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

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.

Understanding Lithium-ion Transport in Sulfolane- and Tetraglyme-Based Electrolytes Using Very Low-Frequency Impedance Spectroscopy

With the increasing interest in highly concentrated electrolyte systems,correct determination of the cation transference number is important.Pulsed-field gradient NMR technique,which measures self-diffusion coefficients,is often applied on liquid electrolytes because of the wide accessibility and simple sample preparation.However,since the assumptions of this technique,that is,complete salt dissociation,all ions participating in motion,and all of them moving independently,no longer hold true in concentrated solutions,the transference numbers,thus obtained are often over-estimated.In the present work,impedance spectroscopy at a frequency range of 1 MHz to 0.1 mHz was used to examine the concentration effect on lithium-ion transference number under anion-blocking conditions T abc Liþfor two electrolytes:lithium bis(fluorosulfonyl)imide(LiFSI)in sulfolane(SL)and lithium bis(trifluorosulfonyl)imide(LiTFSI)in tetraglyme(G4).The T abc Liþof the former was almost an order of magnitude higher than that of the latter.It also appeared to increase with increasing concentration while the latter followed an opposite trend.The faster Li^(+)transport in the SL system is attributed to the formation of a liquid structure consisting of extended chains/bridges of SL molecules and the anions,which facilitate a cation-hopping/ligand-exchanged-typed diffusion mechanism by partially decoupling the cations from the anions and solvent molecules.The G4 system,in contrast,is dominated by the formation of long-lived,stable[Li(G4)]+solvation cages that results in a sluggish Li+transport.The difference between the two transport mechanisms is discussed via comparison of the bulk ionic conductivity,viscosity,ion self-diffusion coefficients,and the Onsager transport coefficients.

Model tests and numerical analyses on horizontal impedance functions of inclined single piles embedded in cohesionless soil

Horizontal impedance functions of inclined single piles are measured experimentally for model soil-pile systems with both the effects of local soil nonlinearity and resonant characteristics.Two practical pile inclinations of 5掳 and 10掳 in addition to a vertical pile embedded in cohesionless soil and subjected to lateral harmonic pile head loadings for a wide range of frequencies are considered.Results obtained with low-to-high amplitude of lateral loadings on model soil-pile systems encased in a laminar shear box show that the local nonlinearities have a profound impact on the horizontal impedance functions of piles.Horizontal impedance functions of inclined piles are found to be smaller than the vertical pile and the values decrease as the angle of pile inclination increases.Distinct values of horizontal impedance functions are obtained for the ＇positive＇ and ＇negative＇ cycles of harmonic loadings,leading to asymmetric force-displacement relationships for the inclined piles.Validation of these experimental results is carried out through three-dimensional nonlinear finite element analyses,and the results from the numerical models are in good agreement with the experimental data.Sensitivity analyses conducted on the numerical models suggest that the consideration of local nonlinearity at the vicinity of the soil-pile interface influence the response of the soil-pile systems.

LOW-FREQUENCY LOW-NOISE CIRCUITS DESIGN USING AN E_n-I_n MODEL

In view of the limitations of a Rn-Gn model in the low frequency range and the defects of an En-In model in common use now, this paper builds a complete En-In model according to the theory of random harmonic. The parameters for the low-noise design such as the equivalent input noisy voltage Ens, the optimum source impedance Zsopt and the minimum noise figure Fmin can be calculated accurately by using this En-In model because it considers the coherence between the noise sources fully. Moreover, this paper points out that it will cause the maximum 30% miscalculation when neglecting the effects of the correlation coefficient 7. Using the series-series circuits as an example, this paper discusses the methods for the En-In noise analysis of electronic circuits preliminarily and demonstrates its correctness through the comparison between the simulated and measured results of the minimum noise figure Fmin of a single current series negative feedback circuit.

