# Power Transformer Fault Diagnosis Based on Dissolved Gas Analysis by Correlation Coefficient-DBSCAN
## 3 Improved CCDBSCAN Algorithm
### Chaotic Sequence Optimization  
Different gases usually play different roles in the process of sample classification. Simulation tests and a large number of field tests show that [3] acetylene is the characteristic gas of discharges, hydrogen is the characteristic gas of partial discharges, and ethylene is the characteristic gas of a thermal fault. However, according to Equation (4), the correlation between two groups of gases cannot reflect the similarity of characteristic gases of different faults, so it is necessary to amplify the less characteristic gases. Therefore, the following calculation method for enlarging the characteristic gases of faults is proposed in this paper. Suppose that the DGA data is  
\[X_{(n\times 5)}=(X_{1}^{T},X_{2}^{T},X_{3}^{T},X_{4}^{T},X_{5}^{T},X_{6}^{T})^ {T}\]  
of \(n\) fault transformers is collected, among which  
\[X_{c}^{T}(c=1,2,\ldots,6)\]  
is the typical fault dataset of transformers, \(c=1\) is the T1 dataset, \(c=2\) is the T2 fault dataset, \(c=3\) is the T3 dataset, \(c=4\) is the PD dataset, \(c=5\) is the D1 dataset, \(c=6\) is the D2 dataset. When \(c=1\),  
\[X_{1(m\times 5)}=(X_{11},X_{12},\ldots,X_{1m})^{T},\]  
where  
\[X_{11(5\times 1)}=(x_{111},x_{112},x_{113},x_{114},x_{115})^{T}\]  
represents the first DGA train vector of T1. The matrix of amplification coefficient  
\[A_{(5\times 5)}=diag(\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{4},\alpha_{5})\]  
is defined, and the amplification matrix \(Y_{(n\times 5)}\) is obtained by multiplying the matrix \(X_{(m\times 5)}\) by the matrix \(A\). \[Y_{(n\times 5)}=X_{(n\times 5)}A_{(5\times 5)} \tag{5}\]  
where the row correlation coefficient \(R_{Y}\) of \(Y\) is  
\[R_{Y}=\left[ \begin{array}{cccc}R_{11}&R_{12}&\cdots&R_{16}\\ R_{21}&R_{22}&\cdots&R_{26}\\ \vdots&\vdots&\vdots&\vdots\\ R_{61}&R_{62}&\cdots&R_{66}\end{array} \right] \tag{6}\]  
where \(R_{ij}\) is the correlation coefficient matrix of type \(i\) and type \(j\) faults  
\[R_{ij}=\left[ \begin{array}{cccc}r_{ij11}&r_{ij12}&\cdots&r_{ij1m}\\ r_{ij21}&r_{ij22}&\cdots&r_{ij2m}\\ \vdots&\vdots&\vdots&\vdots\\ r_{ijm1}&r_{ijm2}&\cdots&r_{ijmm}\end{array} \right] \tag{7}\]  
where \(r_{ijmm}\) is the correlation coefficient between the m-th DGA vector of class \(i\) and the m-th DGA vector of class \(j\). The PC (partition coefficient) can be defined by the above description  
\[PC_{ij}=1-\frac{\sum\limits_{a=1}^{m}\sum\limits_{b=1}^{m}r_{ijnb}}{m\times m} \tag{8}\]  
The AC (aggregation coefficient) is  
\[AC_{ii}=1-PC_{ij}(i=j) \tag{9}\]  
The larger the partition coefficient of class \(i\) and \(j\) faults indicates that the separation is more obvious. When \(i\
eq j\), the larger the partition coefficient indicates that the similarity between class \(i\) and \(j\) faults is lower. When \(i=j\), the higher the partition coefficient indicates that the data correlation within class \(i\) faults is higher. The idea of this chapter is to use chaos sequence to optimize the amplification coefficient matrix, so that the partition coefficient between different types of faults is the largest and the aggregation coefficient of the same type of faults is the largest, to improve the classification and diagnosis effect of CCDBSCAN. Chaos sequence optimization is to search chaos variables in a certain range according to the ergodicity and regularity of chaos sequence, so as to make the search of chaos variables jump out of the local optimum and finally reach the global optimum [34]. Based on the idea of information sharing of each orbit, the next iteration is not only determined by the inertia weight, but also affected by the historical information of the orbit and the global historical information of the rest orbit. Due to the introduction of chaotic sequence, the global feasible solution is fully searched, and the global optimization ability of the search method is obviously improved.