Problem In Time Domain Research Articles

Energy-saving mechanism of series–parallel hybrid transmissions — A dynamic programming method based on matrix operations

The economic evaluation of hybrid transmission is a complicated numerical calculation problem in the finite time domain. Currently, employing traditional dynamic programming methods to evaluate a single design scheme consumes a lot of time, making it arduous to effectively compare performance disparities across various design schemes. This paper introduces a dynamic programming method based on matrix operations, enabling the determination of maximum energy-saving potential in hybrid transmission while reducing the evaluation time for a single design scheme from hours to less than 10 s. It unifies the design variables, constraints, and optimization objectives for multi-gear and multi-mode series–parallel hybrid transmissions (MGMM-SPHTs) during economic evaluation. By solving the performance of tens of thousands of design schemes, it is found that increasing the number of engine direct drive gears from 1 to 2 enhances the economy and power performance of series–parallel hybrid transmissions. For the optimal design scheme of Type-B vehicles, this enhancement results in a 1.712% increase in energy-saving efficiency and a 30.5% increment in power performance. Furthermore, this paper elucidates the adaptive relationship between MGMM-SPHTs and different vehicle types, revealing the energy-saving mechanisms under varied design schemes. This paper holds the promise of offering theoretical underpinnings and methodological instruments for selecting technical routes and optimizing design parameters for MGMM-SPHTs.

Simple, Method of Moments Solution for the Integral Equations for Multiple Dielectric Bodies of Arbitrary Shape in Time Domain

In this work, we present a straightforward and simple method of moments (MOM) solution procedure, with minimum mathematical manipulations, to solve the coupled integral equations for multiple, homogeneous and inhomogeneous, dielectric bodies of arbitrary shape directly in the time domain. The standard surface and volume integral equation formulations are used for homogeneous and inhomogeneous bodies, respectively. The numerical solution procedure does not involve a time-marching process as is usually adopted for time domain problems and seems to be one of the primary reasons for the late-time instabilities as a result of error accumulation. The present solution method is stable for a very long time as evidenced by several representative numerical examples presented for validation.

Research on Piano Curriculum Education and Its Performance Ecosystem Based on Network Flow Optimization

Abstract This paper investigates music education, where an efficient and accurate performance evaluation system in the piano teaching and performance ecosystem is increasingly becoming an essential tool for improving teaching quality and performance level. The objective evaluation of students’ performance skills can be achieved by carefully analyzing piano performances using the network flow optimization technique. This technique optimizes the performance evaluation system’s audio recognition ability by analyzing the piano audio signal and solving the multi-constraint nonlinear optimization problem in a limited time domain. This paper establishes a network flow optimization model, applies the multi-constraint nonlinear optimization technique, and combines the non-negative matrix decomposition and dynamic time regularization algorithm to analyze the piano performance for experiments. After optimization processing, hundreds of piano audio samples were collected, and the audio recognition accuracy was improved by 20%. By optimizing and processing the audio signals from the network stream, the evaluation system could detect polyphony more accurately and track the musical score effectively, improving accuracy and efficiency. Using the non-negative matrix decomposition algorithm, the accuracy of detecting polyphony can reach 85%, while the dynamic temporal regularization algorithm can match the position of the musical score with 95% accuracy. The accuracy of piano performance evaluation is optimized by this network flow optimization method, providing new technical means for music education, and promoting the quality of teaching and performance.

A Dual Neural Network Approach to Topology Optimization for Thermal-Electromagnetic Device Design

Topology optimization for engineering problems often requires multiphysics (dual objective functions) and multi-timescale considerations to be coupled with manufacturing constraints across a range of target values. We present a dual neural network approach to topology optimization to optimize a 3-dimensional thermal-electromagnetic device (optical shutter) for maximum temperature rise across a range of extinction ratios while also considering manufacturing tolerances. One neural network performs the topology optimization, allocating material to each sub-pixel within a repeating unit cell. The size of each sub-pixel is selected with manufacturing considerations in mind. The other neural network is trained to predict performance of the device using extinction ratio and temperature rise over a given time period. Training data is generated using a finite element model for both the electromagnetic wave frequency domain and thermal time domain problems. Optimized designs across a range of targets are shown.

