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Global-local mean square error criterion for equivalent linearization of nonlinear systems under random excitation

ACTA MECHANICA 2015年第9期226卷 3011-3029页

作者： Anh, N. D. Hung, L. X. Viet, L. D. Thang, N. C. VAST Inst Mech Hanoi Vietnam Univ Engn & Technol VNU Hanoi Vietnam Hanoi Metropolitan Rail Board Hanoi Vietnam

The paper presents a dual approach with respect to the local mean square error criterion to multi-degree-of-freedom nonlinear systems under stationary Gaussian random excitation. It results in new values of linearization coefficients that are obtained as global averaged values of all local linearization coefficients. Two examples of typical two-degree-of-freedom nonlinear systems under zero-mean stationary Gaussian random excitation are demonstrated. The results show that the accuracy of solutions by the proposed criterion is significantly improved in comparison with the one by the classical equivalent linearization method, especially when the nonlinearity is strong.

关键词： mean square algorithms EQUIVALENCE (Mathematics) LINEARIZATION (Electronics) NONLINEAR systems DEGREES of freedom GAUSSIAN processes

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mean square Error Based Method for Parameter Ranking and Selection To Obtain Accurate Predictions at Specified Operating Conditions

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INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2014年第14期53卷 6033-6046页

作者： Eghtesadi, Zahra McAuley, Kimberley B. Queens Univ Dept Chem Engn Kingston ON K7L 3N6 Canada

A mean-squared-error-based forward selection methodology is proposed for simultaneous parameter ranking and selection based on the critical ratio r(CCW) [Eghtesadi, Z.;Wu, S.;McAuley, K. B. hid. Eng. Chem. Res, 2013, 52, 12297]. This new technique employs information in the available data set and the operating region of interest to determine the best model with the lowest mean square prediction error. This technique involves relatively simple computations and avoids overfitting of noisy data. This new approach is valuable when data available for parameter estimation arise from correlated experimental designs that make accurate estimation of all the parameters difficult. It is particularly beneficial when the predictions are desired in an operating region that is different from where the data are already available. Monte Carlo simulations of a linear regression example and a nonlinear case study are used to illustrate the effectiveness of the proposed method, demonstrating that results from simulated data agree with theoretical results.

关键词： mean square algorithms ERROR analysis (Mathematics) PARAMETER estimation REGRESSION analysis MONTE Carlo method

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Sliding mode mean square filter design for linear stochastic time delay systems

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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 2014年第12期351卷 5340-5357页

作者： Rodriguez-Ramirez, Pablo Rodriguez-Gonzalez, Jesus IPN Ctr Invest & Estudios Avanzados Unidad Monterrey Apodaca 66600 NL Mexico

This paper investigates the mean-square filtering problem for a linear time delay systems with Gaussian white noises. The obtained solution contains a sliding mode term, signum of the innovations process. It is demonstrated that the estimate produced by the designed filter generates the mean-square estimate, which has the same minimum estimation-error variance as the best estimate given by the classical Kalman-Bucy filter. The theoretical result is applied to an illustrative example: the tryptophan operon of E. coli, verifying the performance of the designed filter. It is demonstrated that the estimates produced by the designed sliding-mode mean-square filter and the Kalman-Bucy filter yield the same estimation-error variance. Simulation graphs demonstrate the better performance of the designed sliding-mode filter and show the potential of the proposed new filter. (C) 2014 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

关键词： SLIDING mode control mean square algorithms KALMAN filtering STOCHASTIC systems LINEAR systems TIME delay systems RANDOM noise theory

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How to understand linear minimum mean-square-error transceiver design for multiple-input-multiple-output systems from quadratic matrix programming

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IET COMMUNICATIONS 2013年第12期7卷 1231-1242页

作者： Xing, Chengwen Li, Shuo Fei, Zesong Kuang, Jingming Beijing Inst Technol Sch Informat & Elect Beijing 100081 Peoples R China

