Robust spectral estimation for speed of sound with phase shift correction applied online in yeast fermentation processes

Ultrasound techniques are well suited to provide real-time characterization of bioprocesses in non-invasive, non-contact, and non-destructive low-power consumption measurements. In this paper, a spectral analysis method was proposed to estimate time of flight (TOF) between the propagated echoes, and its corresponding speed of sound (USV). Instantaneous power spectrum distribution was used for accurate detection of echo start times, and phase shift distribution for correcting the involved phase shifts. The method was validated by reference USV for pure water at 9-30.8°C, presenting a maximum error of 0.22%, which is less than that produced by the crosscorrelation method. Sensitivity analyses indicated a precision of 6.4 × 10^-3% over 50 repeated experiments, and 0.11% over two different configurations. The method was competently implemented online in a yeast fermentation process, and the calculated USV was combined with temperature and nine signal features in an artificial neural network. The network was designed by back propagation algorithm to estimate the instantaneous density of the fermentation mixture, producing a maximum error of 0.95%.