Uncertainty Analysis And Optimization Of Space-coiled Acoustic Metamaterials Based On Evidence Theory

Space-coiled acoustic metamaterials have broad application prospects in high-speed trains,aerospace and other fields because of they have the advantage of perfectly absorbing low frequency noise at subwavelength thicknesses.In practical engineering,due to factors such as limited sample data,processing errors,and environmental uncertainties,uncertainty widely exists in space-coiled acoustic metamaterials.The existing numerical analysis and optimization design methods of space coiled acoustic metamaterials often ignore the influence of these uncertain factors,which may cause the sound absorption performance of space coiled acoustic metamaterials to fail to achive the design requirements.Evidence theory model can flexibly describe uncertainty such as interval uncertainty information and imprecise probability information.Therefore,this thesis will introduce evidence theory to handle with uncertainty,and research on the uncertainty analysis and optimization methods of space-coiled acoustic metamaterials based on evidence theory.The main research contents are as follows:(1)Establish a finite element analysis model of space-coiled acoustic metamaterials.The correctness of the finite element model method is verified by theoretical methods.Impedance tube tests were used for multiple structures in the same batch,and the uncertainty of sound absorption performance was analyzed.The influence of size parameters and environmental factors on the sound absorption performance was researched.The main influence factors of the sound absorption performance of the space-coiled acoustic metamaterial were identified.(2)In order to handle the problem that the calculation amount of the extreme value analysis of the focal element under the evidence theory model is too large,an uncertainty analysis method of the evidence theory based on Gaussian sampling and reduced optimization is proposed.Firstly,the surrogate model is constructed by the orthogonal polynomial expansion method,and the Gaussian integration points are generated based on the optimal weight function.Then the sequence sampling scheme is used to select the sample points.For the 5-variable 5-order expansion problem,the computational efficiency is improved by about 90 times.Secondly,in order to solve the problem that the computational cost increases sharply with the dimension of the problem and the number of focal elements,a reduction optimization method is proposed,which effectively reduces the computational time of extreme analysis of joint focal element.For the problem of 3 variables and 16 focal elements of each variable,the computational efficiency is improved by about 518 times.Finally,the proposed method is applied to the cognitive uncertainty analysis of space-coiled acoustic metamaterials.The results show that the proposed method greatly improves the computational efficiency.(3)The uncertain optimization is a double-layered nested loop.In the optimization process,there will be a lot of uncertain analysis,which will bring a great cost of calculation.Therefore,the propsed evidencetheoretic uncertainty analysis method based on Gaussian sampling and reduced optimization is applied to the optimization of space-coiled acoustic metamaterials.Comparing the optimal design results based on evidence theory with those obtained by deterministic optimization methods.The reliability index of the deterministic optimization cannot satisfy the reliability constraints,while the uncertainty optimization can improve the sound absorption performance and satisfy the high reliability index.Therefore,for the engineering application of spatially coiled acoustic metamaterials,it is necessary to consider the influence of structural parameter uncertainty.In this thesis,a cognitive uncertainty analysis and optimization method for space coiled acoustic metamaterials based on evidence theory will be proposed,which will provide an effective method for the engineering application of space coiled acoustic metamaterials.