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model reduction of fractional impedance spectra for time–frequency analysis of batteries, fuel cells, and supercapacitors

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Carbon Energy 2024年第1期6卷 108-141页

作者： Weiheng Li Qiu-An Huang Yuxuan Bai Jia Wang Linlin Wang Yuyu Liu Yufeng Zhao Xifei Li Jiujun Zhang Institute for Sustainable Energy/College of Sciences Shanghai UniversityShanghaiChina Shanxi Key Laboratory of Nanomaterials and Nanotechnology School of Mechanical and Electrical EngineeringXi'an University of Architecture and TechnologyXi'anShaanxiChina Xi'an Key Laboratory of New Energy Materials and Devices School of Materials Science and EngineeringInstitute of Advanced Electrochemical EnergyXi'an University of TechnologyXi'anShaanxiChina

Joint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells,batteries,and supercapacitors.To increase the reliability of time–frequency analysis,a theoretical correlation between frequency-domain stationary analysis and time-domain transient analysis is urgently required.The present work formularizes a thorough model reduction of fractional impedance spectra for electrochemical energy devices involving not only the model reduction from fractional-order models to integer-order models and from high-to low-order RC circuits but also insight into the evolution of the characteristic time constants during the whole reduction process.The following work has been carried out:(i)the model-reduction theory is addressed for typical Warburg elements and RC circuits based on the continued fraction expansion theory and the response error minimization technique,respectively;(ii)the order effect on the model reduction of typical Warburg elements is quantitatively evaluated by time–frequency analysis;(iii)the results of time–frequency analysis are confirmed to be useful to determine the reduction order in terms of the kinetic information needed to be captured;and(iv)the results of time–frequency analysis are validated for the model reduction of fractional impedance spectra for lithium-ion batteries,supercapacitors,and solid oxide fuel cells.In turn,the numerical validation has demonstrated the powerful function of the joint time–frequency analysis.The thorough model reduction of fractional impedance spectra addressed in the present work not only clarifies the relationship between time-domain transient analysis and frequency-domain stationary analysis but also enhances the reliability of the joint time–frequency analysis for electrochemical energy devices.

关键词： battery,fuel cell,supercapacitor fractional impedance spectroscopy model reduction time-frequency analysis

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Development of stability-preserving time-limited model reduction framework for 2-D and 1-D models with error bound

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Control Theory and Technology 2022年第3期20卷 371-381页

作者： Muhammad Imran Syeda Hira Ambreen Syed Nooh Hamdani Muhammad Imran Muhammad Ejaz Naveed Maria Siddiqui Department of Electrical Engineering Military College of Signals(MCS)National University of Sciences and Technology(NUST)Islamabad43000Pakistan Department of Electrical Engineering Sir Syed(Center For Advanced Studies)Institute of Technology(SSCASE)Islamabad43000Pakistan College of Science and Humanities Rumah Majmaah UniversityRumahKingdom of Saudi Arabia

Due to their complex structure,2-D models are challenging to work with;additionally,simulation,analysis,design,and control get increasingly difficult as the order of the model grows.Moreover,in particular time intervals,Gawronski and Juang’s time-limited model reduction schemes produce an unstable reduced-order model for the 2-D and 1-D models.Researchers revealed some stability preservation solutions to address this key flaw which ensure the stability of 1-D reduced-order systems;nevertheless,these strategies result in large approximation errors.However,to the best of the authors’knowledge,there is no literature available for the stability preserving time-limited-interval Gramian-based model reduction framework for the 2-D discrete-time systems.In this article,2-D models are decomposed into two separate sub-models(i.e.,two cascaded 1-D models)using the condition of minimal rank-decomposition.model reduction procedures are conducted on these obtained two 1-D sub-models using limited-time Gramian.The suggested methodology works for both 2-D and 1-D models.Moreover,the suggested methodology gives the stability of the reduced model as well as a priori error-bound expressions for the 2-D and 1-D models.Numerical results and comparisons between existing and suggested methodologies are provided to demonstrate the effectiveness of the suggested methodology.

关键词： model reduction Weighted Gramian Limited interval Gramian Minimal realization Approximation error Error bound

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model reduction using the genetic algorithmand routh approxi mations

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Journal of Systems Engineering and Electronics 2005年第3期16卷 632-639页

作者：李红星芦金石闫红书 Coll .of Automation Beijing Union Univ Dept .of Information Engineering Dalian Inst .of Light Industry

A new method of model reduction combining the genetic algorithm（GA） with the Routh approximation method is presented. It is suggested that a high-order system can be approximated by a low-order model with a time delay. The denominator parameters of the reduced-order model are determined by the Routh approximation method, then the numerator parameters and time delay are identified by the GAL. The reduced-order models obtained by the proposed method will always be stable if the original system is stable and produce a good approximation to the original system in both the frequency domain and time domain. Two numerical examples show that the method is cornputationally simple and efficient.