In this study, a unified linear minimum mean-square-error (LMMSE) transceiver design framework is investigated, which is suitable for a wide range of wireless systems. The unified design is based on an elegant and powerful mathematical programming technology termed as quadratic matrix programming (QMP). Based on QMP it can be observed that for different wireless systems, there are certain common characteristics which can be exploited to design LMMSE transceivers, for example, the quadratic forms. It is also discovered that evolving from a point-to-point multiple-input-multiple-output (MIMO) system to various advanced wireless systems such as multi-cell coordinated systems, multi-user MIMO systems, MIMO cognitive radio systems, amplify-and-forward MIMO relaying systems and so on, the quadratic nature is always kept and the LMMSE transceiver designs can always be carried out via iteratively solving a number of QMP problems. A comprehensive framework on how to solve QMP problems is also given. The work presented in this study is likely to be the first shot for the transceiver design for the future ever-changing wireless systems.

关键词： mean square algorithms WIRELESS communication systems MATRICES QUADRATIC equations RADIO transmitter-receivers

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mean square exponential synchronization for two classes of Markovian switching complex networks under feedback control from synchronization control cost viewpoint

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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 2015年第8期352卷 3221-3242页

作者： Wang, Xin Fang, Jian-an Dai, Anding Li, Zhen Zhou, Wuneng Donghua Univ Coll Informat Sci & Technol Shanghai 201620 Peoples R China Zhejiang Text & Fash Coll Sch Informat Engn Ningbo 315211 Zhejiang Peoples R China Hunan City Univ Sch Math & Comp Sci Yiyang 413000 Hunan Peoples R China

This paper is concerned with mean square exponential synchronization for two classes of Markovian switching complex networks (MSCNs) under linear negative control scheme from synchronization control cost viewpoint. Two classes of MSCNs are considered. In order to analyze synchronization controllability for the two classes of MSCNs from synchronization control cost viewpoint, synchronization control cost and synchronization controllability are defined, respectively. By utilizing M-matrix properties, a novel Lyapunov function and the stochastic analysis techniques, sufficient criteria of mean square synchronization and global synchronization for the two classes of MSCNs under feedback control are derived. Three numerical examples and simulations are given to illustrate the following conclusions: (1) the two classes of MSCNs under the same linear negative feedback controller can achieve mean square exponential synchronization and global synchronization if they satisfy sufficient conditions of mean square exponential synchronization;(2) by computing synchronization control cost, we obtain that global synchronization controllability for the first class of MSCNs may perhaps stronger or poorer than that of the second class of MSCNs with time-varying delays. (C) 2014 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

关键词： mean square algorithms EXPONENTIAL functions FEEDBACK control systems SYNCHRONIZATION MATRICES

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WEIGHT VECTOR FLUCTUATIONS IN ADAPTIVE ANTENNA ARRAYS TUNED USING THE LEAST-mean-square ERROR ALGORITHM WITH QUADRATIC CONSTRAINT

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RADIOPHYSICS AND QUANTUM ELECTRONICS 2015年第1期58卷 71-77页

作者： Zimina, S. V. NI Lobachevsky State Univ Nizhny Novgorod Nizhnii Novgorod Russia

We present the results of statistical analysis of an adaptive antenna array tuned using the least-mean-square error algorithm with quadratic constraint on the useful-signal amplification with allowance for the weight-coefficient fluctuations. Using the perturbation theory, the expressions for the correlation function and power of the output signal of the adaptive antenna array, as well as the formula for the weight-vector covariance matrix are obtained in the first approximation. The fluctuations are shown to lead to the signal distortions at the antenna-array output. The weight-coefficient fluctuations result in the appearance of additional terms in the statistical characteristics of the antenna array. It is also shown that the weight-vector fluctuations are isotropic, i.e., identical in all directions of the weight-coefficient space.