A New Perspective to Evaluate Doppler Vascular Impedance in Hypertensive Disorders Complicating Pregnancy: Multilevel Modeling Established in a Case Control Study

Background: There have been researches on the evaluation of Doppler vascular impedance in hypertensive disorders complicating pregnancy (HDCP). With respect to the method of analysis used and the conclusions drawn in previous studies, different vessels were usually viewed separately and independently. This study was designed to evaluate Doppler vascular impedance changes in HDCP from a new perspective, with original thought and insight into an ordinary issue. Methods: 273 pregnant women (110 hypertensive pregnancies and 163 normotensive pregnancies) were randomly included in a grouping case-control study conducted from February 10, 2011 to April 30, 2013. All women in the study underwent Doppler measurements of six different vessels including the umbilical artery, the uterine arteries, the placental bed spiral artery, the fetal middle cerebral artery and the fetal renal artery. Doppler vascular impedance was presented as pulsatility index (PI), resistance index (RI), and systolic and diastolic ratio (S/D). Doppler changes in the hypertensive and normotensive groups were assessed by the multilevel modeling approach with univariate and multivariate-adjusted analyses. Results: According to multilevel modeling approach with multivariate-adjusted analysis, a relatively average evaluation on Doppler vascular impedance was provided. Hypertension was significantly associated with positive effects on PI, RI and S/D values (coefficients were 0.10, 0.03 and 0.08, respectively;95% CIs were 0.06 - 0.14, 0.02 - 0.04 and 0.04 - 0.11, respectively;P values were all less than 0.001) in comparison with normotensive group. Conclusion: According to an overall evaluation, Doppler vascular impedance in hypertensive disorders complicating pregnancy was higher than in normotensive pregnancy. The novel thought and approach applied in this research may bring about inspirations for better understanding and assessment of the disease.

Electrode models in electrical impedance tomography

This paper presents different views on electrode modelling, which include electrode electrochemistry models for modelling the effects of electrode-electrolyte interface, electric field electrode models for modelling electrode geometry, and electrode models for modelling the effects of electrode common mode voltage and double layer capacitance. Taking the full electrode models into consideration in electrical impedance tomography (EIT) will greatly help the optimised approach to a good solution and further understanding of the measurement principle.

Stress wave analysis of high-voltage pulse discharge rock fragmentation based on plasma channel impedance model

High-voltage pulse discharge(HVPD)rock fragmentation controls a plasma channel forming inside the rock by adjusting the electrical parameters,electrode type,etc.In this work,an HVPD rock fragmentation test platform was built and the test waveforms were measured.Considering the effects of temperature,channel expansion and electromagnetic radiation,the impedance model of the plasma channel in the rock was established.The parameters and initial values of the model were determined by an iterative computational process.The model calculation results can reasonably characterize the development of the plasma channel in the rock and estimate the shock wave characteristics.Based on the plasma channel impedance model,the temporal and spatial distribution characteristics of the radial stress and tangential stress in the rock were calculated,and the rock fragmentation effect of the HVPD was analyzed.

T-Y TUBE MODEL OF HUMAN ASCENDINGAORTIC INPUT IMPEDANCE

This paper proposed a T- Y tube model to simulate foe input impedance of arterial system. It improves and extends the asymmetric T-tube model which was firstproposed by O' Rourke[1] and developed laier by Liu et al.[2]. Based on foe asymmetricT-tube model. a T-Y tube model was proposed by adding branching tubes whichrepresem the iliac arteries.All the tubes are considered to be uniform,viscoelasticlongitudinally tethered cylindrical tubes.The upper tube terminates with a windkesselmodel, while the terminal arterioles of the lowr tube are expressed as a resistance.After proper eraluation of the parameters.the impedance of the arterial system iscalculated under normal physiological and hypertensive condition.The model canpredict impedance in good agreement with the experimentally obtained data no matterin normal physiological condition or in pathological condition In comparison with theasymmeric T-tube model,T- Y tube model is closer to anatomy structure of the human arlerial system and at the sametime much simpler than the extremely complex multiplebranching tube model Therefore it will be a valuable model in studying the influencesof various parameters on aorta impedance and ventricular-vascular coupling.

