Simulation of second-order RC equivalent circuit model of lithium battery based on variable resistance and capacitance

With the rise of the electric vehicle industry,as the power source of electric vehicles,lithium battery has become a research hotspot.The state of charge(SOC)estimation and modelling of lithium battery are studied in this paper.The ampere-hour(Ah)integration method based on external characteristics is analyzed,and the open-circuit voltage(OCV)method is studied.The two methods are combined to estimate SOC.Considering the accuracy and complexity of the model,the second-order RC equivalent circuit model of lithium battery is selected.Pulse discharge and exponential fitting of lithium battery are used to obtain corresponding parameters.The simulation is carried out by using fixed resistance capacitance and variable resistance capacitor respectively.The accuracy of variable resistance and capacitance model is 2.9%,which verifies the validity of the proposed model.

Time-varying gravity field model of Sichuan-Yunnan region based on the equivalent mass source model

High-precision time-varying gravity field is an effective way to study the internal mass movement and understanding the spatio-temporal evolution process of the geodynamic system.Compared to the satellite gravity measurement,the repeated terrestrial gravity observation can provide a more high-order signal related to the shallow crust and subsurface.However,the suitable and unified method for gravity model estimation is a key problem for further applications.In this study,we introduce the spherical hexahedron element to simulate the field source mass and forward model the change of gravity field located at the Sichuan-Yunnan region(99—104°E,23—29°N)in the four epochs from 2015 to 2017.Compared to the experimental results based on Slepian or spherical harmonics frequency domain method,this alternative approach is suitable for constructing the equivalent mass source model of regional-scale gravity data,by introducing the first-order smooth prior condition of gravity time-varying signal to suppress the high-frequency component of the signal.The results can provide a higher spatial resolution reference for regional gravity field modeling in the Sichuan-Yunnan region.

Research on Equivalent Modeling Method of AC-DC Power Networks Integrating with Renewable Energy Generation

Along with the increasing integration of renewable energy generation in AC-DC power networks,investigating the dynamic behaviors of this complex system with a proper equivalent model is significant.This paper presents an equivalent modeling method for the AC-DC power networks with doubly-fed induction generator(DFIG)based wind farms to decrease the simulation scale and computational burden.For the AC-DC power networks,the equivalent modeling strategy in accordance with the physical structure simplification is stated.Regarding the DFIG-based wind farms,the equivalent modeling based on the sequential identification of multi-machine parameters using the improved chaotic cuckoo search algorithm(ICCSA)is conducted.In light of the MATLAB simulation platform,a two-zone four-DC interconnected power grid with wind farms is built to check the efficacy of the proposed equivalentmodelingmethod.Fromthe simulation analyses and comparative validation in different algorithms and cases,the proposed method can precisely reflect the steady and dynamic performance of the demonstrated system under N-1 and N-2 fault scenarios,and it can efficiently achieve the parameter identification of the wind farms and fulfill the equivalent modeling.Consequently,the proposed approach’s effectiveness and suitability are confirmed.

Second-Order MaxEnt Predictive Modelling Methodology. II: Probabilistically Incorporated Computational Model (2nd-BERRU-PMP)

This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and parameters. This methodology is designated by the acronym 2nd-BERRU-PMP, where the attribute “2nd” indicates that this methodology incorporates second- order uncertainties (means and covariances) and second (and higher) order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best-Estimate Results with Reduced Uncertainties” and the last letter (“P”) in the acronym indicates “probabilistic,” referring to the MaxEnt probabilistic inclusion of the computational model responses. This is in contradistinction to the 2nd-BERRU-PMD methodology, which deterministically combines the computed model responses with the experimental information, as presented in the accompanying work (Part I). Although both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies yield expressions that include second (and higher) order sensitivities of responses to model parameters, the respective expressions for the predicted responses, for the calibrated predicted parameters and for their predicted uncertainties (covariances), are not identical to each other. Nevertheless, the results predicted by both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies encompass, as particular cases, the results produced by the extant data assimilation and data adjustment procedures, which rely on the minimization, in a least-square sense, of a user-defined functional meant to represent the discrepancies between measured and computed model responses.

