A fault detection method based on partition of unity and kernel approximation

Mirzaei, Davoud; Soodbakhsh, Navid

doi:10.1007/s11075-022-01488-4

Cited by 3 publications

(1 citation statement)

References 49 publications

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“…The system predicts faults before occurrence to prevent or minimize their effect on the system. Fault detection, 108 on the other hand, focuses on identifying the presence or occurrence of a specific event, object, or pattern within a given dataset. It involves recognizing and classifying instances that belong to a particular class or category of interest.…”

Section: Taxonomy Of Fault Tolerance Approachesmentioning

confidence: 99%

Fault‐tolerance approaches for distributed and cloud computing environments: A systematic review, taxonomy and future directions

Kirti,

Maurya,

Yadav

2024

Concurrency and Computation

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Fault tolerance is crucial in ensuring smooth working of distributed and cloud computing. It is challenging to implement because of the constantly changing infrastructure and complex configurations in distributed and cloud computing. Implementation of various fault tolerance methods require domain‐specific knowledge as well as in‐depth understanding of the existing techniques and approaches. Recent surveys on fault tolerance in cloud and distributed environments exist, but they have limitations. This article systematically reviews fault tolerance approaches in distributed and cloud computing and discusses their taxonomy. Based on the taxonomy provided, fault‐tolerance approaches are divided into four types, that is, reactive approaches, proactive approaches, adaptive approaches, and hybrid approaches. Reactive approaches provide a preventive measure after the occurrence of faults in the system. Proactive approaches prevent the system or minimize failure effects by predicting in advance. The adaptive approaches predict, learn, and adapt the changes to deal with new faults in the system. The hybrid approaches combine reactive, proactive, and adaptive approaches. The objective of this article is to give a better understanding of handling faults using suitable approaches and further compare them on various parameters. The paper also presents a promising research direction based on the challenges and issues in multiple approaches.

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Section: Taxonomy Of Fault Tolerance Approachesmentioning

confidence: 99%

Fault‐tolerance approaches for distributed and cloud computing environments: A systematic review, taxonomy and future directions

Kirti,

Maurya,

Yadav

2024

Concurrency and Computation

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A regularization–correction approach for adapting subdivision schemes to the presence of discontinuities

Amat,

Levin,

Ruiz-Álvarez

et al. 2024

Bit Numer Math

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Linear approximation methods suffer from Gibbs oscillations when approximating functions with jumps. Essentially non oscillatory subcell-resolution (ENO-SR) is a local technique avoiding oscillations and with a full order of accuracy, but a loss of regularity of the approximant appears. The goal of this paper is to introduce a new approach having both properties of full accuracy and regularity. In order to obtain it, we propose a three-stage algorithm: first, the data is smoothed by subtracting an appropriate non-smooth data sequence; then a chosen high order linear approximation operator is applied to the smoothed data and finally, an approximation with the proper jump or corner (jump in the first order derivative) discontinuity structure is reinstated by correcting the smooth approximation with the non-smooth element used in the first stage. This new procedure can be applied as subdivision scheme to design curves and surfaces both in point-value and in cell-average contexts. Using the proposed algorithm, we are able to construct approximations with high precision, with high piecewise regularity, and without smearing nor oscillations in the presence of discontinuities. These are desired properties in real applications as computer aided design or car design, among others.

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Detecting and approximating decision boundaries in low-dimensional spaces

Grajewski

Kleefeld

2023

Numer Algor

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A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of scattered points along with the corresponding classification algorithm to construct a representation of a decision curve by points with prescribed maximal distance to the true decision curve. Hereby, our algorithm ensures that the representing point set covers the decision curve in its entire extent and features local refinement based on the geometric properties of the decision curve. We demonstrate applications of our method to problems related to the detection of faults, to multi-criteria decision aid and, in combination with Kirsch’s factorization method, to solving an inverse acoustic scattering problem. In all applications we considered in this work, our method requires significantly less pointwise classifications than previously employed algorithms.

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A fault detection method based on partition of unity and kernel approximation

Cited by 3 publications

References 49 publications

Fault‐tolerance approaches for distributed and cloud computing environments: A systematic review, taxonomy and future directions

Fault‐tolerance approaches for distributed and cloud computing environments: A systematic review, taxonomy and future directions

A regularization–correction approach for adapting subdivision schemes to the presence of discontinuities

Detecting and approximating decision boundaries in low-dimensional spaces

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