Moments method (Statistics)

Computational accuracy is widely recognized as a critical issue in applied electromagnetics. Increasing computational power is being applied to solve more complex electromagnetic systems with an emphasis on computational accuracy. The work of this thesis is focused on the implementation of Method of Moments (MoM) to integral equation formulations. The goal of this effort is to use what is known as condition number, and, a heuristic rule-of-thumb is applied to investigate the computational accuracy of MoM in numerical electromagnetics. Other possible applications of condition number of the MoM matrix are also indicated.

It is known that response probability densities, although important in failure analysis, are seldom achievable for stochastically excited systems except for linear systems under additive excitations of Gaussian processes. Most often, statistical moments are obtainable analytically or experimentally. It is proposed in this thesis to determine the probability density from the known statistical moments using artificial neural networks. A multi-layered feed-forward type of neural networks with error back-propagation training algorithm is proposed for the purpose and the parametric method is adopted for identifying the probability density function. Three examples are given to illustrate the applicability of the approach. All three examples show that the neural network approach gives quite accurate results in comparison with either the exact or simulation ones.

For certain wavelength size objects, the frequency range between 100 MHz and 1000 MHz spans a transition region when using low frequency electromagnetic scattering codes based on Method of Moments (MoM) to high frequency codes based on Physical Theory of Diffraction (PTD) and ray tracing techniques. As the wavelength size of the object increased, MoM codes can require prohibitively long computational times and hence the more approximate high frequency codes become more attractive. The Ohio State Material Wire code (MATWRS) was selected as a representative MoM code for characterizing the transition region. XPATCH was selected as a representative high frequency code with ACAD used as the general modeling program. To evaluate these codes, a comparison of Radar Cross Section (RCS) predictions for simple PEC canonical shapes was made. Comparisons were made to both measured data where available and predictions generated by the McDonnell Douglas Body of Revolution (BOR) code.