Construction of a generalized probabilistic-physical model of reliability of a two-level active phased antenna array

Abstract

A generalized probabilistic-physical model of reliability of a two-level active phased antenna array (APAA) of a multifunctional radar station was presented.When constructing the APAA physical model, definitions of failures of the radiating channel and the antenna array as a whole were formulated. Key parameters of the APAA were chosen: radiation power, gain in transmission and the top level of the near side lobes. This has made it possible to formulate generalized criteria of failure of the APAA operating in the modes of transmission and reception as well as determine the permissible number of failures of the radiating channels and receiving modules. The physical model of the APAA reliability was formalized by a system of equations describing deviation of key parameters of the antenna array beyond the permissible limits. At the same time, boundary (permissible) values of the number of failed radiating channels and receiving modules were found that provide critical (minimum permissible) values of key parameters of the antenna array.To construct a probabilistic model of the APAA reliability, the antenna array was defined as an isotropic hierarchical system and a formula was derived for determining the average number of operable radiating channels in the multi-level APAA structure. A block-diagram of reliability of receiving and transmitting sub-arrays, receiving and transmitting APAA has been built and formalized. Definition of failures of the receiving and transmitting sub-arrays, receiving and transmitting APAA was given. This has allowed us to derive analytical expressions for determining mean time to failure, probability of failure-free operation, density of time to failure and failure rates for sub-arrays and the APAA. Exponential distribution (for sudden failures), diffusional non-monotonic distribution (for gradual failures) and composition of exponential and diffusional non-monotonic distributions (at a joint manifestation of sudden and gradual failures) were used as models of failure of SHF elements, transistors, radiating channels and receiving modules. An illustrative example of calculation of the average time to failure of a two-level APAA of a multifunctional RS including 6400 radiating channels was presented.