Optimal placement of triaxial sensors for modal identification using hierarchic wolf algorithm

Summary Optimal triaxial sensor placement plays a crucial role in tridimensional modal identification; however, few studies have been conducted on this topic. In this paper, a holistic approach, including a tridimensional optimal criterion and solution method, is proposed for finding the optimal locations to deploy triaxial sensors. The tridimensional optimal criterion is established by combining the tridimensional modal assurance criterion and the redundancy function. The tridimensional modal assurance criterion is deduced from the one-dimensional modal assurance criterion by using the widely accepted Fisher information matrix, adopted to ensure the linear independence of identified tridimensional mode shapes. The redundancy function, which is defined by the similarity index among nodes, is developed to measure the information redundancy and to maintain effective visualization of the identified tridimensional mode shapes. To efficiently find the optimal triaxial sensor configuration with the proposed tridimensional optimal criterion, the hierarchic wolf algorithm (HWA) is developed by imitating the swarm intelligence embedded in the wolf pack. Five strategies, which are termed as coding and spreading wolves, searching behaviors, attacking behaviors, hierarchic population, and distributing food process, are employed to enhance the global searching ability of the HWA. The proposed approach is verified by a benchmark bridge model. The results indicate that the established tridimensional optimal criterion has the capability of ensuring optimal triaxial sensor configurations that make the identified tridimensional mode shapes have features of excellent linear independence and good visualization, and the HWA has strong ability and high efficiency in determining the global optimal triaxial sensor configuration.