記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：IEEE Sensors Journal  

The characteristics of the sensor selection method based on various algorithms for state estimation in a high-dimensional system using the Kalman filter were investigated. Sensors were selected based on the error covariance matrix of the Kalman filter. The performance of the sensor selection methods based on different algorithms, semidefinite programming (SDP), approximate convex relaxation, and greedy algorithm, including newly formulated methods, were compared by varying the number of potential sensor locations and the number of sensors to be selected under several noise ratio conditions. Two sensor selection methods for state estimation in a high-dimensional system using a Kalman filter were newly proposed based on the SDP with gain formulation and approximate convex relaxation, and the characteristics of the method including the previously proposed method were compared in a high-dimensional system. Although the condition was limited at n < O(103) , the approximate convex relaxation method and its randomized method are effective in terms of computational time and objective value for a small-scale problem. The objective value obtained by the greedy method shows the best performance compared to the other methods in almost all investigated conditions. Particularly, the greedy method outperforms other methods when the number of selected sensors is small. In addition, only the greedy method can handle the large-scale problem of n> O(104). Overall, the greedy-based method is found to be favorable in large-scale problems in terms of computation time and the performance of the obtained sensor set.

DOI： 10.1109/jsen.2024.3388849

Web of Science

Scopus

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Mathematics  

Estimating governing equations from observed time-series data is crucial for understanding dynamical systems. From the perspective of system comprehension, the demand for accurate estimation and interpretable results has been particularly emphasized. Herein, we propose a novel data-driven method for estimating the governing equations of dynamical systems based on machine learning with high accuracy and interpretability. The proposed method enhances the estimation accuracy for dynamical systems using sparse modeling by incorporating physical constraints derived from Hamiltonian mechanics. Unlike conventional approaches used for estimating governing equations for dynamical systems, we employ a sparse representation of Hamiltonian, allowing for the estimation. Using noisy observational data, the proposed method demonstrates a capability to achieve accurate parameter estimation and extraction of essential nonlinear terms. In addition, it is shown that estimations based on energy conservation principles exhibit superior accuracy in long-term predictions. These results collectively indicate that the proposed method accurately estimates dynamical systems while maintaining interpretability.

DOI： 10.3390/math12070974

Web of Science

Scopus

担当区分：筆頭著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：IOP Publishing  

Abstract

This paper investigates the global structures of periodic orbits that appear in Rayleigh–Bénard convection, which is modelled by a two-dimensional perturbed Hamiltonian model, by focusing upon resonance, symmetry and bifurcation of the periodic orbits. First, we show the global structures of periodic orbits in the extended phase space by numerically detecting the associated periodic points on the Poincaré section. Then, we illustrate how resonant periodic orbits appear and specifically clarify that there exist some symmetric properties of such resonant periodic orbits which are projected on the phase space; namely, the period m and the winding number n become odd when an m-periodic orbit is symmetric with respect to the horizontal and vertical centre lines of a cell. Furthermore, the global structures of bifurcations of periodic orbits are depicted when the amplitude ɛ of the perturbation is varied, since in experiments the amplitude of the oscillation of the convection gradually increases when the Rayleigh number is raised.

DOI： 10.1088/1361-6544/aca73b

その他リンク： https://iopscience.iop.org/article/10.1088/1361-6544/aca73b/pdf

担当区分：筆頭著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

担当区分：筆頭著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）