Send Order for Reprint to reprint@benthamcience.ae 488 The Open Automation and Control Sytem Journal, 2014, 6, 488-492 Open Acce Parameter Optimization of Linear Phaed Array Tranducer for Defect Detection Li Li 1,*, Xinliang Yu 1, Fangqin Li 2 and Baojia Chen 1 1 Hubei Key Laboratory of Hydroelectric Machinery Deign & Maintenance, China Three Gorge Univerity, Yichang, 443002, China 2 Department of Electrical and Computer Engineering (ECE) National Univerity of Singapore, 21 Lower Kent Ridge Road, 119077, Singapore Abtract: An optimization deign method wa propoed for linear phaed array ultraonic imaging teting. In the method, main lobe width and the amplitude ratio of ide lobe to main lobe were erved a optimization objective to judge the teting preciion of phaed array beam directivity. The combination of element of width and inter-element pace wa erved a optimize parameter for the optimization objective. The combination of optimal parameter for phaed array tranducer wa finally achieved and applied to phaed array B-mode imaging ultraonic teting on a flat bottom hole in tandard tet block. The reult how that the method can not only obtained the optimal parameter for linear array of phaed array tranducer, but alo improve the accuracy of the location and ize for defect detection. Keyword: Defect detection, linear phaed array tranducer, parameter optimization, phaed array ultraonic B-mode imaging teting. 1. INTRODUCTION Due to the flexibility of control of ultraonic beam directivity and the ize and location of focu, phaed array ultraonic imaging teting technology play a critical role in defect detection among aeropace, railway, hipping and nuclear indutry [1-5]. The reolution of phaed array ultraonic imaging i one of the mot concerned of thee indutrial detection field. According to the reearch, phaed array tranducer parameter are eential to obtain a high ultraonic imaging reolution [6-8]. Improper parameter of phaed array tranducer would lead to a poor phaed array ultraonic beam directivity, and then caue defect reolution artifact, grating lobe or ide lobe effect artifact in the ultraonic imaging [9, 10]. Artifact mean that the poition of echo ignal in ultraonic imaging teting ytem doe not agree with the actual poition in the echo interface for the teting body, or the diplayed ignal amplitude and the change of gray cale doe not relate to the variation of echo interfacial characterization [9,10]. Any artifact can greatly deteriorate the accuracy of the defect detection. Therefore, it i crucial to etablih an appropriate et of deign parameter for phaed array tranducer for obtaining accurate defect ultraonic imaging and defect diagnoi [8]. It i noticed that the current method for a linear phaed array tranducer parameter election (called current method ) i only focued on analyzing or optimizing for ingle parameter. It doe not provide optimal matching parameter for a linear phaed array tranducer [11]. Therefore an optimization deign of a linear phaed array parameter method wa preented in thi paper. The normalized main lobe width and the amplitude ratio of the ide lobe to main lobe were erved a optimization objective to judge the teting preciion of phaed array beam directivity. Element width a and inter-element pacing d were erved a optimized parameter for the optimization objective. The combination of optimal parameter for phaed array tranducer wa finally achieved by analyzing and applied to phaed array B-mode imaging ultraonic teting on a flat bottom hole in tandard tet block. The reult how that the method can not only obtained the optimal parameter for linear array of phaed array tranducer, but alo improve the accuracy of the location and ize for defect detection. 2. BEAM DIRECTIVITY FOR LINEAR PHASED ARRAY TRANSDUCER Beam directivity for linear phaed array tranducer decrip acoutic preure amplitude with the variation of azimuth angle [6-8]. Linear phaed array tranducer conit of N individual element. It beam directivity can be defined a following. D( θ ) = Where, k ka in[ (inθ-in θ )] in( in θ) 2 2 kd ka N in[ (in θ in θ )] in θ 2 2 (1) 1874-4443/14 2014 Bentham Open
Parameter Optimization of Linear Phaed Array Tranducer The Open Automation and Control Sytem Journal, 2014, Volume 6 489 Fig. (1). Beam directivity of linear phaed array tranducer. a --- element width; d --- inter-element pace; k = 2πλ; λ --- wave length; f --- operating frequency for tranducer; θ --- azimuth angle; θ --- teering angle. Beam directivity conit of main lobe, grating lobe and ide lobe, hown in Fig. (1). Well beam directivity can be achieved by minimizing the main lobe width, eliminating grating lobe and uppreing ide lobe, o that it ultraonic beam can be teered and focued on whole teting area. The parameter (N, a) have a great effect on the beam directivity. 