Second-Order MaxEnt Predictive Modelling Methodology. I: Deterministically Incorporated Computational Model (2nd-BERRU-PMD)

This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2nd-BERRU-PMD. The attribute “2nd” indicates that this methodology incorporates second-order uncertainties (means and covariances) and second-order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”) in the acronym indicates “deterministic,” referring to the deterministic inclusion of the computational model responses. The 2nd-BERRU-PMD methodology is fundamentally based on the maximum entropy (MaxEnt) principle. This principle is in contradistinction to the fundamental principle that underlies the extant data assimilation and/or adjustment procedures which minimize in a least-square sense a subjective user-defined functional which is meant to represent the discrepancies between measured and computed model responses. It is shown that the 2nd-BERRU-PMD methodology generalizes and extends current data assimilation and/or data adjustment procedures while overcoming the fundamental limitations of these procedures. In the accompanying work (Part II), the alternative framework for developing the “second- order MaxEnt predictive modelling methodology” is presented by incorporating probabilistically (as opposed to “deterministically”) the computed model responses.

Second-Order MaxEnt Predictive Modelling Methodology. III: Illustrative Application to a Reactor Physics Benchmark

This work illustrates the innovative results obtained by applying the recently developed the 2nd-order predictive modeling methodology called “2nd- BERRU-PM”, where the acronym BERRU denotes “best-estimate results with reduced uncertainties” and “PM” denotes “predictive modeling.” The physical system selected for this illustrative application is a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation (involving 21,976 uncertain parameters), the solution of which is representative of “large-scale computations.” The results obtained in this work confirm the fact that the 2nd-BERRU-PM methodology predicts best-estimate results that fall in between the corresponding computed and measured values, while reducing the predicted standard deviations of the predicted results to values smaller than either the experimentally measured or the computed values of the respective standard deviations. The obtained results also indicate that 2nd-order response sensitivities must always be included to quantify the need for including (or not) the 3rd- and/or 4th-order sensitivities. When the parameters are known with high precision, the contributions of the higher-order sensitivities diminish with increasing order, so that the inclusion of the 1st- and 2nd-order sensitivities may suffice for obtaining accurate predicted best- estimate response values and best-estimate standard deviations. On the other hand, when the parameters’ standard deviations are sufficiently large to approach (or be outside of) the radius of convergence of the multivariate Taylor-series which represents the response in the phase-space of model parameters, the contributions stemming from the 3rd- and even 4th-order sensitivities are necessary to ensure consistency between the computed and measured response. In such cases, the use of only the 1st-order sensitivities erroneously indicates that the computed results are inconsistent with the respective measured response. Ongoing research aims at extending the 2nd-BERRU-PM methodology to fourth-order, thus enabling the computation of third-order response correlations (skewness) and fourth-order response correlations (kurtosis).

Small-Signal Equivalent Circuit Modeling of a Photodetector Chip

A small-signal equivalent circuit model and the ted. The equivalent lumped circuit, which takes the main extraction techniques for photodetector chips are presen- factors that limit a photodetector＇s RF performance into consideration,is first determined based on the device＇s physical structure. The photodetector＇s S parameters are then on-wafer measured, and the measured raw data are processed with further calibration. A genetic algorithm is used to fit the measured data, thereby allowing us to calculate each parameter value of the model. Experimental resuits show that the modeled parameters are well matched to the measurements in a frequency range from 130MHz to 20GHz, and the proposed method is proved feasible. This model can give an exact description of the photodetector chip＇s high frequency performance,which enables an effective circuit-level prediction for photodetector and optoelectronic integrated circuits.

