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Measuring flow speeds in natural waters by training an artificial neural network to analyze high-frequency flow-induced vibrations of tethered floats

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Abstract

Measuring water currents in natural waters is limited by the cost of sensors. Standard sonar-based acoustic current Doppler profilers (ADCPs) are high cost, about $10–20 K per unit. Tilt current meters (TCMs) are much cheaper. They consist of a bottom-mounted subsurface float equipped with an inertial measurement unit (IMU) and data center that records the float’s motion and attitude as a time series. The flow speed is measured by calculating the tilt angle of the float in response to the current. However, tilt-based measurements require the float system to be carefully engineered and its physical response optimized for good results. Even so, high-frequency flow-induced vibrations often dominate the motion and must be averaged and filtered out of the data and discarded. This represents the loss of potentially valuable information, but decoding the high-frequency components for such useful data is difficult. These experiments explored using an artificial neural network (ANN) approach to extract the ambient water current speed from that high-frequency data alone, after the displacement information was filtered out. The methods were informed by the ANN designs and data augmentation techniques used by neurologists to observe the tremors and other motions exhibited by patients experiencing symptoms of Parkinson’s disease. Once the model was trained using carefully selected training and validation sets to prevent overfitting, the results of evaluating previously unseen data by the model are clear and promising. Water current speed was accurately calculated from the high-frequency components of the motion sensor data and agreed with corresponding current speeds measured by established methods. This novel approach could facilitate new sensor system designs that can be empirically or self-calibrated more efficiently and have a lower barrier to application than those currently available.

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Fig. 1

Source: diagram drawn by the author from documentation provided by the manufacturer (Lowell Instruments LLC & North Falmouth MA, 2017) as well as background information from Figurski et al. (2011)

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Source: drawn by the author from direct observation and information in the TCM-1 manual (Lowell Instruments LLC & North Falmouth MA, 2017)

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All data and metadata needed to replicate the work shown in this manuscript are available by request from the author.

Code availability

Program source codes and instructions necessary to run said codes to replicate the work shown in this manuscript are available by request from the author.

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Acknowledgements

I would like to acknowledge my doctoral advisor John Janssen for his valuable input and guidance and the use of his equipment. Doctoral committee members J. Val Kump, James T. Waples, and Hector Bravo provided valuable feedback and encouragement. My colleague Matthew Smith Ph.D. was the primary investigator on the in-house 2015 float meter project and Maureen Schneider deployed the floats in 2015. Hector Bravo allowed my use of his Nortek Aquadopp. Ryan Davis of UW-Madison assisted with the 2018 tilt meter deployments. Michelle N. Hansen provided valuable support and proofreading. Dr. Jake Luo gave precious input and advice in finishing this work. Finally, the University of Wisconsin-Milwaukee School of Freshwater Sciences provided lab space, ship time, and other material support for this research.

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    Thomas F. Hansen Ph.D.

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The abstract for a precursor to this current work appeared in the IAGLR Conference Proceedings 2019 (http://iaglr.org/conference/proceedings/2019/prof493.html). No additional paper or other text was submitted to the IAGLR, and the present manuscript differs substantially from the abstract submitted to IAGLR. I am revealing it here because, at first glance, the work seems similar.

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Hansen, T.F. Measuring flow speeds in natural waters by training an artificial neural network to analyze high-frequency flow-induced vibrations of tethered floats. Environ Monit Assess 194, 129 (2022). https://doi.org/10.1007/s10661-021-09744-1

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