Model-constrained and data-driven double-supervision acoustic impedance inversion

Seismic impedance inversion is an important technique for structure identification and reservoir prediction.Model-based and data-driven impedance inversion are the commonly used inversion methods.In practice,the geophysical inversion problem is essentially an ill-posedness problem,which means that there are many solutions corresponding to the same seismic data.Therefore,regularization schemes,which can provide stable and unique inversion results to some extent,have been introduced into the objective function as constrain terms.Among them,given a low-frequency initial impedance model is the most commonly used regularization method,which can provide a smooth and stable solution.However,this model-based inversion method relies heavily on the initial model and the inversion result is band limited to the effective frequency bandwidth of seismic data,which cannot effectively improve the seismic vertical resolution and is difficult to be applied to complex structural regions.Therefore,we propose a data-driven approach for high-resolution impedance inversion based on the bidirectional long short-term memory recurrent neural network,which regards seismic data as time-series rather than image-like patches.Compared with the model-based inversion method,the data-driven approach provides higher resolution inversion results,which demonstrates the effectiveness of the data-driven method for recovering the high-frequency components.However,judging from the inversion results for characterization the spatial distribution of thin-layer sands,the accuracy of high-frequency components is difficult to guarantee.Therefore,we add the model constraint to the objective function to overcome the shortages of relying only on the data-driven schemes.First,constructing the supervisor1 based on the bidirectional long short-term memory recurrent neural network,which provides the predicted impedance with higher resolution.Then,convolution constraint as supervisor2 is introduced into the objective function to guarantee the reliability and accuracy of the inversion results,which makes the synthetic seismic data obtained from the inversion result consistent with the input data.Finally,we test the proposed scheme based on the synthetic and field seismic data.Compared to model-based and purely data-driven impedance inversion methods,the proposed approach provides more accurate and reliable inversion results while with higher vertical resolution and better spatial continuity.The inversion results accurately characterize the spatial distribution relationship of thin sands.The model tests demonstrate that the model-constrained and data-driven impedance inversion scheme can effectively improve the thin-layer structure characterization based on the seismic data.Moreover,tests on the oil field data indicate the practicality and adaptability of the proposed method.

Harmonic State-Space Based AC-Side Impedance Model of MMC and High Frequency Oscillation Characteristics Analysis

Recently,high-frequency oscillation of themodularmultilevel converter(MMC)based high-voltage direct current(HVDC)projects has attracted great attentions.In order to analyze the small-signal stability,this paper uses the harmonic state-space(HSS)method to establish a detailed frequency domain impedance model of the AC-side of the HVDC transmission system,which considers the internal dynamic characteristics.In addition,the suggested model is also used to assess the system’s high-frequency oscillationmechanism,and the effects of the MMC current inner loop control,feedforward voltage links,and control delay on the high-frequency impedance characteristics and the effect of higher harmonic components.Finally,three oscillation suppression schemes are analyzed for the oscillation problems occurring in actual engineering,and a simplified impedance model considering only the highfrequency impedance characteristics is established to compare the suppression effect with the detailed impedance model to prove its reliability.

Nonlinear Electrical Impedance Tomography Method Using a Complete Electrode Model for the Characterization of Heterogeneous Domains

This paper presents an electrical impedance tomography(EIT)method using a partial-differential-equationconstrained optimization approach.The forward problem in the inversion framework is described by a complete electrodemodel(CEM),which seeks the electric potential within the domain and at surface electrodes considering the contact impedance between them.The finite element solution of the electric potential has been validated using a commercial code.The inverse medium problem for reconstructing the unknown electrical conductivity profile is formulated as an optimization problem constrained by the CEM.The method seeks the optimal solution of the domain’s electrical conductivity to minimize a Lagrangian functional consisting of a least-squares objective functional and a regularization term.Enforcing the stationarity of the Lagrangian leads to state,adjoint,and control problems,which constitute the Karush-Kuhn-Tucker(KKT)first-order optimality conditions.Subsequently,the electrical conductivity profile of the domain is iteratively updated by solving the KKT conditions in the reduced space of the control variable.Numerical results show that the relative error of the measured and calculated electric potentials after the inversion is less than 1%,demonstrating the successful reconstruction of heterogeneous electrical conductivity profiles using the proposed EIT method.This method thus represents an application framework for nondestructive evaluation of structures and geotechnical site characterization.

