XIAO Wen-bin,DONG Wen-cai,WU Hao

(Department of Naval Architecture,Naval University of Engineering,Wuhan 430033,China)

1 Introduction

Six-degree motion response of ship model in waves is one of the important measuring items for the seakeeping test.In the towing tank,the linear displacements,such as the surge,sway and heave motions,are early measured by the potentiometers,whose resistance values are changed through the cordages linking the potentiometers to the ship model with oscillatory motion.According to the resistance data,ship model’s linear displacements at three degree of freedom can then be calculated and acquired.For angular displacements of ship model,the mechanical gyroscope is a kind of common measurement device in the early stage[1].Based on the double integration algorithm for the acceleration to displacement,the acceleration motionmeasuring apparatus is developed and gradually applied to the ship model test[2].The spatial displacements of ship model are directly resolved by the acceleration signals in this apparatus,whose test accuracy mainly depends on the integral error with the accumulative time.The motion-measuring instrument in the mechanical style is also a kind of measurement means for the model’s motion responses at six degree of freedom in the towing tank.The oscillating motion of ship model would move the units of the mechanical instrument,which is connected with the model to get the dynamic data.However,the inertia of this mechanical instrument poses the interaction to the model measurement for the small amplitude or high frequency motion to a certain extent[3].The facilities mentioned above are all installed or linked on the ship model,which can be inducted as the on-board or contact measurement method.

For the wake of developments in the computer vision and digital image technologies,foreign and domestic institutions design and invent many contactless motion-measuring products for towing ship model[4-7].Based on the optical principles,the representative products are the RODYM-DMM of KRYPTON in Belgium and the QTM of QUALISYS in Sweden.The RODYMDMM is mainly made up of the CCD component and the infrared emitting diode,whose measurement error in length is about±0.3 mm for the 6 m range[8].However,the emitter of infrared rays in the QTM,whose full name is Qualisys Tracker Manager,is located in the lens of high-speed camera.Within the scope of the camera view,the detailed motion information of ship model is achieved by the infrared reflection of the reflective targets,which are mounted on the ship model.The calibration test indicates that the measurement uncertainty of optical system QTM is at the similar level with the contact facilities such as gyroscope and string pot[9].Compared with the contact measurement method,the optical contactless motion-measuring system has big superiority in the experimental convenience and data reliability for it can effectively remove the constrict influence of mounted facilities to the ship model.Currently,this kind of contactless system is gradually extended to the odd experiments for the offshore platform model with dynamic positioning performance[10].

In the respect of hydrodynamic interaction exploring for two ships in close proximity,the experimental research now is still not sufficient for its technological complexity in engineering.The main difficulties are as follows:(1)Different from the normal tank,the towing carriage for two-model test should be equipped with another auxiliary towing apparatus[11],which may add to the experimental cost greatly.(2)The transversal and longitudinal separations between two models should be adjustable according to different test conditions.The enlargement of the separations may intensify the difficulty for the setup design of testing device.(3)Various parameters are needed to measure such as the multi degree motion response of every model and the relative motion of two models.If the interface and protocol of all kinds of testing instruments are not unified,the real-time motion measurement is hard to realize for the multichannel data acquisition.In present paper,the optical contactless system QTM is introduced to the motion measurement of two-model test in the towing tank.The spatial layout for the infrared reflective targets and the motion-sensitive cameras is probed based on the limited mounting space in the carriage.Additionally,the acquired testing signals are analyzed by comparing them with the data from the contact instruments.It is expected to provide the model-test technology for the behaviors of two ships advancing under the complex sea condition.

2 Fundamental principle of motion measurement for two ship models

To probe into the hydrodynamic interaction of two ship models in quantity,the optical system QTM is utilized to capture the pose variation in calm water and dynamic motion response in waves.In the towing tank,the two models with certain degree of freedom are moving by the cable traction.Fig.1 illustrates the operating principle of the motion measurement in the two-model test.The QTM system here is mainly composed of the infrared reflective targets,calibration device and motion-sensitive cameras.

Four infrared reflective targets are mounted on each ship model,one of which is on the plumb line with the gravity center of ship model and the other ones are arranged evenly around the center.The location of every target must be the fixed point on ship model and the relative positions of target and model should not be changed in the experimental process.By the coordinates of four infrared reflective targets,a rigid body can be defined in the three dimensional space,which is then to represent the model’s motion at multi degree of freedom.

In the pre-test condition or if the test environment changes significantly,the calibration is needed for the QTM system,which is essentially the process of definition of spatial coordinates,confirmation of motion-sensitive cameras and initialization of working parameters.Within the visible scope of cameras system,the XOY plane of calibration frame should be parallel to the undisturbed free surface and the positive direction of the OX axis is pointing to the advancing speed of ship models.In the calibration process,the dynamic data of calibration bar in different location is automatically logged.For the condition that the calibrating error is within the predefined error range,the current calibration is recognized as a valid.However,the system calibration must be carried out again if the calibrating error is beyond the set value.

