Identifying molecular structures of water and ice helps reveal the chemical nature of liquid and solid water. Real-space geometrical information on molecular systems can be precisely obtained from molecular simulations, but classifying the resulting structure is a non-trivial task. Order parameters are ordinarily introduced to effectively distinguish different structures. Many order parameters have been developed for various kinds of structures, such as body-centered cubic, face-centered cubic, hexagonal close-packed, and liquid. Order parameters for water have also been suggested but need further study. There has been no thorough investigation of the classification capability of many existing order parameters. In this work, we investigate the capability of 493 order parameters to classify the three structures of ice: Ih, Ic, and liquid. A total of 159 767 496 combinations of the order parameters are also considered. The investigation is automatically and systematically performed by machine learning. We find the best set of two bond-orientational order parameters, Q4 and Q8, to distinguish the three structures with high accuracy and robustness. A set of three order parameters is also suggested for better accuracy.