2.1. Influence of Tranducer Parameter on Beam Directivity 2.1.1. Influence on Main Lobe A hown in in Fig. (1), main lobe width q i defined a the ditance of main lobe on the azimuth angle θ axi 1 [in λ (in ) in λ (in )] q = θ + θ (2) π Relationhip between q, N and λ are hown in Fig. (2). In Fig. (2a) main lobe width q decreae with both element number N and inter-element pace d. Since maller q will lead to a higher ultraonic imaging reolution, phaed array beam directivity can be improved by increaing element number N and inter-element pace d. 2.1.2. Influence on Grating Lobe The appearance of grating lobe will lead to both energy leakage and puriou ignal. If inter-element pace d and wavelength λ atify inequality (3), grating lobe would not appear in linear phaed tranducer beam directivity diagram and grating lobe effect artifact [6-8]. d ( N) λ N(1+ in θ ) 2.1.3 Influence on Slide Lobe Fig. (2). Influence of linear phaed array tranducer parameter on the main lobe θ 0 = 30 o, f = 10MHz, c = 5940m/ Influence of element number N on the main lobe width q ( d λ = 0.6 ) Influence of inter-element pace d λ on main lobe width q (N = 32). Side lobe are the mall lobe near to main lobe in beam directivity diagram hown in Fig. (1). The ratio of ide lobe to main lobe ε i a follow. (3)
490 The Open Automation and Control Sytem Journal, 2014, Volume 6 Li et al. Therefore, bigger element number N and maller interelement pace d contribute to le ide lobe. 2.2. Influence of Tranducer Parameter on Teting Area Compared to the axial direction of the teering angle of acoutic preure, the acoutic preure amplitude generated by the linear phaed array tranducer hould not be lower than 6dB, thi range i called teting area angle. β 06. λ a -6dB = 2in ( ) (5) If 0.6 λ/a 1, teting area angle i 180 and the linear phaed array ultraonic beam can be teered and focued. Therefore, the element width of a linear phaed array tranducer hould meet the following condition. a λ 0.6 (6) 2.3. Analyi of Phaed Array Tranducer Parameter Optimization Deign According to the analyi of beam directivity and teting area, everal criterion for election of linear phaed array tranducer are obtained:1) Increae element number N and inter-element pace d to decreae the main lobe width q; 2) Inequality (3) hould be atified to eliminate ide lobe; 3) Increae element number N or decreae element width a to uppre ide lobe amplitude; 4) Inequality (6) hould be atified to make the whole teting area covered. 2.3.1. Variable Selection According to the deign rule for phaed array tranducer parameter, element width a and inter-element pace d play deciive role on the beam directivity of linear phaed array tranducer. X = ( a, d) (7) k ka ka in[ (inθ-in θ)] in( in θ) inθ ε = 2 2 2 kd ka ka N in[ (inθ in θ)] inθ in( in θ) 2 2 2 1 λ 1 2λ where, θ = in θ (in θ ) + in θ (in θ ) 2 2 Fig. (3). Influence of linear phaed array tranducer parameter on ide lobe θ = 0 o, f = 10 MHz, c = 5940m/, a λ = 0.35 Influence of element number N on main lobe width q ( d λ = 0.6 ) Influence of inter-element pace d λ on main lobe width q (N = 32). It can be found in Fig. (3) that ε decreae with element number N, while increae with inter-element pace d (d > a). (4) 2.3.2. Optimization Function Deign Artifact produced by undeirable beam directivity affect the imaging reolution directly. In order to minimize the main lobe width q and uppre ide lobe amplitude, the minimum main lobe width q X ide lobe to main lobe! X ( ) and the ratio of minimum ( ) are taken a optimization function. 1 λ λ f1( X) = min q( X) = min( [in (in θ + ) in (in θ )]) π k ka ka in[ (inθ-in θ)] in( in θ) inθ f 2 2 2 2( X) = min ε ( X) = min kd ka ka N in[ (inθ in θ)] inθ in( in θ) 2 2 2 2.3.3. Contraint Condition Deign Grating lobe elimination and complete coverage of teting area are deigned a optimal contraint condition. (8)
Parameter Optimization of Linear Phaed Array Tranducer The Open Automation and Control Sytem Journal, 2014, Volume 6 491 Fig. (4). Phaed array imaging ultraonic tet to a flat bottom hole 5# in CSII 1 20 tandard tet block. Table 1. Comparion of beam directivity for two phaed array tranducer. Rotation Velocity (rpm) Current Optimization Comparion Main lobe width q 0.0685 0.0359 47.59% Granting lobe No No - Teting area Angle/ o 180 180 - d ( N ) a, 0.6 λ N(1+ in θ ) λ 2.4. Application In order to verify the propoed method, a hown in Fig. (4), a CSII 1 20 tandard tet block with a flat bottom hole 5# i taken a a tet object for defect. A et of reaonable parameter of a linear phaed array tranducer i tudied. In the application, we chooe N = 32, c = 5940 m/, f = 10 MHz, λ = 0.594 mm, array aperture D = 12 mm and teering angleθ = 30 o. Employing the method, an optimized reult wa got a a = 0.107625 mm, d = 0.383625 mm. (9) big error. It indicate that parameter optimization method can tet the location and ize of defect more accurately and quantitatively than current method. The information of tructure defect can be ditinguihed by parameter optimization method. It alo prove the feaibility and validity of thi method. 