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... the scale is taken to a certain value, the logarithm of the scale and its corresponding box number no longer maintain a linear relationship, that is, the signal no longer has fractal characteristics. Table 1 lists the number of boxes with scales from 1 to 30 for a simulated ultrasonic signal with a signal-to-noise ratio of 30 dB. It can be seen the good downward trend is no longer maintained when δ is equal to 19 from table 1, that is, the ultrasonic signal is a non-strict random fractal. ...Citations
... Major parameters include defects in the material, positioning of the sensor, coupling conditions, damping and reflections [5][6][7]. For regular excitation patterns, such as a sine wave or an impulse stimulation, the CCF exhibits many local maxima with similar correlation factors as the global maximum because of the resonant eigenfrequencies of the transducer, causing ambiguity [8][9][10]. ...
The cross-correlation function (CCF) is an established technique to calculate time-of-flight for ultrasonic signals. However, the quality of the CCF depends on the shape of the input signals. In many use cases, the CCF can exhibit secondary maxima in the same order of magnitude as the main maximum, making its interpretation less robust against external disturbances. This paper describes an approach to optimize ultrasonic signals for time-of-flight measurements through coded excitation sequences. The main challenge for applying coded excitation sequences to ultrasonic signals is the influence of the piezoelectric transducer on the outgoing signal. Thus, a simulation model to describe the transfer function of an experimental setup was developed and validated with common code sequences such as pseudo noise sequences (PN), Barker codes and chirp signals. Based on this model an automated optimization of ultrasonic echoes was conducted with random generated sequences, resulting in a decrease in the secondary positive maximum of the CCF to 56.6%. Based on these results, further empiric optimization leveraging the nonlinear regime of the piezoelectric transducer resulted in an even lower secondary positive maximum of the CCF with a height of 25% of the first maximum. Experiments were conducted on different samples to show that the findings hold true for small variations in the experimental setup; however, further work is necessary to develop transfer functions and simulations able to include a wider parameter space, such as varying transducer types or part geometry.
