Aerospace dielectric components of orbital spacecrafts are frequently exposed to harsh space environment, where beam irradiation leads to persistent charging and discharging of these dielectric materials. Here the dynamic charge transport behaviors of advanced aerospace dielectrics under electron beam irradiation are investigated by combining the drift-diffusion electron-hole transport model and synthetic surface charging diagnostics. Based on the measured trap state distribution and surface conductivity, numerical simulation of typical aerospace dielectrics with a focus on the polyimide is performed. The simulation reveals the spatial-temporal evolution of microscopic quantities consisting of the current density, charge density, electric field distribution, in addition to the time evolution of macroscopic quantities namely the sample current, secondary emission yield (SEY) and surface potential. Factors affecting the dielectric charging process, including beam energy, beam current, material type, and sample thickness, are analyzed. Dedicated relation between the beam energy and final surface potential is determined, while the beam current is found to only affect the charging speed. The effects of material type on the charging process are due to a range of combined channels via different primary range, permittivity, surface resistivity, trap state distribution, electron affinity, etc. The observed trends of surface potential, sample current, and SEY in experiment are generally consistent with the model prediction, and possible explanations for the discrepancies are provided. In the end, implications of the obtained conclusions for the electrostatic discharges on aerospace dielectrics are discussed.