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1 – 10 of 200Marissa Condon and Rossen Ivanov
The paper is aimed at the development of novel model reduction techniques for nonlinear systems.
Abstract
Purpose
The paper is aimed at the development of novel model reduction techniques for nonlinear systems.
Design/methodology/approach
The analysis is based on the bilinear and polynomial representation of nonlinear systems and the exact solution of the bilinear system in terms of Volterra series. Two sets of Krylov subspaces are identified which capture the most essential part of the input‐output behaviour of the system.
Findings
The paper proposes two novel model‐reduction strategies for nonlinear systems. The first involves the development, in a novel manner compared with previous approaches, of a reduced‐order model from a bilinear representation of the system, while the second involves reducing a polynomial approximation using Krylov subspaces derived from a related bilinear representation. Both techniques are shown to be effective through the evidence of a standard test example.
Research limitations/implications
The proposed methodology is applicable to so‐called weakly nonlinear systems, where both the bilinear and polynomial representations are valid.
Practical implications
The suggested methods lead to an improvement in the accuracy of nonlinear model reduction, which is of paramount importance for the efficient simulation of state‐of‐the‐art dynamical systems arising in all aspects of engineering.
Originality/value
The proposed novel approaches for model reduction are particularly beneficial for the design of controllers for nonlinear systems and for the design and analysis of radio‐frequency integrated circuits.
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Keywords
José Cruz Nuñez-Perez, José Ricardo Cardenas-Valdez, Christian Gontrand, J. Apolinar Reynoso-Hernandez, Francisco Iwao Hirata-Flores, Rigoberto Jauregui-Duran and Francisco J. Perez-Pinal
The paper aims to focus on the memory-polynomial model (MPM) as special case of Volterra series, implemented in hardware. The behavior of the MPM is fully proved through a…
Abstract
Purpose
The paper aims to focus on the memory-polynomial model (MPM) as special case of Volterra series, implemented in hardware. The behavior of the MPM is fully proved through a comparison with AM-AM and AM-PM measured data. The results show that this simulation technique is able to prove the effectiveness of the MPM implementation as behavioural model for high power radiofrequency amplifiers. The system is able to compensate perturbations caused by modern communication systems.
Design/methodology/approach
The implementation uses Matlab-Simulink, and its digital signal processing (DSP) builder. The first stage allows developing the model in Matlab using the DSP builder blockset through the signal compiler block. Then, the design is downloaded to the DSP board.
Findings
The paper demonstrates a proper behavior of the MPM as a truncation of the Volterra series, with respect to different inputs. This is a key point, because the series truncations allow first to implement this model in real time and second to obtain a correct precision, for instance when modeling amplification of digital signals in high frequency.
Originality/value
The global system approach permits to easily develop, simulate, and validate a wireless system. The efficiency of a complete connected solution based on Agilent Technologies tools, combining simulations and measurements under true operating conditions, seems to be clearly demonstrated.
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Hadi Dehbovid, Habib Adarang and Mohammad Bagher Tavakoli
Charge pump phase locked loops (CPPLLs) are nonlinear systems as a result of the nonlinear behavior of voltage-controlled oscillators (VCO). This paper aims to specify jitter…
Abstract
Purpose
Charge pump phase locked loops (CPPLLs) are nonlinear systems as a result of the nonlinear behavior of voltage-controlled oscillators (VCO). This paper aims to specify jitter generation of voltage controlled oscillator phase noise in CPPLLs, by considering approximated practical model for VCO.
Design/methodology/approach
CPPLL, in practice, shows nonlinear behavior, and usually in LC-VCOs, it follows second-degree polynomial function behavior. Therefore, the nonlinear differential equation of the system is obtained which shows the CPPLLs are a nonlinear system with memory, and that Volterra series expansion is useful for such systems.
Findings
In this paper, by considering approximated practical model for VCO, jitter generation of voltage controlled oscillator phase noise in CPPLLs is specified. Behavioral simulation is used to validate the analytical results. The results show a suitable agreement between analytical equations and simulation results.
