METHOD FOR ALARM PREDICTION

Luis Pastor Sanchez Fernandez

Center for Computing Research. Mexico City, Mexico.

Lazaro Gorostiaga Canepa

Center of Automatization, Robotics and Technologies of the Information and the Manufacture. Spain

Oleksiy Pogrebnyak

Center for Computing Research. Mexico City, Mexico.

Keywords: Alarm, prediction, supervision, trend, identification, neural networks.

Abstract: The goal of this paper is to show a predictive supervisory method for the trending of variables of

technological processes and devices. The data obtained in real time for each variable are used to estimate the

parameters of a mathematical model. This model is continuous and of first-order or second-order (critically

damped, overdamped or underdamped), all of which show time delay. An optimization algorithm is used for

estimating the parameters. Before performing the estimation, the most appropriate model is determined by

means of a backpropagation neural network (NN) previously trained. Virtual Instrumentation was used for

the method programming.

1 INTRODUCTION

The antecedents are methods for supervising

technological processes (Juricek, Seborg and

Larimore, 1998) and more specifically, the

algorithms that devices use to detect special or

abnormal conditions. These conditions will be

determined by the values taken up by their variables

in the chosen algorithm. Alarm algorithms by limits

and hysteresis may be used, but they are limited to

diagnose conditions that exist already or that are

likely to occur in a short period of time. This paper

aims at developing more detailed algorithms using

mathematical models representing the dynamics of

the processes that will be supervised. The presented

method makes it possible to predict, in short time,

possible abnormal conditions. This will give rise to

one of two possibilities. The first is a series of

preventative actions to prevent the system from

operating in such a way. The second is a series of

actions for the successful operation of the process

upon reaching the critical state that may or may not

be abnormal (as it happens with hydraulic canals

whose dynamics are complex).

The backpropagation network (NN) was chosen

due to it’s ability to successfully recognize diverse

patterns. In our case, it is used to recognize signal

patterns of first and second order dynamic systems

(Ogata, 2001) in which the dynamics of a

considerable amount of technological processes can

be represented. The methodology used consists of

estimating the parameters of the models through an

optimization algorithm (Edgar and Himmelblau,

1988). Before such parameters are estimated, the

most appropriate model is determined by means of a

NN, thus reducing the total processing time.

A broad range of mathematical techniques,

ranging from statistics to fuzzy logic, have been

used to great advantage in intelligent data analysis

(Robins, 2003).

The following transfer functions are used:

First order model:

-θs

1

Ke

Gm(s) =

Ts+1

(1)

Second order model:

336

Pastor Sanchez Fernandez L., Gorostiaga Canepa L. and Pogrebnyak O. (2005).

METHOD FOR ALARM PREDICTION.

In Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Signal Processing, Systems Modeling and

Control, pages 336-339

DOI: 10.5220/0001163203360339

Copyright

c

SciTePress

-θs

22

Ke

Gm(s) =

s/ω n+2ξ s/ω n+1

(2)

where the parameters to be estimated are:

1

T : time constant; K : gain; : natural oscillation

frequency

;

θ

: time delay.

n

w

ζ: coefficient of damping. ζ<1 (underdamped). ζ=1

(critically damped). ζ>1 (overdamped).

2 BLOCK CHART OF THE

METHOD

Figure 1 displays the simplified flow chart of a cycle

of the predictive alarm algorithm. A circular buffer

of changeable dimensions is used. This cycle begins

with the permanent storing of N last data of the

variable of the technological process or device under

supervision.

As shown in Figure 2, the instant for

recognizing and estimating the parameters of the

model representing by the points stored in the

circular buffer is determined by an algorithm of

lineal trend prediction. On predicting by lineal trend,

the behavior of the variable is considered to be that

of a straight line from the current sampling instant.

Figure 2 shows an example of a variable versus time

plot V(t) with the following parameters:

HAL: high alarm limit; v(k): current value; v(k-1):

previous value; T: sampling period. The current

sampling instant in this example is 2T.

