Equivalent Modeling Method Research Articles

Equivalent Beam Model for Spatial Repetitive Lattice Structures with Hysteretic Nonlinear Joints

This study presented an equivalent modeling method for analysis of the fundamental harmonic response of the spatial repetitive lattice structures with hysteretic nonlinear joints. Firstly, the joint was modelled as a spatial nonlinear spring-damper system with bilinear hysteresis, the equivalent linear stiffness and viscous damping coefficients of the hysteretic joint were derived using the describing function method. Subsequently, high-precision displacement and rotation fields that consider the warping and distortion of the cross section of the lattice structure were presented for the repeating element and the equivalent continuum modeling method based on the principle of energy equivalence was adopted to obtain an 8-DOFs spatial beam element for the repeating element of the lattice structure. Afterwards, the equations of motion of the equivalent beam model for the lattice structure were established in the frequency domain and solved by using the Newton-Raphson method. In the numerical studies, the joints with axial nonlinearity and rotational nonlinearity were considered, and the influences of joint parameters and excitation amplitude on the dynamic response of the lattice structure were investigated. The correctness of the presented modeling method was verified by comparison with the nonlinear finite element model of the original structure.

Dynamic equivalent modeling for power converter based on LSTM neural network in wide operating range

The internal parameters and topology of the power converter are unknown in some practical cases. Existing modeling methods based on impedance frequency scanning method can only guarantee that the dynamic modeling is effective at a single working point. To make the established dynamic model effective in a wide range, an equivalent modeling method for power converter based LSTM Neural Network is presented. At first, the equivalence of black-box modeling problem and deep loop neural network is studied. Then, dynamic modeling method black-box power converter on wide operating range by using LSTM neural network is proposed. Finally, the simulation results under large disturbance and multi-operating points show that the proposed method is effective under wide operation range.

A survey on energy efficiency intrabody communication techniques for wearable devices

Currently, wireless body area networks (WBANs) are developing rapidly. Miniature wearable devices which are light weight and low power consumption can be developed using modern technology. However, the WBANs research challenge is power consumption. This paper provides the two intrabody communication (IBC) methods review. The equivalent body channel models and modeling methods are analyzed. The conventional IBC WBANs architecture is reviewed and novel energy-efficient architecture and an IBC WBANs data transmission technique are proposed. The experiment was conducted in order to measure the BodyCom mobile module output power. The comparative analysis showed that the power consumption of the IBC proposed technique is 7 times lower than Bluetooth LE, and 14 times lower than ZigBee. The proposed technique can be applied in areas such as home and industrial automation, medical appliances, wearable devices, security, and internet of things.

Mechanical Structural Interference Detection for Dedicated Hybrid Transmissions

Abstract Planetary gear set (PGS) has been one of the best components to constitute a transmission configuration, including the dedicated hybrid transmission (DHT). Using different synthesis approaches, the DHT configurations can be obtained through algorithms. However, different synthesis results correspond to different connection states of the planetary gear system. There are a certain number of results that violate the motion requirements of the mechanical principal need to be detected and removed. Therefore, this paper presents a novel modeling method to systematically remove the interference structures, with graph theory in structural synthesis. Based on the original graph theory, this paper proposes an equivalent replacement modeling method to convert the motor graph model into a brake-like graph model. Based on the conversion, avoid the appearance of the hanging points in the graph model. By applying the proposed approach, a DHT structure proves the feasibility of the method. The proposed detection approach can systematically detect all the PGS-based transmission with multi-PGSs, multi-shifting elements, and multi-power sources.

Robustness-Improved Method for Measurement-Based Equivalent Modeling of Active Distribution Network

Accurate equivalent model can be efficient to analyze the dynamic properties of active distribution network (ADN) as well as assess their impacts on stabilities of interconnected power system. However, due to the stochastic nature of renewable resources and time-varying configurations of load conditions, traditional ADN equivalent model may not be robust enough to different operation conditions. To overcome the limitations, this article proposed a robustness-improved method for dynamic equivalent modeling of ADN. To sketch out the most representative operation conditions of ADN, two-step clustering method with fisher discriminant analysis are used for grouping of operation conditions featured characteristic data sets. With the key parameter based identification technique applied, the multiple solution issue in parameter identification process could be effectively avoided. To further enhance the robustness of equivalent model, long short-term memory neural network is adopted to generalize the identified parameters. The performance of proposed modeling method is comprehensively evaluated by an actual ADN based verification cases.

