{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T14:04:21Z","timestamp":1769522661298,"version":"3.49.0"},"reference-count":38,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,2,6]],"date-time":"2020-02-06T00:00:00Z","timestamp":1580947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51805161"],"award-info":[{"award-number":["51805161"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Hunan Provincial Key Research and Development Program","award":["2017WK2051 and 2018GK2044"],"award-info":[{"award-number":["2017WK2051 and 2018GK2044"]}]},{"DOI":"10.13039\/501100004735","name":"Hunan Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["2017JJ2084 and 2018JJ4084"],"award-info":[{"award-number":["2017JJ2084 and 2018JJ4084"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The tomography technique is an effective way to quantitatively evaluate damage from reconstruction imaging in structure health monitoring (SHM). The reconstruction algorithm for the probabilistic inspection of damage (RAPID) algorithm based on the signal difference coefficient (SDC) feature is a promising approach due to its superior performance. This paper focuses on the influence of different patterns of PZT (Lead Zirconate Titanate) sensor array configurations, i.e., the circular, square, and parallel array, on reconstruction image qualities for evaluating hole and crack damage. Variable shape parameters are applied to account for the unequal damage distances of different actuator-sensor pairs. Considering the directionality scattering fields of cracks, the angular scattering pattern of the SDC values are studied by simulation. The SDC variations for different groups of sensing paths at the same actuator are applied to predict the crack orientation. An improved RAPID algorithm is proposed by defining an additional SDC value of 1 in the path along the predicted crack orientation, which is determined by the point of the actuator causing the minimal SDC variation and the center point of the initial reconstruction image of the crack. The results show that the improved RAPID algorithm is effective for the evaluation of crack damage. Reconstruction image qualities with three PZT sensor array configurations for both holes and cracks are compared. The research is significant for selecting the PZT sensor array configuration in SHM.<\/jats:p>","DOI":"10.3390\/s20030860","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T03:13:27Z","timestamp":1581045207000},"page":"860","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Influence of the PZT Sensor Array Configuration on Lamb Wave Tomography Imaging with the RAPID Algorithm for Hole and Crack Detection"],"prefix":"10.3390","volume":"20","author":[{"given":"Songlai","family":"Wang","sequence":"first","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China"}]},{"given":"Wanrong","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9073-7900","authenticated-orcid":false,"given":"Yiping","family":"Shen","sequence":"additional","affiliation":[{"name":"Hunan Provincial Key Laboratory of Health Maintenance for Mechanical Equipment, Hunan University of Science and Technology, Xiangtan 411201, China"}]},{"given":"Yi","family":"Liu","sequence":"additional","affiliation":[{"name":"Zhuzhou National Innovation Railway Technology Co., Ltd., Zhuzhou 412000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2106-2465","authenticated-orcid":false,"given":"Shuai","family":"Jiang","sequence":"additional","affiliation":[{"name":"Hunan Provincial Key Laboratory of Health Maintenance for Mechanical Equipment, Hunan University of Science and Technology, Xiangtan 411201, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Qing, X., Li, W., Wang, Y., and Sun, H. (2019). Piezoelectric Transducer-Based Structural Health Monitoring for Aircraft Applications. Sensors, 19.","DOI":"10.3390\/s19030545"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"7312","DOI":"10.3390\/s140407312","article-title":"Quantitative damage detection and sparse sensor array optimization of carbon fiber reinforced resin composite laminates for wind turbine blade structural health monitoring","volume":"14","author":"Li","year":"2014","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1016\/j.measurement.2019.06.053","article-title":"Ultrasound computed tomography for material inspection: Principles, design and applications","volume":"146","author":"Khairi","year":"2019","journal-title":"Measurement"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Su, C., Jiang, M., Liang, J., Tian, A., Sun, L., Zhang, L., Zhang, F., and Sui, Q. (2020). Damage Localization of Composites Based on Difference Signal and Lamb Wave Tomography. Materials, 13.","DOI":"10.3390\/ma13010218"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"535","DOI":"10.4028\/www.scientific.net\/KEM.774.535","article-title":"Effectiveness of RAPID and SSM Algorithms on Composite Scarf Repair","volume":"774","author":"Lambinet","year":"2018","journal-title":"Key Eng. Mater."