The cameras system is made up of several high-speed cameras,which are installed at the fixed positions of the towing carriage.Care must be taken to ensure that each camera can capture the motion response of ship model in every test condition.The front lens of high-speed camera is furnished with an infrared ray emitter,which can project infrared light into the space immediately.By the infrared reflection,the spherical targets are always traced in the calibration coordinates.Combined with the definition of rigid body and the digital image processing technology,the optical system QTM can decouple the each model’s motion at six degree of freedom,which is inclusive of the linear displacement,the angular displacement and the velocity and acceleration signals.

3 Spatial arrangement of the targets and cameras

Aiming at the performance of different advancing speed,transversal and longitudinal separations,towing tank test is carried out to explore the hydrodynamic interaction of two ship models in close proximity.If there is a long distance between the two models,the motion-sensitive cameras are still required to capture the dynamic parameters of infrared reflective targets.For the test is involved the front and back position alternation of models and the limiting condition of spatial construction in the carriage,spatial arrangement of the targets and cameras is difficult to design properly.

3.1 Mathematical description of the arrangement problem

Supposing the model A is located on the port side of model B,a moving coordinate system is set up in Fig.2.The xoy place with the positive ox axis pointing to the model speed coincides with the undisturbed water surface and oz axis is oriented positively upward.The origin o is defined at the central lateral plane of model A.Transversal and longitudinal separations between two models are denoted by Dyand Dxrespectively.For Dx>0,model B is ahead of model A.

Fig.2 Three dimensional arrangement of Marker targets and cameras

For the camera a,the field of view,FOV for short,is assumed as θ,the spatial coordinate of its fixed position isand the orientation angles to the three coordinate axes are αa,βaand γa.By the space geometry,the visible scope of the camera is a cone in the three dimensional space,whose intersection with the horizontal plane is a circle or ellipse.Supposing the axial direction vector of camera a is)is on the conical surface formed by its view field,the spatial surface equation for M can be expressed as follows:

Additionally,the spatial coordinates of infrared reflective targets areOn account of the fact that the targets’heights above the water surface are much smaller than the cameras’vertical scales,all the targets can be assumed on the xoy plane,that is to say zi=0.Further,the intersection between the water surface and the spatial conical surface presented in Eq.(1)can be derived as below:

The equation above is generally corresponding to an elliptic equation,which can be rewritten asIn order to meet the requirement that the targets mounted on models are in the visual field of camera a,this kind of elliptic equation can be treated as the discriminant representation.By substituting the coordinates into the elliptic equation,the No.i target can be captured by the camera a ifHowever,some spatial parameters of camera a should be modified if

Similarly,the discriminant representations of other cameras can be derived asIf all the targets are within the view field of the cameras system,the expression below must be satisfied.

The locations of mounted targets in the coordinate system and their limits of variation can be generally determined because the relative position between two models is up to the experimental conditions.Therefore,the orientation angles and position scales of camera(s)should be adjusted if Eq.(3)is not true.The ultimate goal is that all the targets are viewed by all the cameras.

3.2 Instance analyses

According to the theoretical description above,some analysis results are given below for a two-model test in the Ref.[12].The restricted region of carriage in the towing tank here is 5.5 m×6.5 m for the cameras’mounting,which is illustrated in Fig.3.In order to make the uniform distribution of cameras system and the large field of their views,each corner in the carriage should be fully utilized.The infrared reflective targets are mounted near the gravity center of ship model.In terms of the requirement of test condition and the movement redundancy in waves,the distribution ranges of targets in the ox and oy axis are at least 4.5 m and 0.5 m respectively.

Fig.3 Location range of Marker targets and mounting region of cameras

For the rectangular region in the horizontal water plane of-3.25 m≤x≤3.25 m and-4 m≤x≤1.5 m,Eq.(3)is put to numerically discriminate whether the targets are within the visual field of cameras.In accordance with the structural characteristic of carriage,the horizontal mounting region of cameras is presented in Fig.3,whose heights above the water surface are all set as 1.2 m and FOV as 58°[13].A discrimination result is given in Fig.4 for the three motion-sensitive cameras.In the rectangular region,the red zone indicates that the infrared reflective targets are captured into the visual field of corresponding camera and the black zone shows the targets are beyond the field of view.Compared with cameras a and c,the adjustable range of camera b’s orientation angle is relatively small,which demonstrates that great focus should be taken on the installation of camera b in the testing process.For each ship model,the targets mounted on the models are all within the fields of cameras no matter how the transversal and longitudinal separations change.In this instance of two-model test,the orientation angles of cameras are listed as follows.