Retrieving chlorophyll content and equivalent water thickness of Moso bamboo(Phyllostachys pubescens) forests under Pantana phyllostachysae Chao-induced stress from Sentinel-2A/B images in a multiple LUTs-based PROSAIL framework

Biochemical components of Moso bamboo(Phyllostachys pubescens)are critical to physiological and ecological processes and play an important role in the material and energy cycles of the ecosystem.The coupled PROSPECT with SAIL(PROSAIL)radiative transfer model is widely used for vegetation biochemical component content inversion.However,the presence of leaf-eating pests,such as Pantana phyllostachysae Chao(PPC),weakens the performance of the model for estimating biochemical components of Moso bamboo and thus must be considered.Therefore,this study considered pest-induced stress signals associated with Sentinel-2A/B images and field data and established multiple sets of biochemical canopy reflectance look-up tables(LUTs)based on the PROSAIL framework by setting different parameter ranges according to infestation levels.Quantitative inversions of leaf area index(LAI),leaf chlorophyll content(LCC),and leaf equivalent water thickness(LEWT)were derived.The scale conversions from LCC to canopy chlorophyll content(CCC)and LEWT to canopy equivalent water thickness(CEWT)were calculated.The results showed that LAI,CCC,and CEWT were inversely related with PPC-induced stress.When applying multiple LUTs,the p-values were<0.01;the R2 values for LAI,CCC,and CEWT were 0.71,0.68,and 0.65 with root mean square error(RMSE)(normalized RMSE,NRMSE)values of 0.38(0.16),17.56μg cm-2(0.20),and 0.02 cm(0.51),respectively.Compared to the values obtained for the traditional PROSAIL model,for October,R2 values increased by 0.05 and 0.10 and NRMSE decreased by 0.09 and 0.02 for CCC and CEWT,respectively and RMSE decreased by 0.35μg cm-2 for CCC.The feasibility of the inverse strategy for integrating pest-induced stress factors into the PROSAIL model,while establishing multiple LUTs under different pest-induced damage levels,was successfully demonstrated and can potentially enhance future vegetation parameter inversion and monitoring of bamboo forest health and ecosystems.

Equivalent series system to model a multiple friction pendulum system with numerous sliding interfaces for seismic analyses

Current structural analysis software programs offer few if any applicable device-specifi c hysteresis rules or nonlinear elements to simulate the precise mechanical behavior of a multiple friction pendulum system(MFPS) with numerous sliding interfaces.Based on the concept of subsystems,an equivalent series system that adopts existing nonlinear elements with parameters systematically calculated and mathematically proven through rigorous derivations is proposed.The aim is to simulate the characteristics of sliding motions for an MFPS isolation system with numerous concave sliding interfaces without prior knowledge of detailed information on the mobilized forces at various sliding stages.An MFPS with numerous concave sliding interfaces and one articulated or rigid slider located between these interfaces is divided into two subsystems: the fi rst represents the concave sliding interfaces above the slider,and the second represents those below the slider.The equivalent series system for the entire system is then obtained by connecting those for each subsystem in series.The equivalent series system is validated by comparing numerical results for an MFPS with four sliding interfaces obtained from the proposed method with those from a previous study by Fenz and Constantinou.Furthermore,these numerical results demonstrate that an MFPS isolator with numerous concave sliding interfaces,which may have any number of sliding interfaces,is a good isolation device to protect structures from earthquake damage through appropriate designs with controllable mechanisms.

Seepage simulation of high concrete-faced rockfill dams based on generalized equivalent continuum model

This research focused on the three-dimensional(3 D) seepage field simulation of a high concrete-faced rockfill dam(CFRD) under complex hydraulic conditions. A generalized equivalent continuum model of fractured rock mass was used for equivalent continuous seepage field analysis based on the improved node virtual flow method. Using a high CFRD as an example, the generalized equivalent continuum range was determined, and a finite element model was established based on the terrain and geological conditions, as well as structural face characteristics of the dam area. The equivalent seepage coefficients of different material zones or positions in the dam foundation were calculated with the Snow model or inverse analysis. Then, the 3 D seepage field in the dam area was calculated under the normal water storage conditions, and the corresponding water head distribution, seepage flow, seepage gradient, and seepage characteristics in the dam area were analyzed. The results show that the generalized equivalent continuum model can effectively simulate overall seepage patterns of the CFRD under complex hydraulic conditions and provide a reference for seepage analysis of similar CFRDs.

