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- Beilina, Larisa, 1970, et al.
(author)
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Explicit P 1 Finite Element Solution of the Maxwell-Wave Equation Coupling Problem with Absorbing b. c.
- 2024
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In: Mathematics. - 2227-7390. ; 12:7
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Journal article (peer-reviewed)abstract
- In this paper, we address the approximation of the coupling problem for the wave equation and Maxwell’s equations of electromagnetism in the time domain in terms of electric field by means of a nodal linear finite element discretization in space, combined with a classical explicit finite difference scheme for time discretization. Our study applies to a particular case where the dielectric permittivity has a constant value outside a subdomain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this subdomain, Maxwell’s equations hold. Outside this subdomain, the wave equation holds, which may correspond to Maxwell’s equations with a constant permittivity under certain conditions. We consider as a model the case of first-order absorbing boundary conditions. First-order error estimates are proven in the sense of two norms involving first-order time and space derivatives under reasonable assumptions, among which lies a CFL condition for hyperbolic equations. The theoretical estimates are validated by numerical computations, which also show that the scheme is globally of the second order in the maximum norm in time and in the least-squares norm in space.
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| 2. |
- Hosseinzadeh Dadash, Amirhossein, 1986-, et al.
(author)
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Infinite-Horizon Degradation Control Based on Optimization of Degradation-Aware Cost Function
- 2024
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In: Mathematics. - : MDPI. - 2227-7390. ; 12:5
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Journal article (peer-reviewed)abstract
- Controlling machine degradation enhances the accuracy of the remaining-useful-life estimation and offers the ability to control failure type and time. In order to achieve optimal degradation control, the system controller must be cognizant of the consequences of its actions by considering the degradation each action imposes on the system. This article presents a method for designing cost-aware controllers for linear systems, to increase system reliability and availability through degradation control. The proposed framework enables learning independent of the system's physical structure and working conditions, enabling controllers to choose actions that reduce system degradation while increasing system lifetime. To this end, the cost of each controller's action is calculated based on its effect on the state of health. A mathematical structure is proposed, to incorporate these costs into the cost function of the linear-quadratic controller, allowing for optimal feedback for degradation control. A simulation validates the proposed method, demonstrating that the optimal-control method based on the proposed cost function outperforms the linear-quadratic regulator in several ways.
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| 3. |
- Lou, Chuyue, et al.
(author)
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Unknown Health States Recognition with Collective-Decision-Based Deep Learning Networks in Predictive Maintenance Applications
- 2024
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In: Mathematics. - Basel : MDPI. - 2227-7390. ; 12:1
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Journal article (peer-reviewed)abstract
- At present, decision-making solutions developed based on deep learning (DL) models have received extensive attention in predictive maintenance (PM) applications along with the rapid improvement of computing power. Relying on the superior properties of shared weights and spatial pooling, convolutional neural networks (CNNs) can learn effective representations of health states from industrial data. Many developed CNN-based schemes, such as advanced CNNs that introduce residual learning and multi-scale learning, have shown good performance in health states recognition tasks under the assumption that all the classes are known. However, these schemes have no ability to deal with new abnormal samples that belong to state classes not part of the training set. In this paper, a collective decision framework for different CNNs is proposed. It is based on a one-vs.-rest network (OVRN) to simultaneously achieve classification of known and unknown health states. OVRNs learn class-specific discriminative features and enhance the ability to reject new abnormal samples incorporated to different CNNs. According to the validation results on the public dataset of the Tennessee Eastman process (TEP), the proposed CNN-based decision schemes incorporating an OVRN have outstanding recognition ability for samples of unknown heath states while maintaining satisfactory accuracy on known states. The results show that the new DL framework outperforms state-of-the-art CNNs, and the one based on residual and multi-scale learning has the best overall performance. © 2023 by the authors.
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