Algorithm 1 Two-dimensional gradient descent search algorithm

determine the initial conditions by performing a turning operation to produce one low rigidity shaft: determine shaft diameter d determine bending force Fbe determine cutting force component Ff determine the initial distance from the cutting edge to the point at which the workpiece is secured in the spindle a0 determine initial axial force Fx10 determine initial eccentricity e0 record measurements of Fx1, e and deviation y every 0.05 mm by changing the values of parameters Fx1 and e within the pre-defined range use the measurement data to train an ANN to predict $y=f\left(F_{x1},e\right)$ minimize deviation y, which is the output value of the neural network which serves as the objective function $y={\min }_{Fx1,e}\varphi (d,L,F_f,v,a_p,f,a,x,F_{x1},e)$ for the GA