An automatic fire searching and suppression system for large spaces

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302
T. Chen et al. / Fire Safety Journal 39 (2004) 297–307
Y ¼ Y 2 cos o 2 Z 2 sin o 2 þ D sin o 2 ;
Z ¼ Y 2 sin o 2 þ Z 2 cos o 2 þ D cos o 2 :
ð4Þ
Take Eq. (2) into (3) and eliminate Y 1 , the relationshipbetween Y and Z has an
expression
Y ¼ ðy 1 cos o 1 f sin o 1 ÞðZ D cos o 1 Þ
þ D sin o 1 : ð5Þ
y 1 sin o 1 þ f cos o 1
Take Eq. (2) into (4) and eliminate Y 2 , the relation between Y and Z has another
expression
Z ¼ ðy 2 sin o 2 þ f cos o 2 ÞðY D sin o 2 Þ
þ D cos o 2 : ð6Þ
y 2 cos o 2 f sin o 2
Solution of Y and Z can be obtained from Eqs. (5) and (6), as shown in Eq. (7).
Y ¼ Dðy 2 f tan o 2 Þ½ðsin o 2 sin o 1 þ A cos o 1 B cos o 2 Þ=ðA þ BÞ D cos o 2 Š
y 2 tan o 2 þ f
þ D sin o 2 ;
Z ¼
D
A B ðsin o 2 sin o 1 þ A cos o 1 B cos o 2 Þ; ð7Þ
where
A ¼ðy 1 f tan o 1 Þ=ðy 1 tan o 1 þ f Þ;
B ¼ðy 2 f tan o 2 Þ=ðy 2 tan o 2 þ f Þ: ð8Þ
In the above equations, y 1 and y 2 are still unknown. Actually, they can be
calculated from the pixel coordinates (i, j) of the images, because most of the CCD
camera are of the same standard specifications. Suppose the CCD camera’s scanning
area is known as H V pixels and h v m 2 , the relationshipbetween [y 1 , y 2 ] and
[j 1 , j 2 ] can be found.
y 1 ¼ðj 1 V=2Þv=V;
y 2 ¼ðj 2 V=2Þv=V: ð9Þ
Thus the fire position P(d,a) in the space is confirmed and expressed as
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
d ¼ Z 2 þ Y 2 ; ð10Þ
a ¼ tan 1 ðY=ZÞ:
ð11Þ
2.3. Working process
Initially, the fire monitor is set at the horizontal-left limit position. Once a fire is
detected by a fire detector in the system, the corresponding fire monitor will be
activated. It will start searching for fire and be driven to the down-right limit
position step-by-step (shown in Fig. 3). The fire monitor rests for a short time after
each step. During this period of time, continuous images are captured from the CCD