Analytical and Numerical Model Confrontation for Transfer Impedance Extraction in Three-Dimensional Radio Frequency Circuits

3D chip stacking is considered known to overcome conventional 2D-IC issues, using through silicon vias to ensure vertical signal transmission. From any point source, embedded or not, we calculate the impedance spread out;our ultimate goal will to study substrate noise via impedance field method. For this, our approach is twofold: a compact Green function or a Transmission Line Model over a multi-layered substrate is derived by solving Poisson’s equation analytically. The Discrete Cosine Transform (DCT) and its variations are used for rapid evaluation. Using this technique, the substrate coupling and loss in IC’s can be analyzed. We implement our algorithm in MATLAB;it permits to extract impedances between any pair of embedded contacts. Comparisons are performed using finite element methods.

Research on the Mechanism of Impedance Matching for Underwater Acoustic Transmitter based on Mathematical Modelling and Corresponding Balance Transformer

With the progress of power transmission technology, it is necessary for researchers to conduct related research on impedance matching. In this paper, we conduct research on the mechanism of impedance matching for underwater acoustic transmitter based on mathematical modelling and corresponding balance transformer. To realize underwater acoustic signal of wide band and high power emission, in addition to need the bandwidth performance good transducer array yuan, to a large extent also depends on a good matching between the transducer and amplifier. The result shows the feasibility and robustness of our designed system.

Seasonal Characteristics and Interannual Variability of Monthly Scale Low-Frequency Oscillation in a Low-Order Global Spectral Model

Analysis is done of five-year low-pass filtered data by a five-layer low-order global spectral model, indicating that although any non-seasonal external forcing is not considered in the model atmosphere,monthly-scale anomaly takes place which is of remarkable seasonality and interannual variability.Analysis also shows that for the same seasonal external forcing the model atmosphere can exhibit two climatic states,similar in the departure pattern but opposite in sign, indicating that the anomaly is but the manifestation of the adverse states, which supports the theory of multi-equilibria proposed by Charney and Devore(1979) once again.Finally, the source for the low-frequency oscillation of the global atmosphere is found to be the convective heat source / sink inside the tropical atmosphere as discussed before in our study.Therefore, the key approach to the exploration of atmospheric steady low-frequency oscillation and the associated climatic effect lies in the examination of the distribution of convective heat sources / sinks and the variation in the tropical atmosphere.

A 6n-Order Low-Frequency Mathematical Model of Multiple Inverters Based Microgrid

Microgrid stability analysis is a critical issue especially due to the inverters’low-inertia nature.The voltage and current control loops influences on stability are researched frequently most of which focus on medium and high-frequency characteristic.Although the complete state-space model aims at low-frequency characteristic,it is too complicated and the calculation amount is huge with the scale of the microgrid increasing.One available reduced-order model of an inverter is simple,but it is suitable for only single inverter without network dynamic in microgrid.To fill in these gaps,a novel modeling method is proposed in this paper to investigate the low-frequency instability phenomenon and describe the whole DG connected system including network.In consideration of the high penetration level of induction motor(IM)loads and constant power(CP)loads in practical applications,the low-frequency mathematical model of IM and CP loads on the basis of static load is also built in this paper.Simulation and experimental results verify the effectiveness of the proposed model.

High-Impedance Bus Differential Protection Modeling in ATP/MODELS

This paper presents a modeling of a high-impedance bus differential protection logic using the ATP (Alternative Transients Program) MODELS language. The model is validated using ATP simulations on an electrical system consisting of a sectionalized bus arrangement with four transmission lines (TLs) and two autotransformers. The obtained results validate the model and present some of the advantages of using this type of bus protection, such as fast and safe operation, even when under adverse conditions such as current transformers (CTs) magnetic core saturation upon the occurrence of external faults.

