Probabilistic Interval Analysis for the Analytic Prediction of the Pattern Tolerance Distribution in Linear Phased Arrays with Random Excitation Errors

A statistical approach based on the interval analysis (IA) is proposed for the analysis of the effects, on the radiation patterns radiated by phased arrays, of random errors and tolerances in the amplitudes and phases of the array-elements excitations. Starting from the efficient, reliable, and inclusive computation of the bounds of the complex-valued interval array pattern function by means of IA, an analytic method is presented to yield closed-form expressions for the probability of occurrence of a user-chosen value of the power pattern or of its features within the corresponding IA-derived bounds. A set of numerical examples is reported and discussed to assess the reliability of the proposed probabilistic interval analysis (PIA) method with the results from Monte Carlo simulations as well as to point out its effectiveness and potentialities/advantages/efficiency in real applications of great industrial interest.