Fig.4 Capture zones of the cameras at z=0 plane

4 Performance analyses of tested signals

4.1 Motion signals of two models at multi degree of freedom

In the moving coordinate system,the high-speed camera directly obtains the displacement signals of the infrared reflective targets.By the definition of rigid body,the optical system QTM can automatically calculate the motion response of ship model at six degree of freedom.During the whole test period,human touch to the mounted cameras should be avoided to prevent the invalidation of calibration coordinate system.However,the accumulative position change of camera may be caused by various objective reasons such as motor rotating,equipment vibration,and carriage shaking over a long time.In the wave test,large amplitude motion of ship model may make some targets being shadowed.If the missing data of target is relatively little in the signal collection,the QTM system can effectively integrate the gathered data to reconstruct the full motion information for the rigid body,which shows the powerful computing performance of the embedded algorithm in this optical system.

Fig.5 illustrates the time history of the heave,roll and pitch motions,which are of particular concern in the regular waves for two ship models.From this figure,the stable harmonic characteristics of the two-model motion modes are demonstrated if t>17 s.Numerous test conditions and collected data indicate that the optical system QTM is advantageous to realize the real-time synchronous measurement for the dynamic interaction and relative motion between two ship models.

Fig.5 Time history of the motion responses for two ship models

Fig.6 Comparison of the measured pitch-motion signals by attitude indicator and QTM

4.2 Comparison of the pitch signals

To analyze the performance of the QTM and contact measuring device in the dynamic motion measurement of ship model,a contrast test is carried out for the pitch signals in regular waves.The WS-601 attitude indicator,a kind of contact device,is adopted to gather the pitch angles,which is fixed near the bow of ship model.Fig.6 gives the time history of pitch-motion signals by the attitude indicator and QTM.The stable data with t∈[1,1 ]6 is extracted and the amplitude of pitch angle is statistically treated.Results show that the average amplitudes of the signals from the indicator and QTM are 1.722 2°and 1.717 2°,respectively,whose relative error is only 3‰.For the two kinds of pitch signals,numerical characteristics at the peak or valley during the cyclic changes over time show good agreement with each other.Based on the analysis above,the fast response and testing performance of QTM are similar to those of the attitude indicator in the pitch-motion model test.

4.3 Comparison of the acceleration signals

Besides the motion response at multi degree of freedom,the acceleration data at the special positions of ship models is paid great attention in the two-model tank test.In the optical system QTM,the vertical acceleration signal at the gravity center can be obtained from the single target,which is arranged on the plumb line with the gravity center of ship model.For a test condition in regular waves,the vertical acceleration at gravity center is simultaneously measured by the means of acceleration transducer and QTM,which is shown in Fig.7.The acceleration transducer here is attached to the DH5922 donghua dynamic system.The acceleration signal from QTM is the numerical result of quadratic differential to the displacement signal.Therefore,there are many noise components mixed in the acceleration signal,which is mainly the high-frequency noise caused by the numerical operation.Fig.7 also gives the processing result of vertical acceleration signal by the low-pass filtering[14].The average amplitudes of gathered signals are extracted,which are 1.507 5 m/s2and 1.529 9 m/s2for the transducer and QTM,respectively.And the relative error between the two amplitude values is about 1.5%.In this sense,the acceleration signal collected by the optical system QTM is inclusive of many noise components with the high frequency,which puts forward a higher demand for the processing method of digital signal and effective extraction of characteristic quantity.

Fig.7 Acceleration signals and their low-pass filtering results

5 Conclusions

(1)In the seakeeping test of towing tank,optical system QTM is an effective facility to measure the motion response of ship model at six degree of freedom.By the motion-sensitive cameras installed in the carriage of towing tank,the QTM can accurately capture the motion information of the infrared reflective targets mounted on ship model.The significant advantage of QTM system is that it can directly eliminate the contact interference on the tested model.Compared with the contact measuring instruments,the test error is further constricted by the introduction of QTM.

(2)The spatial position and orientation angle of motion-sensitive camera are directly relative to the problem whether the infrared reflective targets are within the cameras’view fields.Combined with the instance of a two-model test,a mathematical model of spatial arrangement is proposed for the targets and cameras.In the existing structure of carriage,the optical system QTM is available to the motion measurement for the two models in complex test conditions.

(3)Performance analysis of the tested signals indicates that QTM possesses the high position resolution and fast response properties.However,the acceleration signals of QTM are mixed with the high-frequency noise,which is mainly the numerical component due to the quadratic differential to the displacement signal.

For the powerful capabilities of optical system QTM,it would be extensively applied in the experimental measurement for the model performance of ship and marine platform.

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