Wavelet-based optical velocimetry: an alternative technique for deepwater oil spill flow rate estimation

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1 Indian Journal of Geo Marine Sciences Vol.46 (1), December 017, pp Wavelet-based optical velocimetry: an alternative technique for deepwater oil spill flow rate estimation Osman A.B 1*, Mar OV 1*, Fahruldin M.H 1 & Faye I 1 Mechanical Engineering Department, Universiti Tenologi PETRONAS 3610 Seri Isandar, Pera, Malaysia Fundamental & Applied Science Department, Universiti Tenologi PETRONAS 3610 Seri Isandar, Pera, Malaysia *[ anotood@yahoo.com, mar_ovinis@utp.edu.my] Received 17 April 017 ; revised 7 October 017 Deepwater oil spill flow rate estimation is a challenge due to the lac of dedicated techniques. As well as the complex nature flow associated with oil jet leads to inaccurate flow rate estimation. In this paper, a novel technique based on discrete wavelet transform was developed. Wavelet transform has the advantage of decomposing signals into numerous levels. This could be useful for flow estimation of the complex signals of oil jet. The jet flow signals were decomposed using discrete wavelet decomposition (DWT), and then the flow was estimated using Fast Fourier Transform (FFT) cross correlation algorithm. The technique was called DWT-FFT. To validate the DWT-FFT, a turbulent jet flow was experimentally simulated by changing the jet nozzle Reynolds number from 1847 to The DWT-FFT estimated the nozzle velocity with an error of 34.8%. However, the DWT-FFT is sensitive to wavelet decomposition level and has less sensitivity to the selection wavelet function. [Keywords: Macondo well, cross correlation, wavelet transform] Introduction Optical velocimetry has a large applications used for flow visualization and measurement. In In 010 during Macondo well incident of oil spill, there was not proven methods for spill flow rate estimation. However, several optical velocimetry that developed in fluid dynamic field were applied to quantify the amount of oil spill as reviewed by McNuttet al. 1 and Lehr et al.. Manual tracing velocimetry such as feature tracing velocimetry (FTV) and large eddy velocimetry (LEV) are suffer from high uncertainty due to the difficulty of tracing the flow features.both the FTV and LEV techniques, which are based on visible tracing of existing features in the fluid flow space, poorly estimated the flow rate. The bad quality of spill videos leads to the inability of these techniques to trac the visible features such as coherent structures. A particle image velocimetry (PIV) is a well-nown technique and extensively used in fluid dynamics.however, the PIV failed to estimate accurately the flow rate of the oil spill in case of Macondo well incident 1,. This due to the limited size of interrogation window usually used in PIV unable to capture the large motion of oil jet. To overcome this limitation, a technique based on temporal averaging rather than spatial averaging

