We present an efficient method to optimize sensor placement for flow
estimation using sensors with time-delay embedding in advection-dominated
flows. Our solution allows identifying promising candidates for sensor
positions using solely preliminary flow field measurements with
non-time-resolved Particle Image Velocimetry (PIV), without introducing
physical probes in the flow. Data-driven estimation in advection-dominated
flows often exploits time-delay embedding to enrich the sensor information for
the reconstruction, i.e. it uses the information embedded in probe time series
to provide a more accurate estimation. Optimizing the probe position is the key
to improving the accuracy of such estimation. Unfortunately, the cost of
performing an online combinatorial search to identify the optimal sensor
placement in experiments is often prohibitive. We leverage the principle that,
in advection-dominated flows, rows of vectors from PIV fields embed similar
information to that of probe time series located at the downstream end of the
domain. We propose thus to optimize the sensor placement using the row data
from non-time-resolved PIV measurements as a surrogate of the data a real probe
would actually capture in time. This optimization is run offline and requires
only one preliminary experiment with standard PIV. Once the optimal positions
are identified, the probes can be installed and operated simultaneously with
the PIV to perform the time-resolved field estimation. We show that the
proposed method outperforms equidistant positioning or greedy optimization
techniques available in the literature.

Questo articolo esplora i giri e le loro implicazioni.

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