Hybrid Model Testing Technique for Deep-Sea Platforms Based on Equivalent Water Depth Truncation

In this paper, an inner turret moored FPSO which works in the water of 320 m depth, is selected to study the socalled ＂passively-truncated ＋ numerical-simulation＂ type of hybrid model testing technique while the tnmcated water depth is 160 m and the model scale ）, = 80. During the investigation, the optimization design of the equivalent-depth truncated system is performed by using the similarity of the static characteristics between the truncated system and the full depth one as the objective function. According to the truncated system, the corresponding physical test model is made. By adopting the coupling time domain simulation method, the tnmcated system model test is numerically reconstructed to carefully verify the computer simulation software and to adjust the corresponding hydrodynamic parameters. Based on the above work, the numerical extrapolation to the full depth system is performed by using the verified computer software and the adjusted hydrodyrmmic parameters. The full depth system model test is then performed in the basin and the results are compared with those from the numerical extrapolation. At last, the implementation procedure and the key technique of the hybrid model testing of the deep-sea platforms are summarized and printed. Through the above investigations, some beneficial conclusions are presented.

EQUIVALENT NORMAL CURVATURE APPROACH MILLING MODEL OF MACHINING FREEFORM SURFACES

A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry. Moreover, a specialized whirlwind milling tool and a 5-axis CNC horizontal milling machine are introduced. This new milling model can efficiently enlarge the material removal volume at the tip of the whirlwind milling tool and improve the producing capacity. The machining strategy of this model is to regulate the orientation of the whirlwind milling tool relatively to the principal directions of the workpiece surface at the point of contact, so as to create a full match with collision avoidance between the workpiece surface and the symmetric rotational surface of the milling tool. The practical results show that this new milling model is an effective method in machining complex three- dimensional surfaces. This model has a good improvement on finishing machining time and scallop height in machining the freeform surfaces over other milling processes. Some actual examples for manufacturing the freeform surfaces with this new model are given.

Simulation study of a magnetocardiogram based on a virtual heart model:effect of a cardiac equivalent source and a volume conductor

In this paper, we present a magnetocardiogram （MCG） simulation study using the boundary element method （BEM） and based on the virtual heart model and the realistic human volume conductor model. The different contributions of cardiac equivalent source models and volume conductor models to the MCG are deeply and comprehensively investigated. The single dipole source model, the multiple dipoles source model and the equivalent double layer （EDL） source model are analysed and compared with the cardiac equivalent source models. Meanwhile, the effect of the volume conductor model on the MCG combined with these cardiac equivalent sources is investigated. The simulation results demonstrate that the cardiac electrophysiological information will be partly missed when only the single dipole source is taken, while the EDL source is a good option for MCG simulation and the effect of the volume conductor is smallest for the EDL source. Therefore, the EDL source is suitable for the study of MCG forward and inverse problems, and more attention should be paid to it in future MCG studies.

NUMERICAL SIMULATION OF METHANE-AIR TURBULENT JET FLAME USING A NEW SECOND-ORDER MOMENT MODEL

A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using the well-known EBU-Arrhenius model and the original second-order moment model. The comparison shows the advantage of the new model that it requires almost the same computational storage and time as that of the original second-order moment model, but its modeling results are in better agreement with experiments than those using other models. Hence, the new second-order moment model is promising in modeling turbulent combustion with NOx formation with finite reaction rate for engineering application.

Equivalent continuum modeling of beam-like truss structures with flexible joints

The paper investigated the equivalent continuum modeling of beam-like repetitive truss structures considering the flexibility of joints,which models the contact between the truss member and joint by spring-damper with six directional stiffnesses and dampings.Firstly,a two-node hybrid joint-beam element was derived for modeling the truss member with flexible end joints,and a condensed model for the repeating element with flexible joints was obtained.Then,the energy equivalence method was adopted to equivalently model the truss structure with flexible joints and material damping as a spatial viscoelastic anisotropic beam model.Afterwards,the equations of motion for the equivalent beam model were derived and solved analytically in the frequency domain.In the numerical studies,the correctness of the presented method was verified by comparisons of the natural frequencies and frequency responses evaluated by the equivalent beam model with the results of the finite element method model.