2 580 INDIAN J. MAR. SCI., VOL. 46, NO. 1, DECEMBER 017 of PIV has been more appropriate for estimating the fluid flow. Optical plume velocimetry (OPV) is a temporal averaging based technique developed by Crone et al. 4 for Deepwater blac smoer flow rate estimation.opv is the most accurate optical technique used for oil spill flow rate estimation 1. The OPV estimates the flow rate based on temporal cross correlation, in which the turbulent flow variation over time is considered. This could be the main reason behind its better accuracy over other techniques. Moreover, the temporal cross correlation of OPV technique is less sensitive to bias in velocity estimation and requires less computational time 3. As a comparison, both PIV and OPV use cross correlation algorithm as the step to estimate the flow. However, the PIV implements the cross correlation spatially, while the OPV uses temporalcross correlation of a pair of intensity signals. PIV has not been not ideal for capturing the fast motion of oil jet due to the variability of this flow over time. The low temporal resolution of PIV and the limited size of standard interrogation windows were behind the inaccurate estimation of oil spill flow rate. Although the large motion can be captured through overlapping the interrogation windows, as well as time-resolved PIV can be used for solve the problem of limited temporal resolution. However, these solutions have not been applied for oil spill flow rate estimation.therefore, the OPV has an advantage of better temporal, spatial resolution and accuracy as compared to PIV. The proposed technique in this paper comprises the advantages of OPV technique in terms of its temporal and spatial resolution, as well as considering the multi-scale behavior of the turbulent flow. Velocity field estimation based on temporal averaging needs to find the local velocity at each point of turbulent flow space. To estimate the local velocity usually four steps are required: (i) setting a distance between two points in the flow space, (ii) extracting the signal from these two points (v) cross correlation of the two signals, and (iv) interpolation and pea detectionof the obtained correlation coefficients. Then the time lag between the two signals is the time that corresponds to the pea of interpolated correlation coefficients. Once the lag is detected then the local velocity can be estimated by dividing the fixed distance over time. Cross correlation (CC) is the main step that control the accuracy of velocity estimation. Several CC functions were extensively applied including direct cross correlation (DCC), Fast Fourier Transform (FFT) cross correlation, average square difference function and normalized cross correlation (NCC). The DCC algorithm is based on signal amplitude in time domain, while the FFT algorithm is based on frequency information of the signal. However, transforming a signal from time to frequency domain is a trade-off between time information and frequency information. On the other hand, the wavelet transforms have the ability to decompose a signal/image into various levels, and to provide both timefrequency information. The wavelet transforms has an extensive applications in fluid dynamics. These includes investigation of self-similarity and intermittency behavior in turbulent signals 4,5, and identification of flow structure 6. A relation between wavelets and turbulence are discussed by Farge et al. 7, while Farge et al. 8 analyzed a turbulent signal based on wavelet coefficients. As well as the wavelet transform used for fluid flow simulation such as the wor of Kim et al. 9. However, in most of these wors, the velocity field is already nown and waveletbased methods were utilized to understand the turbulent flow behavior. In the context of velocity field estimation from image sequences by Dérian et al. 10,11, combined a differential based algorithm with wavelet expansion. This combination improved the accuracy and the performance of motion estimation algorithm. However, this method limited for small motion estimation because of the differential form of algorithm used. Figure 1 shows a comparison between the existing optical techniques that used for oil spill flow rates estimation with the proposed waveletbased optical velocimetry. In this paper, an optical velocimetry is proposed to estimate the

3 OSMAN et al.: WAVELET-BASED OPTICAL VELOCIMETRY 581 velocity of fluid from image sequence. The proposed technique is based on decomposing turbulent signals prior cross correlation stepis proposed. This technique combined discrete wavelet transform (DWT) and FFT cross correlation, from which the new algorithm called DWT-FFT algorithm. The rest of this paper organized as: Section includes a description of method including both proposed technique and experimental facility. Section 3 presents results and discussion followed by conclusion. Method This section presents the overall method of DWT-FFT algorithm as well as the experimental wor. Image Velocity Estimation Image velocity estimation using the wavelet based method several steps are requires includes, extraction of a pair of intensity signals separated by a nown distance from the input image stac, decompose these signals using discrete wavelet transform, cross correlation using FFT algorithm, then the local velocity at the first point can be estimated by finding the time lag by detecting the pea of correlation coefficients. Figure shows the overall procedures for image velocity estimation using DWT-FFT algorithm. Existing optical techniques FTV LEV PIV OPV Proposed technique Algorithm Manual tracing Manual tracing Spatial cross correlation Temporal cross correlation DWT-FFT Spatial resolution Very low Very low Low High High Temporal resolution Low Low Low High High Domain Time Time Time/ frequency Time Wavelet Figure 1: Comparison of existing optical techniques with proposed wavelet-based velocimetry. Discrete Wavelet Transform Wavelet transform is an extension of the windowed Fourier transform, which has the advantage of presenting signal in both timefrequency domains simultaneously. As compared to Fourier transform where only signal frequency can be provided. Discrete wavelet transform (DWT) decompose signals using low-pass g[n] and high-pass h[n] filters into approximate and detailed coefficients. Again the approximate coefficients can be decomposing into several levels. Figure 3 shows the procedure for three level decomposition of signal x[n] using DWT.

