Shipboard Wave Measurement Through Fusion of Wave Radar and Ship Motion Data

Transcription

1 Copy No. Defence Research and Development Canada Recherche et développement pour la défense Canada DEFENCE & DÉFENSE Shipboard Wave Measurement Through Fusion of Wave Radar and Ship Motion Data D.C. Stredulinsky E.M. Thornhill Defence R&D Canada Atlantic Technical Memorandum DRDC Atlantic TM February 2009

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3 Shipboard Wave Measurement Through Fusion of Wave Radar and Ship Motion Data D.C. Stredulinsky E.M. Thornhill Defence R&D Canada Atlantic Technical Memorandum DRDC Atlantic TM February 2009

4 Principal Author Original signed by Dave Stredulinsky Dave Stredulinsky Approved by Original signed by N.G. Pegg N.G. Pegg Head/Warship Performance Approved for release by Original signed by Ron Kuwahara for Calvin Hyatt Chair/Document Review Panel c Her Majesty the Queen in Right of Canada as represented by the Minister of National Defence, 2009 c Sa Majesté la Reine (en droit du Canada), telle que représentée par le ministre de la Défense nationale, 2009

5 Abstract DRDC Atlantic is considering shipboard wave measurement systems for use with seakeeping, slam warning and other ship operator guidance systems. Wave radars which extract wave information from the sea clutter in X-band navigational radar images have been found to provide reasonably accurate wave direction and frequency information but often inaccurate wave heights. A fusion algorithm has been developed which uses ship motion measurements to improve the accuracy of wave heights obtained from the wave radar. The method was tested with data collected using a WaMoS II wave radar processor during a sea trial on CFAV QUEST in January 2006 and in a sea trial aboard HMCS KINGSTON in March Application of the fusion algorithm to the QUEST data demonstrated promising results. During the HMCS KINGSTON sea trial the wave radar generally provided good wave period and direction measurements but poor wave heights (typically a factor of two or three times lower than heights measured with a wave buoy). While the wave fusion method considerably improved the wave height measurements for QUEST, the results were not as good for KINGSTON, and exhibited two to three times more scatter when compared to wave buoy data. Résumé DRDC Atlantique envisage d utiliser des systèmes de mesure des vagues à bord de navires, de concert avec le système de tenue à la mer, le système d avertissement de tossage et d autres systèmes d orientation par l opérateur. On a constaté que les radars de mesure des vagues qui recueillent des données sur la hauteur des vagues en retour de mer par images radar de navigation sur la bande X donnent des renseignements précis sur la direction des vagues et leur fréquence, mais les mesures de leur hauteur sont souvent erronées. On a créé un algorithme de fusion qui a recours aux mesures de mouvement du navire pour améliorer l exactitude des mesures des vagues obtenues du radar de mesure des vagues. Cette méthode a été mise à l épreuve au moyen des données recueillies à l aide d un processeur de radar de mesure des vagues WaMoS II lors d essais à la mer à bord du NAFC QUEST en janvier 2006, et à bord du NCSM KINGSTON en mars L application de l algorithme de fusion aux données du NAFC QUEST a révélé des résultats prometteurs. Lors de l essai à la mer à bord du NCSM KINGSTON, le radar de mesure des vagues donnait en général de bonnes mesures sur la période des vagues et leur direction, mais celles sur leur hauteur étaient erronées (généralement deux à trois fois plus faibles que les valeurs mesurées par une bouée de mesure des vagues). Bien que la méthode de fusion de mesure des vagues ait amélioré de manière considérable les mesures de hauteur des vagues dans de cas du NAFC QUEST, les résultats n ont pas été aussi concluants à bord du NCSM KING- STON et indiquaient deux à trois fois plus de diffusion par rapport aux données provenant de la bouée. DRDC Atlantic TM i

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7 Executive summary Shipboard Wave Measurement Through Fusion of Wave Radar and Ship Motion Data D.C. Stredulinsky, E.M. Thornhill; DRDC Atlantic TM ; Defence R&D Canada Atlantic; February Background: The DRDC Atlantic Warship Performance section has had an interest in shipboard measurement of the wave environment for many years. In recent years there have been significant advances in wave radar technology (systems that extract wave data from backscatter (sea clutter) information contained in X-band navigational radar display images). While wave radars are fairly good at measurement of wave frequency and direction, it is DRDC s experience that it is still difficult to obtain accurate wave heights from these systems. In this research a fusion algorithm has been developed which compares measured and predicted ship motion responses to improve the accuracy of wave radar height measurements. Data from sea trials with a WaMoS II wave radar processor on CFAV QUEST and on HMCS KINGSTON were used to test the fusion algorithm. Principal results: For CFAV QUEST the fusion algorithm produced wave heights that were within ±15 percent of wave buoy measurements for most cases for significant wave heights greater than 2.5 m, reducing the scatter in wave radar height measurements by a factor of three or greater. The study also showed that using a combination of pitch angle and CG heave displacements (to correct wave radar data) provided the best improvement of wave radar height measurements. The results from the KINGSTON data analysis were not as good and require further investigation. Significance of results: Seakeeping and other ship operator guidance systems require accurate knowledge of the seaway wave height, wave frequency and wave direction information in order to provide reliable tactical guidance to operators. The fusion of wave radar and measured ship motion data shows promise for fulfilling this requirement. Future work: Another QUEST trial was conducted in November/December 2008 to demonstrate the use of the wave fusion method in real time. The trial was very successful and detailed data analysis is underway. The KINGSTON trial data will be considered further to try to understand why the fusion algorithm did not perform as well for this ship. Other hydrodynamic codes will be tested as well to see, for example, if 3D panel codes provide better results than the strip theory code ShipMo7 used in this study. If the demonstration of the wave fusion method is successful then the method will be incorporated into the concept demonstration Seakeeping Operator Guidance capability for real time and tactical operator guidance. DRDC Atlantic TM iii