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"105002","DOI":"10.1088\/0964-1726\/20\/10\/105002","article-title":"Ultrasonic Lamb wave tomography in structural health monitoring","volume":"20","author":"Zhao","year":"2011","journal-title":"Smart Mater. Struct."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1177\/1475921709352145","article-title":"Probabilistic damage identification based on correlation analysis using guided wave signals in aluminum plates","volume":"9","author":"Wang","year":"2010","journal-title":"Struct. Health Monit."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"e1919","DOI":"10.1002\/stc.1919","article-title":"Delamination detection in composite plates by synthesizing time-reversed Lamb waves and a modified damage imaging algorithm based on RAPID","volume":"24","author":"Liu","year":"2017","journal-title":"Struct. Control Health Monit."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1007\/s12541-012-0087-2","article-title":"A study on quantitative lamb wave tomogram via modified RAPID algorithm with shape factor optimization","volume":"13","author":"Sheen","year":"2012","journal-title":"Int. J. Precis. Eng. Man."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s12650-015-0290-1","article-title":"Multi-defect tomographic imaging with a variable shape factor for the RAPID algorithm","volume":"19","author":"Lee","year":"2016","journal-title":"J. Visual-Japan"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s42417-018-0032-5","article-title":"Probabilistic Diagnostic Algorithm-Based Damage Detection for Plates with Non-uniform Sections Using the Improved Weight Function","volume":"6","author":"Zhao","year":"2018","journal-title":"J. Vib. Eng. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.polymertesting.2018.12.020","article-title":"Quantitative imaging of surface cracks in polymer bonded explosives by surface wave tomographic approach","volume":"74","author":"Li","year":"2019","journal-title":"Polym. Test."},{"key":"ref_13","first-page":"72951H","article-title":"Quantification of sensor geometry performance for guided wave SHM","volume":"7295","author":"Croxford","year":"2009","journal-title":"SPIE"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1063\/1.3591937","article-title":"Analysis of distributed sparse array configurations for guided wave imaging applications","volume":"1335","author":"Hall","year":"2011","journal-title":"AIP Conf. Proc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1063\/1.4864827","article-title":"Design of distributed sparse arrays for Lamb wave SHM based upon estimated scattering matrices","volume":"1581","author":"Chen","year":"2014","journal-title":"AIP Conf. Proc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2181","DOI":"10.1177\/1045389X14549873","article-title":"Validation and evaluation of damage identification using probability-based diagnostic imaging on a stiffened composite panel","volume":"26","author":"Wu","year":"2015","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.acme.2016.09.005","article-title":"Localizing impact damage of composite structures with modified RAPID algorithm and non-circular PZT arrays. Arch","volume":"17","author":"Dziendzikowski","year":"2017","journal-title":"Civ. Mech. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1088\/0964-1726\/13\/3\/011","article-title":"Optimal placement of sensors for structural health monitoring using improved genetic algorithms","volume":"13","author":"Guo","year":"2004","journal-title":"Smart Mater. Struct."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1687","DOI":"10.1063\/1.2184724","article-title":"Ultrasonic sensor placement optimization in structural health monitoring using evolutionary strategy","volume":"820","author":"Gao","year":"2006","journal-title":"AIP Conf. Proc."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/stc.1898","article-title":"Transducer placement optimisation scheme for a delay and sum damage detection algorithm","volume":"24","author":"Salmanpour","year":"2017","journal-title":"Struct. Control Health Monit."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1177\/1475921719841307","article-title":"Sensor placement optimization on complex and large metallic and composite structures","volume":"19","author":"Ismail","year":"2020","journal-title":"Struct. Health Monit."