Stochastic and sensitivity analysis of shape error of inflatable antenna reflectors

• Published in: Acta astronautica 2017-03, Vol.132, p.170-176
• Main Authors: San, Bingbing, Yang, Qingshan, Yin, Liwei
• Format: Article
• Language: English
• Subjects: Antennas; Apertures; Correlation analysis; Error analysis; Error detection; Global sensitivity analysis; Hypercubes; Inflatable antenna reflectors; Latin hypercube sampling; Modulus of elasticity; Pressure variations; Probability distribution; Random errors; Ranking; Reflectors; Regression analysis; Satellite communications; Satellite observation; Satellites; Sensitivity analysis; Shape error; Shape error control; Space exploration; Statistical analysis; Stochastic analysis; Stochastic models; Weight
• ISSN: 0094-5765; 1879-2030
• DOI: 10.1016/j.actaastro.2016.12.015

Inflatable antennas are promising candidates to realize future satellite communications and space observations since they are lightweight, low-cost and small-packaged-volume. However, due to their high flexibility, inflatable reflectors are difficult to manufacture accurately, which may result in undesirable shape errors, and thus affect their performance negatively. In this paper, the stochastic characteristics of shape errors induced during manufacturing process are investigated using Latin hypercube sampling coupled with manufacture simulations. Four main random error sources are involved, including errors in membrane thickness, errors in elastic modulus of membrane, boundary deviations and pressure variations. Using regression and correlation analysis, a global sensitivity study is conducted to rank the importance of these error sources. This global sensitivity analysis is novel in that it can take into account the random variation and the interaction between error sources. Analyses are parametrically carried out with various focal-length-to-diameter ratios (F/D) and aperture sizes (D) of reflectors to investigate their effects on significance ranking of error sources. The research reveals that RMS (Root Mean Square) of shape error is a random quantity with an exponent probability distribution and features great dispersion; with the increase of F/D and D, both mean value and standard deviation of shape errors are increased; in the proposed range, the significance ranking of error sources is independent of F/D and D; boundary deviation imposes the greatest effect with a much higher weight than the others; pressure variation ranks the second; error in thickness and elastic modulus of membrane ranks the last with very close sensitivities to pressure variation. Finally, suggestions are given for the control of the shape accuracy of reflectors and allowable values of error sources are proposed from the perspective of reliability. •We conduct a stochastic study on the shape error of initially curved antennas.•A global sensitivity analysis ranks the effects of manufacturing error sources.•Suggestions are given in controlling the shape of reflectors.