Simultaneous-Fault Diagnosis of Gas Turbine Generator Systems Using a Pairwise-Coupled Probabilistic Classifier

Table 3

Definition of common statistical features in time-domain.

Time-domain feature	Equation
(1) Mean	𝑥𝑚=1𝑁^𝑁𝑖∑=1𝑥𝑖
(2) Standard deviation	𝑥std=∑^𝑁𝑖=1(𝑥𝑖−𝑥𝑚)^2𝑁−1
(3) Root mean square	𝑥rms=1𝑁^𝑁𝑖∑=1𝑥^2𝑖
(4) Peak	𝑥pk=max𝑥𝑖
(5) Skewness	𝑥ske=∑^𝑁𝑖=1(𝑥𝑖−𝑥𝑚)^3(𝑁−1)𝑥^3std
(6) Kurtosis	𝑥kur=∑^𝑁𝑖=1(𝑥𝑖−𝑥𝑚)^4(𝑁−1)𝑥^4std
(7) Crest factor	𝑥CF=^pk𝑥rms
(8) Clearance factor	𝑥CLF=^pk(1/𝑁)∑^𝑁𝑖=1𝑥𝑖^2
(9) Shape factor	𝑥SF=^rms(1/𝑁)∑^𝑁𝑖=1𝑥𝑖
(10) Impulse factor	𝑥IF=^pk(1/𝑁)∑^𝑁𝑖=1𝑥𝑖

Note: 𝑥_𝑖 represents a signal series for 𝑖=1,2,…, N, where N is the number of data points of a raw signal.