Length measurement of curved pipes and branch pipes using stationary waves

The author previously proposed an on-line length measurement system for straight pipes using stationary waves which were generated in the pipes. The measurement system regarded several of the stationary waves as state variables of a linear dynamic system and realized an online high-accurate length measurement of the pipes. This paper presents length measurement systems for curved and branch pipes by extending the pre-proposed measurement system. Experimental results show that accurate pipe length measurement is realized with the methods