Information Technology Reference
In-Depth Information
To increase the generalisation offered by the system, a degree of approximation be-
tween the n-grams held in the database and the test n-grams was also introduced.
The advantage of the n-gram technique is that it will work with data in any format
and it should even work with some forms of encrypted data. A further benefit is that it
does not depend upon mathematical relationships between the data readings and so it
is a natural complement to invariant induction. The limitation of this approach is that
it has difficulty detecting errors that occur close together because a single error cre-
ates a zero response for the entire time that the sliding window is over it.
4.2
Invariant Induction
This approach builds up a normal model of the data by looking for relationships be-
tween the different data readings. These are expressed as invariants, i.e. facts which
should always hold in the current context. In the data from electricity networks this
approach is particularly effective since most of the data is interrelated in a systematic
manner. For example, in the networks that we have experimented on, the relationship
between the power flow readings at either end of a line are, to a high degree of accu-
racy, of the form P1 = kP2 + C, where k and C are constants. Initially a certain num-
ber of invariants are hypothesised for the readings from the network. Some relation-
ships are based on physical relationships, but others will simply be empirical
relationships that are found in the training data. As more data comes in, some of these
relationships will be discarded because they no longer hold and eventually one is left
with a set of relationships which hold for all of the training data. A simplified exam-
ple of this technique now follows.
Suppose that this approach is being applied to the three bus network in Fig. 2.
P2
P1
P6
P5
P3
P4
Bus 1
Bus 3
Bus 2
Fig. 2. Three bus electricity network
Table 1. Real power readings for three bus network
Time
P1
P2
P3
P4
P5
P6
T1
200
-190
60
-59.4
-70
67.9
T2
220
-209
50
-49.5
-100
97
T3
240
-228
80
-79.2
-150
145.5
Table 1 shows three sets of real power readings for this network. If the only rela-
tionships that are hypothesised are linear equations through the origin, then at time T1
it is possible to hypothesise the following six equations:
 
Search WWH ::




Custom Search