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In order to solve the problem of extracting ultrasonic signals from strong background noise, a novel method, which is termed APSO-SD algorithm and based on improved adaptive particle swarm optimization (APSO) and sparse decomposition (SD) theory, is proposed in this paper. This method can convert the ultrasonic signal denoising problem into optimizing the function on the infinite parameter set. First, based on the sparse decomposition theory and the structural characteristics of ultrasonic signal, the objective function of particle swarm optimization algorithm and the reconstruction algorithm of the denoised signal are constructed, so that particle swarm optimization and ultrasonic signal denoising can be combined. Second, in order to improve the robustness of the proposed approach, an APSO algorithm is proposed. What is more, because particle swarm optimization algorithm can be used to optimize in continuous parameter space, and according to the empirical characteristics of the ultrasonic signals used in practical engineering, a continuous super complete dictionary for matching ultrasonic signals is established. Since the super complete dictionary is continuous, there are an infinite number of atoms in the established dictionary. The redundancy of dictionaries is enhanced by the method in this paper. Based on the fact that the inner product of the optimal atom and the ultrasonic signal is one and the inner product of the noise and the optimal atom is zero in the established dictionary, the objective optimization function of APSO-SD algorithm is established. Finally, the optimal atom is determined based on the optimization result of the objective function. In this way, the denoising ultrasonic signal can be reconstructed by using the optimal atom according to the reconstruction algorithm. The processing results of simulated ultrasonic signals and measured ultrasonic signals show that the proposed method can effectively extract weak ultrasonic signals from strong background noise whose signal-to-noise ratio is lowest, as low as-4 dB. In addition, compared with the adaptive threshold based wavelet method, the proposed method in this paper shows the good denoising performance. In this paper, it is demonstrated that the problem of ultrasonic signal denoising can be transformed into the optimization of constraint functions. Furthermore, the ability of the proposed APSO-SD algorithm to accurately recover signals from noisy acoustic signals is better than that of the common wavelet method.
[1] Kharrat M, Gaillet L 2015 Ultrasonics 61 52
[2] Burkov M V, Eremin A V, Lyubutin P S, Byakov A V, Panin S V 2017 Russ. J. Nondestruct. 53 817
[3] Demcenko A, Mainini L, Korneev V A 2015 Ultrasonics 57 179
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[12] San E, Rodriguez H 2015 J. Nondestruct Eval. 34 270
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[15] Wang L, Cai G G, Gao G Q, Zhou F, Yang S Y, Zhu Z K 2017 J. Vib. Shock 36 176 (in Chinese)[王林, 蔡改改, 高冠琪, 周菲, 杨思远, 朱忠奎 2017 振动与冲击 36 176]
[16] Zhao Z G, Zhang C J, Gou X F, Sang H T 2015 Acta Phys. Sin. 64 088801 (in Chinese)[赵志刚, 张纯杰, 苟向锋, 桑虎堂 2015 物理学报 64 088801]
