A new two dimensional inverse Laplace transform algorithm using analytic expressions for the gradient and the Hessian matrix,

Increased running speeds and the requirement for rotating machinery to operate within specified levels of vibration mean that the control of machinery vibration is essential in today’s industry. In this work, the flexible rotor balancing problem based on the influence coefficient method and holospectrum technique is formulated as a minimax optimization problem. This formulation can solve the minimax high-speed rotating machinery’s balancing problem under practical balancing constraints effectively while ensuring the balancing machinery runs up safely. Imperialist Competitive Algorithm (ICA) method is employed to solve the minimax balancing problem. An experimental and a real world balancing example are given to demonstrate the effect of this formulation. The performance of ICA is compared with that of other established approaches; some conclusions are derived.