Combined backbone application on numerical simulations and a model experiment of a 20,000 TEU container ship

For the large-scale development and large opening characteristics of container ships, the characteristics of springing in waves has become more complex. It is thus urgent to find reasonable equivalent principles to solve the dilemma of simultaneously simulating vertical, horizontal and torsional vibrations in model tests. Meanwhile, to avoid the complexity and time-consuming nature of full three-dimensional modelling, a large-scale combined beam model is adopted to simulate three-dimensional coupled vibrations and the positions of the neutral axis and torsion centre. Combined with the finite element method, a 3D equivalent modelling method of the combined model is analysed in detail, and the stiffness influence of transverse bulkheads on the coupled vibrations mode is revealed. Furthermore, the elastic modal responses, vibration principles and waves load in the fluid-structure interaction vibrations are assessed and investigated by the three-dimensional linear hydroelastic mechanics method in the frequency- and time-domains. Then, the scheme and load measurement method in the model test in the wave basin are put forward, and the experimental data and numerical calculation results are compared and found to be consistent. The proposed the equivalent combined beam model is of great significance for model tests and numerical analyses of very large container ships.

Evaluation of equivalent friction damping ratios at bearings of welded large-scale domes subjected to earthquakes

The major sources of damping in steel structures are within the joints and the structural material. For welded large-scale single-layer lattice domes subjected to earthquake ground motions, the stick-slip phenomenon at the bearings is an important source of the energy dissipation. However, it has not been extensively investigated. In this study, the equivalent friction damping ratio (EFDR) at the bearings of a welded large-scale single-layer lattice dome subjected to earthquake ground motions is quantified using an approximate method based on the energy balance concept. The complex friction behavior and energy dissipation between contact surfaces are investigated by employing an equivalent modeling method. The proposed method uses the stick-slip-hook components with a pair of circular isotropic friction surfaces having a variable friction coefficient to model the energy loss at the bearings, and the effect of the normal force on the friction force is also considered. The results show that the EFDR is amplitude-dependent and is related to the intensity of the ground motions; it exhibits complex characteristics that cannot be described by the conventional models for damping ratios. A parametric analysis is performed to investigate in detail the effects of important factors on the EFDR. Finally, the friction damping mechanism at bearings is discussed. This study enables researchers and engineers to have a better understanding of the essential characteristics of friction damping under earthquake ground motions.

Joint estimation of SOC and SOH for lithium-ion batteries based on EKF multiple time scales

PurposeThe operation state of lithium-ion battery for vehicle is unknown and the remaining life is uncertain. In order to improve the performance of battery state prediction, in this paper, a joint estimation method of state of charge (SOC) and state of health (SOH) for lithium-ion batteries based on multi-scale theory is designed.Design/methodology/approachIn this paper, a joint estimation method of SOC and SOH for lithium-ion batteries based on multi-scale theory is designed. The venin equivalent circuit model and fast static calibration method are used to fit the relationship between open-circuit voltage and SOC, and the resistance and capacitance parameters in the model are identified based on exponential fitting method. A battery capacity model for SOH estimation is established. A multi-time scale EKF filtering algorithm is used to estimate the SOC and SOH of lithium-ion batteries.FindingsThe SOC and SOH changes in dynamic operation of lithium-ion batteries are accurately predicted so that batteries can be recycled more effectively in the whole vehicle process.Originality/valueA joint estimation method of SOC and SOH for lithium-ion batteries based on multi-scale theory is accurately predicted and can be recycled more effectively in the whole vehicle process.

A Novel Dual Correction Extended Kalman Filtering Algorithm for The State of Charge Real-Time Estimation of Packing Lithium-Ion Batteries

This paper explores the state estimation method of lithium-ion battery pack through theoretical analysis and experimental research. Combining the advantages of the empirical models of various electrochemical models, a new type of composite electrochemistry-dual circuit polarization (E-DCP) model is proposed to better reflect the dynamic performance of the power lithium-ion battery under the conditions of meeting its safe and reliable energy supply requirements. Using the multi-innovation least squares (MILS) algorithm to identify the parameters in the E-DCP model online, so that it has the characteristics of high data utilization efficiency and high parameter identification accuracy. The battery charge and discharge efficiency function is introduced to dynamically modify the battery capacity, and the dynamic function is used to improve the Kalman gain in the extended Kalman filter (EKF), a new type of based on dynamic function improvement and combined with actual capacity correction (FC-DEKF) algorithm is applied to the estimation of battery pack operating characteristics, which solves the problem that the traditional EKF algorithm is difficult to estimate errors when the system input change rate is large. The experimental results of urban dynamometer driving schedule (UDDS) and complex charge-discharge cycle test show that the maximum error of terminal voltage does not exceed 0.04V, the accuracy is 99.05%, and the errors of MILS algorithm combined with FC-DEKF algorithm for SOC estimation are all within 1%. The proposed equivalent circuit modeling method and state estimation correction strategy provide a theoretical basis for the reliable application of high-power lithium-ion battery packs.

