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Fictitious time integration method for seeking periodic orbits of nonlinear dynamical systems

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 2023年 152卷

作者： Liu, Chein-Shan Atluri, Satya N. Dai, Honghua Natl Taiwan Ocean Univ Ctr Excellence Ocean Engn Keelung 202301 Taiwan Texas Tech Univ Ctr Adv Res Engn Sci Lubbock TX USA Northwestern Polytech Univ Coll Astronaut Xian 710072 Peoples R China

In the paper, we compute the period and periodic orbit of an n-dimensional nonlinear dynamical system by developing two iterative algorithms based on the fictitious time integration method (FTIM). Periodicity condition, also known as the Poincare map, is a necessary condition for the existence of a periodic motion in the state space, which consists of n implicit nonlinear algebraic equations (NAEs). Instead of solving the NAEs by the Newton-Raphson method, we derive an equivalent nonlinear scalar equation to determine unknown period by using the FTIM. The resulting sequence of the iterated periods monotonically converges to a desired period, wherein the unknown initial point on the periodic orbit is determined simultaneously. We find that the second iterative algorithm using the matrix shape function to convert the periodic problem into a corresponding initial value problem is convergent faster than the first iterative algorithm. A key point is that the periodicity condition is satisfied automatically by the second iterative algorithm when the terminal values of the new variables are convergent. Numerical examples exhibit some major advantages of these two iterative algorithms.

关键词： Nonlinear dynamical system Periodic orbit Matrix shape function Fictitious time integration method iterative algorithm

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A study on ultrasonic process tomography for dispersed small particle system visualisation

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INTERNATIONAL JOURNAL OF COMPUTER APPLICATIONS IN TECHNOLOGY 2021年第2-3期67卷 176-184页

作者： Meng, Zhiheng Gu, Jianfei Chou, Yongxin Changshu Inst Technol Sch Elect & Automat Engn Changshu Jiangsu Peoples R China

The present challenge in the ultrasonic process tomography on dispersed small particle systems is that it is hard to obtain the accurate algorithm for reconstruction. For more accurate reconstruction, this work proposes an improved GMRES (Generalised Minimal Residual) algorithm based on generalised minimal residual iteration and mean filtering method. To verify the feasibility of the algorithm for dispersed small particle system visualisation, a linear acoustic attenuation model is developed to obtain the projection data of ultrasonic array. Then, we compared it with the current mainstream reconstruction algorithms under the conditions of the less effective information by solving the underdetermined equations. It is shown that this method can present a high reconstruction precision in the cases of numerical simulations, and reasonably reflect the cross section of dispersed small particle distribution. In the numerical simulations, the imaging accuracy of improved GMRES algorithm can reach about 90%.

关键词： ultrasonic method dispersed particle particulate two-phase flow back projection iterative algorithm

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Alternative threshold-based channel estimation and message-passing-based symbol detection in MIMO-OTFS systems using superimposed pilots

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PHYSICAL COMMUNICATION 2023年第1期59卷

作者： Ouchikh, Rabah Aissa-El-Bey, Abdeldjalil Chonavel, Thierry Djeddou, Mustapha Ecole Mil Polytech Lab Telecommun Bordj El Bahri Algeria CNRS UMR 6285 IMT Atlantique Lab STICC F-29238 Brest France

In this work, we investigate the challenging problem of channel estimation in high-mobility environ-ments for advanced mobile communication systems (5G and beyond). First, we propose an iterative algorithm for channel estimation and symbol detection in the delay-Doppler domain for multiple-input multiple-output orthogonal time-frequency space (OTFS) system. The proposed algorithm is based on a superimposed pilot pattern to improve the spectral efficiency of the system. It iterates between data-aided channel estimation and message-passing-aided data detection. The channel estimation step is based on a threshold method. This step considers interference-plus-noise caused by the data symbols and the additive noise to adapt the threshold at each iteration. The data detection step is based on an adapted version of the message-passing algorithm proposed in the literature for uncoded OTFS. Then, to improve the channel estimation efficiency, we suggest an interference cancellation scheme executed at each iteration of the proposed algorithm. Finally, we compare the computational complexity and the achieved performance in terms of normalized mean square error of channel estimation, bit error rate, and spectral efficiency against five state-of the-art methods.(c) 2023 Elsevier B.V. All rights reserved.

