Receptance-based antiresonant frequency assignment of an uncertain dynamic system using interval multiobjective optimization method

This study addresses the antiresonant frequency assignment problem of vibrating systems with uncertainty, which is solved using an interval multi-objective optimization method. The study accounts for several uncertain factors, including in the structural parameters and test data, and defines them as interval variables. The bounds of interval variation of the receptance (frequency response function or FRF) are determined from a small number of numerical or experimental results; thus, it is unnecessary to collect a large amount of data to construct the sample space. The antiresonant frequency assignment problem of uncertain systems is formulated as an interval multi-objective optimization. Optimal solutions (the structural modifications that assign the desired antiresonant frequency frequencies) are determined through the MI-NSGA-II algorithm proposed in this work. It employs the basic framework of the interval multi-objective genetic algorithm INSGA-II and redefines the interval confidence level to evaluate the merits and demerits between individual feasible solutions and improve the stability of INSGA-II. The obtained modifications not only accurately achieve the goal of antiresonant frequency assignment but also stably maximize the robustness of the antiresonant frequency frequencies after modifications. From the perspective of enhancing the applicability of the receptance method, the proposed method can overcome the problems of unsuccessful antiresonant frequency assignment due to measurement inaccuracies and the uncertainty of physical parameters to a certain extent. Numerical and experimental examples have been provided to demonstrate the effectiveness of the proposed method.