Rotation-based sampling Multi-Particle Collision Algorithm with Hooke-Jeeves for Vibration-based Damage Identification

The structural vibration-based damage identification can be formulated as an optimization problem. The objective functional is expressed by a least square difference between measured and computed forward model displacements. The latter functional is minimized by using a hybrid scheme combining Rotation-based sampling Multi-Particle Collision Algorithm with Hooke-Jeeves heuristic (RMPCA-HJ). Multi-Particle Collision Algorithm (MPCA) is a stochastic optimization method inspired by the physics in the nuclear reactor, where absorption and scattering phenomena are represented. In the MPCA algorithm, a set of particles (solutions) travels in the search space. After a certain number of function evaluations, they share the best particle solution found. MPCA, working together with the Rotation-Based Learning (RBL), is used as a first stage of the hybrid method performing a global exploratory search. RBL is a novel extension of Opposition-based Learning (OBL). In RBL, a rotated solution is calculated by applying a specific rotation angle to the original solution. Here, the new Rotation-Based Sampling (RBS) solution projects a point between the original solution and its rotated solution. RBS could be more flexible than RBL, and also OBL, to find the promising candidate solutions. The intensification search stage of the hybrid metaheuristic is addressed by the direct search Hooke-Jeeves (HJ) method. HJ consists of the repeated application of exploratory searches for all dimensions around a base point. If the exploration has success finding a better solution, a pattern move is performed. The hybrid algorithm is tested to identify damages on a truss structure. Experimental data was generated in silico, using time-invariant damages. Experiments with noiseless and noisy data, under several levels of noise, were carried out. Good estimations of damage location and severity are achieved.