  Galactic black hole X-ray binaries (BHXBs) provide excellent laboratories to
study accretion, as their relatively quick evolution allows us to monitor large
changes in the in-flowing and/or out-flowing material over human timescales.
However, the details of how the inflow-outflow coupling evolves during a BHXB
outburst remain an area of active debate. In this work we attempt to probe the
physical changes underlying the system evolution, by performing a systematic
analysis of the multi-wavelength data of three BHXB sources: XTE J1752-223,
MAXI J1659-152, and XTE J1650-500, during hard and hard-intermediate states.
Using the power spectral hue which characterises the X-ray variability
properties, we identify several clusters of BHXB epochs and perform the joint
multi-wavelength spectral modelling to test their commonality with a physical
jet model. Under the assumption that the corona is related to the base of the
jet, we find that the power spectral hue traces the variation of the coronal
radius(from ~10Rg - ~40Rg) in multiple BHXBs at hard and hard-intermediate
states, and that the data are consistent with moderately truncated accretion
discs (<25Rg) during hard-intermediate states. We also find that all epochs of
low disc reflection have high hue located near the hard-intermediate to
soft-intermediate state transition, indicating that in these states the
vertical extent of the corona and/or its bulk speed are increasing. Our results
link the geometrical similarity in the corona among multiple BHXB sources to
their timing characteristics, and probe the corona responding to the disc-jet
interactions at hard and intermediate states during outbursts.
