Information Technology Reference
In-Depth Information
It is easy to convert common algebra equations and differential equations into
qualitative equations. The process of qualitative reasoning is to give explanation
with qualitative equations. Now we take the qualitative analysis of the pressure
regulator as example to explain the approach of qualitative model reasoning.
The pressure regulator controls the flow valve through spring, so as to make
the flow value a certain settled value, and not influenced by the influent flow and
the change of load. According to the physics:
P
Q
=
CA
2
P
>
0
ρ
dQ
P
dA
CA
ρ
dP
C
2
+
dt
ρ
dt
ρ
2
P
dt
Among them Q denotes the flow value through the valve, P denotes the
pressure, A denotes the area that the valve opens, C is constant coefficient, and ρ
denotes quality density of fluid. Qualitative equations are gained according to the
operation and convert rules:
[Q] = [P]
µ
Q
=
µ
A
+
µ
P
(if A > 0)
We can also build up related qualitative equations according to the physical
rules such as consistency and continuity, etc. Then we can get qualitative
explanation by these qualitative equations. The regulator is described with three
special states: OPEN state, WORKING state and CLOSE state:
Qualitative
equation
µ
P = 0
OPEN state
A = Amax
[P] = 0
Qualitative
equation
µ
P +
µ
A =
µ
Q
WORKING state
0<A<Amax
[P] = [Q]
Qualitative
equation
µ
Q = 0
CLOSED state
A = 0
[Q] = 0
Besides discussing the qualitative analyses of each state, we can also discuss
the qualitative analyses of states variation. De Kleer has built ENVSION system
using constraint propagation and producing testing approach for qualitative
equations solution.
