classification accuracy, it trains faster while SVM is computationally most expensive. 

Table 2 compares the results of the networks designed in terms of accuracy, training time and testing time to classify bushing conditions into thermal fault, PD faults and faults caused by an unknown source bushing faults and this is called second level classification. This table shows that the MLP classifier gives 98.62% classification accuracy while RBF and SVM classifier give 81.73% and 96.9%, respectively. In the second level classification, the MLP classifier performs better than the RBF and SVM. 

Table 2: Comparison of the performance of different frameworks for second level of fault diagnosis 

|                         | MLP    | RBF   | SVM    |
|-------------------------|--------|-------|--------|
| Accuracy (%)            | 98.62  | 81.73 | 96.90  |
| Training Time (s)       | 30.016 | 1.038 | 83.906 |
| Classification Time (s) | 0.780  | 0.05  | 1.094  |

Because the MLP gives the best results compared with RBF and MLP on condition monitoring of bushings, it is therefore selected as the most appropriate learning engine and thus it is chosen for on-line learning. 

## 9 On-Line Learning

As indicated earlier in the paper, on-line learning is suitable for modelling dynamically time-varying systems, where the operating region changes with time. It is also suitable, if the data available is not adequate and does not fully represent the system. 

Another advantage of on-line learning is that it is able to accommodate new conditions that may be introduced by incoming data. An on-line bushing condition monitoring system must have incremental learning capability if it is to be used for automatic and continuous on-line monitoring. The on-line bushing monitoring system improves reliability, reduces maintenance cost and minimizes out-of-service time for a transformer. The basis of on-line learning is incremental learning, which has been studied by a number of researchers [15][16][17][18]. The difficulty in on-line learning is the tendency of an online learner to forget information gathered during the early stages of learning [19]. The method of on-line learning adopted in this paper is Learn++ [20]. 

## 4.1. Learn++

Learn++ is an incremental learning algorithm that uses an ensemble of classifiers that are combined using weighted majority voting [19]. Learn++ was developed by Polikar [19] and was inspired by a boosting algorithm called adaptive boosting 
(AdaBoost). Each classifier is trained using a training subset that is drawn according to a distribution. The classifiers are trained using a weakLearn algorithm. 

The requirement for the weakLearn algorithm is that it must be able to give a classification rate of less than 50% initially [20]. For each database Dk **that contains** 
training sequence, S, **where S contains learning** 
examples and their corresponding classes, Learn++ 
starts by initialising the weights, w**, according to the** 
distribution DT, where T **is the number of hypothesis.** 
Initially the weights are initialised to be uniform, which gives equal probability for all instances to be selected to the first training subset and the distribution is given by: 
m D = 1 **(7)** 
where m **represents the number of training examples** 
in Sk**. The training data are then divided into training** 
subset TR and testing subset TE **to ensure weakLearn** 
capability. The distribution is then used to select the training subset TR and testing subset TE from Sk**. After** 
the training and testing subset have been selected, the weakLearn algorithm is implemented. The weakLearner is trained using subset, TR**. A** 
hypothesis, ht, **obtained from weakLearner is tested** 
using both the training and testing subsets to obtain an error, εt: 
)(
: ( )
D i i i i t h x y t ∑ t
≠
ε = **(8)** 
The error is required to be less than 0.5; a normalized error βt **is computed using:** 

t t t ε ε β− =1 (9) 
$$({\mathfrak{g}})$$
If the error is greater than 0.5, the hypothesis is discarded and new training and testing subsets are selected according to DT **and another hypothesis is** 
computed. All classifiers generated are then combined using weighted majority voting to obtain composite hypothesis, Ht:

$$H_{t}=\arg\operatorname*{max}_{y\in Y}\sum_{t\in h_{t}(x)=y}\log(1/\beta_{t})$$

Weighted majority voting gives higher voting weights to a hypothesis that performs well on the training and testing subsets. The error of the composite hypothesis is computed by: 

$$\mathbf{l}\mathbf{l}.$$
