{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T17:04:47Z","timestamp":1772643887814,"version":"3.50.1"},"reference-count":25,"publisher":"Acoustical Society of America (ASA)","issue":"3","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52371311"],"award-info":[{"award-number":["52371311"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12274100"],"award-info":[{"award-number":["12274100"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fund of the Key Laboratory of Hydroacoustics","award":["KY10500240097"],"award-info":[{"award-number":["KY10500240097"]}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,3,1]]},"abstract":"<jats:p>This paper investigates the acoustic radiation produced by water entry of objects. While current research predominantly focuses on the fluid dynamic characteristics of object submersion, studies on acoustic radiation are limited. Most existing studies derive conclusions from open-water or laboratory measurements of sound pressure, which are highly susceptible to experimental conditions such as measurement distance, water depth, and medium. This study focuses on solid steel balls and uses total sound energy to characterize the acoustic properties of underwater objects. Different methods are employed in near-field and far-field areas to measure water entry sound, and an optimized segmented calculation method suitable for the total sound energy of water entry sounds is proposed. This method reduces the impact of echo signals from the initial impact sound on bubble pulsation sounds in near-field measurements and avoids the influence of the cutoff frequency of the reverberation tank in far-field measurements. Additionally, the calculation results are integrated with a neural network-based data fitting method to establish a small-scale predictive model for the total sound energy of water entry sound. The measurement-calculation-modeling approach proposed in this study provides a theoretical foundation for engineering applications such as extracting acoustic characteristics of underwater targets in shallow marine environments and acoustically locating water entry events.<\/jats:p>","DOI":"10.1121\/10.0042826","type":"journal-article","created":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T12:54:58Z","timestamp":1772628898000},"page":"1930-1947","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Measured acoustic energy and neural network models for low-speed water entry by steel spheres"],"prefix":"10.1121","volume":"159","author":[{"given":"Yihan","family":"Yang","sequence":"first","affiliation":[{"name":"National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University 1 , Harbin 150001,","place":["China"]},{"name":"Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology 2 ; Harbin 150001,","place":["China"]},{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University 3 , Harbin 150001,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"Li","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University 1 , Harbin 150001,","place":["China"]},{"name":"Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology 2 ; Harbin 150001,","place":["China"]},{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University 3 , Harbin 150001,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dajing","family":"Shang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University 1 , Harbin 150001,","place":["China"]},{"name":"Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology 2 ; Harbin 150001,","place":["China"]},{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University 3 , Harbin 150001,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Tang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University 1 , Harbin 150001,","place":["China"]},{"name":"Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology 2 ; Harbin 150001,","place":["China"]},{"name":"College of Underwater Acoustic Engineering, Harbin Engineering University 3 , Harbin 150001,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ping","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Computing, The Hong Kong Polytechnic University 4 , Hong Kong,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"231","published-online":{"date-parts":[[2026,3,4]]},"reference":[{"issue":"3","key":"2026030407545204600_c1","doi-asserted-by":"publisher","first-page":"695","DOI":"10.1080\/17445302.2020.1835053","article-title":"Recent developments on the water entry impact of wedges and projectiles","volume":"17","year":"2022","journal-title":"Ships Offshore Struct."},{"key":"2026030407545204600_c2","first-page":"2","article-title":"Acoustic effects on water impact","year":"1995"},{"issue":"1_Supplement","key":"2026030407545204600_c3","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1121\/1.1917863","article-title":"Theory of the sound radiated into the liquid by the gas-to-liquid entry of an object","volume":"27","year":"1955","journal-title":"J. Acoust. Soc. Am."},{"issue":"8","key":"2026030407545204600_c4","doi-asserted-by":"publisher","first-page":"1080","DOI":"10.1121\/1.1907831","article-title":"Splashes as sources of sound in liquids","volume":"31","year":"1959","journal-title":"J. Acoust. Soc. Am."},{"issue":"6","key":"2026030407545204600_c5","doi-asserted-by":"publisher","first-page":"1138","DOI":"10.1121\/1.1919174","article-title":"Underwater noise produced by bullet entry","volume":"36","year":"1964","journal-title":"J. Acoust. Soc. Am."},{"key":"2026030407545204600_c6","volume-title":"Underwater Acoustics","year":"1965"},{"key":"2026030407545204600_c7","first-page":"27","article-title":"Research on the sound characteristics of water impact","volume":"01","year":"1981","journal-title":"J. Ship Mech."