A method based on an interval arithmetic is proposed to analyze uncertain factors such as the curvature radii, excitation amplitude, and excitation phase of a spherical conformal array antenna. An interval description of element factors under different curvature radii of spherical substrates is established using the surrogate model based on the data obtained through a full-wave analysis method. The interval formula of the spherical curvature radius and array element position error is derived and the effects of the spherical radius tolerance, excitation amplitude tolerance, and excitation phase tolerance on the antenna power pattern are studied. To evaluate the effectiveness and reliability of the proposed method, a set of representative numerical results are reported and discussed and a comparison with the Monte Carlo methods and full-wave simulation is described. This method can be widely used during the antenna design and before the antenna prototyping/manufacturing to predict the effects, on the radiation performance, of possible errors/tolerances in the antenna structure to guarantee the antenna working 'in operation'.
Keywords: interval arithmetic; spherical conformal array antenna; surrogate model; tolerance analysis.