Measurement of deflections and of oscillation frequencies of engineering structures using Robotic Theodolites (RTS)

The Robotic Theodolite or Robotic Total Station (RTS) is a new generation geodetic instrument that can automatically record the changing coordinates of a moving target (reflector). RTS was so far used for monitoring of static and very slow displacements. This limitation was imposed by some characteristics of these instruments (real sampling rate <2 Hz and non-constant, noisy results in high frequency sampling, etc.). A study of a new generation of RTS based on: (1) systematic experiments using an apparatus producing oscillations of known, computer-determined characteristics (frequency and amplitude of oscillation) which were compared with those recorded by the RTS; (2) upgrading of the instrument’s built-in software to display measurements with a 0.01 s resolution; and (3) spectral analysis of the obtained non-equidistant data with a least-squares based software without prior interpolations, permitted us to show that the range of application of RTS may be safely extended to higher frequency oscillations.In particular, it was shown that: (1) the maximum real sampling rate of RTS is 6–7 Hz, but since sampling rate is variable, aliasing-free results can be obtained above the Nyquist frequency. (2) The potential to record oscillations depends on the maximum angular velocity of the instrument and on the maximum velocity of the moving target; for velocities up to about 10 cm/s in field studies, results are very precise. On the contrary, for targets moving with maximum velocities > 15 cm/s, some displacements cycles are not well-defined or are lost, and hence, the accuracy of the oscillation amplitude and frequency are lower. (3) RTS can be used to measure small (on the order of a few mm) amplitudes of oscillation, and to some degree of frequencies of oscillation of various relatively stiff engineering structures (modal frequencies > 1 Hz, up to 3–4 Hz). This potential is demonstrated on the basis of several field examples, including the monitoring of two bridges with dominant modal frequencies > 1.5 Hz.Obviously, these limits reflect the most unfavorable cases of application of RTS, and higher period/larger amplitude oscillations or other deflections can be successfully measured if the main requirement for this type of instrument is satisfied: an unobstructed view of a reflector at a maximum distance of a few hundred meters from an RTS set on stable ground.