Article
Engineering, Geological
Ahmed M. El-Kholy, Sayed M. Sayed, Mohamed M. El-Assaly
Summary: This paper presents a nonlinear macromodeling strategy for predicting the structural behavior of multistory reinforced concrete buildings with masonry infill walls during earthquakes. The strategy uses different models for the frame elements and joints, masonry infill walls, and shear walls, and has been validated to be accurate and reliable.
BULLETIN OF EARTHQUAKE ENGINEERING
(2023)
Article
Engineering, Electrical & Electronic
Fatemeh Charoosaei, Amin Faraji, Sayed Alireza Sadrossadat, Ali Mirvakili, Weicong Na, Feng Feng, Qi-Jun Zhang
Summary: In the field of computer-aided design (CAD), the use of recurrent neural networks (RNN) has proven to be highly effective in generating fast and high-performance models. One key challenge in this area is predicting time sequences, which requires identifying the dependencies between sequences. Conventional RNNs face limitations in terms of accuracy and the number of parameters. To address this, we propose a new macromodeling method called Clockwork-RNN (CWRNN) and its hybrid version, which simplifies the architecture and reduces model complexity while still accurately capturing complex dependencies. The CWRNN also offers lower computational cost and greater flexibility in architectural configuration.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2023)
Article
Engineering, Mechanical
Qian Wang, Heng Liu, Yi Liu, Yupeng Yu, Minqing Jing
Summary: This study investigates the multiple periodic solution branch distribution of a four-degree-of-freedom dynamical system with a piecewise linear NES and develops a method based on polynomial homotopy to capture ISBs. The harmonic balance method with high harmonic orders and alternating frequency/time-domain technique are employed to distinguish true periodic solutions.
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE
(2022)
Article
Mathematics, Applied
Oleg Davydov, Wee Ping Yeo
Summary: The method presents a construction of C-1 piecewise quadratic hierarchical bases on arbitrary polygonal domains, which are Riesz bases for Sobolev spaces. Homogeneous boundary conditions can be taken into account in a natural way using this method.
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
(2021)
Article
Mathematics, Interdisciplinary Applications
Dan Sun, Linping Peng
Summary: This paper investigates the limit cycle bifurcation from a reversible differential center of degree 2n + 2 due to small piecewise smooth homogeneous polynomial perturbations. By using averaging theory and the complex method based on the Argument Principle, lower and upper bounds for the maximum number of limit cycles bifurcating from the period annulus around the center of the unperturbed system are obtained.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
Article
Mathematics, Interdisciplinary Applications
M. H. Heydari, M. Razzaghi
Summary: This study introduces a novel category of fractional optimal control problems by utilizing piecewise fractional derivatives based on Caputo fractional derivative. It considers using piecewise Chebyshev cardinal functions as an appropriate family of basis functions to construct a numerical method for solving such problems. The proposed technique transforms the solution of these problems into finding the solution of algebraic systems of equations by approximating the state and control variables using the mentioned basis functions, with the accuracy of the approach investigated through solving examples.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Xiaoer Qin, Li Yan
Summary: Constructing permutation polynomials in finite fields is a popular topic. This paper investigates the construction of permutation polynomials over F-q3, using the AGW criterion and piecewise method. Several classes of permutation polynomials of the form (x(q2) + x(q) + x + delta)(q3-1/d) +1 + L(x), where d = 2, 3, 4, 6 and L(x) is a linearized polynomial over F-q, are constructed.
Article
Automation & Control Systems
Xiaoqiang Sun, Yulin Wang, Weiwei Hu, Yingfeng Cai, Chen Huang, Long Chen
Summary: This paper introduces a novel control strategy to improve the path tracking control performance of the intelligent vehicle under critical maneuvers. A three-dimensional piecewise affine identification method is proposed to model the nonlinear tire cornering characteristics. Based on this, a driver direction control model and a linear quadratic optimal control method are used to design path tracking controllers and generate optimal steering angles for the front wheels. The proposed control strategy shows significant performance advantages and satisfactory path tracking control performance.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Automation & Control Systems
R. Sakthivel, N. Aravinth, T. Satheesh, O. M. Kwon
Summary: This paper addresses the input-output finite-time stabilisation problem for a class of continuous-time periodic piecewise polynomial systems with immeasurable states and external disturbances. A state estimation-based robust reliable controller is proposed to solve this problem, and a periodic piecewise polynomial observer is designed to estimate the immeasurable states. The stability conditions are obtained by combining Lyapunov stability theory, linear matrix inequality technique and IO-FT stability theory. Simulation results demonstrate the effectiveness and utility of the proposed control protocol.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
(2023)
Article
Mathematics, Applied
Juyoung Jeong, Yoon Mo Jung, Soo Hyun Kim, Sangwoon Yun
Summary: Trend filtering is a regression problem that estimates underlying trends in time series data. This method utilizes adaptive piecewise polynomials to achieve better fitting and provides a simplified form and brief summary of the given data.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Computer Science, Software Engineering
Miguel Crespo, Adrian Jarabo, Adolfo Munoz
Summary: The algorithm combines quadrature and Monte Carlo integration to handle low-frequency regions and high-frequency details of multidimensional integrals. It leverages importance sampling techniques and can be applied to complex multidimensional integrals. Through demonstrations in various applications, it shows effective results and faster convergence compared to previous approaches.
ACM TRANSACTIONS ON GRAPHICS
(2021)
Article
Mathematics, Applied
Xiaoyan Chen, Dingheng Pi
Summary: This paper focuses on the nonlinear sliding mode and nonlinear regularization of piecewise smooth systems. Conditions to guarantee the existence of a sliding periodic orbit for the piecewise smooth system are presented using Jeffrey's nonlinear method. The nonlinear regularization of the piecewise smooth system with a sliding periodic orbit is then discussed, considering both planar and higher-dimensional cases. Sufficient conditions are established for the existence of a periodic orbit in the regularized system. Additionally, it is proven that the periodic orbit of the regularized system remains close to the sliding periodic orbit of the original piecewise smooth system as the small regularization parameter approaches 0.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Applied
Xuli Han, Jing Yang
Summary: This paper presents a new method for constructing piecewise polynomial curves, where the first and second derivatives of the given curve are determined by non-negative combinations of the first and second order divided differences of the control points. Shape parameters are introduced to allow for local adjustment of the curve, with proper ranges and optimal values established for minimizing the combination coefficients of the second derivatives. Geometric examples are provided to demonstrate the feasibility of this curve representation and its approximation effect on the control polygon.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Multidisciplinary Sciences
Surapol Naowarat, Shabir Ahmad, Sayed Saifullah, Manuel De la Sen, Ali Akguel
Summary: This research investigates the evolution of rotavirus and the impact of vaccination using a piecewise derivative framework. The numerical solution is deduced using the Adam-Bashforth numerical method and Newton polynomial. Stability analysis is conducted using the Ulam-Hyres concept and nonlinear analysis. The proposed approach is validated by comparing simulated results with real data.
Article
Engineering, Mechanical
Xiao-Feng Geng, Hu Ding, Xiao-Ye Mao, Li-Qun Chen
Summary: Research on a limited nonlinear energy sink using a piecewise spring device to restrict vibration amplitude shows that the vibration of the nonlinear energy sink can be effectively suppressed, although the vibration damping effect on the linear oscillator is weakened after the introduction of the piecewise spring.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)