$M$	the system’s mass	$\Gamma (\lambda )$	standard gamma function
$B$	damping coefficient	$x_j^t,x_k^t$	random pollen
$K$	stiffness	$\epsilon$	random number in [0, 1]
$C$	scale factor	$p$	switching probability
$x(t)$	state variable	$v_t^i$	particle $i$ speed at iteration $t$
$h(t)$	output of the hysteresis part	$p_t^i$	particle $i$ optimal solution
$D$	ratio coefficient	$p_t^g$	population optimal solution
$A,B$	hysteresis parameter	$c_1,c_2$	learning factor
$\gamma ,n$	hysteresis parameter	$r_1,r_2$	random number in [0, 1]
$u(t)$	input signal	$w_t$	inertia weight
$u^{\prime }(t)$	first derivative of $u(t)$	$w_{\min }$	minimum value of $w_t$
$c_0,c_1,c_2$	coefficient to be identified	$w_{\max }$	maximum value of $w_t$
$y(t)$	output displacement of the system	$t_{\max }$	maximum number of iterations
$x_i^t$	solution $i$ at iteration $t$	$Max\_T$	maximum number of iterations
$x_i^{t+1}$	solution $i$ at iteration $t+1$	$t$	current iteration number
$g_{best}^{*}$	global optimal solution	$r$	$r=(c_0,c_1,c_2,A,\beta ,\gamma ,n)$
$\gamma$	scale factor of the control step	$N$	total number of data
$L(\lambda )$	Lévy flight	$x_{\exp }$	experimental data
$S$	step length	$x_{mdl}$	model data