8 Sommaire Shipboard Wave Measurement Through Fusion of Wave Radar and Ship Motion Data D.C. Stredulinsky, E.M. Thornhill; DRDC Atlantic TM ; R & D pour la défense Canada Atlantique; février Introduction: La section de l évaluation de la performance des navires de combat de RDDC Atlantique est intéressée depuis nombre d années à la mesure des vagues à partir du navire. Au cours des dernières années, des progrès importants ont été réalisés dans la technologie des radars de mesure des vagues (des systèmes qui recueillent des données à partir des renseignements du retour de mer contenus dans les images des radars de navigation dans la bande X). Bien que ce type de radar soit passablement précis dans la mesure de la fréquence et de la direction des vagues, l expérience de RDDC en la matière démontre qu il est toujours difficile d obtenir de tels systèmes des mesures précises de hauteur des vagues. Au cours de la présente recherche, on a créé un algorithme de fusion qui compare les mesures et les prévisions de la réponse en mouvement du navire afin d améliorer la précision des mesures de hauteur de vagues des radars de ce genre. Des données d essais à la mer obtenues d un processeur de radar de mesure de vagues WaMoS II à bord du NAFC QUEST et à bord du NCSM KINGSTON ont servi à mettre à l épreuve l algorithme de fusion. Résultats principaux: Dans le cas du NAFC QUEST, l algorithme de fusion a produit dans la plupart des cas des mesures de hauteur de vagues qui étaient précises à 15 % près des mesures provenant d une bouée de mesure des vagues pour des hauteurs de vagues de plus de 2,5 m. On obtenait une réduction par un facteur de trois ou plus de la diffusion des mesures de hauteur de vagues par radar. L étude a également démontré que l utilisation d une combinaison d angle de tangage et de déplacement vers le haut du CG (pour corriger les données du radar de mesure des vagues) donnait la plus grande amélioration des mesures de hauteur par un radar de mesure des vagues. Les résultats de l analyse des données du NCSM KINGSTON n étaient pas aussi précis et exigent des recherches plus approfondies. Portée: Le système de tenue à la mer et les autres systèmes d orientation pour l opérateur nécessitent une connaissance précise de la hauteur des vagues de mer, de leur fréquence et de leur direction afin de procurer aux opérateurs une orientation tactique fiable. La fusion des données des radars de mesure des vagues et de mesure des mouvements du navire est prometteuse pour ce aui est de satisfaire à cette exigence. iv DRDC Atlantic TM

9 Recherches futures: Un autre essai à bord du NAFC QUEST a eu lieu en novembre/décembre 2008 afin de démontrer l utilisation de la méthode de fusion de mesure des vagues en temps réel. L essai a été couronné de succès et une analyse détaillée des données est en cours. Les données de l essai du NCSM KINGSTON feront l objet d une analyse plus poussée afin de comprendre la raison pour laquelle l algorithme de fusion ne s est pas comporté aussi bien dans le cas de ce navire. D autres codes hydrodynamiques seront testés également, par exemple pour voir si des codes de panneaux tridimensionnels donnent de meilleurs résultats que le code de prévision de tenue à la mer ShipMo7 utilisé dans la présente étude. Si la démonstration de la méthode de fusion des mesures de vagues s avère réussie, la méthode sera alors intégrée dans la démonstration du concept de capacité d orientation sur la tenue à la mer pour l opérateur en temps réel et d orientation tactique de l opérateur. DRDC Atlantic TM v

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11 Table of contents Abstract i Résumé i Executive summary Sommaire iii iv Table of contents vii List of figures List of tables ix xii 1 Introduction Wave Radar Measurement Method Wave Fusion Method QUEST Q293 Sea Trial Data Analysis Wave Measurements Ship Motion Measurements Radar Wave Spectra for Runs ShipMo7 Motion Response Predictions Fusion Algorithm Results KINGSTON 2007 Sea Trial Data Analysis Wave Measurements Trial Measurements ShipMo7 Validation Wave Fusion Results Summary and Conclusions Future Work DRDC Atlantic TM vii

