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The paper describes a new theory for correcting track irregularities by applying their restored waveforms and carrying out experimental leveling and lining work. In this theory, the optimum shifting/lifting values are obtained as solutions for a typical quadratic programming problem. Restrictions on shifting rails are formulated as constraint conditions of the optimization problem. Furthermore, in the case of levelling work, a designed cross level can be realized. From experimental work on ballasted and slab track, the effectiveness of this theory has been confirmed. In the range of long wavelengths up to 50 m (164 ft), the amplitude of track irregularity has decreased.

Theory and Practice of Optimum Correction using Restored Track Irregularity Waveform.