de chaleur

interne. (a) eÂtage 1: R1 en absorption, R2 en deÂsorption. (b) eÂtage

2: R1 en deÂsorption, R2 en absorption.

Fig. 2. Neural network architecture.

Fig. 2. Architecture du reÂseau neuronal.

layer. The inputs to this neurone consist of an N-dimensional

vector x and a bias (threshold value, uj) whose value is 1.

Each of the inputs has a weight wij associated with it. The

®rst calculation within the neurone j consists in calculating

the weighted sum Sj of the input as:

Sj �XNi�1

wijxi 1 wN11; juj �1�

Next the output xj of the neurone j is calculated as the

sigmoid function of Sj as:

xj � s�Sj� �2�where for a generic neurone, assuming z � Sj

s�z� � 1

1 1 e2z�3�

Once the outputs of the hidden layer have been calculated,

they are passed to the output layer. The output layer carries

out the same calculations, except that the input vector x is

replaced by the hidden layer output vector and the weights

in the Eq. (1) are those between the hidden and output layer

wjk.

The objective is to minimise the overall network error

E �X

p

Ep �4�

for all input patterns p in the training set. In practice, this is

often performed in an iterative fashion by minimising the

error over the n output units after presenting each pattern p:

Ep � 1

2

Xj

�dj 2 aj�2p �5�

where dj is the desired output and aj is the neural net output.

A backpropagation net learns by making changes in its

weights. These changes are de®ned as proportional to the

negative derivative of the error with respect the weight:

Dwjk � 2gdEp

dwjk

�6�

4. Modelling the chilling sorption machine using

conservation equations

A classical approach to calculate a cycle under given

operating conditions is to integrate the set of differential

equations derived for the gas/solid reactor coupled to the

condenser or the evaporator [7±10,12±18]. This way may

be dif®cult for a gas/solid reactor where simultaneous mass

and heat transfer processes coupled to the gas/solid kinetics

take place in a non-isotropic solid. The system of equations

can only be solved quickly by standard computers when

using relatively simple models. Nevertheless, the assump-

tions made to derive such models, i.e. neglecting heat or

mass transfer limitations [7], lead to an inaccurate prediction

of the machine performance. Additionally, some model

parameters, i.e. the solid porosity or the solid-to-wall heat

transfer coef®cient, change with the reaction advancement.

In a previous work, Hermes et al. [14] developed a

computer program orientated to the simulation of the

dynamic behaviour of such systems (see Fig. 4). It is

shown in Fig. 4 that the instantaneous cold production

(power taken in the evaporator) is high during the ®rst

step and very low during the internal recovery step.

A. Palau et al. / International Journal of Refrigeration 22 (1999) 59±6662

Fig. 3. Single neurone.

Fig. 3. Neurone simple.

Fig. 4. Released power at the condenser and at the evaporator (after

Hermes et al. [13]).

Fig. 4. Puissance libeÂreÂe au condenseur et aÁ l'eÂvaporateur (d'apreÁs

HermeÁs et al. [13]).

Additionally, the time consumed to complete the second

step is much longer than the one for the ®rst step.

5. Modelling the chilling machine with neural networks

In this work, the backpropagation training algorithm is

considered, which has been used successfully in training

the neural nets with one input layer, one hidden layer and

one output layer, for wide applications. The backpropaga-

tion algorithm adjusts the weights in feedforward neural nets

consisting of several layers, and an output layer. The goal to

reach is to have the network associate speci®c output states,

called targets states, to each of several input states. Once the

neural network has learned the fundamental relationships

between inputs and outputs, it can produce the correct

output for a new and previously unseen input.

Four neural networks have been created that could prog-

nosticate the mean cooling power and the cycle time for the

two main stages under different operating conditions. For

feedforward control purposes, it is necessary to predict the

machine operating conditions which will give a desired

mean power under given environment temperatures. There-

fore, one additional neural network with this functionality

has been added.

The ®rst step was to ®nd the relevant inputs to the neural

networks for each output and to prepare different training

patterns and test patterns. From this work it results, that the

relevant inputs are the environment temperature and the

external heat source temperature. The second step was to

train these neural networks. The number of hidden neurones

in the hidden layer, the RMS error and the learning rate are

shown on Table 1.

Due to the lack of experimental data, training patterns

were obtained by using a simulation program developed

by Hermes et al. [14] which supplies the transient perfor-

mance data of a given machine. The mean chilling power

was calculated from the off-line analysis of the simulated

data. Further work contemplates extended validation of the

method by using experimental data from a chilling machine

prototype, already designed and being built.

