Reduced Space Optimization-Based Evidence Theory Method for Response Analysis of Space-Coiled Acoustic Metamaterials with Epistemic Uncertainty

Acoustic metamaterials have been widely concerned by researchers because of their excellent sound absorption properties. Traditional uncertainty analysis methods for response analysis of acoustic metamaterials with evidence variables have limitations. The excessive time spent on repetitive extreme analysis of focal elements severely impedes the practical application of evidence theory. To reduce the computational costs of uncertainty quantification for acoustic metamaterials under the evidence theory, a reduced space optimization-based evidence theory method (RSO-ETM) is proposed. In RSO-ETM, a simplified surrogate model is first constructed by a modified adaptive arbitrary orthogonal polynomial (MAAOP) expansion method, and then, the monotonicity of the response surface is examined to reduce the space. Subsequently, the Newton iteration technique and a transformation boundary method are used to obtain the extreme points in the reduced space, through which the boundary of the response over each focal element can be readily obtained. By using RSO-ETM, the optimization for each focal element can be avoided, and correspondingly the computational costs are reduced. Two mathematical examples and acoustic problems are employed to demonstrate the practicality of the methods.