{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:36:16Z","timestamp":1760240176845,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,3,31]],"date-time":"2019-03-31T00:00:00Z","timestamp":1553990400000},"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":["No. 61871283"],"award-info":[{"award-number":["No. 61871283"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Foundation of Pre-Research on Equipment of China","award":["No.61403120103"],"award-info":[{"award-number":["No.61403120103"]}]},{"name":"Joint Foundation of pre-Research on Equipment from Education Department of China","award":["No.6141A02022336"],"award-info":[{"award-number":["No.6141A02022336"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>With the explosive growth of ocean data, it is of great significance to use ocean observation data to analyze ocean pycnocline data in military field. However, due to natural factors, most of the time the ocean hydrological data is not complete. In this case, predicting the ocean hydrological data by partial data has become a hot spot in marine science. In this paper, based on the traditional statistical analysis literature, we propose a machine-learning ocean hydrological data processing process under big data. At the same time, based on the traditional pycnocline gradient determination method, the open Argo data set is analyzed, and the local characteristics of pycnocline are verified from several aspects combined with the current research about pycnocline. Most importantly, in this paper, the combination of kernel function and support vector machine(SVM) is extended to nonlinear learning by using the idea of machine learning and convex optimization technology. Based on this, the known pycnocline training set is trained, and an accurate model is obtained to predict the pycnocline in unknown domains. In the specific steps, this paper combines the classification problem with the regression problem, and determines the proportion of training set and test formula set by polynomial regression. Subsequently, the feature scaling of the input data accelerated the gradient convergence, and a grid search algorithm with variable step size was proposed to determine the super parameter c and gamma of the SVM model. The prediction results not only used the confusion matrix to analyze the accuracy of GridSearch-SVM with variable step size, but also compared the traditional SVM and the similar algorithm. At the end of the experiment, two features which have the greatest influence on the Marine density thermocline are found out by the feature ranking algorithm based on learning.<\/jats:p>","DOI":"10.3390\/s19071562","type":"journal-article","created":{"date-parts":[[2019,4,2]],"date-time":"2019-04-02T03:21:26Z","timestamp":1554175286000},"page":"1562","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Prediction of Marine Pycnocline Based on Kernel Support Vector Machine and Convex Optimization Technology"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2558-552X","authenticated-orcid":false,"given":"Jiachen","family":"Yang","sequence":"first","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, 92 Weijin Road, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, 92 Weijin Road, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linfeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, 92 Weijin Road, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gen","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, 92 Weijin Road, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhonghao","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, 92 Weijin Road, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2631-9223","authenticated-orcid":false,"given":"Houbing","family":"Song","sequence":"additional","affiliation":[{"name":"Department of Electrical, Computer, Software and Systems Engineering, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,31]]},"reference":[{"key":"ref_1","first-page":"150413133522004","article-title":"Theoretical Investigation of the Atlantic Multidecadal Oscillation","volume":"45","author":"Slevellec","year":"2017","journal-title":"J. Phys. Oceanogr."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.jmarsys.2015.05.002","article-title":"Distribution of hypoxia and pycnocline off the Changjiang Estuary, China","volume":"154","author":"Zhu","year":"2016","journal-title":"J. Mar. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1134\/S0001437012030071","article-title":"Effects of the wind and thermal conditions variability on the structure and dynamics of the seawater in the Northeastern Black Sea","volume":"52","author":"Krivosheya","year":"2012","journal-title":"Oceanology"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1175\/JPO-D-11-040.1","article-title":"Source and Pathway of the Western Arctic Upper Halocline in a DataConstrained Coupled Ocean and Sea Ice Model","volume":"42","author":"Nguyen","year":"2012","journal-title":"J. Phys. Oceanogr."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.csr.2013.11.016","article-title":"Assessment of coastal density gradients near a macro-tidal estuary: Application to the Mersey and Liverpool Bay","volume":"87","author":"Howarth","year":"2014","journal-title":"Cont. Shelf Res."},{"key":"ref_6","unstructured":"Ofan, A., Ahmad, I., Greene, J.P., Paul, M., Pellin, M.J., and Savina, M.R. (2006, January 13\u201317). A Search for Live 244Pu in Deep-Sea Sediments: Development of an Efficient Detection Method. Proceedings of the Annual Lunar and Planetary Science Conference, League City, TX, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/j.pocean.2006.12.005","article-title":"Ventilation of the North Pacific subtropical pycnocline and mode water formation","volume":"77","author":"Suga","year":"2008","journal-title":"Prog. Oceanogr."},{"key":"ref_8","unstructured":"Dias, G.M., Bellalta, B., and Oechsner, S. (arXiv, 2016). On the importance and feasibility of forecasting data in sensors, arXiv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.jhydrol.2010.05.040","article-title":"Prediction of rainfall time series using modular artificial neural networks coupled with datapreprocessing techniques","volume":"389","author":"Wu","year":"2010","journal-title":"J. Hydrol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1064","DOI":"10.1109\/TIA.2012.2190816","article-title":"Forecasting Power Output of Photovoltaic Systems Based on Weather Classification and Support Vector Machines","volume":"48","author":"Shi","year":"2015","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.solener.2016.04.020","article-title":"Forecasting shortterm solar irradiance based on artificial neural networks and data from neighboring meteorological stations","volume":"134","author":"GutierrezCorea","year":"2016","journal-title":"Sol. Energy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1965","DOI":"10.1175\/1520-0477(2001)082<1965:TEOMWF>2.3.CO;2","article-title":"The Effects of Marine Winds from Scatterometer Data on Weather Analysis and Forecasting","volume":"82","author":"Atlas","year":"2010","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Jiang, Y., Gou, Y., Zhang, T., Wang, K., and Hu, C. (2017). A Machine Learning Approach to Argo Data Analysis in a Thermocline. Sensors, 17.","DOI":"10.3390\/s17102225"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2013","DOI":"10.1162\/089976600300015042","article-title":"Bounds on Error Expectation for Support Vector Machines","volume":"12","author":"Vapnik","year":"2000","journal-title":"Neural Comput."