12 References Annex A: QUEST Q293 Trial Significant Wave Height Measurements Annex B: Sample ShipMo7 Input Files B.1 Main Input File B.2 Sample ShipMo7 Directional Wave Spectrum Input File Annex C: QUEST Fusion Algorithm Results for Input of Various Motion Components C.1 Fusion of Measured Heave Acceleration with Radar and Buoy Wave Spectra C.2 Fusion of Measured Heave Displacement with Radar and Buoy Wave Spectra C.3 Fusion of Measured Pitch Angle with Radar and Buoy Wave Spectra C.4 Fusion of Measured Heave Acceleration and Pitch Angle with Radar and Buoy Wave Spectra C.5 Fusion of Measured Heave Displacement and Pitch Angle with Radar and Buoy Wave Spectra C.6 Fusion of Measured Heave Acceleration and Heave Displacement with Radar and Buoy Wave Spectra viii DRDC Atlantic TM

13 List of figures Figure 1: Radar image from WaMoS II on QUEST Figure 2: Example 2D Wave Spectra for QUEST Q279 Sea Trial Figure 3: Nominal Run Pattern Figure 4: Uncertainty in wave height measurements for the wave buoys Figure 5: Wave height measurements for the WaMoS wave radar Figure 6: Significant wave height versus time for each 2-minute radar file in Run 2.0a Figure 7: Wave frequency spectrum for each 2-minute radar file in Run 2.0a.. 13 Figure 8: Wave heading spectrum for each 2-minute radar file in Run 2.0a Figure 9: Significant wave height versus time for each 2-minute radar file in Run Figure 10: Wave frequency spectrum for each 2-minute radar file in Run Figure 11: Wave heading spectrum for each 2-minute radar file in Run Figure 12: Figure 13: Figure 14: Figure 15: Figure 16: Figure 17: Comparison of WaMoS original spectrum and conversion for ShipMo7 versus wave frequency (Run 6.4) Comparison of WaMoS original spectrum and conversion for ShipMo7 versus wave heading (Run 5.7a) Fusion results for input of RMS heave and pitch displacement and Triaxys DREA wave spectra Fusion results for input of RMS heave and pitch displacement and Triaxys DRDC wave spectra Fusion results for input of RMS heave and pitch displacement and WaMoS trial wave spectra Fusion results for input of RMS heave and pitch displacement and WaMoS reprocessed wave spectra Figure 18: Wave frequency and heading spectra for Run 4.2 (H s = 1.4 m) DRDC Atlantic TM ix

14 Figure 19: Wave frequency and heading spectra for Run 9.2 (H s = 4.4 m) Figure 20: Map showing locations and dates of data collection sets Figure 21: KINGSTON Run pattern No. 5 March 23, 2007 (1112 to 1344 UTC) 27 Figure 22: Significant Wave Height During Trial) Figure 23: Peak Wave Period During Trial) Figure 24: Predicted vs. Measured RMS Pitch) Figure 25: Predicted vs. Measured RMS Vert. Acc. at BTC Figure 26: Predicted vs. Measured RMS Vert. Acc. at CG Figure 27: Wave Fusion Results: Pitch Figure 28: Wave Fusion Results: BTC Vert. Acc Figure 29: Wave Fusion Results: CG Vert. Acc Figure 30: Wave Fusion Results: Triaxys Input Figure C.1: Figure C.2: Figure C.3: Figure C.4: Figure C.5: Figure C.6: Figure C.7: Fusion results for input of heave acceleration and Triaxys DREA wave spectra Fusion results for input of heave acceleration and Triaxys DRDC wave spectra Fusion results for input of heave acceleration and WaMoS Trial wave spectra Fusion results for input of heave acceleration and WaMoS Reprocessed wave spectra Fusion results for input of heave displacement and Triaxys DREA wave spectra Fusion results for input of heave displacement and Triaxys DRDC wave spectra Fusion results for input of heave displacement and WaMoS Trial wave spectra x DRDC Atlantic TM

15 Figure C.8: Fusion results for input of heave displacement and WaMoS Reprocessed wave spectra Figure C.9: Fusion results for input of pitch angle and Triaxys DREA wave spectra 58 Figure C.10: Fusion results for input of pitch angle and Triaxys DRDC wave spectra 58 Figure C.11: Fusion results for input of pitch angle and WaMoS Trial wave spectra. 59 Figure C.12: Figure C.13: Figure C.14: Figure C.15: Figure C.16: Figure C.17: Figure C.18: Figure C.19: Figure C.20: Figure C.21: Figure C.22: Figure C.23: Fusion results for input of pitch angle and WaMoS Reprocessed wave spectra Fusion results for input of heave acceleration and pitch angle and Triaxys DREA wave spectra Fusion results for input of heave acceleration and pitch angle and Triaxys DRDC wave spectra Fusion results for input of heave acceleration and pitch angle and WaMoS Trial wave spectra Fusion results for input of heave acceleration and pitch angle and WaMoS Reprocessed wave spectra Fusion results for input of heave displacement and pitch angle and Triaxys DREA wave spectra Fusion results for input of heave displacement and pitch angle and Triaxys DRDC wave spectra Fusion results for input of heave displacement and pitch angle and WaMoS Trial wave spectra Fusion results for input of heave displacement and pitch angle and WaMoS Reprocessed wave spectra Fusion results for input of heave acceleration and heave displacement and Triaxys DREA wave spectra Fusion results for input of heave acceleration and heave displacement and Triaxys DRDC wave spectra Fusion results for input of heave acceleration and heave displacement and WaMoS Trial wave spectra DRDC Atlantic TM xi