2.5. Comparative Analyi The reult of optimal parameter deign for phaed array tranducer (N = 32, f = 10 MHz, d = 0.38 mm, a = 0.11 mm) are compared with the reult of current method (N = 32, f = 10 MHz, d = 0.20 mm, a = 0.11 mm) in Table 1 and Fig. (5). A hown in Table 1, main lobe width and ide lobe amplitude of optimal parameter deigning for phaed array tranducer are of 47.59% and 0.42% maller than current method repectively, but the beam directivity for both i fine. Fig. (5) how the phaed array B-mode imaging imulation reult of a flat bottom hole 5# uing thee two tranducer [12]. After convert thee two B-mode graycale image to binary image baed on threhold, accordingly, defect edge are extracted in Fig. (5c) (dah curve and full curve). We can ee that the location (approximately 0.25 mm) and ize ( Φ= 2 mm) of defect detection after parameter optimization (dah curve) are obviouly conitent with the real poition (0.25 mm) and ize Φ= 2 mm (bold red curve), but the current method on defect evaluation (the full curve) have a
492 The Open Automation and Control Sytem Journal, 2014, Volume 6 Li et al. (2) The application indicate that: the optimal parameter combination for phaed array tranducer obtained by the parameter optimization method i N=32, f = 10 MHz, d = 0.38 mm, a = 0.11 mm, the location (0.25 mm) and the ize ( Φ= 2 mm) of the flat bottom hole 5# defect teting by the phaed array B-mode imaging imulation agree well with reality, it prove that the parameter method can really improve the accuracy of the location and ize for defect detection. CONFLICT OF INTEREST The author confirm that thi article content ha no conflict of interet. ACKNOWLEDGEMENTS Thi work decribed in the paper wa upported by National Natural Science Foundation of China (No. 51175401 and No.51205230). (c) Fig. (5). Comparion of phaed array B-mode imaging imulation reult to a 5# flat bottom hole in CSII /20 tandard tet block Current method Parameter optimization (c) Comparion CONCLUSION Aimed at improving defect detection quality of linear phaed array ultraonic imaging tet, an optimization deign for a linear phaed array parameter method wa preented in thi paper. The effectivene of thi method ha been verified by a cae tudy. It can be concluded that: (1) A parameter optimization method for linear phaed array ultraonic ha been propoed. Thi method i baed on the analyi of beam directivity of phaed array ultraonic and electing the minimum main lobe width and the ratio of ide lobe to main lobe a optimization function, the elimination of ide lobe and effective teting area a the contrain condition, and then the main parameter of phaed array, i.e. element width a and inter-element pace d, were analyed and deigned, the optimal parameter combination of phaed array tranducer were finally obtained. REFERENCES [1] B. W. Drinkwater, and P. D. Wilcox, Ultraonic array for nondetructive evaluation: A review, NDT and E International, vol. 39, no. 7 pp. 525-541, October 2006. [2] H. Li, Y. Li, G. Lu, and K. Tian, Ultraonic phaed array technology in the detection of compoite material application, Fiber Reinforced Platic/Compoite, no. 2, pp. 86-88, March 2010. [3] X. Zhan, J. Li, Y. Zhang, S. Chen, Z. Zeng, and S. Jin Ultraonic phaed array ytem applied in flaw detection of pipe girth weld, Chinee Journal of Scientific Intrument, vol. 27, no. 6, pp. 1427-1428, June 2006. [4] Y. Ji, and J. Li, Application of LX Portable Phaed Array Wheel Rim Flaw Detection Device in EMU Wheelet Flaw Detection, Chinee Railway, no. 2, pp. 89-92, February 2011. [5] S. Song, H. Shin, and Y. Jang, Development of an ultraonic phaed array ytem for non-detructive tet of nuclear power plant component, Nuclear Engineering and Deign, vol. 214, no. 2, pp. 151-161, 2002. [6] Clay, S. Wooh, L. Azar, and J. Wang, Experimental tudy of phaed array beam teering characteritic, Journal of Nondetructive Evaluation, vol. 18, no. 2, pp. 59-71, June 1999. [7] S. Wooh, and Y. Shi, Optimum beam teering of linear phaed array, Wave Motion, vol. 29, no. 3, pp. 245-265, April 1999. [8] S. Wooh, and Y. Shi, Three-dimenional directivity of phaed teered ultraound, Journal of the Acoutical Society of America, vol. 105, no. 6, pp. 3275-3282, 1999. [9] K. Shi, and Y. Guo, Phaed Array Ultraonic Imaging, Higher Education Pre: China, 2010. [10] R. Feng, Principle and Deign of ultraonic diagnotic equipment. China Medical, Science and Technology Pre: China, 1993. [11] H. Jing, S. Zhou, and P. Que, Optimization of Parameter for Linear Phaed Array Tranducer, Piezoelectric and Acoutooptic, vol. 32, no. 1, pp. 51-54, February, 2010. [12] J. A. Jenen, Uer' guide for the Field II program, Verion 3.20. Department of Information Technology, Technical Univerity of Denmark, 2011. Received: February 13, 2014 Revied: February 28, 2014 Accepted: October 28, 2014 Li et al.; Licenee Bentham Open. Thi i an open acce article licened under the term of the Creative Common Attribution Non-Commercial Licene (http://creativecommon.org/licene/by-nc/3.0/) which permit unretricted, non-commercial ue, ditribution and reproduction in any medium, provided the work i properly cited.