4 58 INDIAN J. MAR. SCI., VOL. 46, NO. 1, DECEMBER 017 Start Input image sequence Extraction of two signals Wavelet transform using DWT Cross correlation using FFT algorithm. Pea detection of correlation coefficients Velocity estimation for each wavelet level Average of velocity Extract another point where D( is the wavelet transform of the signal, ( ) is a wavelet function used to t correlation with the original signals, and the wavelet coefficients. are The discrete wavelet phase, ( can be written as: S p ( D( () The remaining part of the time domain signal in DWT, r ( can be given by: S p r( x( n), ( n) (3) j where ( ) denotes the scaling function of the wavelet n 1/ j ( n ) (4) x[n] End Figure : Image velocity field estimation using the proposed wavelet-based algorithm. g[n] h[n] g[n] h[n] Level 1 coefficients g[n] h[n] Level coefficients Level 3 coefficients Figure 3: Signal decomposition using discrete wavelet transform. For each level the signal length reduces by factor of two. To transform signal x(n) using DWT, the can the following equation is used: D ( x( n) ( n) (1) n Wavelet coefficients for each level can be reconstructed again in time domain by finding the inverse of DWT using Equation (5): x n) r( ( n) D( i, ( n) (5) ( j In this study, five levels of wavelet decomposition were applied, while three wavelet functions were used for comparison purpose. The selection of these functions is based on their ability to provide local information of signal, which could be useful for velocity estimation. Cross correlation of wavelet coefficients Since the signal is transformed in wavelet domain, the second step for velocity estimation is cross correlation between wavelet coefficients in order to find the time lag which requires several steps: estimation of correlation coefficients, interpolation, and pea detection of obtained coefficients. Figure 4 shows the bloc diagram for finding time lag between two signals S(t) and S(t-D) delayed by a value of D.

5 OSMAN et al.: WAVELET-BASED OPTICAL VELOCIMETRY 583 S(t) S(t-D) FFT FFT x t IFFT Adjust t to maximize correlation coefficient Pea detection Lag Figure 4: Bloc diagram for estimating time lag between two signals using FFT cross correlation. FFT algorithm was used to cross correlate between the wavelet coefficients and can be given by Equation (6): R FFT ifft fft ( D(. conj ( fft ( D( ) ) (6) ( 1 where R FFT is correlation coefficients, D ( 1, ( D ( are wavelet coefficients for extracted signals. The FFT of signal S can be given by: S ( i N 1 n0 S ( n). e i j n N (7) the inverse of FFT is given by using equation (8): S ( j) i N 1 0 S (. e i j n N (8) To find an accurate time lag value between the extracted two signals, an interpolation procedure is required, in which a parabola interpolation was used. Then, the required time lag can be obtained by detecting the pea of interpolated correlation coefficients. Then the local velocity u can be calculated using Equation (9): d u (9) t where d is the separation distance between extracted two points which was empirically fixed to be 5 pixels, and t is the detected time lag. By repeating the same steps for local velocity estimation, the image velocity field can be obtained. Finally, due to the presence of noise in the output velocity field, a median filter with size of 10 by 10 pixels was applied for smoothing. Experimental Facility Figure 5 shows the layout of experimental rig setup used for simulating the turbulent jet flow. For each experimental run the jet flow was simulated by allowing a fluid from overhead tan to pass into the main tan through a nozzle has a diameter of 10 mm. The nozzle flow rate was controlled by a control valve fixed between the overhead tan and the nozzle. The fluid in the overhead tan is a mixer of tap water, colloidal graphite, and salt (i.e. NaCl of 5 % weight), while the main tan filled by tap water. The graphite used to provide a better visualization of the flow and for improving the quality of video, while the salt used to provide the buoyancy effect in the turbulent jet flow as done by Crone et al. 3.The mixed fluid was first prepared in the supply tan and pumped to the overhead tan using a submersible pump. During the runs of experiments the level of fluid in overhead tan should be constant to provide constant flow rate for the nozzle, and any extra amount of fluid will return bac to the supply tan through drainage pipe. The main tan was made of a transparent acrylic material with a size of (900x900x000 mm), which is big enough to accommodate the fluid mixture. A momentum diffuser put inside the main tan to eep the blac fluid in the bottom of the tan, while a valve fixed at the bottom of the main tan for drainage purpose. Nozzle flow rates were measured in order to validate the proposed wavelet-based technique. Five cases of flow rate were measured by calibrating the opening of control valve as applied by Crone et al. 3. By opening the control valve the fluid will go to the main tan and simulate the turbulent jet flow for that valve opening. For each flow rate case the control valve was calibrated by opening the valve and measuring the time that allowed passing five liters of fluid into the main tan.