16 Figure C.24: Fusion results for input of heave acceleration and heave displacement and WaMoS Reprocessed wave spectra List of tables Table 1: Nominal Run Pattern Details Table 2: WaMoS Wave statistics for run patterns No. 1 to Table 3: WaMoS Wave statistics for run patterns No. 5 to Table 4: WaMoS wave statistics for run patterns No. 9 to Table 5: Fusion normalized wave height statistics for all runs and wave heights 20 Table 6: Fusion normalized wave height statistics for all runs where significant wave heights greater than 3m Table 7: Star pattern nominal run headings and typical run duration Table A.1: Comparison of significant wave heights for run patterns No. 1 to Table A.2: Comparison of significant wave heights for run patterns No. 5 to Table A.3: Comparison of significant wave heights for run patterns No. 9 to xii DRDC Atlantic TM

17 1 Introduction DRDC Atlantic is interested in the development of a shipboard system to obtain accurate measurements of directional wave spectra and wave statistics. Such a system could provide an important input to ship structural health monitoring systems and provide information on seaway wave characteristics to various ship operator guidance systems. The system could also be used in long-term sea trials to validate ship response predictions and to provide seaway information during test and evaluation trials where it is inconvenient or impossible to conduct the trials in the vicinity of wave buoys. It is anticipated that a wave radar would be the core of this system and that fusion of data from other shipboard systems would be used to improve the quality of measurements. A WaMoS II wave radar processor [1, 2] was first employed on CFAV QUEST in January 2004 [3] and more recently in two sea trials, one on QUEST [4] denoted as QUEST trial Q293, conducted in January 2006, and one on HMCS KINGSTON [5], conducted in March These trials and previous DRDC experience have shown that while the wave radar generally gave good wave heading and frequency information, the measurement of wave height was not very reliable. The main purpose of the sea trial on HMCS KINGSTON was to test a commercially developed slam warning operator guidance system. The system derived wave height, frequency and heading from measured ship motions using a ship-as-a-wave-buoy algorithm. The algorithm performed very poorly. During the Cooperative Research Ships (CRS) project Ship Monitoring, Analysis and Comparative Studies (SMACS) both a Wavex wave radar processor [6] and a TSK overthe-bow wave height meter were used to measure wave conditions during several trans- Atlantic and Pacific voyages of the A.P. Moller containership, Margrethe Maersk. Ship motion and structural response were also measured during the Margrethe Maersk voyages. There were significant differences and scatter in comparisons of wave heights from the Wavex, TSK, crew observations and the few wave buoy locations available for comparison. After the voyages, an algorithm was developed that used the Wavex directional spectra as input to a prediction of the ship CG heave and the relative wave height at the bow. A weighted comparison of these predictions to measurements of the heave motion and the relative wave height from the TSK was used to correct the input Wavex wave height. Use of this corrected Wavex data seemed to significantly reduce the scatter in a comparison of measured and predicted RMS vertical bending moments but there was very limited independent wave data to test the method. Data from the QUEST Q293 trial and the KINGSTON trial are used in this study to test a similar fusion algorithm and determine the best combination of ship motion measurements for use in the fusion algorithm. The first section of this report briefly describes how the wave radar makes its measurements, followed by a description of the fusion algorithm used to improve the wave radar height measurements. This is followed by a section considering the testing of this algorithm using the QUEST data, a section considering DRDC Atlantic TM

18 the KINGSTON trial data, and finally sections providing a summary and conclusions and suggestions for future work. This work was conducted under the Seakeeping Operator Guidance project (ARP 11gw) which has the objective to develop a concept demonstration Seakeeping Operator Guidance (SOG) capability for real time and tactical operator guidance with accurate measurement of wave height and directional spectra using shipboard sensors. The project is focusing on seakeeping and slam warning operator guidance. 2 Wave Radar Measurement Method Wave radars, such as the WaMoS II system, analyze the back scatter signatures (so called sea clutter ) from images captured from X-band navigational radar. The sea clutter is created by the backscatter of the transmitted radar electromagnetic waves from the short ripples on the sea surface. The example radar image in Figure 1 from the QUEST 279 sea trial [3] clearly shows the pattern of sea surface waves. The 2D wave spectrum is derived by the WaMoS II system through spatial and temporal processing of three rectangular areas extracted from each radar image in a series of 32 radar images acquired in each two-minute measurement interval. The system provides a direct measurement of the wave spectrum frequency and directional characteristics which are generally in reasonable agreement with wave frequency and directional data measured with a wave buoy. This is illustrated in Figure 2 which shows two 2D wave spectra from the QUEST 279 sea trial, one from the Triaxys wave buoy and one from the WaMoS wave radar. The angular direction in the polar plot represents the direction that the waves are coming from and the radii show the wave frequency. While the plots, normalized to the peak energy density, are quite similar, the peak energy density and significant wave height differ by a factor of roughly two in this case. The significant wave height is an indirect measurement and is estimated from the radar signal-to-noise ratio. Since this parameter is a function of more than just wave height, it must be calibrated for each configuration of ship/radar geometry and radar type. This signal-to-noise ratio is also a function of parameters such as wind and other environmental conditions which may not always be correctly accounted for in the system s processing, leading to inaccuracies in wave height measurements. The large difference between the wave height measured with the wave buoy and wave radar shown in Figure 2 may be caused in part by incorrect calibration settings for the QUEST radar configuration. But as indicated in Section 4.1, even with the best-fit calibration parameters, there were still significant errors and scatter in the radar wave height measurements for the WaMoS system on QUEST. 2 DRDC Atlantic TM

