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TRIAXYS g3 Wave Sensor Validation
WHITEPAPER
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DOCUMENT DESCRIPTION
Document Title TRIAXYS g3 Wave Sensor Validation
Document Release Date September 14, 2016
Prepared by:
AXYS Technologies
Head Office European Office 2045 Mills Road Esplanadestraat 1
Sidney, British Columbia 8400 Oostende Canada Belgium +1 250 655
5850 +32 (0) 470 102220
[email protected]
www.axystechnologies.com
mailto:[email protected]://www.axystechnologies.com/
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Executive Summary As part of the wave sensor validation to date,
the TRIAXYS g3 has been deployed in three sea trials with varying
ocean conditions. The test platform was a standard TRIAXYS 1m
directional wave buoy with both TRIAXYS Next Wave II (TRIAXYS NWII)
and TRIAXYS g3 sensors integrated into a single payload. These
co-located sensors gives the unique opportunity to directly compare
wave sensing technologies on a single platform removing any biases
from independently moored platforms. The study design follows
similar procedures WMO-JCOMM1 is using for the evaluation of
different Wave Measurement technologies in the PP-WET Study2. The
wave sensors were configured to sample motion data for 20 minute
durations with variable intervals.
This whitepaper demonstrates and discusses the TRIAXYS g3 wave
sensor and how this sensor compares to the previous model, the
TRIAXYS NWII, in wave sensing capabilities and performance. The
study concludes that the TRIAXYS g3 measures waves and sea states
with the equivalent accuracy of the TRIAXYS NWII wave sensor.
Introduction The TRIAXYS g3 is the culmination of nearly 20
years of wave sensing development work by AXYS Technologies (AXYS).
When the TRIAXYS sensor was introduced in the year 2000 it was a
pioneer in the field of solid state wave sensing, combining market
leading sensor technology with high accuracy wave algorithms
developed by AXYS and the Canadian Hydraulics Centre (CHC) of the
National Research Council of Canada (NRC). The software was derived
from the well-proven CHC GEDAPTM software package that has been
developed over many years at the CHC to satisfy a broad range of
real-world project requirements with particular emphasis on random
wave generation and data analysis in hydrodynamic laboratories.
GEDAPTM has also been used extensively to analyze full-scale
data.
Since the initial introduction of the sensor there has been a
series of iterations to improve the onboard data processing
capacity of the sensor, as well as functional enhancements such as
reduced power consumption and data storage capacity. The core
functionality has, however, remained consistent, ensuring a
long-term dataset of consistent, reliable, accurate wave data from
around the world.
The newest version of the sensor, the g3, combines a radically
reduced form factor with further power reduction and a significant
enhancement in processing features including:
- Continuous wave data output on a rolling one minute average
basis - Optimised compressed messages to reduce the cost of remote
telemetry - Enhanced onboard memory capacity to support a minimum
two year raw data storage - Full wave spectrum reporting and the
capacity to report on up to three user specified frequency
ranges in near real time
1 http://www.jcomm.info/ 2
ftp://ftp.wmo.int/Documents/PublicWeb/amp/mmop/documents/JCOMM-TR/J-TR-59-MARCDAT-III/ppts/G2-Swai-PP-WET.pdf
http://www.jcomm.info/ftp://ftp.wmo.int/Documents/PublicWeb/amp/mmop/documents/JCOMM-TR/J-TR-59-MARCDAT-III/ppts/G2-Swai-PP-WET.pdfftp://ftp.wmo.int/Documents/PublicWeb/amp/mmop/documents/JCOMM-TR/J-TR-59-MARCDAT-III/ppts/G2-Swai-PP-WET.pdf
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Initial Validation Studies In order to validate the accuracy of
the new TRIAXYS g3 wave sensor, the following three studies were
conducted:
Deployment Locations
Deployment Coordinates (deg) Mean Sea Level (m)
Number of Records
Deployment
Florencia Bay 48.95398, -125.61247 30 1313 September 2015 –
November 2015
Port Renfrew 48.53587, -124.48870 25 3155 November 2015 –
January 2016 German North Sea
54.53587, 6.48870 30 1870 November 2015 –
February 2016
Deployment Conditions Florencia Bay Port Renfrew North Sea
Parameter Min Max Min Max Min Max Hmax (m) 0.98 6.31 0.62 11.48
0.65 16.61 Hav (m) 0.34 2.45 0.23 4.59 0.27 4.3 Hsig (m) 0.57 3.72
0.35 6.93 0.41 6.62 H10 (m) 0.79 4.68 0.44 8.35 0.51 8.05 Tsig (s)
5.44 12.62 3.38 16.02 2.76 10.81 Tav (s) 3.84 8.52 2.77 12.99 2.35
8.83 T10 (s) 5.4 15.75 3.58 19.01 2.77 15.6 Hm0 (m) 0.69 3.76 0.42
7.00 0.43 6.87 Te (s) 5.67 14.65 4.32 16.61 3.29 18.46 Tmean(s)
4.11 8.08 2.95 12.69 2.54 9.32 TP (s) 4.76 20 3.57 28.57 2.53
28.57
The wave statistics comparison is split into 2 groups: the
Heave, zero crossing, based wave parameters and the spectra,
frequency, based parameters.