},{"issue":"4","key":"2026030407545204600_c8","doi-asserted-by":"publisher","first-page":"1518","DOI":"10.1121\/1.397353","article-title":"Underwater sound produced by individual drop impacts and rainfall","volume":"85","year":"1989","journal-title":"J. Acoust. Soc. Am."},{"issue":"4","key":"2026030407545204600_c9","doi-asserted-by":"publisher","first-page":"352","DOI":"10.15949\/j.cnki.0217-9776.2009.04.002","article-title":"Research on detection and azimuth estimation for the splash sound of target's water entry based on empirical mode decomposition","volume":"28","year":"2009","journal-title":"Chin. J. Acoust."},{"issue":"1","key":"2026030407545204600_c10","doi-asserted-by":"publisher","first-page":"10","DOI":"10.7776\/ASK.2014.33.1.010","article-title":"Experimental study on underwater transient noise generated by water-entry impact","volume":"33","year":"2014","journal-title":"J. Acoust. Soc. Korea"},{"key":"2026030407545204600_c11","doi-asserted-by":"publisher","first-page":"102649","DOI":"10.1016\/j.apor.2021.102649","article-title":"A contribution to underwater acoustic problem in water entry of wedge-shaped bodies","volume":"111","year":"2021","journal-title":"Appl. Ocean Res."},{"key":"2026030407545204600_c12","doi-asserted-by":"publisher","first-page":"108659","DOI":"10.1016\/j.ymssp.2021.108659","article-title":"A noise reduction method for force measurements in water entry experiments based on the Ensemble Empirical Mode Decomposition","volume":"168","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"2026030407545204600_c13","doi-asserted-by":"publisher","first-page":"115299","DOI":"10.1016\/j.oceaneng.2023.115299","article-title":"Probability density function analysis of water entry sound based on \u03b1 stable distribution model","volume":"285","year":"2023","journal-title":"Ocean Eng."},{"key":"2026030407545204600_c14","doi-asserted-by":"publisher","first-page":"109761","DOI":"10.1016\/j.apacoust.2023.109761","article-title":"The line-of-sight peak detection and tracking of underwater acoustic DSSS communications in the doubly spread channel","volume":"216","year":"2024","journal-title":"Appl. Acoust."},{"issue":"1","key":"2026030407545204600_c15","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1121\/10.0034786","article-title":"A combined noise source model based on vertical coherence to quantify the proportions of two types of noise power","volume":"157","year":"2025","journal-title":"J. Acoust. Soc. Am."},{"issue":"1","key":"2026030407545204600_c16","doi-asserted-by":"publisher","first-page":"4345419","DOI":"10.1155\/2021\/4345419","article-title":"Near-field measurements of water-entry sound of low-speed metal balls in a non-anechoic tank","volume":"2021","year":"2021","journal-title":"Math. Problems Eng."},{"key":"2026030407545204600_c17","first-page":"70","volume-title":"Fundamentals of Acoustics","year":"1981"},{"issue":"7","key":"2026030407545204600_c18","doi-asserted-by":"publisher","first-page":"075006","DOI":"10.1088\/1361-6501\/ab1034","article-title":"A new application for reverberation tanks: Measurement of underwater impulsive sound characteristics","volume":"30","year":"2019","journal-title":"Meas. Sci. Technol."},{"key":"2026030407545204600_c19","doi-asserted-by":"publisher","first-page":"115071","DOI":"10.1016\/j.jsv.2019.115071","article-title":"Measurement of radiated sound power from a complex underwater sound source in a non-anechoic pool based on spatial averaging","volume":"468","year":"2020","journal-title":"J. Sound Vib."},{"issue":"1971","key":"2026030407545204600_c20","doi-asserted-by":"publisher","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","year":"1998","journal-title":"Proc. R. Soc. Lond. A Math. Phys. Eng. Sci."},{"key":"2026030407545204600_c21","volume-title":"Neural Networks and Learning Machines","year":"2009","edition":"3"},{"key":"2026030407545204600_c22","volume-title":"The Elements of Statistical Learning: Data Mining, Inference, and Prediction","year":"2009","edition":"2"},{"key":"2026030407545204600_c23","volume-title":"Classification and Regression Trees","year":"2017"},{"issue":"1","key":"2026030407545204600_c24","doi-asserted-by":"publisher","first-page":"1929","DOI":"10.5555\/2627435.2670313","article-title":"Dropout: A simple way to prevent neural networks from overfitting","volume":"15","year":"2014","journal-title":"J. Mach. Learn. Res."},{"issue":"9","key":"2026030407545204600_c25","doi-asserted-by":"publisher","first-page":"6486","DOI":"10.1109\/TPAMI.2024.3382294","article-title":"Towards understanding convergence and generalization of AdamW","volume":"46","year":"2024","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."}],"container-title":["The Journal of the Acoustical Society of America"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/159\/3\/1930\/20928467\/1930_1_10.0042826.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/159\/3\/1930\/20928467\/1930_1_10.0042826.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T12:55:00Z","timestamp":1772628900000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jasa\/article\/159\/3\/1930\/3382244\/Measured-acoustic-energy-and-neural-network-models"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,1]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,3,1]]}},"URL":"https:\/\/doi.org\/10.1121\/10.0042826","relation":{},"ISSN":["1520-8524"],"issn-type":[{"value":"1520-8524","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,3]]},"published":{"date-parts":[[2026,3,1]]}}}