Judith Angel , Jörn Behrens , Sebastian Götschel , Marten Hollm , Daniel Ruprecht , Robert Seifried
{"title":"利用 PDE 约束优化法根据实验数据重建水深测量数据","authors":"Judith Angel , Jörn Behrens , Sebastian Götschel , Marten Hollm , Daniel Ruprecht , Robert Seifried","doi":"10.1016/j.compfluid.2024.106321","DOIUrl":null,"url":null,"abstract":"<div><p>Knowledge of the bottom topography, also called bathymetry, of rivers, seas or the ocean is important for many areas of maritime science and civil engineering. While direct measurements are possible, they are time consuming, expensive and inaccurate. Therefore, many approaches have been proposed how to infer the bathymetry from measurements of surface waves. Mathematically, this is an inverse problem where an unknown system state needs to be reconstructed from observations with a suitable model for the flow as constraint. In many cases, the shallow water equations can be used to describe the flow. While theoretical studies of the efficacy of such a PDE-constrained optimisation approach for bathymetry reconstruction exist, there seem to be few publications that study its application to data obtained from real-world measurements. This paper shows that the approach can, at least qualitatively, reconstruct a Gaussian-shaped bathymetry in a wave flume from measurements of the free surface level at up to three points. Achieved normalised root mean square errors (NRMSE) are in line with other approaches.</p></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0045793024001531/pdfft?md5=6b1dd691cad04dcb29fbba43f3927cbd&pid=1-s2.0-S0045793024001531-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Bathymetry reconstruction from experimental data using PDE-constrained optimisation\",\"authors\":\"Judith Angel , Jörn Behrens , Sebastian Götschel , Marten Hollm , Daniel Ruprecht , Robert Seifried\",\"doi\":\"10.1016/j.compfluid.2024.106321\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Knowledge of the bottom topography, also called bathymetry, of rivers, seas or the ocean is important for many areas of maritime science and civil engineering. While direct measurements are possible, they are time consuming, expensive and inaccurate. Therefore, many approaches have been proposed how to infer the bathymetry from measurements of surface waves. Mathematically, this is an inverse problem where an unknown system state needs to be reconstructed from observations with a suitable model for the flow as constraint. In many cases, the shallow water equations can be used to describe the flow. While theoretical studies of the efficacy of such a PDE-constrained optimisation approach for bathymetry reconstruction exist, there seem to be few publications that study its application to data obtained from real-world measurements. This paper shows that the approach can, at least qualitatively, reconstruct a Gaussian-shaped bathymetry in a wave flume from measurements of the free surface level at up to three points. Achieved normalised root mean square errors (NRMSE) are in line with other approaches.</p></div>\",\"PeriodicalId\":287,\"journal\":{\"name\":\"Computers & Fluids\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2024-05-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0045793024001531/pdfft?md5=6b1dd691cad04dcb29fbba43f3927cbd&pid=1-s2.0-S0045793024001531-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computers & Fluids\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0045793024001531\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Fluids","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0045793024001531","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Bathymetry reconstruction from experimental data using PDE-constrained optimisation
Knowledge of the bottom topography, also called bathymetry, of rivers, seas or the ocean is important for many areas of maritime science and civil engineering. While direct measurements are possible, they are time consuming, expensive and inaccurate. Therefore, many approaches have been proposed how to infer the bathymetry from measurements of surface waves. Mathematically, this is an inverse problem where an unknown system state needs to be reconstructed from observations with a suitable model for the flow as constraint. In many cases, the shallow water equations can be used to describe the flow. While theoretical studies of the efficacy of such a PDE-constrained optimisation approach for bathymetry reconstruction exist, there seem to be few publications that study its application to data obtained from real-world measurements. This paper shows that the approach can, at least qualitatively, reconstruct a Gaussian-shaped bathymetry in a wave flume from measurements of the free surface level at up to three points. Achieved normalised root mean square errors (NRMSE) are in line with other approaches.
期刊介绍:
Computers & Fluids is multidisciplinary. The term ''fluid'' is interpreted in the broadest sense. Hydro- and aerodynamics, high-speed and physical gas dynamics, turbulence and flow stability, multiphase flow, rheology, tribology and fluid-structure interaction are all of interest, provided that computer technique plays a significant role in the associated studies or design methodology.