Ultrasonic Measurement of
Wave Height
Liping Huang
Project Description
• Tasks
– Simulate a wave in the water surface.
– Design a ultrasonic system to measure the
distances between the water surface and the
transducer fixed in the bottom of water pool.
– Calculate the spectrum of the surface wave.
Ocean Surface Wave
•
•
•
Related to wind over the ocean.
Various wavelengths and wave frequencies.
Simplified mathematical expression at one position:
y = f (t )
A short record of wave
amplitude measured by
a wave buoy in the
North Atlantic.
[R. H. Stewart, 2005]
Spectrum of Wave
•
Spectrum of digitized wave
record (with length T). one
periodogram.
•
Describe waves in certain
frequency range:
1
1
< f <
T
2Δ
•
Energy spectrum/wave-height
spectrum:
– Average 10-30 periodograms.
– Needed data for three hours
typically.
[R. H. Stewart, 2005]
Spectrum of Wave
• Spectrum ÅÆ Wind speed.
– F.ex: 10 kt ÅÆ fmax = 0.248 Hz
• Various idealized ocean wave spectra ÅÆ
Sepecified wind, such as speed, time, area.
• Applications:
– Estimate the biggest waves produced by a given
wind in designing ships or offshore structures.
– Wave forecasting following the wave spectrum
together with wind models. (by meteorological
agencies)
Measurement of Waves
•
•
•
•
Sea state estimated by observers at sea.
Satellite altimeters.
Synthetic aperture radars on satellite.
Accelerometer mounted on meteorological
or other buoy.
• Wave gages.
Measurement System Using
Ultrasound
t = ti
d i = cΔti
2
h i = di − d0
Spectrum Estimation
• ARMA process
q
p
k =0
i =0
x (nT ) = ∑ bk u (nT − kT ) − ∑ ai x(nT − iT )
• Estimate the (p+q) parameters: ai and bk
• Spectrum
q
S( f ) =
T ∑ bk exp(−2πjkTf )
2
k =0
p
1 + ∑ ai exp(−2πjiTf )
i =0
2
Spectrum Estimation
-Maximum Entropy Method
• AR process
p
x (nT ) = b 0 u (n) − ∑ ai x(nT − iT )
i =0
• Estimate the (p+1) parameters: ai and b0
• Spectrum
2
S( f ) =
b0 T
p
1 + ∑ ai exp(−2πjiTf )
i =0
2
Spectrum Estimation
• Benefits:
– Reduce needed amount of data.
– Keep the information content significantly.