Originality/value
The proposed method in this paper has two advantages over the conventional design and analysis methods. First, in contrast to an ideal CPPLL, in which the characteristic of the VCO’s output frequency based on the control voltage is linear, in the present paper, a nonlinear behavior was considered for this characteristic in accordance with the real situations. Besides, regarding the simulations in this paper, a behavior similar to the second-degree polynomial was considered, which caused the dependence of the produced jitter’s characteristic corner frequency on the jitter’s amplitude. Second, some new nonlinear differential equations were proposed for the system, which ensured the calculation of the produced jitter of the VCO phase noise in CPPLLs. The presented method is general enough to be used for designing the CPPLL.
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Lorenzo Codecasa, Federico Moro and Piergiorgio Alotto
This paper aims to propose a fast and accurate simulation of large-scale induction heating problems by using nonlinear reduced-order models.
Abstract
Purpose
This paper aims to propose a fast and accurate simulation of large-scale induction heating problems by using nonlinear reduced-order models.
Design/methodology/approach
A projection space for model order reduction (MOR) is quickly generated from the first kernels of Volterra’s series to the problem solution. The nonlinear reduced model can be solved with time-harmonic phasor approximation, as the nonlinear quadratic structure of the full problem is preserved by the projection.
Findings
The solution of induction heating problems is still computationally expensive, even with a time-harmonic eddy current approximation. Numerical results show that the construction of the nonlinear reduced model has a computational cost which is orders of magnitude smaller than that required for the solution of the full problem.
Research limitations/implications
Only linear magnetic materials are considered in the present formulation.
Practical implications
The proposed MOR approach is suitable for the solution of industrial problems with a computing time which is orders of magnitude smaller than that required for the full unreduced problem, solved by traditional discretization methods such as finite element method.
Originality/value
The most common technique for MOR is the proper orthogonal decomposition. It requires solving the full nonlinear problem several times. The present MOR approach can be built directly at a negligible computational cost instead. From the reduced model, magnetic and temperature fields can be accurately reconstructed in whole time and space domains.
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Yanqing Shi, Hongye Cao and Si Chen
Online question-and-answer (Q&A) communities serve as important channels for knowledge diffusion. The purpose of this study is to investigate the dynamic development process of…
Abstract
Purpose
Online question-and-answer (Q&A) communities serve as important channels for knowledge diffusion. The purpose of this study is to investigate the dynamic development process of online knowledge systems and explore the final or progressive state of system development. By measuring the nonlinear characteristics of knowledge systems from the perspective of complexity science, the authors aim to enrich the perspective and method of the research on the dynamics of knowledge systems, and to deeply understand the behavior rules of knowledge systems.
Design/methodology/approach
The authors collected data from the programming-related Q&A site Stack Overflow for a ten-year period (2008–2017) and included 48,373 tags in the analyses. The number of tags is taken as the time series, the correlation dimension and the maximum Lyapunov index are used to examine the chaos of the system and the Volterra series multistep forecast method is used to predict the system state.
Findings
There are strange attractors in the system, the whole system is complex but bounded and its evolution is bound to approach a relatively stable range. Empirical analyses indicate that chaos exists in the process of knowledge sharing in this social labeling system, and the period of change over time is about one week.
Originality/value
This study contributes to revealing the evolutionary cycle of knowledge stock in online knowledge systems and further indicates how this dynamic evolution can help in the setting of platform mechanics and resource inputs.
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Fen‐May Liou and Chien‐Hui Yang
The objective of this paper is to stress the importance of detecting financial frauds in predicting business failures disclosed by the unexpected financial crisis brought by…
Abstract
Purpose
The objective of this paper is to stress the importance of detecting financial frauds in predicting business failures disclosed by the unexpected financial crisis brought by Enron, Worldcom and other corporate distresses involving accounting irregularities.
Design/methodology/approach
The most frequently used methodologies in predicting business failures, discriminant analysis and neural network (NN) (based on the Kolmogorov‐Gabor polynomial Volterra series algorithm) are used. This paper suggests a two‐stage NN procedure: the first stage detected the false financial statements, which were excluded from samples that used to predict the business failures at the second stage. The one‐stage discriminant analysis and the NN model are used to contrast the two‐stage approach in terms of accuracy rate.
Findings
The one‐stage NN model has a higher accuracy rate in identifying failed firms than the discriminant analysis, while the two‐stage NN approach has an even higher accuracy rate than the one‐stage NN model.
Practical implications
Detecting the fraudulent reporting in advance can effectively improve the accuracy rate of business failure predictions.
Originality/value
The paper draws attention to the importance of excluding fraudulent financial reporting to increase the accuracy rate in predicting business failures.
