Symbol or Abbreviation	Explanation
a	distance from spindle to the tip of the cutting tool bit
e	eccentricity of tensile force under tension
Fbe	bending force exerted by the cutting tool bit
Fr	reaction along the x axis
Fx	tensile force along the x axis
Fx 1	moving tensile force
L	length of shaft
M0, Q0	initial parameters: moment and transverse force at the holding point, respectively
M1	moment generated by the axial component of cutting force
M2	moment generated at the holding point at which the part is secured to the tailstock of the turning machine
R	regression coefficient
x1, x2, y1, y2	current coordinates at each section of the workpiece
$y_i^{\prime }$	reference value for the i-th shaft section;
$y_i^{*}$	predicted value for the i-th shaft section
${\sigma }_i^{\prime }$	standard deviation of reference values
${\sigma }_i^{*}$	standard deviation of predicted values
ADAM	adaptive moment estimation optimization method
ANN	artificial neural network
BiLSTM	bidirectional LSTM layer
DBN	deep belief network
GA	genetic algorithms
LMA	Levenberg-Marquardt optimization algorithm
LSTM	long short-term memory neural network, which is a recurrent deep learning network
MLP	multilayer perceptron
MSE	mean square error
NARX	flat nonlinear autoregressive network with exogenous input designed for the prediction of multidimensional time series and signals
RBM	restricted Boltzmann machine
RMSE	rooted MSE
SVM	support vector machine