Abstract
This paper is dedicated to the development of robust optimization and decision making techniques taking into account the uncertain parameters of linear and nonlinear dynamic vibration absorbers. In this case, novel approaches are proposed regarding different fuzzy logic optimization strategies. The uncertain parameters of the considered mechanical systems are treated as fuzzy variables. Consequently, the associated optimization problem is described as a fuzzy function that maps the fuzzy inputs. The proposed techniques are applied to the design of dynamic vibration absorbers. This numerical study illustrates the versatility and convenience of the proposed fuzzy logic optimization strategies.
Highlights
The design process and operation limits of mechanical systems are currently obtained from the analysis of deterministic models, which should be able to represent the associated dynamic phenomena
The proposed fuzzy robust optimization techniques were applied to the design of the systems depicted in Figure 8 (DVA, Figure 8(a), and Nonlinear Dynamic Vibration Absorber (nDVA), Figure 8(b))
Considering the robust design of the dynamic vibration absorber (DVA), the uncertain parameters were modeled as fuzzy triangular numbers with an uncertainty of ±10% with respect to the nominal value of the parameter
Summary
The design process and operation limits of mechanical systems are currently obtained from the analysis of deterministic models, which should be able to represent the associated dynamic phenomena. Parametric or nonparametric uncertainties are inherent to dynamic systems due to manufacturing errors and tolerances, damage, wear, and influence of environmental conditions that should be taken into account to obtain reliable mathematical models These fluctuations are disregarded in ordinary deterministic approaches. The present contribution aims at proposing different fuzzy robust optimization techniques These methodologies were evaluated for the design of linear and nonlinear robust dynamic vibration absorbers (DVA and nDVA, resp.), considering parametric uncertainties affecting the mechanical system. A fuzzy evaluation of the optimization problem can be conceived through the evaluation of the pessimistic and optimistic values of the fuzzy sets (i.e., the uncertain information) This is the basic concept of the techniques conveyed in the present contribution. X2αk r x2 z μ(z) max f(x) min f(x) zαk r zαk r zαk Figure 1: The α-level optimization
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