19 Figure 1: Radar image from WaMoS II on QUEST 3 Wave Fusion Method As indicated in the previous section, the wave radar generally gives a reasonable measurement of the normalized 2D wave spectrum (wave frequency and direction characteristics). It was anticipated that if this wave spectrum is input to a ship motion prediction code then the resulting motion predictions could be compared to measured ship motions and this comparison used to scale (and hopefully improve) the wave radar height measurement. The details of the method developed are described here. DRDC has developed a linear hydrodynamic strip-theory code called ShipMo7 [7] which can provide predictions of the irregular wave motions (RMS response) in a seaway defined by a directional wave spectrum. This code is computationally very efficient so that it can be used in real time to calculate ship CG motion responses for comparison with RMS response measured over a time period T run. The average measured wave spectral density from the wave radar during this time period is defined here as S(ω,β s ) where ω is the wave frequency and β s is the the sea direction relative to the ship heading and wave radar significant wave height is defined as Hs radar. Under the ShipMo7 convention, β s = 0 deg. is a following sea, β s = 90 deg. is a port beam sea, and β s = 180 deg. is a head sea. If δ shipmo is one of the the RMS motion components (for example, heave displacement or pitch angle at the ship CG), predicted by ShipMo7 using the uncorrected measured directional wave spectrum from the wave radar, and δ meas is the RMS motion component measured during the time period T run then the fusion corrected significant wave height Hs is given by H s = r corr H radar s (1) DRDC Atlantic TM

20 0 0.2 Hz TRIAXYS DREA H s = 3.3 m T p = 10.7 s Peak = m 2 /(Hz-deg) Hz WAMOS TRIAL Decca H s = 6.5 m T p = 10.7 s Peak = m 2 /(Hz-deg) 180 Contours at 10, 20, 40, 60 and 80 % of peak Figure 2: Example 2D Wave Spectra for QUEST Q279 Sea Trial 4 DRDC Atlantic TM

21 where the correction ratio r corr is given by r corr = δmeas. (2) δshipmo Similarly the fusion corrected directional wave spectral density S (ω,β s ) is then given by S (ω,β s ) = (r corr ) 2 S(ω,β s ). (3) Since in different ship operational conditions the accuracy of prediction of different motion components can vary, an extension to the above method was considered in which the corrections from different motion components were combined to check if this would improve the results. If n motion components are considered, δ i,i = 1,n, and the correction ratio for the i th motion component is r corr i = δmeas i δ shipmo i (4) then a mean r corr for application in Equations 1 and 3 can be defined by r corr = n i=1 r corr i /n (5) The application of this method of fusion of measured motion data, ShipMo7 motion predictions and the wave spectra derived from a wave radar processor are considered for the QUEST Q93 sea trial in the following section. 4 QUEST Q293 Sea Trial Data Analysis The QUEST Q293 sea trial is described in detail in a DRDC Technical Memorandum [4]. The trial was conducted approximately 120 miles South of Halifax in the vicinity of the MEDS (Marine Environmental Data Service) La Have Bank moored buoy. Over ninety dedicated runs each of approximately 25-minute duration were conducted over the period of January 11 to January 18, 2006 inclusive. Each run was conducted at a constant heading and speed. The nominal run pattern consisted of station keeping in head seas in the vicinity of the Endeco buoy (nominal speed 1 knot), followed by 6 legs conducted at either a 6 or 12 knot ship speed as shown in Figure 3, followed by additional measurements while station keeping. The details of the nominal pattern are summarized in Table 1. The Scanner DRDC Atlantic TM

22 Table 1: Nominal Run Pattern Details Run Day in Duration Radar ID* Jan 2007 (minutes) Scanner P.0a Station Keep 25 Scanner 1 P.0b Station Keep 25 Scanner 2 P.1 Head 25 Scanner 2 P.2 Following 25 Scanner 2 P.3 Starboard Bow 25 Scanner 2 P.4 Port Quarter 25 Scanner 2 P.5 Port Beam 25 Scanner 2 P.6 Starboard Beam 25 Scanner 2 P.7a Station Keep 25 Scanner 2 P.7b Station Keep 25 Scanner 1 * P is the Pattern ID number Figure 3: Nominal Run Pattern 1 and Scanner 2 entries refer to either QUEST s Decca X-band navigational radar or a Furuno X-band scanner dedicated to scientific purposes. 4.1 Wave Measurements Data from four wave buoys was collected during the sea trial, three drifting buoys deployed from the ship (two Triaxys buoys, identified as DREA and DRDC, and an older Endeco type 1156 wave buoy) and the MEDS moored buoy C44142 (La Have Bank, at deg. N, deg. W) operated by Environment Canada. Since all wave buoys were drifting, from time to time the buoys ranged from a few miles apart to about 20 miles apart by the end of the trial. This included the MEDS La Have Bank buoy which started drifting and was found at a new location on two occasions during the trial. For each trial run, a 6 DRDC Atlantic TM

