Satyam Panda , Breiffni Fitzgerald , Budhaditya Hazra
{"title":"球形(S2)流形上随机激发系统的实时异常检测","authors":"Satyam Panda , Breiffni Fitzgerald , Budhaditya Hazra","doi":"10.1016/j.probengmech.2024.103689","DOIUrl":null,"url":null,"abstract":"<div><div>Advanced analytical tools have become crucial in today’s constantly changing and complex systems. Real-time Principal Geodesic Analysis (RPGA) is a novel technique that provides a unique perspective for analyzing nonlinear data on differentiable manifolds. Traditional linear methods are often inadequate when exploring the complexities of such data. Orthogonal transformation techniques such as Principal Component Analysis (PCA) and Principal Geodesic Analysis (PGA) are highly desirable for condition monitoring stochastically excited systems in domains like mechanical, aerospace, and civil engineering. However, uncertainties and dynamic fluctuations necessitate robust analytical methods for early change detection to ensure safety, performance, and cost-effectiveness. Limitations posed by linear orthogonal transformation techniques such as PCA and its recursive counterparts make it imperative to adapt these techniques to nonlinear situations where data does not evolve in a flat Euclidean space. Significant advancements have been made in this field over recent decades, with data-driven real-time algorithms such as RPCA, RCCA, and RSSA providing reliable solutions for complex multidimensional problems. However, for curved space, the nonlinear RPGA technique takes center stage. It is known for its effectiveness in extracting meaningful information from the complex data stream. This paper explores the foundational concepts and methodologies underlying the transition from linear to nonlinear data analysis. By examining examples such as stochastic geometric oscillator on <span><math><msup><mrow><mtext>S</mtext></mrow><mrow><mn>2</mn></mrow></msup></math></span>, and the inverted spherical pendulum cart system navigating a rough surface, we illustrate the significance of reliable, real-time damage detection techniques provided by tools such as RPGA.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":null,"pages":null},"PeriodicalIF":3.0000,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Real-time anomaly detection of the stochastically excited systems on spherical (S2) manifold\",\"authors\":\"Satyam Panda , Breiffni Fitzgerald , Budhaditya Hazra\",\"doi\":\"10.1016/j.probengmech.2024.103689\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Advanced analytical tools have become crucial in today’s constantly changing and complex systems. Real-time Principal Geodesic Analysis (RPGA) is a novel technique that provides a unique perspective for analyzing nonlinear data on differentiable manifolds. Traditional linear methods are often inadequate when exploring the complexities of such data. Orthogonal transformation techniques such as Principal Component Analysis (PCA) and Principal Geodesic Analysis (PGA) are highly desirable for condition monitoring stochastically excited systems in domains like mechanical, aerospace, and civil engineering. However, uncertainties and dynamic fluctuations necessitate robust analytical methods for early change detection to ensure safety, performance, and cost-effectiveness. Limitations posed by linear orthogonal transformation techniques such as PCA and its recursive counterparts make it imperative to adapt these techniques to nonlinear situations where data does not evolve in a flat Euclidean space. Significant advancements have been made in this field over recent decades, with data-driven real-time algorithms such as RPCA, RCCA, and RSSA providing reliable solutions for complex multidimensional problems. However, for curved space, the nonlinear RPGA technique takes center stage. It is known for its effectiveness in extracting meaningful information from the complex data stream. This paper explores the foundational concepts and methodologies underlying the transition from linear to nonlinear data analysis. By examining examples such as stochastic geometric oscillator on <span><math><msup><mrow><mtext>S</mtext></mrow><mrow><mn>2</mn></mrow></msup></math></span>, and the inverted spherical pendulum cart system navigating a rough surface, we illustrate the significance of reliable, real-time damage detection techniques provided by tools such as RPGA.</div></div>\",\"PeriodicalId\":54583,\"journal\":{\"name\":\"Probabilistic Engineering Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2024-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probabilistic Engineering Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0266892024001115\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probabilistic Engineering Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0266892024001115","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Real-time anomaly detection of the stochastically excited systems on spherical (S2) manifold
Advanced analytical tools have become crucial in today’s constantly changing and complex systems. Real-time Principal Geodesic Analysis (RPGA) is a novel technique that provides a unique perspective for analyzing nonlinear data on differentiable manifolds. Traditional linear methods are often inadequate when exploring the complexities of such data. Orthogonal transformation techniques such as Principal Component Analysis (PCA) and Principal Geodesic Analysis (PGA) are highly desirable for condition monitoring stochastically excited systems in domains like mechanical, aerospace, and civil engineering. However, uncertainties and dynamic fluctuations necessitate robust analytical methods for early change detection to ensure safety, performance, and cost-effectiveness. Limitations posed by linear orthogonal transformation techniques such as PCA and its recursive counterparts make it imperative to adapt these techniques to nonlinear situations where data does not evolve in a flat Euclidean space. Significant advancements have been made in this field over recent decades, with data-driven real-time algorithms such as RPCA, RCCA, and RSSA providing reliable solutions for complex multidimensional problems. However, for curved space, the nonlinear RPGA technique takes center stage. It is known for its effectiveness in extracting meaningful information from the complex data stream. This paper explores the foundational concepts and methodologies underlying the transition from linear to nonlinear data analysis. By examining examples such as stochastic geometric oscillator on , and the inverted spherical pendulum cart system navigating a rough surface, we illustrate the significance of reliable, real-time damage detection techniques provided by tools such as RPGA.
期刊介绍:
This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.