Improving correlation accuracy of crashworthiness applications by combining the CORA and MADM methods

With the increasing use of Computer Aided Engineering, it has become vital to be able to evaluate the accuracy of numerical models. This research poses the problem of selection of the most accurate and relevant correlation solution to a set of corridor variations. Specific methods such as CORA, widely accepted in industry, are developed to objectively evaluate the correlation between monotonic functions, while the Minimum Area Discrepancy Method, or MADM, is the only method to address the correlation of non-injective mathematical variations, usually related to force/acceleration versus displacement problems. Often, it is not possible to differentiate objectively various solutions proposed by CORA, which this paper proposes to answer. This research is original, as it proposes a new innovative correlation optimisation framework, which can select the best CORA solution by including MADM as a subsequent process. The paper and the methods are rigorous, having used an industry standard driver airbag computer model, built virtual test corridors and compared the relationship between different CORA and MADM ratings from 100 Latin Hypercube samples. For the same CORA value of ‘1’ (perfect correlation), MADM was capable to objectively differentiate between 13 of them and provide the best correlation possible. The paper has recommended the MADM settings n = 1; m = 2 or n = 3; m = 2 for a congruent relationship with CORA. As MADM is performed subsequently, this new framework can be implemented in already existing industrial processes and provide automotive manufacturers and Original Equipment Manufacturers (OEM) with a new tool to generate more accurate computer models.

The method of simple iterations with correction of convergence and the minimal discrepancy method for plasmonic problems

The problem of searching for complex roots of the dispersion equations of plasmon-polaritons along the boundaries of the layered structure-vacuum interface is considered. Such problems arise when determining proper waves along the interface of structures supporting surface and leakage waves, including plasmons and polaritons along metal, dielectric and other surfaces. For the numerical solution of the problem, we consider a modification of the method of simple iterations with a variable iteration parameter leading to a zero derivative of the right side of the equation at each step, i.e. convergent iterations, as well as a modification of the minimum residuals method. It is shown that the method of minimal residuals with linearization coincides with the method of simple iterations with the specified correction. Convergent methods of higher orders are considered. The results are demonstrated by examples, including complex solutions of dispersion equations for plasmon-polaritons. The advantage of the method over other methods of searching for complex roots in electrodynamics problems is the possibility of ordering the roots and constructing dispersion branches without discontinuities. This allows you to classify modes.