{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T16:08:10Z","timestamp":1778602090584,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T00:00:00Z","timestamp":1655164800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Liaoning Provincial Department of Education Basic Research Projects for Higher Education Institutions, China","award":["LJKZ0301"],"award-info":[{"award-number":["LJKZ0301"]}]},{"name":"Liaoning Provincial Department of Education Basic Research Projects for Higher Education Institutions, China","award":["2017LNQN22"],"award-info":[{"award-number":["2017LNQN22"]}]},{"name":"Liaoning Provincial Department of Education Basic Research Projects for Higher Education Institutions, China","award":["2017QN04"],"award-info":[{"award-number":["2017QN04"]}]},{"name":"The Scientific Research Foundation of the Education Department of Liaoning Province, China","award":["LJKZ0301"],"award-info":[{"award-number":["LJKZ0301"]}]},{"name":"The Scientific Research Foundation of the Education Department of Liaoning Province, China","award":["2017LNQN22"],"award-info":[{"award-number":["2017LNQN22"]}]},{"name":"The Scientific Research Foundation of the Education Department of Liaoning Province, China","award":["2017QN04"],"award-info":[{"award-number":["2017QN04"]}]},{"name":"Young Teachers Foundation of University of Science and Technology Liaoning, China","award":["LJKZ0301"],"award-info":[{"award-number":["LJKZ0301"]}]},{"name":"Young Teachers Foundation of University of Science and Technology Liaoning, China","award":["2017LNQN22"],"award-info":[{"award-number":["2017LNQN22"]}]},{"name":"Young Teachers Foundation of University of Science and Technology Liaoning, China","award":["2017QN04"],"award-info":[{"award-number":["2017QN04"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Pipeline corrosion prediction (PCP) is an important technology for pipeline maintenance and management. How to accurately predict pipeline corrosion is a challenging task. To address the drawback of the poor prediction accuracy of the grey model (GM(1,1)), this paper proposes a method named ETGM(1,1)-RABC. The proposed method consists of two parts. First, the exponentially transformed grey model (ETGM(1,1)) is an improvement of the GM(1,1), in which exponential transformation (ET) is used to preprocess the raw data. Next, dynamic coefficients, instead of background fixed coefficients, are optimized by the reformative artificial bee colony (RABC) algorithm, which is a variation of the artificial bee colony (ABC) algorithm. Experiments are performed on actual pipe corrosion data, and four different methods are included in the comparative study, including GM(1,1), ETGM(1,1), and three ETGM(1,1)-ABC variants. The results show that the proposed method proves to be superior for the PCP in terms of Taylor diagram and absolute error.<\/jats:p>","DOI":"10.3390\/axioms11060289","type":"journal-article","created":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T23:50:14Z","timestamp":1655250614000},"page":"289","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Pipeline Corrosion Prediction Using the Grey Model and Artificial Bee Colony Algorithm"],"prefix":"10.3390","volume":"11","author":[{"given":"Shiguo","family":"Li","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering and Automation, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hualong","family":"Du","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and Automation, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiuyu","family":"Cui","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and Automation, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pengfei","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and Automation, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and Automation, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0987-640X","authenticated-orcid":false,"given":"He","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and Automation, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,14]]},"reference":[{"key":"ref_1","first-page":"116","article-title":"Review on Evaluation Technology of Oil-Gas Pipelines with Corrosion Defect","volume":"47","author":"Huang","year":"2018","journal-title":"Surf. Technol."},{"key":"ref_2","first-page":"927","article-title":"Diagnostic and prognostic analysis of oil and gas pipeline with allowable corrosion rate in Niger Delta Area, Nigeria","volume":"23","author":"Obaseki","year":"2019","journal-title":"J. Appl. Sci. Environ. Manag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1504\/IJRS.2010.029562","article-title":"A study on the corrosion process of gas pipeline applying grey dynamic model","volume":"4","author":"Li","year":"2010","journal-title":"Int. J. Reliab. Saf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"14771","DOI":"10.1007\/s00521-021-06116-1","article-title":"An intelligent model to predict the life condition of crude oil pipelines using artificial neural networks","volume":"33","author":"Shaik","year":"2021","journal-title":"Neural Comput. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jlp.2019.03.010","article-title":"An optimization of artificial neural network modeling methodology for the reliability assessment of corroding natural gas pipelines","volume":"60","author":"Wen","year":"2019","journal-title":"J. Loss Prev. Process Ind."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Shaik, N.B., Pedapati, S.R., Taqvi, S.A.A., Othman, A.R., and Abd Dzubir, F.A. (2020). A feed-forward back propagation neural network approach to predict the life condition of crude oil pipeline. Processes, 8.","DOI":"10.3390\/pr8060661"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"022025","DOI":"10.1088\/1757-899X\/490\/2\/022025","article-title":"Study on corrosion rate of buried gas steel pipeline in Nanjing based on the GM (1, N) optimization model","volume":"490","author":"Liao","year":"2019","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"012106","DOI":"10.1088\/1742-6596\/1894\/1\/012106","article-title":"Prediction of Submarine Pipeline Corrosion Based on the Improved Grey Prediction Model","volume":"1894","author":"Gao","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_9","first-page":"96","article-title":"GM-RBF model based error compensation for prediction of submarine pipeline corrosion","volume":"28","author":"Zhengshan","year":"2018","journal-title":"China Saf. Sci. J."