Zero Crossing Based Statistics • The r2 parameter of the wave
heights in all deployments is >0.99. • The ME illustrates an
average bias in the Havg and Hsig parameters of 0.01m and the Tavg
and
Tsig not exceeding 0.13s. • The MAE of the Havg and Hsig
parameters do not exceed 0.01m, with a maximum difference in
Hmax to be 0.04m. The periods show similar results with the MAE
of the Tavg and Tsig parameters not exceeding 0.17s.
• The RMSE has a maximum Havg and Hsig value of 0.02m with a
maximum Tavg and Tsig value of 0.2s.
https://www.google.com/maps/preview/@54.5358704,6.4887027,15z
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These differences equate to an excellent agreement between the
two wave sensing technologies and that the TRIAXYS g3 is capable of
measuring the equivalent heave based wave statistics as the TRIAXYS
NWII.
Florencia Bay Havg (m) Tavg
(s) Hsig (m)
Tsig (s)
H1_10 (m)
T1_10 (s)
Hmax (m)
r2 0.9974 0.9710 0.9992 0.9781 0.9991 0.9785 0.9962 g3 ME (m)
(s) 0.00 -0.13 0.00 -0.08 0.01 -0.05 0.02 g3 MAE (m) (s) 0.01 0.15
0.01 0.13 0.01 0.17 0.04 g3 MPE (%) -0.22 -2.21 0.26 -0.94 0.39
-0.51 0.65 g3 RMSE (m) (s) 0.02 0.19 0.01 0.20 0.02 0.25 0.05
Renfrew Havg (m) Tavg
(s) Hsig (m)
Tsig (s)
H1_10 (m)
T1_10 (s)
Hmax (m)
r2 0.9991 0.9961 0.9997 0.9969 0.9997 0.9940 0.9991 g3 ME (m)
(s) 0.00 0.01 0.00 0.01 0.00 0.01 0.00 g3 MAE (m) (s) 0.01 0.09
0.01 0.10 0.01 0.13 0.02 g3 MPE (%) 0.02 0.17 0.01 0.17 -0.01 0.14
-0.06 g3 RMSE (m) (s) 0.01 0.12 0.01 0.14 0.02 0.20 0.03
German North Sea Havg (m) Tavg
(s) Hsig (m)
Tsig (s)
H1_10 (m)
T1_10 (s)
Hmax (m)
r2 0.9994 0.9969 0.9998 0.9982 0.9996 0.9955 0.9938 g3 ME (m)
(s) 0.00 0.00 -0.01 0.00 -0.01 0.00 -0.01 g3 MAE (m) (s) 0.01 0.05
0.01 0.04 0.01 0.05 0.03 g3 MPE (%) -0.17 0.04 -0.20 0.05 -0.23
0.00 -0.26 g3 RMSE (m) (s) 0.02 0.06 0.02 0.05 0.03 0.09 0.13
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Spectral Based Statistics • The Hm0, Te and Tmean parameters
have excellent r2 values being >0.99. • The ME shows little bias
in Hm0 with a value of 0.01m and the Te and Tmean values resulting
in
a bias < 0.08s. • The mean direction of the Florencia Bay
deployment shows excellent correlation between the
two heading values of the sensors. With a mean absolute error of
1.75°. Similarly with the heave based wave statistics, the TRIAXYS
g3 is tightly coupled with the TRIAXYS NWII. Showing that the
TRIAXYS g3 can represent the equivalent spectral based wave
statistics as the TRIAXYS NWII.
Florencia Bay Hm0 (m) Te (s)
Tmean (s)
Tp (s)
Tp5 (s)
Mean Direction
(deg)
Mean Spread (deg)
r2 0.9998 0.9980 0.9972 0.9422 0.9972 0.9932 0.9534 g3 ME 0.01
-0.03 -0.08 -0.01 -0.02 0.67 -1.23 g3 MAE 0.01 0.05 0.08 0.13 0.07
1.75 1.24 g3 MPE (%) 0.33 -0.37 -1.28 0.37 -0.21 0.35 -3.17 g3 RMSE
0.01 0.07 0.09 0.93 0.17 2.35 1.65
Renfrew Hm0 (m) Te (s)
Tmean (s)
Tp (s)
Tp5 (s)
Mean Direction
(deg)
Mean Spread (deg)
r2 1.0000 0.9996 0.9999 0.9772 0.9986 0.7518a 0.9713 g3 ME 0.00
0.01 0.01 0.00 0.00 6.64a 0.05 g3 MAE 0.00 0.02 0.01 0.05 0.05
12.33a 0.72 g3 MPE (%) -0.02 0.10 0.10 0.13 0.04 3.29a 0.14 g3 RMSE
0.01 0.04 0.02 0.48 0.11 13.93a 1.00
German North Sea
Hm0 (m)
Te (s)
Tmean (s)
Tp (s)
Tp5 (s)
Mean Direction
(deg)
Mean Spread (deg)
r2 0.9995 0.9968 0.9997 0.9890 0.9988 0.8677a 0.9939 g3 ME -0.01
0.01 0.00 0.00 0.00 -4.87a 0.08 g3 MAE 0.01 0.02 0.01 0.03 0.02
7.04a 0.34 g3 MPE (%) -0.19 0.17 0.00 0.02 0.00 49.97a 0.25 g3 RMSE
0.02 0.07 0.02 0.22 0.06 23.95a 0.47
a Magnetic Calibration error
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Example Correlation Plots The correlation plots of the Hm0 and
Tmean parameters of the Port Renfrew deployment are illustrated
below. These graphs illustrate the tight correlation between the
TRIAXYS g3 and the NWII. The graphs represented in the following
figures are only shown for the Renfrew deployment. The Florencia
Bay and FINO 1 deployments have been omitted for brevity.
