Unknown Design Parameters Research Articles

Estimation of Membership Function of Design Variables Using HDMR and FFT

This paper presents an inverse reliability analysis to determine the unknown design parameters such that prescribed reliability indices are attained in the presence of mixed uncertain variables. The proposed computational procedure involves the failure probability estimation using High Dimensional Model Representation, transformation technique to obtain the contribution of the fuzzy variables to the convolution integral, convolution using fast Fourier transform, and update of reliability index and most probable point. This is aversatile method that can solve even highly nonlinear problems or the problems with multiple parameters. The methodology developed is applicable for inverse reliability analysis involving any number of fuzzy variables and random variables with any kind of distribution. The accuracy and efficiency of the proposed method is demonstrated through three examples involving explicit/implicit performance functions.

Design of three-layer antireflection coatings: a generalized approach

A generalized theoretical formulation for multilayer antireflection coatings (ARCs) has been established, which has scope for considering both zero and nonzero reflectance at one or more than one wavelength. Starting with this, a new design method for three-layer ARCs making use of input reflectance parameters at two wavelengths (R(1) and R(2) at lambda(1) and lambda(2)) has been developed. It allows for determination of all the unknown design parameters explicitly without any a priori conditions on them. The scope of the method has been extended by incorporating optimization of the resultant solutions through an optimizing parameter, integrated reflection loss R* to obtain efficient designs with respect to spectral bandwidth, residual reflection loss, etc. The resulting hybrid methodology is found to be generalized in that it can be used to design a wide range of ARC systems, broad band to V-type, irrespective of the nature of the substrate (absorbing or nonabsorbing) and spectral region of use, with adaptability to simpler/complex ARC systems and other thin film systems such as dichroics/beam splitters and achromatic reflectors.