Modeling of Loaded Nonuniform Grid Power Distribution Network With Arbitrary Shapes

This article presents an equivalent circuit modeling method for the impedance calculation of the loaded power distribution network (PDN). The topology of the proposed equivalent circuit is based on the modal field analysis of the PDN, so that the elements in the circuit possess certain physical meaning. The element values in the equivalent circuit are extracted from a circuit perspective. Using the proposed equivalent circuit and the interpolation method, the calculation efficiency of the proposed method is greatly improved. Compared with the traditional mode method which is limited for the modeling of the regular-shaped PDN, the proposed equivalent circuit method can be used for the modeling of both grid-type and plane PDNs with nonuniform, irregular-shaped, and shorting via-loaded structures. To verify the accuracy of the proposed equivalent circuit, two different samples are simulated and fabricated, and the impedance obtained from the measurement shows good agreements with that obtained from the proposed method.

Finding a better fit for lithium ion batteries: A simple, novel, load dependent, modified equivalent circuit model and parameterization method

Equivalent circuit models (ECM) of lithium ion batteries are used in many applications because of their ease of implementation and low complexity. The accuracy of an ECM is critical to the functionality and usefulness of the battery management system (BMS). The ECM accuracy depends on the parametrization method, and therefore different experimental techniques and model parameter identification methods (PIM) have been widely studied. Yet, how to account for significant changes in time constants between operation under load and during relaxation has not been resolved. In this work a novel PIM and modified ECM is presented that increases accuracy by 77.4% during drive cycle validation and 87.6% during constant current load validation for a large format lithium iron phosphate prismatic cell. The modified ECM uses switching RC network values for each phase, which is significant for this cell and particularly at low state-of-charge for all lithium ion batteries. Different characterisation tests and the corresponding experimental data have been trained together across a complete State-of-Charge (SoC) and temperature range, which enables a smooth transition between identified parameters. Ultimately, the model created using parameters captured by the proposed PIM shows an improved model accuracy in comparison with conventional PIM techniques.

Nonlinear dynamic responses of beamlike truss based on the equivalent nonlinear beam model

The main goal of this paper is to develop an equivalent nonlinear beam model (ENBM) for forced vibration analysis of the nonlinear beamlike truss (NBT) and its numerical implementation for describing the nonlinear behaviors of the periodic NBT. For the equivalent dynamic modeling method based on the energy equivalence principle of the truss structures, most of the existing approaches focus on studying the linear characteristic which cannot satisfy the nonlinear dynamic analytical requirement. Here, we extend the equivalent dynamic modeling to nonlinear forced vibration responses of the large NBT civil engineering structure with two pinned ends. We introduce the geometric nonlinearity into the equivalent dynamic model using the von Karman nonlinear strain-displacement relationship to imitate the nonlinear behaviors of the beamlike truss. On the basis of the Hamilton principle, the fourth-order governing partial differential equations of motion of the ENBM are obtained and solved utilizing the Galerkin method. It is shown that the ENBM accurately captures the nonlinear dynamic response of the beamlike truss subjected to external load by using the first four order modes. In order to showcase the efficiency and accuracy of the ENBM, time histories, phase maps and fast Fourier transform frequency spectra are investigated for the NBT and the ENBM under different external excitation magnitudes and frequencies. Comparisons between results of the ENBM and those obtained from the finite element simulations of the NBT show good agreements and identify the periodic motions of them. Furthermore, the effect of the external loading and damping parameters on the frequency-response and force-response curves is discussed. In addition, computing time of the proposed ENBM are compared with that of the full-scale finite element model in ANSYS so as to highlight the significant less computational cost of the equivalent nonlinear dynamic modeling. Particularly, the proposed ENBM can achieve the nonlinear mechanism of the NBT in analytical method and design the low-order control law conveniently.

