Study on Health Assessment Method of a Braking System of a Mine Hoist

. 2019 Feb 13;19(4):769. doi: 10.3390/s19040769

HD	health degree
PHM	Prognostics Health Management
CBM	condition based maintenance
TLFCA	three-level fuzzy comprehensive assessment
BPNN	BP neural network
FCA	fuzzy comprehensive assessment
FCAV	fuzzy comprehensive assessment value
AHP	analytic hierarchy process
HS	health state
SH	sub-health
CF	critical fault
FS	fault state
BC	brake clearance
HC	health condition
$X_{i}$	the monitored values of the ith sensor, $X_{i} = [x_{1}^{i}, x_{2}^{i}, \dots, x_{k}^{i}]$
$H D_{S E N S O R}$	HD of sensor
$H D_{S U B - S Y S}$	HD of subsystem
$H D_{S Y S}$	HD of system
$F C A V_{S E N S O R}$	FCAVs of sensor
$F C A V_{S U B - S Y S}$	FCAVs of subsystem
$F C A V_{S Y S}$	FCAVs of system
$U$	factor sets, $U = [U_{1}, U_{2}, \dots, U_{S}]$
$U_{i}$	factor classes, $i = 1, 2, \dots, s$
$U_{i j}$	the jth factor in ith factor class.
$V$	assessment sets, $V = [V_{1}, V_{2}, \dots, V_{m}]$
$W$	weight sets of the factor sets, $W = [W_{1}, W_{2}, \dots, W_{s}]$
$ω_{i}$	weight sets of the ith factor class or subsystem, $ω_{i} = [ω_{i 1}, ω_{i 2}, \dots, ω_{i k_{i}}]$
$w_{i}$	weight sets of the ith sensor, $w_{i} = [w_{i 1}, w_{i 2}, \dots, w_{i k}]$ .
$w_{i}^{1}$	weight sets of time point obtained by experts scoring method.
$w_{i}^{2}$	weight sets of the ith sensor obtained by hierarchy method
$R$	transfer matrix of factor sets and assessment sets
$R_{i}$	transfer matrix of the ith factor class or subsystem and assessment sets
$r_{i}$	transfer matrix of the ith sensor
$R_{j l}^{i}$	fuzzy conversion value between the jth factor in the ith factor class and the lth assessment subset
$F C A V$	FCAVs of factor sets
$F C A V_{i}$	FCAVs of the ith factor class, sensor or subsystem.
$F C A V^{l}$	FCAV of the factor sets belongs to the lth assessment factor.
$F C A V_{i l}$	FCAV of the lth assessment factor in the ith factor class
$x$	the monitored value of the sensor.
$x_{\min 1}$	the lower limit value of the lowest operation
$x_{\min 2}$	the lower limit value of the best operation
$x_{\max 2}$	the upper limit value of the best operation
$x_{\max 1}$	the upper limit value of the lowest operation
$f_{V_{l}} (x)$	membership function of assessment sets
$V_{l}$	different HC, $l = 1, 2, 3, 4$ .
$δ_{l}$	standard deviation of the lth HC
$μ_{l}$	the optimal expected value of the lth HC.
$d_{i j}$	the scale value of the ith parameter at jth point.
$c_{i j}$	the absolute value of the difference between the monitored and optimal expected value of the ith parameter at jth point.
$s_{i j}$	the absolute value of the difference between the optimal expectation of the health and fault of the ith parameter.
$F_{H S n}^{i}$	FCAV of the ith sensor at nth point is in HS
$F_{S H n}^{i}$	FCAV of the ith sensor at nth point is in SH
$F_{C F n}^{i}$	FCAV of the ith sensor at nth point is in CF
$F_{F S n}^{i}$	FCAV of the ith sensor at nth point is in FS
$F C A V_{H S}^{i}$	FCAV of the ith sensor or ith subsystem is in HS
$F C A V_{S H}^{i}$	FCAV of the ith sensor or ith subsystem is in SH
$F C A V_{C F}^{i}$	FCAV of the ith sensor or ith subsystem is in CF
$F C A V_{F S}^{i}$	FCAV of the ith sensor or ith subsystem is in FS