关键词： ANTENNAS (Electronics) mean square algorithms QUADRATIC equations PERTURBATION (Mathematics) APPROXIMATION theory

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Joint bit loading and power allocation for downlink minimum mean square error combining based multi-carrier code division multiple access systems

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IET COMMUNICATIONS 2013年第10期7卷 1015-1023页

作者： Kuo, Yaw-Wen Yang, Chen-Kao Lin, Jia-Hong Natl Chi Nan Univ Dept Elect Engn Puli 54561 Nan Tou Taiwan

The performance of a downlink multi-carrier code-division multiple-access (MC-CDMA) system heavily depends on the receiver type at the user side. The minimum mean square error-combining scheme possesses the finest performance. However, the resource allocation problem becomes a highly complex task because of multiple access interference. This study investigates a realistic scenario, where the base station determines the bit loading and power for all downlink users with both the power and bit error rate (BER) constraints to maximise the overall system throughput. The authors first derive the instantaneous signal to interference and noise ratio (SINR) and then approximate data transmission as an equivalent M-QAM system with a signal-to-noise ratio (SNR) equal to the instantaneous SINR of that user. Combined with accurate BER formulas of M-QAM system, the authors estimate the BER for each user given a set of power and bit loading configuration. Finally, the authors develop an iterative joint bit loading and power allocation algorithm to maximise the system throughput. The simulation results show that the proposed solution achieves performance close to the optimal one and maintains the BER close to the desired target.

关键词： MULTICARRIER modulation (Data processing) mean square algorithms BIT error rate SIGNAL-to-noise ratio DATA transmission systems COMPUTER simulation

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mean-square exponential stability for a class of discrete-time nonlinear singular Markovian jump systems with time-varying delay

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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 2014年第10期351卷 4688-4723页

作者： Long, Shaohua Zhong, Shouming Chongqing Univ Technol Sch Math & Stat Chongqing 400054 Peoples R China Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Peoples R China

This paper investigates the problem of mean-square exponential stability for a class of discrete-time nonlinear singular Markovian jump systems with time-varying delay. The considered systems are with mode-dependent singular matrices E-r(k). By using the free-weighting matrix method and the Lyapunov functional method, delay-dependent sufficient conditions which guarantee the considered systems to be mean-square exponentially stable are presented. Finally, some numerical examples are employed to demonstrate the effectiveness of the proposed methods. (C) 2014 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

关键词： mean square algorithms LYAPUNOV functions NUMERICAL analysis EXPONENTIAL stability TIME delay systems

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Dual approach to local mean square error criterion for stochastic equivalent linearization

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ACTA MECHANICA 2013年第2期224卷 241-253页

作者： Anh, N. D. Hung, L. X. Viet, L. D. Inst Mech VAST 264 Hanoi Vietnam Hanoi Metropolitan Rail Board Hanoi Vietnam

Based on the dual conception, the paper suggests a consideration at global level to the local mean square error criterion of the stochastic equivalent linearization method. It results in new values of linearization coefficients that are obtained as global averaged values of all local linearization coefficients. The numerical analysis of some typical nonlinear systems under white noise excitation shows that the accuracy of the proposed criterion is significantly improved in comparison with the one of the classical mean square error criterion.

关键词： mean square algorithms ERROR analysis (Mathematics) STOCHASTIC analysis COEFFICIENTS (Statistics) NONLINEAR systems NUMERICAL analysis

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Radial basis function network assisted single-user channel estimation by using a linear minimum mean square error detector under impulsive noise

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COMPUTERS & ELECTRICAL ENGINEERING 2013年第4期39卷 1288-1299页

作者： Rizaner, Ahmet Eastern Mediterranean Univ Dept Informat Technol Famagusta North Cyprus Turkey

This paper proposes a novel robust channel estimator for direct-sequence code-division multiple-access systems with time-varying multipath fading channels under impulsive noise. The channel estimation approach presented is based on the linear single-user minimum mean square error criteria and uses a radial basis function network to eliminate the effect of impulsive noise. A threshold mechanism is also developed to eliminate the disadvantage of the proposed estimator under Gaussian noise. Simulation results clearly show that the proposed estimator eliminates the effect of impulsive noise and improves the performance of channel estimation under impulsive noise. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： RADIAL basis functions COMPUTER users PARAMETER estimation mean square algorithms ERROR analysis (Mathematics) SIGNAL-to-noise ratio PERFORMANCE evaluation

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