Figure 1 - Port Renfrew Correlation Plots
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Energy Spectra The wave spectra can be compiled into bins which
are defined by energy and frequency, the following graphs
illustrate 3 sets of information:
• Number of Observations – The number of measurements detected
by the TRIAXYS g3 sensor in the specified bin throughout the
deployment.
• Height Average Bias – The average bias in wave height for each
specified bin of the TRIAXYS g3 referenced to the TRIAXYS NWII.
Equivalent to the MPE equation in the wave statistics analysis.
• Height NRMSE Bias Removed – The normalized root-mean-square
error of the wave heights with the bias removed is the average
error percentage of the errors against the average errors of the
bin
The graphs below depict the wave spectra comparison of the Port
Renfrew deployment. Similarly with the wave statistics, only the
Renfrew data sets are presented for brevity.
The dotted line represents the theoretical wave spectra with an
Hs of 20m. The left axis depicts a logarithmic scale of the energy
in meters squared (m2) while the right axis shows the wave height
in meters (m). The x or bottom axis represents the scale for the
frequencies and periods.
The number of observations graph shows darker shaded bins
representing a higher observation count as described by the colour
bar. The comparison graphs of wave height and NRMSEBiasRemoved, are
filtered to a minimum observation count of 10.
The average wave height bias shows an excellent comparison with
little to no bias between the TRIAXYS g3 and the TRIAXYS NWII.
There are homogenous errors, approaching 0%, across significant
energies and frequencies. The NRMSEBiasRemoved graph shows
throughout the wave spectrum the two sensors show excellent
comparisons with the significant energies and frequency bins with a
results of
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Conclusion The typical wave height and period parameters: Havg,
Hsig, Hm0, Tavg, Tsig, Te and Tmean of the TRIAXYS g3 show
excellent correlation with the TRIAXYS NWII.
• The r2 values all exceed 0.99, with little variance and bias.
• The wave heights MAE does not exceed 0.01m with the Hmax MAE not
exceeding 0.04m. • The wave spectra reported by the TRIAXYS g3
compares with a typical error approaching 0%
when compared to the TRIAXYS NWII across significant energies
and frequencies. The TRIAXYS g3 measures waves and sea states with
the equivalent accuracy of the TRIAXYS NWII wave sensor.
Appendix – Wave Statistics Glossary
Parameter Description
Number of Zero Crossings
The number of zero down crossing waves in the heave
displacement
Havd Average wave height of zero down crossing waves Tavd
Average wave period of zero down crossing waves Hmax Maximum wave
height of zero down crossing waves
Tmax Wave period associated with Hmax
Peak Crest Peak wave amplitude above the mean water level.
Hsig Average wave height of highest 1/3 of waves
Tsig Average wave period of highest 1/3 of waves
H110 Average wave height of highest 1/10 of waves T110 Average
wave period of highest 1/10 of waves Tmean Mean wave period,
calculated from the spectral moments. Equal to sqrt(m0/m2) TP Peak
wave period in seconds. Tp = 1.0/fp where fp is the frequency at
which the wave
spectrum S(f) has its maximum value (Energy). TP Direction Mean
wave direction for the frequency corresponding to peak Period
TP Spread Wave directional spread (deviation) for the frequency
corresponding to peak Period
TP5 Peak wave period in seconds as computed by the Read method.
TP5 has less statistical variability than TP because it is based on
spectral moments.
Hm0 Significant wave height in meters as estimated from spectral
moment mo. HM0 = 4.0 * Sqrt(mo) where mo is the integral of
S(f)*df
Te Wave energy period in seconds, calculated from spectral
moments Mean Direction A single value representing the average wave
direction for the frequency spectrum.
(weighted by energy) Mean Spread A single value representing the
average wave spread for the frequency spectrum.
(weighted by energy)
TRIAXYS g3 wave sensor validation whitepaper.pdfExecutive
SummaryIntroductionInitial Validation StudiesDeployment
LocationsDeployment Conditions
Zero Crossing Based StatisticsSpectral Based StatisticsExample
Correlation PlotsEnergy SpectraConclusionAppendix – Wave Statistics
Glossary