The ®ve neural nets (see Table 1) were trained with 150

different input±output patterns. The range of the input

values for nets 1±4 had been:

1. Environment temperature (EnvT): 278±303 K

2. External source temperature (ExtT): 573±608 K

3. Testing number of patterns: 150

Fig. 5 shows the comparison between the test data and the

trained neural net output for the second neural net (NN),

which predicts the mean chilling power produced in the

evaporator during stage 2 (internal heat recovery). In order

to get the best topology we have used an heuristic approach

by selecting several neural net topologies and comparing

their results. As for overlearning effects in our training,

we have not studied. It will be examined in future work

with real data. As can be seen, there is a good agreement

between test data and the output of the net after it has been

trained. Then, the network is able to learn and can be used to

predict the mean power produced by the chilling machine

under different external and environment temperatures.

Obviously the output of these neural nets is quite instan-

taneous while the computer program simulation takes an

A. Palau et al. / International Journal of Refrigeration 22 (1999) 59±66 63

Table 1

Neural network functionality and RMS error

Tableau 1.

Fonctionnement du reÂseau neuronal et erreur RMS

Neural net (Output) NN number RMS error Learning rate Neurons in hidden layer

Mean power stage 1 1 0.017 0.1 2

Mean power stage 2 2 0.0004 0.1 2

Time stage 1 3 0.011 0.1 2

Time stage 2 4 0.0003 0.1 2

ExtT stage 1 5 0.0004 0.1 6

Fig. 5. Neural net test set for the mean power during stage 2.

Fig. 5. Essai de reÂseau neuronal pour la puissance moyenne

pendant l'eÂtape 2.

average of 20 s to obtain the output. The computer program

has still to be validated with the real chilling-machine. If the

validation is not good we will train the neural nets using

experimental data.

6. System stage control

Instead of using a programmable automata, we have

trained several neural nets, which were then used by an

expert system application. The main objective of this expert

system is to control the stages of the chilling machine. For

the real system, it is very dif®cult to detect the end of every

stage only from the measured variables (pressure or

temperature). Therefore, the expert system uses the neural

nets 3 and 4 to predict the end time of each stage so it can

decide when to operate a set of control valves. We have

tested this control system by using the simulation program

by Hermes et al. [14]. Table 2 shows several computer runs.

A good agreement has been obtained between the results

given by the simulation program run itself and the simula-

tion program controlled by the expert system. We have

obtained good agreement (deviation , 20%) between the

simulation program run itself and the simulation program

controlled by the expert system. In the ®rst case, the simula-

tion program can decide when to operate a valve because it

predicts the reactor conversion and knows when a given

stage has been completed. In the second case, the expert

system predicts the stage time from the output of the neural

network (the reactor conversion is unknown for the expert

system) and gives to the simulation program the order to

open or close the valves.

7. Predicting the temperature of the external heat source

The temperature of the external heat source cannot be

directly predicted with the computer simulation program

because the mean cooling power is not an input of the

program, but it is an output. Then, the simulation program

must use a trial-and-error algorithm to ®nd the source

temperature, which will last several minutes. Thus, neural

net 5 will be used in further expert systems to achieve this

objective.

It is important to notice that the neural nets always give an

output for any input. Therefore, it is possible that the mean

cooling power demand may be too high or too low for a

given machine at a given environment temperature. In this

case, the neural net output will be the maximum or the

minimum value of the training set. Neural net 1 can be

used to check these events.

Table 3 shows how neural network 1 predicts that the

mean power given by a single machine will be not enough

to provide all the power needed by the chilling system. If the

environmental temperature is 278.15 K, and the needed

power is 2.1 kW, the output of the neural network 5 will

inform the control system that the required source tempera-

ture must be 608.1 K, which is the maximum allowable

temperature. Nevertheless, in this case, a single machine

will be not able to provide 2.1 kW. This is checked by neural

network 1, which will inform the control system that for an

environmental temperature of 278.15 K and a source

temperature of 608.1 K, the mean power given by a single

machine will be 1.639 kW. Then, the expert system will

conclude that another chilling machine must be connected.

When the power needed is too low, neural net 5 will give

A. Palau et al. / International Journal of Refrigeration 22 (1999) 59±6664

Table 2

Comparison of the results given by the simulation program controlled by itself and the simulation program controlled by using the neural nets

Tableau 2.