关键词： model reduction time delay genetic algorithm Routh approximation.

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model reduction Methods for High-Rise Buildings with Active Mass Damper Control Systems

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Journal of Harbin Institute of Technology(New Series) 2013年第6期20卷 37-45页

作者： Jun Teng Hou-Bing Xing Cheng-Yin Liu Shenzhen Key Lab of Urban & Civil Engineering Disaster Prevention & reduction Harbin Institute of Technology Shenzhen Graduate School

To improve the performance of an active mass damper control system,the controller should be designed based on a reduced-order model. An improved method based on balanced truncation method was proposed to reduce the dimension of high-rise buildings,and was compared with other widely used reduction methods by using a framework with ten floors. This optimized method has improvement of reduction process and choice of the order. Based on the reduced-order model obtained by the improved method and pole-assignment algorithm,a controller was designed. Finally,a comparative analysis of structural responses,transfer functions,and poles was conducted on an actual high-rise building. The results show the effectiveness of the improved method.

关键词： high-rise building active mass damper model reduction controller design

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Correlation analysis of PCB and comparison of test-analysis model reduction methods

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Chinese Journal of Aeronautics 2014年第4期27卷 835-845页

作者： Xu Fei Li Chuanri Jiang Tongmin Rong Shuanglong School of Reliability and Systems Engineering Beihang University

The validity of correlation analysis between finite element model（FEM） and modal test data is strongly affected by three factors, i.e., quality of excitation and measurement points in modal test,FEM reduction methods, and correlation check techniques. A new criterion based on modified mode participation（MMP） for choosing the best excitation point is presented. Comparison between this new criterion and mode participation（MP） criterion is made by using Case 1 with a simple printed circuit board（PCB）. The result indicates that this new criterion produces better results. In Case 2, 35 measurement points are selected to perform modal test and correlation analysis while 9 selected in Case 3.System equivalent reduction expansion process（SEREP）, modal assurance criteria（MAC）, coordinate modal assurance criteria（CoMAC）, pseudo orthogonality check（POC） and coordinate orthogonality check（CORTHOG） are used to show the error introduced by modal test in Cases 2 and 3. Case 2 shows that additional errors which cannot be identified by using CoMAC can be found by using CORTHOG.In both Cases 2 and 3, Guyan reduction, improved reduced system（IRS） method, SEREP and Hybrid reduction are compared for accuracy and robustness. The results suggest that the quality of the reduction process is problem dependent. However, the IRS method is an improvement over the Guyan reduction, and the Hybrid reduction is an improvement over the SEREP reduction.

关键词： Correlation analysis Excitation and measurementpoint Finite element method Modal analysis model reduction PCB

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An Improved model reduction Method on AIMs for N-S Equations Using Multilevel Finite Element Method and Hierarchical Basis

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Numerical Mathematics(Theory,Methods and Applications) 2019年第1期12卷 115-133页

作者： M.Nauman Aslam Jiazhong Zhang Nannan Dang Riaz Ahmad School of Energy and Power Engineering Xi’an Jiaotong UniversityXi’an 710049China

A numerical method is proposed to approach the Approximate Inertial Man-ifolds(AIMs)in unsteady incompressible Navier-Stokes equations,using multilevel fi-nite element method with hierarchical basis functions.Following AIMS,the unknown variables,velocity and pressure in the governing equations,are divided into two com-ponents,namely low modes and high modes.Then,the couplings between low modes and high modes,which are not accounted by standard Galerkin method,are consid-ered by AIMs,to improve the accuracy of the numerical results.Further,the multilevel finite element method with hierarchical basis functions is introduced to approach low modes and high modes in an efficient way.As an example,the flow around airfoil NACA0012 at different angles of attack has been simulated by the method presented,and the comparisons show that there is a good agreement between the present method and experimental results.In particular,the proposed method takes less computing time than the traditional method.As a conclusion,the present method is efficient in numer-ical analysis of fluid dynamics,especially in computing time.