Optimum design of equivalent accelerated life testing plans based on proportional hazards-proportional odds model

The optimum design of equivalent accelerated life testing plan based on proportional hazards-proportional odds model using D-optimality is presented. The defined equivalent test plan is the test plan that has the same value of the determinant of Fisher information matrix. The equivalent test plan of step stress accelerated life testing （SSALT） to a baseline optimum constant stress accelerated life testing （CSALT） plan is obtained by adjusting the censoring time of SSALT and solving the optimization problem for each case to achieve the same value of the determinant of Fisher information matrix as in the baseline optimum CSALT plan. Numer- ical examples are given finally which demonstrate the equivalent SSALT plan to the baseline optimum CSALT plan reduces almost half of the test time while achieving approximately the same estimation errors of model parameters.

Modelling of Quasi 3-D Groundwater Flow and Studying of Equivalent Drainage Boundary in Beihai Peninsula,Guangxi

This paper describes a quasi 3-D finite element model of the groundwater flow in two -aquifer system which is constructed from a sequence of aquifer flow equations coupled by leakage terms representing flow through the aquitard . It is applied to evaluate the maximum rate of groundwater resources exploited from the coastal aquifer without seawater intrusion . The main task in this model is to determine the drainage boundary of the aquifer extending under the sea . The information of the boundary can be obtained from the fluctuations of the groundwater level caused by sea-tide fluctuations . A new idea, Equivalent Drainage Boundary (EDB), is proposed and the corresponding methods , determining the EDB, are developed with tidal fluctuations data observed in boreholes . The quasi 3-D model and the methods determining EDB have been applied to the aquifer system of Beihai peninsula , Guangxi Autonomous Region of China for calculating the available groundwater resources .

Comparison of a Full Second-Order Moment Model and an Algebraic Stress Two-Phase Turbulence Model for Simulating Bubble-Liquid Flows in a Bubble Column

A full second-order moment (FSM) model and an algebraic stress (ASM) two-phase turbulence modelare proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column. Predictiongives the bubble and liquid velocities, bubble volume fraction, bubble and liquid Reynolds stresses and bubble-liquidvelocity correlation. For predicted two-phase velocities and bubble volume fraction there is only slight differencebetween these two models, and the simulation results using both two models are in good agreement with the particleimage velocimetry (PIV) measurements. Although the predicted two-phase Reynolds stresses using the FSM are insomewhat better agreement with the PIV measurements than those predicted using the ASM, the Reynolds stressespredicted using both two models are in general agreement with the experiments. Therefore, it is suggested to usethe ASM two-phase turbulence model in engineering application for saving the computation time.

Closed-form steady-state solutions for forced vibration of second-order axially moving systems

Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.

Calculation Model of Equivalent Strength for Induced Crack Based on Double-K Fracture Theory and Its Optimizing Setting in RCC Arch Dam

By means of fracture testing on roller-compacted concrete （RCC） three-point bending beams with two different specimen sizes, the P-CMOD complete curve for RCC was gained. Furthermore, by applying double-K fracture theory, KiniⅠC,KunⅠC, as well as the critical effective crack length and the critical crack tip opening displacement, were evaluated. Based on the double-K fracture parameters above, the calculation model of equivalent strength for induced crack was established, thus the calculation method on its initiation, stable propagation and unstable fracture was ascertained. Moreover, the finite element simulation analysis of stress field in ShaPai arch dam and the on-site observational splaying points of induced crack at different altitudes validated the reliability of the model. Finally, crack inducer′s optimal setting in RCC arch dam was studied. It improves the design level of induced crack in RCC arch dam and satisfies the necessity of engineering practice.