6 584 INDIAN J. MAR. SCI., VOL. 46, NO. 1, DECEMBER 017 Main tan Halogen lights Supply tan Video camera Nozzle Upper tan Computer Figure 5: Experimental rig setup used for simulating a turbulent jet flow. Table 1 summarizes the five cases of jet flow rates that considered in this study. For each case the flow rate Q i was calculated by dividing the volume of mixer fluid overtime required for passing this volume through the control valve. An average flow rate Q m with its percentage of standard deviation S normalized by the average flow rates were calculated. The nozzle velocity U m was calculated by dividing the averaged flow rate Q m over the cross section area of nozzle A. While the corresponding Reynolds number (Re) was calculated from Equation: Re Ud (11) where ρ is the fluid density, U nozzle velocity, is d the nozzle diameter, and µ is the fluid viscosity. To convert unit of velocity field from frame/pixel to m/sec, a scale of 4 pixels per every one millimeter was used, which obtained from the chec-board used for camera calibration before running each experiment. Table 1: Actual nozzle flow rates measured from experimental wors. Run No. Time (sec) Q i (liter/sec) Q m (liter/sec) S (%) U m Re

7 OSMAN et al.: WAVELET-BASED OPTICAL VELOCIMETRY 585 Results and Discussion Image Velocity Field Figure 6 shows the image velocity field estimated of DWT-TCC algorithm, in which Symlet wavelet function with five level of decomposition was applied. All the velocity fields were scaled between zero to the value of experimental nozzle velocity (i.e. refer to Table 1) for ease comparison. Generally the DWT- TCC algorithm under-estimated the jet velocity field and none of the obtained velocity field is as predicted from jet flow theory. Moreover, the similarity velocity distribution is observed for all the five cases of jet flow considered. This suggests the existence of non linear estimation in the velocity field when using DWT-TCC algorithm. A possible reason for this result is the effect of wavelet decomposition. The decomposition of signal using DWT is usually leads in reducing the signal. As a result a poor correlation between wavelet coefficients was obtained due to reduction of length. Figure 6: Estimated image velocity field using DWT-TCC algorithm by applying Symlet wavelet function with five wavelet levels for different nozzle flow rate (a) 0.18 m/sec, (b) 0.3 m/sec, (c) 0.45 m/sec, (d) 0.6 m/sec and (e) 1.17 m/sec.

8 Up (m/sec) Up (m/sec) Relative Error (%) 586 INDIAN J. MAR. SCI., VOL. 46, NO. 1, DECEMBER 017 Nozzle Velocity The nozzle velocity was estimated by averaging the velocities under the red-dash line in Figure 6, which equal x/d = 1. Figure 7 shows the estimated nozzle velocity U p using DWT- TCC algorithm against the experimental velocity value W P, where a linear relationship is expected. The difference between the estimated and experimental nozzle velocity increases with increasing the nozzle velocity. This could be for some problem associated with the input images or the DWT-TCC algorithm. To quantify the accuracy of the DWT-TCC, the relative error (RE) was calculated. Figure 8 shows that the overall accuracy of DWT-TCC reduces with increasing wavelet levels, in which an error of 37.8% was obtained at the first level, while an error of 67 % resulted when using level five. This means that the estimated nozzle velocity at first level is closer to the actual nozzle velocity. By more wavelet decomposition the length of signal reduced leading in inaccurate velocity estimation. Moreover the filtering of signal using DWT was lead in losing some information from the original signals. However, the error obtained by DWT-TCC is still too much, to proof that inaccuracy of proposed algorithm when using Symlet wavelet with five levels. 1. Experimental DWT-TCC Wp (m/sec) Figure 7: Estimated nozzle velocity against experimental nozzle velocity Wavelet Decomposition Level Figure 8: Relative errors in nozzle velocity estimation using various wavelet levels. The proposer selection wavelet function, as well as the wavelet level is important factors for the accuracy of DWT-TCC. The accuracy of DWT-TCC algorithm is evaluated by utilizing two different wavelets namely as Meyer, and Coiflet, as compared to the Symlet wavelet. Figure 9 shows the estimated nozzle velocity using three different wavelets with decomposing signals only one time. Both Symlet and Coiflet estimated with large difference as compared to the experimental trend with error of 38.8% and 37.8% respectively. While Meyer wavelet was estimated with an error of 34.6%. This difference is due to the variations of wavelet function properties. By comparing the three wavelet functions, a difference is observed in term of their shape, center frequency as well as the wavelet width Meyer Coiflet Symlet Experimental Wp (m/sec) Figure 9: Effect of wavelet functions in the accuracy of DWT-FFT.

