A Genetic-Continuation Algorithm-Based Nonlinear Rotordynamic Analysis: Application to Tilting Pad Journal Bearing System

Abstract This study introduced a combined structure of a genetic algorithm and continuation method to solve a nonlinear rotordynamic problem known as multiple coexisting solutions. Here, the chromosomes consist of dynamic state elements of a rotor-bearing system, and the genetic objective is the completion of periodicity of the responses in the nonlinear system during the consecutive generations. For the pilot implementation, two exemplary nonlinear models, such as Duffing and Van der Pol, were tested to ensure the capability and compared with the shooting method. Then, a Jeffcott-type rotor supported on two identical six-pad tilting pad journal bearings was employed as a rotor-bearing application. The bearing has rocker-back type pivots, and the fluid film force on each pad is calculated using the finite element method. To find a multiple coexisting solution, 200 initial conditions composed of the dynamic states of the journal and pad were randomly created as the first generation. The optimal results were selected by evaluating the fitness for each generation, and the offspring were created through the processes of crossover, mutation, and elitism: this lasted up to 15 generations. Then Newton–Raphson method takes a role to refine the final candidates to examine whether they meet the convergent criteria. The branches of the solutions were extended concerning a control parameter using the arc-length continuation method to obtain a broader perspective of nonlinear behaviors. As a result, multiple coexisting responses and various bifurcation events, such as periodic doubling, saddle-node, could be discovered by the developed combined numerical scheme.