},{"key":"ref_15","first-page":"281","article-title":"Background papers and supporting data on the International Equation of State of Seawater 1980","volume":"62","author":"Millero","year":"1981","journal-title":"Vet. Immunol. Immunopathol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1713","DOI":"10.1007\/s00227-010-1445-1","article-title":"The ecological significance of lipid\/fatty acid synthesis in developing eggs and newly hatched larvae of Pacific cod (Gadus macrocephalus)","volume":"157","author":"Laurel","year":"2010","journal-title":"Mar. Biol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1080\/17451000.2014.943239","article-title":"Red sea urchins (Echinus esculentus) and water flow influence epiphytic macroalgae density","volume":"11","author":"Bekkby","year":"2015","journal-title":"Mar. Biol. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"T90","DOI":"10.4188\/transjtmsj.25.12_T90","article-title":"A Method of Deciding the Point of the Maximum Curvature on the LoadElongation Curve of Covered Yarn","volume":"25","author":"Yoshimura","year":"2009","journal-title":"Sen I Kikai Gakkaishi"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7305","DOI":"10.1029\/92JC00407","article-title":"Evidence of the barrier layer in the surface layer of the tropics","volume":"97","author":"Sprintall","year":"1992","journal-title":"J. Geophys. Res. Ocean."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1175\/2008JPO3984.1","article-title":"A Diagnostic Model for Mixed Layer Depth Estimation with Application to Ocean Station P in the Northeast Pacific","volume":"39","author":"Thomson","year":"2010","journal-title":"J. Phys. Oceanogr."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1190\/1.1441974","article-title":"Method for depth estimation on aeromagnetic vertical gradient anomalies","volume":"50","author":"Barongo","year":"2012","journal-title":"Geophysics"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1002\/crat.201300006","article-title":"Melt growth and postgrown annealing of semiinsulating (CdZn)Te by vertical gradient freeze method","volume":"48","author":"Franc","year":"2013","journal-title":"Cryst. Res. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2639","DOI":"10.1162\/0899766042321814","article-title":"Canonical Correlation Analysis: An Overview with Application to Learning Methods","volume":"16","author":"Hardoon","year":"2014","journal-title":"Neural Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1565","DOI":"10.1038\/nbt1206-1565","article-title":"What is a support vector machine?","volume":"24","author":"Noble","year":"2006","journal-title":"Nat. Biotechnol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2874","DOI":"10.1016\/j.patcog.2008.02.010","article-title":"Robust and efficient multiclass SVM models for phrase pattern recognition","volume":"41","author":"Wu","year":"2008","journal-title":"Pattern Recognit."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1016\/j.patcog.2013.07.002","article-title":"Multiple rank multilinear SVM for matrix data classification","volume":"47","author":"Hou","year":"2014","journal-title":"Pattern Recognit."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.foodchem.2013.10.020","article-title":"Simultaneous data preprocessing and SVM classification model selection based on a parallel genetic algorithm applied to spectroscopic data of olive oils","volume":"148","author":"Devos","year":"2014","journal-title":"Food Chem."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.jhydrol.2018.02.061","article-title":"Modelling Daily Dissolved Oxygen Concentration Using Least Square Support Vector Machine, Multivariate Adaptive Regression Splines and M5 model Tree","volume":"559","author":"Heddam","year":"2018","journal-title":"J. Hydrol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1978","DOI":"10.1093\/bioinformatics\/btg255","article-title":"Application of support vector machines for Tcell epitopes prediction","volume":"19","author":"Zhao","year":"2017","journal-title":"Bioinformatics"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10489-016-0801-3","article-title":"Novel hybrid SVMTLBO forecasting model incorporating dimensionality reduction techniques","volume":"45","author":"Das","year":"2016","journal-title":"Appl. Intell."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1023\/A:1012450327387","article-title":"Choosing multiple parameters for SVM","volume":"46","author":"Chapelle","year":"2002","journal-title":"Mach. Learn."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1663","DOI":"10.1109\/TPWRD.2006.874114","article-title":"Automated classification of powerquality disturbances using SVM and RBF networks","volume":"21","author":"Janik","year":"2006","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1387","DOI":"10.1016\/j.ijrefrig.2011.03.019","article-title":"Application of the output dependent feature scaling in modeling and prediction of performance of counter flow vortex tube having various nozzles numbers at different inlet pressures of air, oxygen, nitrogen and argon","volume":"34","author":"Polat","year":"2011","journal-title":"Int. J. Refrig."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s11063-013-9301-1","article-title":"Efficient Feature Scaling for Support Vector Machines with a Quadratic Kernel","volume":"39","author":"Liang","year":"2014","journal-title":"Neural Process. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.compag.2018.10.017","article-title":"Wheat yellow rust monitoring by learning from multispectral UAV aerial imagery","volume":"155","author":"Su","year":"2018","journal-title":"Comput. Electron. Agric."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Su, J., Yi, D., Liu, C., Guo, L., and Chen, W.H. (2017). Dimension Reduction Aided Hyperspectral Image Classification with a Small-sized Training Dataset: Experimental Comparisons. Sensors, 17.","DOI":"10.3390\/s17122726"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/7\/1562\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:41:55Z","timestamp":1760186515000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/7\/1562"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,31]]},"references-count":36,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["s19071562"],"URL":"https:\/\/doi.org\/10.3390\/s19071562","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,3,31]]}}}