9 OSMAN et al.: WAVELET-BASED OPTICAL VELOCIMETRY 587 DWT-FFT estimated the nozzle velocity with an error of 34.6% as an optimum accuracy. Applying of this technique for estimating the flow rate of real oil spill might result in inaccurate estimation. This because of the high flow rate of oil jet, since the DWT-FFT accuracy reduces with increasing the flow rate. Moreover, the noisy video data that can be collected from deepwater environment due to the lac of proper lighting as well as the movement of camera will increase the estimation error. This will directly affect the accuracy, since the DWT-FFT is sensitive to the length of signal. This problem can be solved by using continuous wavelet transform, in which the signal length will not be reduced. Conclusion In this paper, a new technique called DWT- FFT was proposed for estimating image velocity field. The DWT-FFT is based on combining discrete wavelet transform and FFT cross correlation. An experimental investigation on the accuracy of the DWT-FFT showed large error in nozzle velocity estimation associated by increasing the level of wavelet decomposition applied to the turbulent signals. The error was ranged from 37.8% to 67% when using one to five wavelet levels. DWT-FFT is less sensitive to wavelet function as compared to wavelet decomposition, where a range of error from 34.6% to 38.8% was obtained using Meyer and Symlet function respectively. However, the wavelet-based technique is a promising technique which accurately estimates the flow rate of oil spill. This is due to the advantage of the wavelet-based technique in decomposing the turbulent signals into multi-scale, while the turbulent flow has a multi-scale behaviour. Due to the limitation of discrete wavelet in dealing with the non-stationary signals of turbulent flow, a continuous wavelet transform will be utilized to develop an alternative optical technique for oil spill flow rate estimation. Acnowledgment The authors would lie to express their appreciation to Universiti Tenologi PETRONAS for supporting this wor under I- Gen 0153AA B30. References 1. M. K. McNutt, R. Camilli, T. J. Crone, G. D. Guthrie, P. A. Hsieh, T. B. Ryerson, et al., "Review of flow rate estimates of the Deepwater Horizon oil spil," Proceedings of the National Academy of Sciences, vol. 109, pp , 01.. B. Lehr, A. Aliseda, P. Bommer, P. Espina, O. Flores, J. Lasheras, et al., "Deepwater horizon release estimate of rate by PIV" Report to the US Dept of interior, T. J. Crone, R. E. McDuff, and W. S. Wilcoc, "Optical plume velocimetry: A new flow measurement technique for use in seafloor hydrothermal systems" Experiments in fluids, vol. 45, pp , G. Xu, B. Wan, and W. Zhang, "Application of wavelet multiresolution analysis to the study of selfsimilarity and intermittency of plasma turbulence" Review of scientific instruments, vol. 77, p , J. Ruppert-Felsot, M. Farge, and P. Petitjeans, "Wavelet tools to study intermittency: application to vortex bursting", Journal of Fluid Mechanics, vol. 636, pp , L. Hui, "Flow structure identification of a turbulent shear flow with use of wavelet statistics" M. Farge, N. Kevlahan, V. Perrier, and E. Goirand, "Wavelets and turbulence" Proceedings of the IEEE, vol. 84, pp , M. Farge, "Wavelet transforms and their applications to turbulence", Annual review of fluid mechanics, vol. 4, pp , T. Kim, N. Thürey, D. James, and M. Gross, "Wavelet turbulence for fluid simulation" in ACM Transactions on Graphics (TOG), 008, p P. Dérian, P. Héas, C. Herzet, and É. Mémin, "Wavelet-based fluid motion estimation" in Scale Space and Variational Methods in Computer Vision, Springer, 01, pp P. Dérian, "Wavelets and Fluid Motion Estimation" Université Rennes 1, J. Ferré-Giné, R. Rallo, A. Arenas, and F. Giralt, "Extraction of structures from turbulent signals" Artificial intelligence in engineering, vol. 11, pp , 1997.

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