23 baseline wave measurement was derived by interpolating (in time) the wave height of each buoy over the run time period. These interpolated heights were weighted by the inverse of the distance of the ship from each buoy and averaged over the run time period to obtain a baseline significant wave height for each run. The Endeco wave heights were not used in the determination of the baseline wave height since the Endeco heights seemed to be more variable and were only available for about one-third of the runs. Figure 4 (taken from the Q293 trial report [4]) shows the normalised wave heights for each wave buoy, for each run, plotted as a function of the baseline significant wave height. The normalised wave height is defined here as the ratio of the significant wave height measured by each buoy to the baseline significant wave height. Significant wave heights during the trial ranged from 1.3 m to 5 m and the figure shows that the mean and the scatter of results are independent of wave height over this range. The figure also shows bands of ± 2.5 standard deviations calculated over 1 m wide bands of wave height. These bands should encompass 99 percent of the points if the data are normally distributed. Most points lie within ± ten percent of the baseline values. Figure 5 shows the normalised wave heights for the WaMoS II wave radar processor plotted as a function of the baseline significant wave height. The results for the sea trial show large scatter with some points over twice the baseline significant wave height and others at almost half the baseline values. Following the sea trial new WaMoS calibration parameters were derived which gave the best fit to the trial data. These reprocessed data still showed large scatter (standard deviation of 0.23). The wave height data used to generate Figures 4 and 5 is provided in Annex A. The Q293 trial report [4] also considered peak wave period and wave direction. There was much better agreement between wave buoy and wave radar measurement wave period and directions measurements and these will not be considered in detail here, since the goal is to develop methods to reduce the large errors and scatter in the wave radar significant wave height measurements. 4.2 Ship Motion Measurements The DRDC Ship motion package, located at the ship CG, provided time series of roll angle, roll rate, pitch angle, pitch rate, yaw rate and longitudinal, lateral, and vertical acceleration sampled at 20 Hz. In this analysis the vertical acceleration signal was integrated twice to provide a time series of heave displacement. The time series of relative vertical displacement at the bow, measured by the TSK was also recorded (20 Hz sampling rate). The RMS response was computed for each time series over the time period for each run. 4.3 Radar Wave Spectra for Runs The WaMoS II wave radar system sampled 32 radar images to produce and store a directional wave spectrum every two minutes (file extension.fth). All of the WaMoS two- DRDC Atlantic TM

24 NORMALISED WAVE HEIGHT Endeco mean: 1.06, sdev: MEDS mean: 0.99, sdev: DREA mean: 0.98, sdev: DRDC mean: 1.02, sdev: BOUNDS OF PLUS/MINUS 2.5 STANDARD DEVIATIONS SIGNIFICANT WAVE HEIGHT (m) Figure 4: Uncertainty in wave height measurements for the wave buoys NORMALISED WAVE HEIGHT WaMoS Reprocess mean: 1.04, sdev: WaMoS Trial mean: 1.51, sdev: SIGNIFICANT WAVE HEIGHT (m) Figure 5: Wave height measurements for the WaMoS wave radar 8 DRDC Atlantic TM

25 Hs (m) TIME (minutes) Figure 6: Significant wave height versus time for each 2-minute radar file in Run 2.0a minute spectra within the time period of each run were averaged and then converted to the ShipMo7 format. It was noted that in some cases there were large variations in the WaMoS spectra within the run time period. The WaMoS wave statistics for the spectra used for each run are given in Tables 2, 3 and 4. The tables give the mean and coefficient of variation (COV = standard deviation/mean) for the significant wave height, peak wave period and peak wave direction from the WaMoS wave measurements collected for each 2-minute period during the run. The last column of the table gives the number of WaMoS measurements during each run. The mean, maximum and minima of the coefficient of variation over all runs are shown at the bottom of Table 4. The significant wave height showed the greatest variability (typically the COV for significant wave height was 3 or 4 times that for peak period and peak wave direction). The largest COV for significant wave height occurred during measurement for Run 2.0a, a station keeping run (COV = 0.45). A graph of the wave height versus time during this run (Figure 6) shows the WaMoS significant wave height varying between about 0.5 m and 3 m over this run. The Q293 trials report [4] shows that the significant wave height (measured by the wave buoys) was fairly constant and increased from 2.1 m to 2.3 m over this run. Figure 7 and Figure 8 show the individual wave spectra over the run, summed over the heading dimension and over the frequency dimension respectively. These show some differences in spectrum shape as well as the large height variation. Similar graphs are shown in Figures 9, 10, and 11 for Run No. 8.3 which showed scatter closer to the mean values calculated over all runs. Again there is a variation in shape as well as height. DRDC Atlantic TM