关键词： MIMO OTFS Channel estimation iterative algorithm Superimposed pilot

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Reducing metal artifacts by restricting negative pixels

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Visual Computing for Industry,Biomedicine,and Art 2021年第1期4卷 142-151页

作者： Gengsheng L.Zeng Megan Zeng Department of Computer Science Utah Valley UniversityOremUT 84058USA Department of Radiology and Imaging Sciences University of UtahSalt Lake CityUT 84108USA Department of Electrical Engineering and Computer Science University of California at BerkeleyBerkeleyCA 94720USA

When the object contains metals,its x-ray computed tomography(CT)images are normally affected by streaking *** artifacts are mainly caused by the x-ray beam hardening effects,which deviate the measurements from their true *** interesting observation of the metal artifacts is that certain regions of the metal artifacts often appear as negative pixel *** novel idea in this paper is to set up an objective function that restricts the negative pixel values in the *** must point out that the naïve idea of setting the negative pixel values in the reconstructed image to zero does not give the same *** paper proposes an iterative algorithm to optimize this objective function,and the unknowns are the metal affected *** the metal affected projections are estimated,the filtered backprojection algorithm is used to reconstruct the final *** paper applies the proposed algorithm to some airport bag CT *** bags all contain unknown metallic *** metal artifacts are effectively reduced by the proposed algorithm.

关键词： Filtered backprojection image reconstruction iterative algorithm Metal artifact reduction Objective function X-ray computed tomography

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Poisson reduced-rank models with sparse loadings

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2021年第4期50卷 1079-1097页

作者： Lee, Eun Ryung Park, Seyoung Sungkyunkwan Univ Dept Stat Seoul South Korea

High-dimensional Poisson reduced-rank models have been considered for statistical inference on low-dimensional locations of the individuals based on the observations of high-dimensional count vectors. In this study, we assume sparsity on a so-called loading matrix to enhance its interpretability. The sparsity assumption leads to the use of L-1 penalty, for the estimation of the loading. We provide novel computational and theoretical analyses for the corresponding penalized Poisson maximum likelihood estimation. We establish theoretical convergence rates for the parameters under weak-dependence conditions;this implies consistency even in large-dimensional problems. To implement the proposed method involving several computational issues, including nonconvex log-likelihoods, L-1 penalty, and orthogonal constraints, we developed an iterative algorithm. Further, we propose a Bayesian-Information-Criteria-based penalty parameter selection, which works well in the implementation. Some numerical evidence is provided by conducting real-data-based simulation analyses and the proposed method is illustrated with the analysis of German party manifesto data.

关键词： Poisson reduced-rank models Interpretation Sparsity Rotation LASSO L-1 Orthogonal constraint iterative algorithm

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A Heuristic algorithm for Arbitrary-criterion Optimization of Quantization Scales

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OPTICAL MEMORY AND NEURAL NETWORKS 2021年第2期30卷 140-145页

作者： Gashnikov, M., V Samara Natl Res Univ Samara 443086 Russia RAS IPSI RAS Branch FSRC Crystallog & Photon Samara 443001 Russia

The paper considers the generation of effective quantization scales which meet any quality criteria under any constrains. The analysis of work of available methods allows a concept of a heuristic iterative algorithm for generating near-optimal quantization scales. The concept uses a uniform scale as an initial approach followed by an iterative target-criterion-optimizing recalculation of quantization interval boundaries with adhering to the constrains at each iteration. The formal description of the algorithm is presented. The software implementation of the algorithm is incorporated into the hierarchical image-compression method. The numerical experiments are carried out to test the efficiency of the algorithm and substantiate the convergence of the algorithm to the best solution.

