Efficient Modeling of Stationary Interval Processes with Spline and Convolution-based Kernels

Efficient Modeling of Stationary Interval Processes with Spline and Convolution-based Kernels | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Efficient Modeling of Stationary Interval Processes with Spline and Convolution-based Kernels Chen Li, Feng Wu, Yuxiang Yang, Xiaopeng Zhang, Xindi Wei, Li Zhu, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5845393/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Practical engineering dynamical analyses suffer from time-variant epistemic uncertainty variables. Precise description of time-variant epistemic uncertainties with only limited samples is a challenge to the safe and reliable assessment of engineering structures. Based on the interval process theory, a systematic study on the modeling of time-variant uncertainty quantities with stationary characteristics under the condition of limited samples is conducted. Firstly, by combining the B-spline function with the convolution theory, a novel spline and convolution-based kernel (SCK) method is developed for constructing general stationary covariance functions. Then, by combining the SCK method, stationary characteristics and the nonlinear elimination method, two unconstrained optimization formulations for modeling stationary interval processes are finally established. These two methods can respectively obtain ellipsoids with the minimum volume and the minimum radius that can enclose the time-variant uncertainty samples, thus realizing the efficient modeling of stationary interval processes. Through two numerical examples and two engineering examples, the high efficiency and accuracy of the two proposed SCK-based stationary interval process modeling methods are demonstrated. Mechanical Engineering Computational Mathematics Uncertainty Interval analysis Optimization formulations Stationary time-variant epistemic uncertainty B-spline Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5845393","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":403264453,"identity":"688d6923-639f-43b7-8398-a6f29353adba","order_by":0,"name":"Chen Li","email":"","orcid":"","institution":"DaLian University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Chen","middleName":"","lastName":"Li","suffix":""},{"id":403264454,"identity":"f918e504-4d7c-4b39-a9ff-abac57d0683f","order_by":1,"name":"Feng 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Precise description of time-variant epistemic uncertainties with only limited samples is a challenge to the safe and reliable assessment of engineering structures. Based on the interval process theory, a systematic study on the modeling of time-variant uncertainty quantities with stationary characteristics under the condition of limited samples is conducted. Firstly, by combining the B-spline function with the convolution theory, a novel spline and convolution-based kernel (SCK) method is developed for constructing general stationary covariance functions. Then, by combining the SCK method, stationary characteristics and the nonlinear elimination method, two unconstrained optimization formulations for modeling stationary interval processes are finally established. 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