26 Table 2: WaMoS Wave statistics for run patterns No. 1 to 4 Run H s H s T p T p ν p ν p n spec ID (m) COV (sec) COV (deg) COV 1.0a b a b a a a b a b a b H s = Significant Wave Height T p = Peak Wave Period ν p = Peak Wave Direction, re True N. COV = Coefficient of Variation (standard.dev/mean) n spec = number of spectra averaged for run 10 DRDC Atlantic TM

27 Table 3: WaMoS Wave statistics for run patterns No. 5 to 8 Run H s H s T p T p ν p ν p n spec ID (m) COV (sec) COV (deg) COV 5.0a b a b a b a b a b a b H s = Significant Wave Height T p = Peak Wave Period ν p = Peak Wave Direction, re True N. COV = Coefficient of Variation (standard.dev/mean) n spec = number of spectra averaged for run DRDC Atlantic TM

28 Table 4: WaMoS wave statistics for run patterns No. 9 to 11 Run H s H s T p T p ν p ν p n spec ID (m) COV (sec) COV (deg) COV 9.0a b a b a b a b Mean* Max* Min* H s = Significant Wave Height T p = Peak Wave Period ν p = Peak Wave Direction, re True N. COV = Coefficient of Variation (standard.dev/mean) n spec = number of spectra averaged for run *All runs in Tables 2 to 4 inclusive. 12 DRDC Atlantic TM

29 Spectral Density (m 2 /Hz) Wave Frequency (Hz) Figure 7: Wave frequency spectrum for each 2-minute radar file in Run 2.0a Spectral Density (m 2 /deg) Wave Heading (degrees True N) Figure 8: Wave heading spectrum for each 2-minute radar file in Run 2.0a DRDC Atlantic TM

30 6 Hs (m) TIME (minutes) Figure 9: Significant wave height versus time for each 2-minute radar file in Run Spectral Density (m 2 /Hz) Wave Frequency (Hz) Figure 10: Wave frequency spectrum for each 2-minute radar file in Run DRDC Atlantic TM

31 0.030 Spectral Density (m 2 /deg) Wave Heading (degrees True N) Figure 11: Wave heading spectrum for each 2-minute radar file in Run ShipMo7 Motion Response Predictions The DRDC hydrodynamic code ShipMo7 [7] was used to predict the irregular-wave ship motion response (RMS and zero-crossing periods) with input of the directional wave spectra. A QUEST ShipMo7 model for Deep Departure, based on the April 1999 trim and stability manual, was adjusted to Q293 draft and trim conditions (a draft at midships of m and a trim by stern of 2.08 m). Example ShipMo7 input files are given in Annex B which used the User Input Directional Spectrum option (SPECTRUM = INPUTDIR) and defines an array of wave spectral density values for a maximum of 30 wave frequencies and 36 sea directions (0 to 350 degrees). The method was tested here using directional spectra from the Triaxys buoys and from the WaMoS II wave radar processor. In the Q293 trial report [4], in anticipation of the wave fusion algorithm development, the ShipMo7 predictions with input of the closest Triaxys wave buoy directional spectra to each run were compared to the measured RMS responses. Roll angle, pitch angle, heave acceleration, and heave displacement were considered, all at the ship CG. Also the relative vertical displacement at the bow, predicted by ShipMo7, were compared to the TSK relative vertical displacement. Both the ship roll and bow relative vertical displacement comparisons showed fairly large scatter with correlation coefficients of 0.65 to The heave displacement, heave acceleration and pitch angle showed better agreement with correlation coefficients for pitch of 0.85 and 0.92, and for heave of 0.88 and 0.95 respectively for the two Triaxys buoys. Based on this analysis it was decided to explore use of pitch angles, DRDC Atlantic TM

32 heave acceleration and heave displacement as the most promising motion components to use in the wave fusion algorithms. As mentioned above, the ShipMo7 input file format requires the wave spectrum to be specified using a fixed set of 36 headings (0 to 350 deg.) and a maximum of 30 wave frequencies. The headings are defined as the directions that the waves are coming from in degrees clockwise relative to True North. The WaMoS II directional wave spectra contained 90 headings (from 2 deg. to 358 deg. at 4 deg. spacing) and 64 frequencies ranging from Hz to 0.35 Hz. In order to maintain the highest frequency resolution, the tails of the measured spectra at the frequency extremes were ignored where the spectral density was less that times the maximum spectral density and 30 equally spaced frequency values were used over the remaining frequency span. Bilinear interpolation of the spectral density surface in wave heading and frequency space was used to obtain the spectral density array at the required 30 frequencies and 36 headings for ShipMo7. It was also necessary to convert the WaMoS frequencies (Hz) and spectral density (m 2 /Hz/deg) respectively to frequencies (rad/s) and spectral density (m 2 /(rad/s)/deg). For the irregular wave calculations, the ShipMo7 formatted ASCII postprocessing output file, QUEST.dat (name defined in the sample ShipMo7 input file given in Annex B), contained the RMS accelerations, velocities and displacements for the CG motions (surge,sway, heave, roll, pitch and yaw). The responses were computed and written to the ShipMo7 output file for ship headings (deg. True N.) of 0 to 355 degrees at 5 degree increments. The file also contained the motions for a seakeeping position at the bow including the relative displacement for comparison to the relative vertical displacement measured with the TSK. The response values from ShipMo7 were interpolated at the mean ship compass heading for the run. The reduction in resolution for direction and heading caused minor changes to the spectra. Changes to the frequencies of the peak in the spectrum ranged from Hz to Hz with the mean of the absolute value of the difference over most runs of Hz. Similarly changes in the wave heading at the spectrum peak ranged from 0 degrees to 14 degrees with a mean of the absolute value of the difference of 4 degrees. In a few runs there were large differences in the frequency and heading of the spectrum peaks (up to 0.07 Hz and 108 degrees respectively). These occurred in spectra with two or more peaks of similar value such that the highest peak switched to the alternative peak in the creation of the spectrum for ShipMo7. The ratio of RMS response of the ShipMo7 spectra to the original WaMoS spectra (calculated from the square root of the zeroth spectral moment m0) ranged from 0.99 to 1.02 for all runs and the mean change in zero-crossing frequency (calculated from m0 and m2) was only Hz (a maximum difference of ) suggesting that the changes to the spectra were not very significant. Figure 12 shows an example of the frequency spectrum with the largest change in peak frequency (0.015 Hz). Figure 13 shows an example with the largest direction shift (14 degrees) in the spectrum peak. The fusion algorithm was also tested using the Triaxys wave buoy spectra as input to ShipMo7 as will be discuss in the following section. The Triaxys directional spectra used 16 DRDC Atlantic TM