[17] Subasi A 2013 Comput. Biol. Med. 43 576
[18] Cho M Y, Hoang T T 2017 Adv. Electr. Comput. En. 17 51
[19] Gao F, Tong H Q 2006 Acta Phys. Sin. 55 577 (in Chinese)[高飞, 童恒庆 2006 物理学报 55 577]
[20] Zhang H L, Song L L 2013 Acta Phys. Sin. 62 190508 (in Chinese)[张宏立, 宋莉莉 2013 物理学报 62 190508]
[21] Armaghani D J, Shoib R S, Faizi K, Rashid A S 2017 Neural Comput. Appl. 28 391
[22] Wei D Z, Chen F J, Zheng X Y 2015 Acta Phys. Sin. 64 110503 (in Chinese)[魏德志, 陈福集, 郑小雪 2015 物理学报 64 110503]
[23] Yuan H D, Chen J, Dong G M 2017 Math. Probl. Eng. 2017 7257603
[24] Ghasemi M, Aghaei J, Hadipour M 2017 Electron. Lett. 53 1360
[25] Demirli R, Saniie J 2001 IEEE Trans. Ultrason. Ferr. 48 787
[26] Zhu J J, Li X L 2017 Healthcare Technol. Lett. 4 134
[27] Tang J, Gao L, Peng L, Zhou Q 2007 High Voltage Eng. 12 66 (in Chinese)[唐炬, 高丽, 彭莉, 周倩 2007 高电压技术 12 66]
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[1] Kharrat M, Gaillet L 2015 Ultrasonics 61 52
[2] Burkov M V, Eremin A V, Lyubutin P S, Byakov A V, Panin S V 2017 Russ. J. Nondestruct. 53 817
[3] Demcenko A, Mainini L, Korneev V A 2015 Ultrasonics 57 179
[4] Mcgovern M E, Reis H 2017 Res. Nondestruct Eval. 28 226
[5] Li W, Cho Y 2014 Exp. Mech. 54 1309
[6] Li W B, Deng M X, Xiang Y X 2017 Chin. Phys. B 26 114302
[7] Demenko A, Koissin V, Korneev V A 2014 Ultrasonics 54 684
[8] Jiang N 2015 Ph. D. Dissertation (Taiyuan: North University of China) (in Chinese)[江念 2015博士学位论文 (太原: 中北大学)]
[9] Mohamed I, Hutchins D, Davis L, Laureti S, Ricci M 2017 Nondestruct. Test Eva. 32 343
[10] Sinding K M, Drapaca C S, Tittmann B R 2016 IEEE Trans. Ultrason Ferr. 63 1172
[11] Wu J, Zhu J G, Yang L H, Shen M T, Xue B, Liu Z X 2014 Measurement 47 433
[12] San E, Rodriguez H 2015 J. Nondestruct Eval. 34 270
[13] Li Y, Guo S X 2012 Acta Phys. Sin. 61 034208 (in Chinese)[李扬, 郭树旭 2012 物理学报 61 034208]
[14] Mallat S G, Zhang Z 1993 IEEE Trans. Signal Process. 41 3397
[15] Wang L, Cai G G, Gao G Q, Zhou F, Yang S Y, Zhu Z K 2017 J. Vib. Shock 36 176 (in Chinese)[王林, 蔡改改, 高冠琪, 周菲, 杨思远, 朱忠奎 2017 振动与冲击 36 176]
[16] Zhao Z G, Zhang C J, Gou X F, Sang H T 2015 Acta Phys. Sin. 64 088801 (in Chinese)[赵志刚, 张纯杰, 苟向锋, 桑虎堂 2015 物理学报 64 088801]
[17] Subasi A 2013 Comput. Biol. Med. 43 576
[18] Cho M Y, Hoang T T 2017 Adv. Electr. Comput. En. 17 51
[19] Gao F, Tong H Q 2006 Acta Phys. Sin. 55 577 (in Chinese)[高飞, 童恒庆 2006 物理学报 55 577]
[20] Zhang H L, Song L L 2013 Acta Phys. Sin. 62 190508 (in Chinese)[张宏立, 宋莉莉 2013 物理学报 62 190508]
[21] Armaghani D J, Shoib R S, Faizi K, Rashid A S 2017 Neural Comput. Appl. 28 391
[22] Wei D Z, Chen F J, Zheng X Y 2015 Acta Phys. Sin. 64 110503 (in Chinese)[魏德志, 陈福集, 郑小雪 2015 物理学报 64 110503]
[23] Yuan H D, Chen J, Dong G M 2017 Math. Probl. Eng. 2017 7257603
[24] Ghasemi M, Aghaei J, Hadipour M 2017 Electron. Lett. 53 1360
[25] Demirli R, Saniie J 2001 IEEE Trans. Ultrason. Ferr. 48 787
[26] Zhu J J, Li X L 2017 Healthcare Technol. Lett. 4 134
[27] Tang J, Gao L, Peng L, Zhou Q 2007 High Voltage Eng. 12 66 (in Chinese)[唐炬, 高丽, 彭莉, 周倩 2007 高电压技术 12 66]
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