An edge-based smoothed finite element method combined with Newmark method for time domain acoustic wave scattering problem

Time domain obstacle scattering widely exists in the scientific fields of geophysics, remote sensing, seismology, and medicine. However, it is difficult to solve the time domain scattering problems with arbitrarily shaped obstacles only within the fixed domain of interest. In this paper, an edge-based smoothed finite element method using linear triangular elements (ES-FEM-T3) combined with the Newmark method is proposed for the two-dimensional time domain acoustic scattering by an arbitrarily shaped obstacle. In the algorithm, a time domain transparent boundary condition (TBC) and the Newmark method are introduced to transform the time domain problem in an unbounded domain into a series of steady-state PDEs on a bounded domain, which is suitable for an arbitrary shaped obstacle scattering problem. In the numerical discretization, ES-FEM-T3 is used to construct a close-to-exact stiffness matrix by the smoothed gradient technique, making it space stable and obtaining more accurate results compared to FEM-T3. Especially, through in advance calculating the function σ(t), the convolution term in the time-domain TBC can be quickly calculated. Finally, through the numerical experiments, the effectiveness of the proposed method is demonstrated. Especially, ES-FEM-T3 can better improve the time convergence stability of the Newmark method and have better accuracy at γ = 0.5 compared to FEM-T3.

Static and dynamic analysis of couple-stress elastic structures by using peridynamic differential operator

In this paper, a peridynamic differential operator (PDDO) method is developed to analyze the static and dynamic responses of size-dependent elastic structures in the frame of a consistent couple stress theory (CCST). The displacement governing equations together with the boundary conditions of the couple-stress static problems are transformed from the local differential form to the nonlocal integral form through a fourth-order PDDO and then solved by a meshfree scheme. For dynamic cases, the time-domain problems are first transformed into frequency domain by Fourier transform, then solved by the PDDO meshless method in the frequency domain. The time-domain results are finally obtained by using an exponential window method (EWM). The size effects on the static and dynamic responses of some typical elastic problems are investigated by the developed PDDO method. A very high level of computational accuracy is achieved by comparing with the analytical solutions and the existing numerical results.

Multiple-scattering frequency-time hybrid solver for the wave equation in interior domains

This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensional interior spatial domains. The approach relies on four main elements, namely, (1) A multiple scattering strategy that decomposes a given interior time-domain problem into a sequence of limited-duration time-domain problems of scattering by overlapping open arcs, each one of which is reduced (by means of the Fourier transform) to a sequence of Helmholtz frequency-domain problems; (2) Boundary integral equations on overlapping boundary patches for the solution of the frequency-domain problems in point (1); (3) A smooth “Time-windowing and recentering” methodology that enables both treatment of incident signals of long duration and long time simulation; and, (4) A Fourier transform algorithm that delivers numerically dispersionless, spectrally-accurate time evolution for given incident fields. By recasting the interior time-domain problem in terms of a sequence of open-arc multiple scattering events, the proposed approach regularizes the full interior frequency domain problem—which, if obtained by either Fourier or Laplace transformation of the corresponding interior time-domain problem, must encapsulate infinitely many scattering events, giving rise to non-uniqueness and eigenfunctions in the Fourier case, and ill conditioning in the Laplace case. Numerical examples are included which demonstrate the accuracy and efficiency of the proposed methodology.

A novel engine and battery coupled thermal management strategy for connected HEVs based on switched model predictive control under low temperature

Under a low-temperature environment, electric vehicles face serious environmental adaptability problems, and efficient vehicle thermal management strategies are urgently needed. This paper presents a novel engine–battery coupled thermal management strategy for connected hybrid electric vehicles (HEVs). An improved system structure for an engine–battery coupled thermal management system (engine–battery CTMS) is designed to avoid unnecessary heat loss. The control requirements of the engine–battery CTMS include minimum engine fuel consumption, minimum power battery aging damage and minimum system energy consumption, which constitutes a multi-objective optimal control problem in a finite time domain. Based on model predictive control (MPC) theory, a switched nonlinear MPC (NMPC) control strategy is proposed to solve the optimal control problem of the complex coupled multi-input multi-output system. To verify the effectiveness of the proposed strategy, three comparative experiments of the centralized NMPC-based and rule-based methods combined with the improved system structure and the unimproved system structure are designed. The results of the cosimulation experiment between MATLAB/Simulink and AMEsim under various driving cycles and different ambient temperatures show that the improved structure and switched control strategy confer great advantages in reducing the controller computation burden, engine fuel consumption, and power battery aging damage.