关键词： quantization optimization iterative algorithm uniform scale error

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A Sparse Learning Approach to Relative-Volatility-Managed Portfolio Selection

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SIAM JOURNAL ON FINANCIAL MATHEMATICS 2021年第1期12卷 410-445页

作者： Pun, Chi Seng Nanyang Technol Univ Sch Phys & Math Sci Singapore 637371 Singapore

This paper proposes a self-calibrated sparse learning approach for estimating a sparse target vector, which is a product of a precision matrix and a vector, and investigates its application to finance to provide an innovative construction of a relative-volatility-managed portfolio. The proposed iterative algorithm, called DECODE, jointly estimates a performance measure of the market and the effective parameter vector in the optimal portfolio solution, where the relative-volatility timing is introduced into the risk exposure of an efficient portfolio via the control of its sparsity. The portfolio's risk exposure level, which is linked to its sparsity in the proposed framework, is automatically tuned with the latest market condition without using cross validation. The algorithm is efficient as it costs only a few computations of quadratic programming. We prove that the iterative algorithm converges and show the oracle inequalities of the DECODE, which provide sufficient conditions for a consistent estimate of an optimal portfolio. The algorithm can also handle the curse of dimensionality in that the number of training samples is less than the number of assets. Our empirical studies of over-12-year backtest illustrate the relative-volatility timing feature of the DECODE and the superior out-of-sample performance of the DECODE portfolio, which beats the equally weighted portfolio and improves over the shrinkage portfolio.

关键词： direct estimation iterative algorithm self-calibrated regularization oracle inequality relative-volatility timing market-sensitive asset selection

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Hierarchical Principle-Based iterative Parameter Estimation algorithm for Dual-Frequency Signals

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2019年第7期38卷 3251-3268页

作者： Liu, Siyu Ding, Feng Xu, Ling Hayat, Tasawar Jiangnan Univ Sch Internet Things Engn Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Jiangsu Peoples R China Hubei Univ Technol Sch Elect & Elect Engn Wuhan 430068 Hubei Peoples R China King Abdulaziz Univ Dept Math Fac Sci Jeddah 21589 Saudi Arabia

In this paper, we consider the parameter estimation problem of dual-frequency signals disturbed by stochastic noise. The signal model is a highly nonlinear function with respect to the frequencies and phases, and the gradient method cannot obtain the accurate parameter estimates. Based on the Newton search, we derive an iterative algorithm for estimating all parameters, including the unknown amplitudes, frequencies, and phases. Furthermore, by using the parameter decomposition, a hierarchical least squares and gradient-based iterative algorithm is proposed for improving the computational efficiency. A gradient-based iterative algorithm is given for comparisons. The numerical examples are provided to demonstrate the validity of the proposed algorithms.

关键词： iterative algorithm Signal modeling Hierarchical identification Least squares Newton search Gradient search

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Identification of MISO Wiener systems using the LMI algorithm

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2021年第3-4期37卷 285-291页

作者： Zhou, Lincheng Li, Xiangli Changshu Inst Technol Sch Elect Engn & Automat Changshu Jiangsu Peoples R China

This paper focuses on a new identification method for multiple-input single output (MISO) Wiener nonlinear systems, in which the static nonlinear block is assumed to be a polynomial. The basic idea is to establish a MISO Wiener nonlinear identification model with polynomial nonlinearities by means of the key term separation principle. Then, a new identification method based on Levenberg-Marquardt iterative (LMI) search techniques, which can make full use of all the measured input and output data, but also automatically change the search step-size according to the change values of the quadratic criterion function, is derived to obtain an accurate and fast parameter estimation of the model. Finally, the simulation results demonstrate the efficacy of this method.

关键词： LMI search parameter estimation iterative algorithm multiple-input single-output system Wiener nonlinear system

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Frequency-Limited Reduced Models for Linear and Bilinear Systems on the Riemannian Manifold

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2021年第9期66卷 3938-3951页

作者： Jiang, Yao-Lin Xu, Kang-Li Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China

In this article, we propose two new iterative algorithms to solve the frequency-limited Riemannian optimization model order reduction problems of linear and bilinear systems. Different from the existing Riemannian optimization methods, we design a new Riemannian conjugate gradient scheme based on the Riemannian geometry notions on a product manifold, and then generate a new search direction. Theoretical analysis shows that the resulting search direction is always descent with depending neither on the line search used, nor on the convexity of the cost function. The proposed algorithms are also suitable for generating reduced systems over a frequency interval in bandpass form. Finally, two numerical examples are simulated to demonstrate the efficiency of our algorithms.

关键词： Manifolds Optimization Nonlinear systems Linear systems Frequency control Geometry Time-frequency analysis Finite frequency frequency-limited controllability and observability Gramians iterative algorithm model order reduction (MOR) product manifold Riemannian optimization

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