Comparative study of dynamically equivalent modeling methods for honeycomb sandwich structure: numerical simulations and experiments

Abstract. The structure of the lightweight honeycomb sandwich panel is complex. Thus, establishing an equivalent simplified model is indispensable to improve the efficiency of the dynamic analysis of honeycomb sandwich panels. In this paper, three commonly used dynamically equivalent modeling methods for honeycomb sandwich panel are studied: a dynamically equivalent method based on laminated plate theory, a single-layer plate equivalent method based on the theory of Hoff (1948), and an improved equivalent method based on Allen (1969). Using theoretical study, numerical simulations, and experiments, the applicability of these equivalent methods and the effect of design parameters on the dynamic characteristics are studied, and the optimal dynamically equivalent method for honeycomb sandwich panels is obtained.

Ring coils heat source numerical modeling and thermal interference characteristics analysis of truncated cone helix energy pile

The truncated cone helix energy pile (CoHEP) is a new type of environmentally-friendly and cost-effective ground heat exchanger with a strong heat transfer capacity. However, its heat transfer characteristics, especially thermal interference, have not yet been fully interpreted due to its complex geometry and semi-infinite medium. In order to understand the thermal interference in the radial and generatrix directions, an efficient modeling method that regards a spiral pipe as a series of ring coils was proposed in this paper based on their structural characteristics and makes these ring coils equivalent to heat sources that are based on heat transfer in the pipe. The thermal interference index based on the temperatures at typical locations was defined to describe the thermal interference of CoHEP. And the accuracy and high efficiency of equivalent heat source modeling method was verified by field experiments. Finally, the CoHEPs of cylindrical energy pile at a cone angle of 0°, 5°, 10°, 15° and 20° were numerically simulated. The results show that the thermal interference intensity decreased with the increase of the cone angle, the maximum thermal interference intensity in the radial direction was 4.54 m·°C/W, 4.41 m·°C/W, 4.37 m·°C/W, 4.31 m·°C/W, and 4.23 m·°C/W respectively, and that in the generatrix direction was 3.96 m·°C/W, 3.91 m·°C/W, 3.88 m·°C/W, 3.84 m·°C/W and 3.77 m·°C/W, respectively, proving that the CoHEP with a large cone angle can significantly reduce thermal interference. Meanwhile, a scientific zone criterion of the heat transfer characteristics of CoHEP was given quantitatively to evaluate the thermal interference of CoHEP from the interference intensity in the radial direction and directions. Particularly, three zones of weak thermal interference zone, transition thermal interference zone and serious thermal interference zone were presented. There was no difference in the proportions of weak zone, transition zone and serious zone for 0°5°, 10° and 15°, which were 7.69%, 15.38% and 76.92%, respectively. The proportions of thermal interference weak zone, transition zone and serious zone in the radial direction of 20° CoHEP were 7.69%, 23.08% and 69.23% respectively, and that of thermal interference in the generatrix direction were 7.69%, 17.05% and 75.26%, respectively, implying that CoHEP with a large cone angle exhibits better heat transfer characteristics and is not easy to develop into a region with severe thermal interference.

Experimental and theoretical investigation of bifurcated wafer warpage evolution in the wafer level packaging processes

Wafer warpage, which mainly originated from thermal mismatch between the materials, has become serious in wafer level packaging (WLP) as larger diameter and thinner wafers are required currently. In this paper, three-dimensional wafer warpage profile and the warpage evolution during typical fan-in WLP processes including wafer thinning process were characterized in situ. Special attention was paid to the bifurcated phenomenon. Prior to the wafer thinning process, the wafer deformed into a bowl shape which was caused by polyimide (PI) curing. A distinct bifurcation behavior appeared and the wafer warped into a cylindrical shape when the wafer was thinned below 270 μm. This bifurcation behavior was systematically analyzed by theoretical analysis and finite element analysis (FEA). Equivalent material model method and perturbation method were employed to simplify the FEA model and incur the bifurcation behavior, respectively.

Probabilistic active distribution network equivalence with correlated uncertain injections for grid analysis

Equivalent modelling for active distribution networks (ADNs) is essential for improving the efficiency of analysing transmission networks. Current equivalent modelling methods for ADNs neglect the probabilistic characteristics of renewable energy sources (RESs) and loads. To address this issue, this study proposes a probabilistic equivalent modelling method (PEMM) for ADNs considering the uncertainty of RESs and loads. The uncertainty of the RESs and loads is transferred to the equivalent boundary bus injection using the properties of cumulant and power transfer matrices. The PEMM is extended to incorporate the correlations of RESs through an orthogonal transformation. A sampling method using the Gaussian copula function is employed to generate the correlated samples and the joint cumulants, providing the input data for the PEMM. The comparative results of the case studies on two different test systems demonstrate the effectiveness of the PEMM. The equivalent model developed in this study is a practical solution for analysing the transmission network efficiently and taking the uncertainty of RESs and loads in the ADNs into account simultaneously.

