# Application of fuzzy entropy in gear fault classification

Suppose that the original time series of gear fault signal is: [x (n)] = x (1), X (2) Then the fuzzy entropy of the sampling sequence of the gear fault signal can be obtained according to the following steps:

1) The sampling time series of gear fault signal is composed of a group of m-dimensional vectors according to the sampling sequence number.

2) The distance d [XM (I), XM (J)] (I ≠ J) between different vectors XM (I) and XM (J) is defined as the maximum difference between the corresponding elements of two vectors.

3) The similarity between vector XM (I) and XM (J) is defined by fuzzy function μ (dmij, R).

4) Define function

5) By analogy, increase the dimension to m + 1, and repeat steps (1) to (4)

6) The time series fuzzy entropy of gear fault signal is as follows

When n is a finite number, the formula can be expressed as follows:

Where: m is the pattern dimension; R is the similarity tolerance; n is the data length. 