Low-frequency data analysis and expansion

The use of low-frequency seismic data improves the seismic resolution, and the imaging and inversion quality. Furthermore, low-frequency data are applied in hydrocarbon exploration; thus, we need to better use low-frequency data. In seismic wavelets, the loss of low-frequency data decreases the main lobe amplitude and increases the first side lobe amplitude and results in the periodic shocking attenuation of the secondary side lobe. The loss of low frequencies likely produces pseudo-events and the false appearance of higher resolution. We use models to examine the removal of low-frequency data in seismic data processing. The results suggest that the removal of low frequencies create distortions, especially for steep structures and thin layers. We also perform low-frequency expansion using compressed sensing and sparse constraints and develop the corresponding module. Finally, we apply the proposed method to real common image point gathers with good results.

Effect of sediment on vertical dynamic impedance of rock-socketed pile with large diameter

Based on the fictitious soil pile model, the effect of sediment on the vertical dynamic impedance of rock-socketed pile with large diameter was theoretically studied by means of Laplace transform technique and impedance function transfer method. Firstly, the sediment under rock-socketed pile was assumed to be fictitious soil pile with the same sectional area. The Rayleigh-Love rode model was used to simulate the rock-socketed pile and the fictitious soil pile with the consideration of the lateral inertial effect of large-diameter pile. The layered surrounding soils and bedrock were modeled by the plane strain model. Then, by virtue of the initial conditions and boundary conditions of the soil pile system, the analytical solution of the vertical dynamic impedance at the head of rock-socketed pile was derived for the arbitrary excitation acting on the pile head. Lastly, based on the presented analytical solution, the effect of sediment properties, bedrock property and lateral inertial effect on the vertical dynamic impedance at rock-socketed pile head were investigated in detail. It is shown that the sediment properties have significant effect on the vertical dynamic impedance at the rock-socketed pile head. The ability of soil-pile system to resist dynamic vertical deformation is weakened with the increase of sediment thickness, but amplified with the increase of shear wave velocity of sediment. The ability of soil pile system to resist dynamic vertical deformation is amplified with the bedrock property improving, but the ability of soil-pile system to resist vertical vibration is weakened with the improvement of bedrock property.

Human Interaction Dynamics for Its Use in Mobile Robotics:Impedance Control for Leader-follower Formation

A complete characterization of the behavior in human-robot interactions(HRI) includes both: the behavioral dynamics and the control laws that characterize how the behavior is regulated with the perception data. In this way, this work proposes a leader-follower coordinate control based on an impedance control that allows to establish a dynamic relation between social forces and motion error. For this, a scheme is presented to identify the impedance based on fictitious social forces, which are described by distance-based potential fields.As part of the validation procedure, we present an experimental comparison to select the better of two different fictitious force structures. The criteria are determined by two qualities: least impedance errors during the validation procedure and least parameter variance during the recursive estimation procedure.Finally, with the best fictitious force and its identified impedance,an impedance control is designed for a mobile robot Pioneer 3AT,which is programmed to follow a human in a structured scenario.According to results, and under the hypothesis that moving like humans will be acceptable by humans, it is believed that the proposed control improves the social acceptance of the robot for this kind of interaction.

Two-dimensional regularized inversion of AMT data based on rotation invariant of Central impedance tensor

Considering the uncertainty of the electrical axis for two-dimensional audo-magnetotelluric(AMT) data processing, an AMT inversion method with the Central impedance tensor was presented. First, we present a calculation expression of the Central impedance tensor in AMT, which can be considered as the arithmetic mean of TE-polarization mode and TM-polarization mode in the twodimensional geo-electrical model. Second, a least-squares iterative inversion algorithm is established, based on a smoothnessconstrained model, and an improved L-curve method is adopted to determine the best regularization parameters. We then test the above inversion method with synthetic data and field data. The test results show that this two-dimensional AMT inversion scheme for the responses of Central impedance is effective and can reconstruct reasonable two-dimensional subsurface resistivity structures. We conclude that the Central impedance tensor is a useful tool for two-dimensional inversion of AMT data.