High-Speed Electromagnetic Transient (EMT) Equivalent Modelling of Power Electronic Transformers

The high-speed accurate electromagnetic transient (EMT) simulation of the power electronic transformers (PET) has become a challenge, due to the microsecond-range time steps and the large number of high-frequency semiconductor switches and isolating transformers. Taking the input-series-output-parallel (ISOP) connected cascaded H-bridge (CHB) type dual active bridge (DAB) based PET as an example, this paper proposes a general high-speed equivalent EMT modelling method of PET. First, the isolating transformer within each DAB is discretized into two-port Norton circuits. Second, each CHB-DAB is equivalent to two single-port circuits by eliminating the internal nodes. And the input-side is represented by a Thévenin circuit and the output-side is represented by a Norton circuit. Third, all the CHB-DABs are equivalent to a two-port circuit with all the internal node information preserved. Fourth, the implementation of PET blocking is also considered for startup and fault protective actions. Fifth, the stability of the proposed discrete decoupling method of the PET is verified that it does not introduce specific limitation on the simulation step size. Finally, the developed PET models on PSCAD/EMTDC are shown to be two orders of magnitude faster than the currently available fully-detailed models with negligible loss of accuracy.

Seismic site period studies for nonlinear soil in the city of Ottawa, Canada

Site period maps at various strain levels were developed for the combined cities of Ottawa and Gatineau in eastern Ontario and western Quebec. These maps were developed to support earthquake response studies in areas containing post-glacial, soft, silty-clayey sediments, which comprise 60% of the urban areas. Approximately 21,700 boreholes and over 1000 surface and downhole geophysical measurements were utilized to prepare the maps.The maps include the following:1) A T0,ESL map is based on an equivalent single-layer modelling method (ESL) as described in the National Building Code of Canada using the 4H/V approach.2) A T0,HVSR map is based on the micro-tremor HVSR method, which systematically deviates from T0,ESL for weak motion. Such variances between the calculated T0,ESL and measured T0,HVSR may be associated with significant shear wave velocity-depth gradients in the near-surface soft sediments.3) A T0,100 map is based on finite element modelling at the 100 cm/s/s level of shaking (0.1 g) at the onset of the “gray zone” between the linear and nonlinear soil responses.4) A T0,400 map is developed from a finite element model at the 400 cm/s/s level of shaking (0.4 g being the “design” earthquake for the city of Ottawa) This model evaluates the effect of nonlinear soft soil behaviour.The differences between these maps were examined and compared. The results indicated that nonlinear soil response at high levels of shaking strongly altered the resonance response toward much longer fundamental periods over large areas within the two cities.

Robust Design Optimization of SPMSM for Robotic Actuator Considering Assembly Imperfection of Segmented Stator Core

To be used as a robotic actuator, a surface-mounted permanent magnet synchronous motor (SPMSM) requires a low cogging torque characteristic. The aim of this study is to analyze and reduce the cogging torque's variation due to the assembly imperfection of the segmented stator that is widely used in the SPMSM. Considering the interconnection of the stator segments, an equivalent modeling method of the segmented stator with assembly imperfection is introduced. In addition, the variation in the cogging torque caused by the assembly imperfection is mathematically evaluated. Then, a robust design process that incorporates a sensitivity analysis and a robust design optimization is proposed. By using the proposed design, a robust optimum design model was built and its validity was verified through Monte Carlo simulation and tests.

Research of ASW-FCM-Based Algorithm for Clustered Wind Turbine Group Equivalent Modeling

A new dynamic equivalent modeling method for a wind farm composed of direct-drive wind turbines is proposed. Firstly, the effective input wind speed is calculated considering the wake effect and wind direction change between wind turbines, the operating characteristics is analyzed, the effective wind speed, rotor speed, pitch angle and output power that reflect the wind turbine operating characteristics are selected as the multi-grouping indicators. Secondly, an adaptive sample weighting fuzzy C-means clustering algorithm (ASW-FCM) considering the differences and correlations among turbines operating conditions is designed to cluster the wind farm optimally. Then the equivalent model of the clustered wind turbine group is established based on the principle that the output characteristics before and after the equivalence are equal. Finally, an actual wind farm system is used as an example for modeling and simulation to verify the rationality and accuracy of the equivalent modeling method.