*2.4. Homogeneity*

In image classification, homogeneity is a textural attribute that estimates the variability of the gray level in the pixels from an image. It is derived from the gray level co-occurrence matrix (GLCM) [22], and it measures the closeness of the element distribution in the GLCM regarding its diagonal. The GLCM shows how many times each gray level comes about at a pixel situated at a predetermined geometric position regarding any other pixel through a function of their gray levels. Homogeneity ranges from 0 to 1 and reaches its maximum value when the diagonal elements have a value of 1. Homogeneity can be computed by

$$H = \sum\_{i} \sum\_{j} \frac{1}{1 + \left(i - j\right)^{2}} p(i, j) \tag{5}$$

where *p*(*i*, *j*) is the (*i*, *j*)th element of the normalized GLCM. Homogeneity can be used as an index for fault detection and classification in SCIM since distinct fault-associated frequency elements are induced in the electrical current signal, changing its uniformity [23].

#### *2.5. Kurtosis*

Kurtosis has the capability of measuring the deviation, i.e., tailedness, of a probability distribution, and discriminating between distributions with different shapes; therefore, it can be used as an efficient indicator for SCIM fault detection. Kurtosis is the fourth-order moment that describes the shape of a probability distribution from a signal. If there is a high impulsive component, with a sharp signal intensity distribution, then there is a high kurtosis value. Kurtosis of a random event *X* is computed as

$$\text{Kurt}[X] = \frac{\frac{1}{N} \sum\_{i=1}^{N} (\mathbf{x}\_i - \boldsymbol{\mu})^4}{\left(\frac{1}{N} \sum\_{i=1}^{N} (\mathbf{x}\_i - \boldsymbol{\mu})^2\right)^2} = \frac{\mu\_4}{\sigma^4} \tag{6}$$

where *N* is the number of samples, *x*<sup>i</sup> is the time raw-signal sample for *i* = 1, 2, ... , *N*, and *μ* is the mean of the random event *X* = [*x*1, *x*2, *x*3,... , *x*N].