Three-dimensional axisymmetric transient response of an unsaturated poroelastic transversely isotropic half-space

This paper investigates the three-dimensional (3D) axisymmetric dynamic response of an unsaturated poroelastic transversely isotropic half-space subjected to different vertical transient loading types. Taking into account the compression deformation of soil particles, pore fluid, the viscous and inertial coupling between different phases, as well as the material anisotropy of soil skeleton, the dynamic governing equations of unsaturated poroelastic transversely isotropic half-space medium in cylindrical coordinate system are established. Then, the general solutions for the soil skeleton’s displacement and stress, as well as the relative displacements and pressures of pore-water and pore-air, are obtained by using Laplace-Hankel transform. Finally, the Durbin numerical inversion method and Gauss-Kronod algorithm are applied to solve the transient Lamb’s problem in time domain. After validating the correctness of the proposed solution, the numerical examples focused on the effect of material anisotropy, transient loading type, the degree of saturation and distance from the loading source on the vertical and radial surface displacements of an unsaturated transversely isotropic poroelastic half-space are investigated.

Adjoint variable method for transient nonlinear electroquasistatic problems

Many optimization problems in electrical engineering consider a large number of design parameters. A sensitivity analysis identifies the design parameters with the strongest influence on the problem of interest. This paper introduces the adjoint variable method as an efficient approach to study sensitivities of nonlinear electroquasistatic problems in time domain. In contrast to the more common direct sensitivity method, the adjoint variable method has a computational cost nearly independent of the number of parameters. The method is applied to study the sensitivity of the field grading material parameters on the performance of a 320 kV cable joint specimen, which is modeled as a finite element nonlinear transient electroquasistatic problem. Special attention is paid to the treatment of quantities of interest, which are evaluated at specific points in time or space. It is shown that the method is a valuable tool to study this strongly nonlinear and highly transient technical example.

Wave resonances in the presence of current and the frequency and time-domain interconnection

The current work investigates the relationship between frequency and time domain problems associated with flexural gravity wave motion with oblique incidence and current. Different types of wave resonances such as buckling resonance, primary and secondary blocking resonance, Bragg resonance and interaction among them are discussed. Three propagating wave modes are observed between the primary and secondary blocking points, two of which are associated with positive group velocities and the third one is related to negative group velocities. Again, the Bragg resonance is analyzed for wave scattering problems. The complex porosity parameter is found to have a significant effect on the buckling and blocking resonance but does not affect Bragg resonance. The discontinuity of Bragg reflection is observed at primary and secondary blocking points and the peak values of Bragg reflection increase in the blocking zone. Again, we establish the interconnection between the frequency and time domain by deriving the time-domain solution from the frequency-domain solution and vice versa. The derivation of time-domain solutions using the dispersion relation and method of stationary phase is an intriguing finding. Wave energy and wave packets move faster in co-propagating waves than in counter-propagating waves and shallow water than in finite water depth. To validate the results, time-domain simulation and spectral methods are used.

Exact artificial boundary condition and 1D time-domain method for seismic response analysis of layered saturated poroelastic half-space

This study proposed a one-dimensional (1D) time-domain finite element method (FEM) for seismic response analysis of a layered saturated soil half-space under obliquely incident plane waves, based on Biot's u-w wave equations. The spatially two-dimensional problem was transformed into an equivalent 1D time-domain problem along the depth according to Snell's law. An exact artificial boundary condition for saturated poroelastic media was developed to simulate the wave absorption and input effects of the truncated half-space. Using the displacement and stress continuity conditions between the adjacent saturated poroelastic-medium layers and combining all finite elements and the exact artificial boundary condition, the total dynamic equation for the spatially 1D problem was obtained. The 1D dynamic equation was solved using the FEM with explicit time integration. The proposed method was verified by analyzing two engineering sites in the time domain and a comparison with the frequency-domain transfer matrix method with fast Fourier transform.

Element Differential Method for Computational Acoustics in Time Domain

In this paper, a new robust numerical method, named element differential method (EDM), is developed to solve computational acoustic problems in time domain. The key aspect of the method is the direct differentiation of shape functions of the isoparametric elements used to characterize the geometry and physical variables, which can be utilized to evaluate the spatial partial derivatives of the physical variables appearing in the governing equations and boundary conditions. Moreover, a unique collocation technique is proposed to form the system of equations, in which the governing equation is collocated at internal nodes of elements and the acceleration equilibrium equation is collocated at interface nodes between elements and outer surface nodes. EDM is a strong-form numerical method that doesn’t require a variational principle or a control volume to set up the computational scheme, and no integration is performed. Based on the Newmark difference technique, a time marching solution scheme is developed for solving the time-dependent system of equations. For the point sound source expressed in terms of the Dirac function, a sound source density function is proposed to approximate the point sound source to make it handleable in EDM. Three numerical examples are given to demonstrate the correctness and application potential of the developed method.