Comparaison des reÂsultats obtenus avec le programme de simulation autoreÂgule et par le programme de simulation reÂgule par les reÂseau

neuronaux

EnvT ExtT Q stage 1

HERMES

Q stage 1

EXPERT

Time stage 1

HERMES

Time stage 1

EXPERT

Q stage 2

HERMES

Q stage 2

EXPERT

Time stage 2

HERMES

Time stage 2

EXPERT

278.15 573.15 2.08 2.372 138.4 136.9 0.27 0.247 1419.1 1687.7

278.15 608.15 2.14 2.358 190.7 182.7 0.23 0.208 1653.4 1759.7

303.15 608.15 1.54 1.728 130.1 130.0 0.06 0.060 6429.2 6491.7

308.15 605.17 1.45 1.324 153.4 153.0 0.05 0.050 7410.2 6905.6

290.11 576.94 1.81 1.942 133.2 132.8 0.13 0.119 2915.0 2912.6

Table 3

Use of the neural network 1 to detect the maximum output of the neural network 5

Tableau 3.

Utilisation du reÂseau neuronal 1 pour deÂtecter quand le reÂsultat donne par le reÂseau neuronal 5 est plafonneÂ

EnvT (K) Q stage 1 (needed) (kW) ExtT (neural net 5) (K) Q stage 1 (neural net 1) (kW)

278.15 2.1 608.1 1.639

295.05 1.7 608.1 1.364

the minimum temperature (573 K). Then neural net 1 can

predict that the power supplied by the set of chilling

machines will be too high, and the expert will disconnect

one of them. If only one machine is working, then the expert

system will stop it.

8. Fault diagnosis

Venkatasubramanian and Chan [19], who proposed the

use of Neural Networks on fault diagnosis, tried to evaluate

the generalising capabilities of neural networks. They

trained the neural networks with the observation vectors

(symptoms resulting from a fault) and its associated class

(the fault or malfunction). Similar to classical decision

theory, neural networks perform the classi®cation by creat-

ing decision boundaries to separate the N different pattern

classes. Neural networks were supposed to lead to novel

generalisations in future classi®cation activities involving

new or slightly modi®ed fault symptoms. In a ®rst approach

to fault diagnosis we implemented the same approach using

our fault diagnosis patterns. The result was a bad response

for simultaneous multiple faults and partial symptom

patterns.

A new approach has been developed trying to exploit the

information storage capabilities rather than the generalising

capabilities of the neural networks. Thus a neural network

was trained with all the combinations of symptom patterns,

including the partial patterns. The ®rst step to implement

this neural network was to create a ®le with the probabilities

of every single symptom for every fault. For those faults or

malfunctions with a single symptom, a 100% probability

was given to the single symptom. For those faults or

malfunctions with more than a single symptom with an

AND connection, equal parts of the total probability was

given to each symptom. For those faults or malfunctions

with more than a single symptom with an OR connection

a 100% probability was given to each single symptom.

Afterwards a whole combination of the single symptoms

was created, adding the probability of the faults for those

single symptoms that results for AND connections and

taking the higher probability for those single symptoms

that result for OR connections. The last step was to train a

neural network with this complete ®le. This neural network

has as many input layer neurons as single symptoms, and as

many output layer neurons as faults or malfunctions.

The complete combined symptoms and faults pattern ®le

contains 2k patterns, were k is the number of single symp-

toms. This can be a problem for those systems with a large

amount of single symptoms. For those cases, the fault diag-

nosis can be divided in smaller groups containing different

types of faults or different types of symptoms.

In our case we have a total of 21 single symptoms and 26

faults for the four operation stages. These single symptoms

and faults were divided in different groups: Reactor 1 in

stage 1 (12 single symptoms, nine faults), Reactor 2 in

stage 1 (nine single symptoms, eight faults), Reactor 1 and

2 in stage 2 (13 single symptoms, 11 faults). The neural nets

were created with 27 hidden layer neurons. The learning

capability of these was perfect.

The ®nal RMS error in the three neural networks created

has been less than 0.0001. So it can be considered an excel-

lent result. Also, we have no problems with over training the

neural networks because we train them with all the possible

patterns.

9. Conclusions

Neural networks and expert systems were used as an

alternative approach for modelling, control and fault diag-

nosis of gas/solid sorption chilling machines. The main

advantage of neural nets is that it is not necessary to have

a priori knowledge of the process phenomena due to their

learning capability. Using this approach to predict the cold

production of a chilling machine under different operating

conditions, can reduce the engineering effort required in the

design and control strategies. The ®nal RMS error in all

neural networks was very low. So it can be considered an

excellent result. Also, the small size of the neural nets makes

them a very fast tool, so they can be applied in real time

control systems.

The expert system used to control the stages of the chil-

ling machines gives excellent results. The time when the

expert system opens or closes the valves to begin a new

stage agrees well with the prediction make by the simulation

program, which knows the solid conversion at any time.

Using neural networks to the fault diagnosis of our system

gives excellent results. Although our approach cannot be

used for large systems, it gives better con®dence and faster

diagnosis than other approaches for small systems.

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