Regarding Figure 2, it can be stated that:

() ( ) ()

V k -V k-1 LSA-V k

=

2T - T tp

(3)

Obtaining tp as:

() ( )

()

T

tp = LSA - V k

Vk-Vk-1

⎛⎞

⎟

⎜

⎡⎤

⎟

⎜

⎟

⎢⎥

⎜

⎣⎦

⎟

⎜

⎟

⎜

⎟

⎝⎠

(4)

The minimum prediction time T

mp

must be set,

such that if tp < T

mp,

then the recognition process of

the signal pattern represented by the samples stored

in the circular buffer begins.

Afterwards,

digital filtering by the moving

average filter (Oppenheim, Schafer and Buck, 1999)

is performed according to the following expression:

+M

1

Y(k) = X(k -i)

2M +1

i=-M

∑

(5)

where

M = 2 was used.

The latest data are selected if it is the time for

recognizing and estimating the parameters of the

model.

Then, a sampling

frequency conversion with a

non-integer factor combining interpolation and

decimation is performed (Oppenheim, Schafer and

Buck, 1999) which makes it possible to obtain 30

points. This is the number of input neurons of the

NN. Later, the

selection of the weights of the NN is

accomplished in accordance with the sign of the 30-

point-curve slope, since it was trained for the

patterns with a positive and negative slope. As an

output, the NN will produce the most suitable model

with its parameters estimated through an

Figure 1: Flow diagram of the predictive alarm algorithm

cycle

Instant for

recognizing

and estimating

the

p

arameters

Data circular

buffer

No

Yes

•

The latest data

are selected

• Digital filtering.

• Frequency conversion

• Selection of the

weights of the NN

Suitable model

Optimization algorithm

for the fitting of curves

(estimation of the

parameters of the model)

The curve

fitting is

good

No

Yes

•

Prediction by

means of the model

• Prediction error is

calculated (

Pe)

Prediction by

lineal trend

Pe<

ε

Yes

No

METHOD FOR ALARM PREDICTION

337

optimization algorithm for the fitting of curves

using all the selected points

. Hooke and Jeeves´s

(Hooke and Jeeves, 1961) optimization method of

direct search is used. This method returns the

minimized index. If the returned index is smaller

than a value that has been pre-established as fair,

then it is considered that the curve

fitting is good

(estimation of the parameters of the model), and the

prediction by means of the model will be made in

order to predict the time when the variable will

reach its limit value. The algorithm establishes the

value considered as fair for the optimization index

by default. The user can increase or reduce this

value considered as fair if he wants the model to

have more or less accuracy. The

prediction error is

calculated periodically. If the fitting of the model is

not good

, the prediction by lineal trend is made.

2.1 Prediction error

Whenever the prediction is made, an approximate

prediction error (

Pe) is calculated. If this error is

smaller than a pre-established value

ε (Pe<

ε

), the

prediction is continued according to the model;

otherwise, as points keep on being stored in the

circular buffer, another process for estimating

parameters is performed. \

3 NEURAL NETWORK

TRAINING PATTERNS

The selection of the NN training patterns was based

on the behavior of the dynamic responses of first-

and second-order systems to step input function,

because this is the most frequent type of disturbance.

In other cases, even though it might not strictly be an

ideal step, it can be considered as such, provided that

for instance, the time constants of the process are

relatively larger than the time constants of an

exponential signal. Figure 3 displays the responses

of critically damped second order systems, with

natural oscillation frequencies w

n

equal to 1, 0.5 and

0.25 respectively. 30 points are shown for every

curve. They have been taken up from sampling

frequencies of 4, 2 and 1 samples per second,

respectively. That is why every time interval in axis

X will be the sampling period of each curve. If the

points of the three curves were graphically

represented using the same time interval for axis X,

they would be superimposed, as shown in Figure 4.