Learning-Based UAV Trajectory Optimization With Collision Avoidance and Connectivity Constraints

Unmanned aerial vehicles (UAVs) are expected to be an integral part of wireless networks, and determining collision-free trajectories for multiple UAVs while satisfying requirements of connectivity with ground base stations (GBSs) is a challenging task. In this paper, we first reformulate the multi-UAV trajectory optimization problem with collision avoidance and wireless connectivity constraints as a sequential decision making problem in the discrete time domain. We, then, propose a decentralized deep reinforcement learning approach to solve the problem. More specifically, a value network is developed to encode the expected time to destination given the agent’s joint state (including the agent’s information, the nearby agents’ observable information, and the locations of the nearby GBSs). An SINR-prediction network is also designed, using accumulated SINR measurements obtained when interacting with the cellular network, to map the GBSs’ locations into the SINR levels in order to predict the UAV’s SINR. Numerical results show that with the value network and SINR-prediction network, real-time navigation for multi-UAVs can be efficiently performed in various environments with high success rate.

Finite volume based asymptotic homogenization of viscoelastic unidirectional composites

The previously developed finite volume based asymptotic homogenization theory designed for unidirectional composites with finite-sized microstructures is further extended to non-ageing linear viscoelastic region via correspondence principle. The theory is a unified framework able to accommodate general loadings, both out-of-plane and in-plane. It first transforms the problems in time domain to Laplace domain via elastic–viscoelastic correspondence principle, solves the problems in transformed region, and transforms the solutions back to time domain through numerical inversion technique. In Laplace domain, the microscale problems are solved up to the third term of expansion, and the homogenized stiffness tensors of all orders are passed to the macroscale, leading to the solutions of macroscale displacements. The method’s capability is assessed through comparison with direct numerical solution, showing increasing accuracy with increasing truncation order and decreasing scale ratio, and further enhancement by reconstructing boundary layer. The robustness of theory is verified through parametric studies. The possibility of reducing the highest order of spatial derivative of homogenized displacement is also investigated. The finite volume based methodology marks the theory’s uniqueness among the existing higher order asymptotic homogenization methods, providing an efficient alternative to solve the viscoelastic composite structural problems.

Transient Thermal Stresses in FG Porous Rotating Truncated Cones Reinforced by Graphene Platelets

The present work studies an axisymmetric rotating truncated cone made of functionally graded (FG) porous materials reinforced by graphene platelets (GPLs) under a thermal loading. The problem is tackled theoretically based on a classical linear thermoelasticity approach. The truncated cone consists of a layered material with a uniform or non-uniform dispersion of GPLs in a metal matrix with open-cell internal pores, whose effective properties are determined according to the extended rule of mixture and modified Halpin–Tsai model. A graded finite element method (FEM) based on Rayleigh–Ritz energy formulation and Crank–Nicolson algorithm is here applied to solve the problem both in time and space domain. The thermo-mechanical response is checked for different porosity distributions (uniform and functionally graded), together with different types of GPL patterns across the cone thickness. A parametric study is performed to analyze the effect of porosity coefficients, weight fractions of GPL, semi-vertex angles of cone, and circular velocity, on the thermal, kinematic, and stress response of the structural member.

Adaptive Isogeometric analysis for transient dynamics: Space–time refinement based on hierarchical a-posteriori error estimations