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1121\/1.1448338","article-title":"Measurement of the scattering of a Lamb wave by a through hole in a plate","volume":"111","author":"Fromme","year":"2002","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.ultras.2018.08.004","article-title":"Incremental scattering of the A0 Lamb wave mode from a notch emanating from a through-hole","volume":"91","author":"Liu","year":"2019","journal-title":"Ultrasonics"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1177\/1550147719843860","article-title":"Study on the orientation detection of surface cracks by electromagnetic acoustic emission","volume":"15","author":"Cai","year":"2019","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2974","DOI":"10.1177\/0954406216686996","article-title":"Interaction of Lamb waves with rivet hole cracks from multiple directions","volume":"231","author":"Shen","year":"2017","journal-title":"Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"76501M","DOI":"10.1117\/12.848621","article-title":"Influence of guided ultrasonic wave scattering directionality on the detection sensitivity for SHM of fatigue cracks","volume":"7650","author":"Fromme","year":"2010","journal-title":"Proc. SPIE"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2021","DOI":"10.1121\/1.2968697","article-title":"Angular influence on the scattering of fundamental shear horizontal guided waves by a through-thickness crack in an isotropic plate","volume":"124","author":"Rajagopal","year":"2008","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1907","DOI":"10.1088\/0964-1726\/16\/5\/047","article-title":"Quantitative evaluation of crack orientation in aluminium plates based on Lamb waves","volume":"16","author":"Lu","year":"2007","journal-title":"Smart Mater. Struct."},{"key":"ref_29","first-page":"1","article-title":"An Enhanced Time-Reversal Imaging Algorithm-Driven Sparse Linear Array for Progressive and Quantitative Monitoring of Cracks","volume":"9456","author":"Wang","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1138","DOI":"10.1177\/1045389X12469452","article-title":"Lamb wave\u2013based quantitative crack detection using a focusing array algorithm","volume":"24","author":"Yu","year":"2013","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"105007","DOI":"10.1088\/0964-1726\/22\/10\/105007","article-title":"A multi-feature integration method for fatigue crack detection and crack length estimation in riveted lap joints using Lamb waves","volume":"22","author":"He","year":"2013","journal-title":"Smart Mater. Struct."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2135","DOI":"10.1016\/j.ymssp.2011.02.001","article-title":"Quantitative evaluation of orientation-specific damage using elastic waves and probability-based diagnostic imaging","volume":"25","author":"Zhou","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1088\/0964-1726\/13\/4\/002","article-title":"Detection of cracks in plates using piezo-actuated Lamb waves","volume":"13","author":"Tua","year":"2004","journal-title":"Smart Mater. Struct."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"30","DOI":"10.3901\/JME.2016.06.030","article-title":"Lamb wave tomography technique for crack damage detection","volume":"52","author":"Wang","year":"2016","journal-title":"Mech. Eng. J."},{"key":"ref_35","unstructured":"Wang, Q., Wang, M., Yue, D., and Su, Z. (2016, January 5\u20138). A Lamb Wave-based Crack Diagnosis Method Using an Improved RAPID Algorithm. Proceedings of the 8th European Workshop On Structure Health Monitoring, Bilbao, Spain."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1177\/1045389X05050106","article-title":"Tuned Lamb Wave Excitation and Detection with Piezoelectric Wafer Active Sensors for Structural Health Monitoring","volume":"16","author":"Giurgiutiu","year":"2005","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1088\/0964-1726\/15\/4\/022","article-title":"Modeling and testing of PZT and PVDF piezoelectric wafer active sensors","volume":"15","author":"Lin","year":"2006","journal-title":"Smart Mater. Struct."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.ultras.2016.03.019","article-title":"Combined analytical FEM approach for efficient simulation of Lamb wave damage detection","volume":"69","author":"Shen","year":"2016","journal-title":"Ultrasonics"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/3\/860\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:55:13Z","timestamp":1760172913000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/3\/860"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,6]]},"references-count":38,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["s20030860"],"URL":"https:\/\/doi.org\/10.3390\/s20030860","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,6]]}}}