关键词： Fluid dynamics model reduction inertial manifolds multilevel finite element method hierarchical basis functions nonlinear dynamics

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Statistical detection of structural damage based on model reduction

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Applied Mathematics and Mechanics(English Edition) 2009年第7期30卷 875-888页

作者：尹涛林向晖朱宏平 Department of Building and Construction City University of Hong Kong School of Civil Engineering and Mechanics Huazhong University of Science and Technology

This paper proposes a statistical method for damage detection based on the finite element （FE） model reduction technique that utilizes measured modal data with a limited number of sensors. A deterministic damage detection process is formulated based on the model reduction technique. The probabilistie process is integrated into the deterministic damage detection process using a perturbation technique, resulting in a statistical structural damage detection method. This is achieved by deriving the first- and second-order partial derivatives of uncertain parameters, such as elasticity of the damaged member, with respect to the measurement noise, which allows expectation and covariance matrix of the uncertain parameters to be calculated. Besides the theoretical development, this paper reports numerical verification of the proposed method using a portal frame example and Monte Carlo simulation.

关键词： damage detection model reduction perturbation technique Monte Carlo simulation

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A new dynamic bacterial foraging optimization and its application on model reduction

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International Journal of modeling, Simulation, and Scientific Computing 2015年第2期6卷 107-131页

作者： Shenli Wu Sun’an Wang Xiaohu Li School of Mechanical Engineering Xi’an Jiaotong University Xi’an Shannxi710049P.R.China

Inspired by the foraging behavior of E.coli bacteria,bacterial foraging optimization(BFO)has emerged as a powerful technique for solving optimization problems.However,BFO shows poor performance on complex and high-dimensional optimization problems.In order to improve the performance of BFO,a new dynamic bacterial foraging optimization based on clonal selection(DBFO-CS)is proposed.Instead of fixed step size in the chemotaxis operator,a new piecewise strategy adjusts the step size dynamically by regulatory factor in order to balance between exploration and exploitation during optimization process,which can improve convergence speed.Furthermore,reproduction operator based on clonal selection can add excellent genes to bacterial populations in order to improve bacterial natural selection and help good individuals to be protected,which can enhance convergence precision.Then,a set of benchmark functions have been used to test the proposed algorithm.The results show that DBFO-CS offers significant improvements than BFO on convergence,accuracy and robustness.A complex optimization problem of model reduction on stable and unstable linear systems based on DBFO-CS is presented.Results show that the proposed algorithm can efficiently approximate the systems.

关键词： Bacterial foraging optimization dynamic adjustment clonal selection model reduction

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Comparison of Invariant Manifolds for model reduction in Chemical Kinetics

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Communications in Computational Physics 2007年第5期2卷 964-992页

作者： Eliodoro Chiavazzo Alexander N.Gorban Iliya V.Karlin Aerothermochemistry and Combustion Systems Laboratory LAV ETH Zurich8092 ZurichSwitzerland Department of Mathematics University of LeicesterLeicester LE17RHUK.

A modern approach to model reduction in chemical kinetics is often based on the notion of slow invariant manifold.The goal of this paper is to give a comparison of various methods of construction of slow invariant manifolds using a simple Michaelis-Menten catalytic reaction.We explore a recently introduced Method of Invariant Grids(MIG)for iteratively solving the invariance equation.Various initial approximations for the grid are considered such as Quasi Equilibrium Manifold,Spectral Quasi Equilibrium Manifold,Intrinsic Low Dimensional Manifold and Symmetric Entropic Intrinsic Low Dimensional Manifold.Slow invariant manifold was also computed using the Computational Singular Perturbation(CSP)method.A comparison between MIG and CSP is also reported.

关键词： Chemical kinetics model reduction invariant manifold entropy nonlinear dynamics mathematical modeling.

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The Role of Thermodynamics in model reduction when Using Invariant Grids

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Communications in Computational Physics 2010年第9期8卷 701-734页

作者： Eliodoro Chiavazzo Iliya V.Karlin Alexander N.Gorban Aerothermochemistry and Combustion Systems Lab ETH Zurich8092 ZurichSwitzerland School of Engineering Sciences University of SouthamptonSO171BJ SouthamptonUnited Kingdom Department of Mathematics University of LeicesterLE17RH LeicesterUnited Kingdom

In the present work,we develop in detail the process leading to reduction of models in chemical kinetics when using the Method of Invariant Grids(MIG).To this end,reduced models(invariant grids)are obtained by refining initial approximations of slow invariant manifolds,and used for integrating smaller and less stiff systems of equations capable to recover the detailed description with high accuracy.Moreover,we clarify the role played by thermodynamics in model reduction,and carry out a comparison between detailed and reduced solutions for a model hydrogen oxidation reaction.

关键词： Chemical kinetics model reduction invariant manifold entropy

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