},{"key":"ref_10","first-page":"210","article-title":"Grey Relational Analysis and Fuzzy Neural Network Method for Predicting Corrosion Rate of Marine Pipeline","volume":"2","author":"Deng","year":"2021","journal-title":"Int. J. High. Educ. Teach. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"012210","DOI":"10.1088\/1742-6596\/2033\/1\/012210","article-title":"Combined Grey Prediction and Neural Network Model for Oil and Gas Pipeline Wall Thinning","volume":"2033","author":"Jiang","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"103716","DOI":"10.1016\/j.jngse.2020.103716","article-title":"A new hybrid algorithm model for prediction of internal corrosion rate of multiphase pipeline","volume":"85","author":"Peng","year":"2021","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.psep.2021.07.031","article-title":"A data-driven corrosion prediction model to support digitization of subsea operations","volume":"153","author":"Li","year":"2021","journal-title":"Process Saf. Environ. Prot."},{"key":"ref_14","first-page":"1","article-title":"Analysis of magnetic-flux leakage (MFL) data for pipeline corrosion assessment","volume":"56","author":"Peng","year":"2020","journal-title":"IEEE Trans. Magn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"104449","DOI":"10.1016\/j.ijpvp.2021.104449","article-title":"A new approach for finite element based reliability evaluation of offshore corroded pipelines","volume":"193","author":"Abyani","year":"2021","journal-title":"Int. J. Press. Vessel. Pip."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"8868","DOI":"10.1109\/TIE.2019.2949520","article-title":"Multiresonant chipless RFID array system for coating defect detection and corrosion prediction","volume":"67","author":"Deif","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1853","DOI":"10.1109\/TII.2018.2857198","article-title":"An improved artificial bee colony algorithm with its application","volume":"15","author":"Gao","year":"2018","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Brezo\u010dnik, L., Fister, I., and Podgorelec, V. (2018). Swarm intelligence algorithms for feature selection: A review. Appl. Sci., 8.","DOI":"10.3390\/app8091521"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Li, C., Gao, H., Qiu, J., Yang, Y., Qu, X., Wang, Y., and Bi, Z. (2018). Grey model optimized by particle swarm optimization for data analysis and application of multi-sensors. Sensors, 18.","DOI":"10.3390\/s18082503"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"116464","DOI":"10.1016\/j.eswa.2021.116464","article-title":"A novel genetic algorithm based system for the scheduling of medical treatments","volume":"195","author":"Squires","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5277","DOI":"10.1007\/s00500-020-05527-x","article-title":"An improved differential evolution algorithm and its application in optimization problem","volume":"25","author":"Deng","year":"2021","journal-title":"Soft Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"e12812","DOI":"10.1111\/exsy.12812","article-title":"Evolutionary state-based novel multi-objective periodic bacterial foraging optimization algorithm for data clustering","volume":"39","author":"Guo","year":"2022","journal-title":"Expert Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"101024","DOI":"10.1016\/j.swevo.2021.101024","article-title":"Preference incorporation into many-objective optimization: An Ant colony algorithm based on interval outranking","volume":"69","author":"Rivera","year":"2022","journal-title":"Swarm Evol. Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1896","DOI":"10.1016\/j.apm.2013.10.004","article-title":"The modeling mechanism, extension and optimization of grey GM (1, 1) model","volume":"38","author":"Xiao","year":"2014","journal-title":"Appl. Math. Model."},{"key":"ref_25","first-page":"973","article-title":"Optimum design of fractional order PID controller for an AVR system using an improved artificial bee colony algorithm","volume":"40","author":"Zhang","year":"2014","journal-title":"Acta Autom. Sin."},{"key":"ref_26","first-page":"122","article-title":"Improvement of GM (1, 1) model based on data transformation","volume":"44","author":"Bian","year":"2019","journal-title":"J. Geomat."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Cheng, M., Li, J., Liu, Y., and Liu, B. (2020). Forecasting clean energy consumption in China by 2025: Using improved grey model GM (1, N). Sustainability, 12.","DOI":"10.3390\/su12020698"},{"key":"ref_28","first-page":"74","article-title":"Pipeline corrosion prediction based on an improved artificial bee colony algorithm and a grey model","volume":"48","author":"XieXun","year":"2021","journal-title":"J. Beijing Univ. Chem. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1007\/s00500-014-1549-5","article-title":"Gaussian bare-bones artificial bee colony algorithm","volume":"20","author":"Zhou","year":"2016","journal-title":"Soft Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"7183","DOI":"10.1029\/2000JD900719","article-title":"Summarizing multiple aspects of model performance in a single diagram","volume":"106","author":"Taylor","year":"2001","journal-title":"J. Geophys. Res. Atmos."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/6\/289\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:31:30Z","timestamp":1760139090000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/6\/289"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,14]]},"references-count":30,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["axioms11060289"],"URL":"https:\/\/doi.org\/10.3390\/axioms11060289","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,14]]}}}