33 Spectral Density (m2/hz) WaMoS SHIPMO Wave Frequency (Hz) Figure 12: Comparison of WaMoS original spectrum and conversion for ShipMo7 versus wave frequency (Run 6.4) Spectral Density (m2/deg) WaMoS SHIPMO Wave Direction (deg) Figure 13: Comparison of WaMoS original spectrum and conversion for ShipMo7 versus wave heading (Run 5.7a) DRDC Atlantic TM

34 121 wave directions (0 to 360 degrees at 3 degree increments) and 129 frequencies (0 Hz to 0.64 Hz inclusive). In a manner similar to that used with the WaMoS spectra, the frequency range of the Triaxys spectrum was reduced to exclude tails of the spectrum where the spectral density was less that times the maximum density value, and the spectral density surface interpolated bilinearly at the headings and frequencies required by ShipMo7. Also the spectra were adjusted from frequencies in Hz to rad/s. The Triaxys buoys were set to provide a directional wave spectrum for each 30 minute period. To avoid simultaneous radio transmission of data from the buoys, one buoy was set to measure and transmit spectra on the hour and half-hour while the other set to transmit at 15 minutes before and after the hour. The closest spectra to the run time period were used as input to the ShipMo7 calculations. 4.5 Fusion Algorithm Results The Triaxys buoy spectra were input to the fusion algorithm as an initial test of the method. This provided a baseline for the best result that could likely be achieved by the method, since these were likely the most accurate measured wave spectra available for the seaway experienced by the ship. The individual CG motion components used to correct the input wave spectrum and significant wave height (used Equations 1, 2 and 3) were heave acceleration, heave displacement, and pitch angular displacement. Combinations of pairs of these three components were also tested (applied Equations 4 and 5) and finally the combination of all three of these motion components was considered. The combination of pitch angle and heave displacement gave the lowest scatter in the corrected significant wave height when compared to the wave buoy baseline wave heights. Figure 14 shows the normalised wave height (ratio of the fusion method corrected significant wave height to the baseline significant wave height) plotted as a function of the baseline significant wave height with a point for each run considered. The plot also shows the mean and bands of ±2.5 standard deviations for 1 m bands of wave height (the bands should encompass 99 percent of the points if normally distributed). In this plot the Triaxys buoy DREA was used as the input wave spectra to the fusion algorithm. A similar plot showing slightly more scatter is given in Figure 15 for the other Triaxs buoy identified as DRDC. There appeared to be a slight trend of lower corrected wave heights and more scatter at lower significant wave heights. The standard deviations of the normalized wave heights were approximately twice that found for the scatter in the wave buoy measurements alone (Figure 4), suggesting about equal contribution of wave buoy measurement error and ShipMo7 prediction error to the scatter in the results. Table 5 gives the mean and standard deviations of the normalised wave heights calculated with the fusion algorithms for input of the two Triaxys buoy wave spectra and for the WaMoS wave spectra (sea trial data and reprocessed data with best-fit calibration parameters). Results are shown with use of individual motion and combinations of motion 18 DRDC Atlantic TM

35 NORMALISED WAVE HEIGHT Response mean: 1.00, sdev: BOUNDS OF PLUS/MINUS 2.5 STANDARD DEVIATIONS SIGNIFICANT WAVE HEIGHT (m) Figure 14: Fusion results for input of RMS heave and pitch displacement and Triaxys DREA wave spectra NORMALISED WAVE HEIGHT Response mean: 0.97, sdev: BOUNDS OF PLUS/MINUS 2.5 STANDARD DEVIATIONS SIGNIFICANT WAVE HEIGHT (m) Figure 15: Fusion results for input of RMS heave and pitch displacement and Triaxys DRDC wave spectra DRDC Atlantic TM