Figure 3: Responses of critically damped systems

w

n

=1

w

n

=0.5

w

n

=0.25

Figure 4: The three curves of Figure 3, superimposed

Figure 2: Prediction based on the linear-trend of the

variable

w

n

=1

w

n

=0.5

w

n

=0.25

ICINCO 2005 - SIGNAL PROCESSING, SYSTEMS MODELING AND CONTROL

338

A similar behavior will occur in first order

systems with respect to the time constant, as well as

in overdamped and underdamped second order

systems, in which only its coefficient of damping

will show any difference.

For NN training patterns, the variations in signal

amplitude are taken up in %, standardized, from

40% to 90%.

After numerous tests, training was carried out

with 858 input patterns, distributed in the following

way:

• For overdamped second order systems (OSO):

For every

ζ value, 11 patterns are obtained

corresponding to the variations of the

amplitude from 40 to 90, with an increase of 5

(40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90).

The

ζ varies from 1.2 to 3, with an increase of

0.09, thus obtaining a total of

220 patterns.

For ζ greater than 3, the behavior of the system

is similar to a first order system.

• For underdamped second-order systems (USO):

As for every

ζ value, 11 patterns corresponding

to amplitude variations are obtained.

The

ζ varies from 0.1 to 0.7, with an increase

of 0.0667, thus obtaining a total of

99

patterns.

• For first- (F) and critically damped second-order

(CSO) systems,

11 patterns are created,

respectively, corresponding to amplitude

variations from 40 to 90.

In order to have a similar number of patterns for

each model and achieve a better training of the NN,

the F and CSO patterns are repeated 20 times,

respectively, for a total of 440 patterns. For the USO

pattern they are repeated twice for 198 patterns. 858

PATTERNS IN ALL.

Once the patterns were chosen, varied topologies

were used until the simplest with the most suitable

response was obtained. Eventually, a 30-input neural

network was used, 11 neurons in the hidden layer

and four-output neurons. Very good results were

obtained in the training and generalization of the

NN. The training error was 0.15%. Over 1000 test

patterns were used, obtaining a correct response,

with an error of 0.9% of failures.

4 CONCLUSIONS AND FUTURE

WORK

Satisfactory results were obtained on training the

neural network, having a high level of

generalization. During the operation, the neural

network recognized the signals used, even those

affected by noise.

The research and the technological advances

presented are a satisfactory step forward in

facilitating the use of advanced and efficient

algorithms of predictive alarm by trend, with

minimum processing time. The presented algorithm

guarantees that the prediction will be corrected in

each period of analysis of the alarm condition states.

This method of predictive alarm has been applied

with good results on several occasions, in managing

hydraulic canals for irrigation and research purposes,

and in controlling sequential processes. For

example, a more efficient operation of a set of tanks

was developed by predicting the time in which a

tank level will reach a limit value.

Moreover, work has began to enhance the neural

network to not only select the most appropriate

model, but also make a pre-estimation of such a

model. This optimization algorithm would be

extremely efficient as its initial operation conditions

would be the values pre-estimated by the neural

network.

REFERENCES

Edgar, T.F. and Himmelblau, D.M., 1988. Optimization of

chemical processes, NY, MacGraw-Hill.

Hooke, R.A. and Jeeves, T.A., 1961. Direct Search

Solution for Numerical and Statistical Problems.

Journal ACM 8, 212-221.

Juricek, B.C., D.E. Seborg and W.E. Larimore, 1998.

"Early Detection of Alarm Situations Using Model

Predictions," Proc. IFAC Workshop on On-Line Fault

Detection and Supervision in the Chemical Process

Industries, Solaize, France.

Ogata, K.. 2001. Modern Control Engineering, 4th

Edition. Prentice Hall, NY.

Oppenheim, A.V., Schafer, R.W. and Buck, J.R., 1999.

Discrete-Time Signal Processing, 2nd Edition.

Prentice-Hall Int. Editions.

Robins, V. et al., 2003. Topology and Intelligent Data,

Advances in Intelligent Data Analysis V, Lecture

Notes in Computer Science, Springer-Verlag GmbH,

Vol. 2810, 275–285

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