In this paper, based on our proposed IsoGeometric Analysis (IGA)-based adaptivity technique for plate vibration (Yu et al., 2018) the space–time adaptivity strategies used for transient dynamics are established. Specifically, the Geometry Independent Field approximaTion (GIFT) method is applied to discretize the spatial domain, and time discretization is proceeded by Newmark method. In the framework of GIFT/Newmark, three kinds of space–time adaptivity strategies based on hierarchical a-posteriori error estimations are developed successively, that is, Unidirectional Multi-level Space-Time Adaptive GIFT/Newmark (UM-STAGN), Energy-based Space-Time Adaptive GIFT/Newmark (E-STAGN), and Goal-oriented Space-Time Adaptive GIFT/ Newmark (G-STAGN) methods respectively. The main concept of UM-STAGN approach is to get rid of the elements where the error estimators reach the prescribed accuracy at each adaptation step, and then assemble the rest elements as the new subsystems to be solved at the next stage. By reducing the scale of the computational domains gradually, this method achieves efficiency to some degree, though, since it fails to transfer the error information across subsystems, the error of Quantity of Interest (QoI) cannot arrive at an expected precision. For this reason, we introduce E-STAGN methodology, wherein the error indicator of each element is reassessed at every adaptive cycle through solving the whole system again. In this case, the QoI error is able to be convergent to an acceptable accuracy. Nevertheless, as the error is accumulated with time in the time-domain problem, E-STAGN method based on the energy-norm error estimation is unable to expose the source of the error so that it fails to offer an efficient refinement. This is the motivation to establish the G-STAGN technique, where the error estimation drives from our proposed first-order Dual Weight Residual (DWR) method. G-STAGN strategy can detect the origin of QoI error, and hence it leads to a remarkably economical refinement. Numerical examples are carried out in both single-patch and multi-patch structures. It is demonstrated that both UM-STAGN and E-STAGN methods can catch the propagation of stress wave for the primal problem, while G-STAGN technique is capable to track the travel path of dual stress. Therefore, the G-STAGN strategy achieves an optimal convergent rate, compared to that obtained by UM-STAGN, E-STAGN and uniform space–time h-refinement approaches.

Reliability analysis ofN-equationsN-unknowns method for the solution of the finite-difference time-domain (FDTD) problems

AbstractFinite-difference time-domain (FDTD) solution of electromagnetic problems at high-frequency (HF) range is a challenging task. This is due to two requirements of accurate geometrical modeling for small objects/antennas and proper modeling of skin-depth effect. Generally, the fine meshes are used to overcome these problems. However, this leads to a large number of time iterations because of the small unit time step. To decrease the computational time,N-equationsN-unknowns (NE-NU) method is developed for multi-frequency sources. Therefore, utilizing wideband nature of the FDTD method, NE-NU method is valuable. However, the reliability analysis of the NE-NU method has not been investigated in the literature. This study is the first numerical application of the NE-NU method that the reliability analysis of the NE-NU method is performed by using condition number calculation and it is validated by time-domain signals of an illustrative numerical example of a HF radar problem. A successful case and a failing case of the NE-NU method are clearly revealed. The effect of using a double-precision floating-point number and a single-precision floating-point number is also discussed. It is proved that a crucial value of the condition number can be found for the reliable NE-NU results.

Applying Frequency-Domain Unsteady Lifting-Line Theory to Time-Domain Problems

Frequency-domain unsteady lifting-line theory is better developed than its time-domain counterpart. To take advantage of this, this paper proposes a method to transform time-domain kinematics to the frequency domain, perform a convolution, and then return the results back to the time domain. This paper demonstrates how well-developed frequency-domain methods can be easily applied to time-domain problems, enabling prediction of forces and moments on finite wings undergoing arbitrary kinematics. Results are presented for rectangular wings of various aspect ratios, undergoing pitch and heave kinematics. Computational fluid dynamics is used to test the effectiveness of the method in the Euler and low-Reynolds-number () regimes. Overall, the proposed method provides fast and reasonably accurate predictions of lift and moment coefficients, particularly in comparison to strip theory, which is commonly used for problems involving arbitrary kinematics.

Time Domain Response Analyses of Multiconductor Transmission Lines Using L-Stable Single Step Multistage Block Method

In order to solve the non-physical oscillation problem of the traditional finite difference time domain(FDTD) scheme at the discontinuous solution, the L-stable single step multistage block method is proposed to analyze the time domain transient response of multiconductor transmission lines. In order to avoid the repeated inversion of the coefficient matrix of the system state equation when the boundary conditions are imposed, the more general Sherman-Morrison formula is used to solve the inverse matrix of the coefficient matrix after the boundary conditions are applied. This method is used to simulate uniform lossless multiconductor transmission lines (MTLs) and non-uniform lossy MTLs, and its simulation result is compared with the results given by FDTD algorithm. The results showed that the single step multistage block method can effectively suppress the numerical oscillation and is not limited by step size of simulation in time domain.