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This paper aims to analyze soil electrical properties based on fractional calculus theory due to the fact that the frequency dependence of soil electrical parameters at high…
Abstract
Purpose
This paper aims to analyze soil electrical properties based on fractional calculus theory due to the fact that the frequency dependence of soil electrical parameters at high frequencies exhibits a fractional effect. In addition, for the fractional-order formulation, this paper aims to provide a more accurate numerical algorithm for solving the fractional differential equations.
Design/methodology/approach
This paper analyzes the frequency-dependence of soil electrical properties based on fractional calculus theory. A collocation method based on the Puiseux series is proposed to solve fractional differential equations.
Findings
The algorithm proposed in this paper can be used to solve fractional differential equations of arbitrary order, especially for 0.5th-order equations, obtaining accurate numerical solutions. Calculating the impact response of the grounding electrode based on the fractional calculus theory can obtain a more accurate result.
Originality/value
This paper proposes an algorithm for solving fractional differential equations of arbitrary order, especially for 0.5th-order equations. Using fractional calculus theory to analyze the frequency-dependent effect of soil electrical properties, provides a new idea for ground-related transient calculation.
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Amir Bahrami and Saeed Reza Ostadzadeh
The purpose of this paper is to calculate the back scattering response from single, finite and infinite arrays of nonlinear antennas like the case where the antennas are exposed…
Abstract
Purpose
The purpose of this paper is to calculate the back scattering response from single, finite and infinite arrays of nonlinear antennas like the case where the antennas are exposed to high-value signals such as lightning strokes.
Design/methodology/approach
In this paper, the authors have used a recently introduced optimization technique called intelligent water drop.
Findings
The results exhibit that the method used by the authors is faster and more accurate than other conventional optimization algorithms, i.e. particle swarm optimization and genetic algorithm.
Originality/value
A new optimization algorithm is used to solve nonlinear problem accurately and sufficiently. Although the technique is not confined to the mentioned examples in the paper, it can be applied to other nonlinear circuits.
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Janne P. Aikio, Timo Rahkonen and Ville Karanko
The purpose of this paper is to propose methods to improve the least square error polynomial fitting of multi-input nonlinear sources that suffer from strong correlating inputs…
Abstract
Purpose
The purpose of this paper is to propose methods to improve the least square error polynomial fitting of multi-input nonlinear sources that suffer from strong correlating inputs.
Design/methodology/approach
The polynomial fitting is improved by amplitude normalization, reducing the order of the model, utilizing Chebychev polynomials and finally perturbing the correlating controlling voltage spectra. The fitting process is estimated by the reliability figure and the condition number.
Findings
It is shown in the paper that perturbing one of the controlling voltages reduces the correlation to a large extend especially in the cross-terms of the multi-input polynomials. Chebychev polynomials reduce the correlation between the higher-order spectra derived from the same input signal, but cannot break the correlation between correlating input and output voltages.
Research limitations/implications
Optimal perturbations are sought in a separate optimization loop, which slows down the fitting process. This is due to the fact that each nonlinear source that suffers from the correlation needs a different perturbation.
Originality/value
The perturbation, harmonic balance run and refitting of an individual nonlinear source inside a device model is new and original way to characterize and fit polynomial models.
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Keywords
Yunfeng Zhou and Feng Wan
The purpose of this paper is to present a neural network approach to control performance assessment.
Abstract
Purpose
The purpose of this paper is to present a neural network approach to control performance assessment.
Design/methodology/approach
The performance index under study is based on the minimum variance control benchmark, a radial basis function network (RBFN) is used as the pre‐whitening filter to estimate the white noise sequence, and a stable filtering and correlation analysis method is adopted to calculate the performance index by estimating innovations sequence using the RBFN pre‐whitening filter. The new approach is compared with the auto‐regressive moving average model and the Laguerre model methods, for both linear and nonlinear cases.
Findings
Simulation results show that the RBFN approach works satisfactorily for both linear and nonlinear examples. In particular, the proposed scheme shows merits in assessing controller performance for nonlinear systems and surpasses the Laguerre model method in parameter selection.
Originality/value
A RBFN approach is proposed for control performance assessment. This new approach, in comparison with some well‐known methods, provides satisfactory performance and potentials for both linear and nonlinear cases.
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