scholarly journals Efficient Algorithm to Calculate a Time-Domain Echo Signal from Moving Targets Based on Physical Optics and the Application to an Autonomous Driving Simulation

2021 ◽  
Vol 21 (5) ◽  
pp. 351-358
Author(s):  
Jihyo Choi ◽  
Il-Suek Koh
Keyword(s):  
Time Domain ◽  
Autonomous Driving ◽  
Computational Time ◽  
Physical Optics ◽  
Echo Signal ◽  
Automotive Radar ◽  
Baseband Signal ◽  
Driving Scenario ◽  
Radar Simulator ◽  
The Time Domain

An automotive radar simulator is proposed that can consider a dynamic driving scenario. The impulse response is computed based on the distance between the radar and the mesh position and the radar equation. The first-order physical optics technique is used to calculate the backscattering by the meshes, which can efficiently consider the shape of the target; however, because the radar operating frequency is very high, the required amount of mesh for discretization is large. Hence, the calculation of the time-domain echo signal requires considerable computational time. To reduce this numerical complexity, a new scheme is proposed to accurately approximate the time-domain baseband signal generated by the large number of meshes. The radar adopts the frequency modulated continuous waveform. Range-Doppler processing is used to estimate the range and relative velocity of the targets based on which simulation results are numerically verified for a driving scenario.

High Dimensional Harmonic Balance Analysis for Dynamic Piecewise Aeroelastic Systems

2008 ◽  
Author(s):  
Liping Liu ◽  
Earl H. Dowell
Keyword(s):  
Frequency Domain ◽  
Limit Cycle ◽  
Time Domain ◽  
Harmonic Balance ◽  
Solution Method ◽  
Computational Time ◽  
High Dimensional ◽  
Aeroelastic System ◽  
Time Marching ◽  
The Time Domain

This paper describes the extension and application of a novel solution method for the periodic nonlinear oscillations of an aeroelastic system. This solution method is a very attractive alternative to time marching algorithms in that it is much faster and may track unstable as well as stable limit cycles. The method is employed to analyze the nonlinear aeroelastic response of a two dimensional airfoil including a control surface with freeplay placed in an incompressible flow. The mathematical model for this piecewise aeroelastic system is initially formulated as a set of first order ordinary differential equations. A frequency domain solution for the limit cycle oscillations is derived by a novel high dimensional harmonic balance (HDHB) method. By an inverse Fourier transformation, the system in the frequency domain is then converted into the time domain. Finally, the airfoil motions are obtained by solving the system in the time domain for only one period of limit cycle oscillation. This process can be easily implemented into computer programs without going through the complex algebraic manipulations for the nonlinearities typical of a more conventional harmonic balance solution method. The solutions found using this new HDHB method have been shown to be the same as those found using a more traditional time marching (e.g. Runge-Kutta) approach and also a conventional harmonic balance approach in the frequency domain with a considerable computational time saving.

scholarly journals A new iterative solver for the time-harmonic wave equation

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. E57-E63 ◽  
Author(s):  
C. D. Riyanti ◽  
Y. A. Erlangga ◽  
R.-E. Plessix ◽  
W. A. Mulder ◽  
C. Vuik ◽  
...  
Keyword(s):  
Wave Equation ◽  
Linear System ◽  
Time Domain ◽  
Multigrid Method ◽  
Harmonic Wave ◽  
Computational Time ◽  
Full Time ◽  
Iterative Solver ◽  
Time Harmonic ◽  
The Time Domain

The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can be solved efficiently by a direct method. In three dimensions, direct methods cannot be used for problems of practical sizes because the computational time and the amount of memory required become too large. Iterative methods are an alternative. These methods are often based on a conjugate gradient iterative scheme with a preconditioner that accelerates its convergence. The iterative solution of the time-harmonic wave equation has long been a notoriously difficult problem in numerical analysis. Recently, a new preconditioner based on a strongly damped wave equation has heralded a breakthrough. The solution of the linear system associated with the preconditioner is approximated by another iterative method, the multigrid method. The multigrid method fails for the original wave equation but performs well on the damped version. The performance of the new iterative solver is investigated on a number of 2D test problems. The results suggest that the number of required iterations increases linearly with frequency, even for a strongly heterogeneous model where earlier iterative schemes fail to converge. Complexity analysis shows that the new iterative solver is still slower than a time-domain solver to generate a full time series. We compare the time-domain numeric results obtained using the new iterative solver with those using the direct solver and conclude that they agree very well quantitatively. The new iterative solver can be applied straightforwardly to 3D problems.

The Development and Application of a Time-Domain Harmonic Balance Flow Solver

2012 ◽  
Author(s):  
Pengcheng Du ◽  
Fangfei Ning
Keyword(s):  
Time Domain ◽  
Harmonic Balance ◽  
Unsteady Flows ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Computational Time ◽  
Test Cases ◽  
Flow Solver ◽  
The Time Domain ◽  
Time Periodic

Time periodic unsteady flows are often encountered in turbomachinery. Simulating such flows using conventional time marching approach is very time-consuming and hence expensive. To handle this problem, several Fourier-based reduced order models have been developed recently. Among these, the time-domain harmonic balance method solves the governing equations purely in the time domain and there is also no need for the turbulence model to be linearized, making it easy to be implemented in an existing RANS code. Thus, the time-domain harmonic balance method was chosen and incorporated into an in-house Navier-Stokes flow solver. Several test cases were performed for the validations of the developed code. They cover standard unsteady test cases such as the low speed vortex shedding cylinder flow and the Sajben transonic diffuser under periodically oscillating back pressure. Further, two different practical turbomachinery unsteady flows were considered. One is a transonic fan under circumferential inlet distortion and the other is the rotor-stator interactions in a single stage compressor. The results illustrate the capability of the harmonic balance method in capturing the dominant nonlinear effects. The number of harmonics should be retained in the harmonic balance method is depend on the strength of the nonlinear unsteady effects and differs from case to case. With appropriate number of harmonics retained, it can resolve the unsteady flow field satisfactory, meanwhile, reducing the computational time significantly. In a word, the harmonic balance method promise to be an effective way to simulate time periodic unsteady flows.

scholarly journals Time-domain non-linear aeroelastic analysis via a projection-based reduced-order model

2020 ◽  
Vol 124 (1281) ◽  
pp. 1798-1818 ◽  
Author(s):  
S. Lee ◽  
H. Cho ◽  
H. Kim ◽  
S.-J. Shin
Keyword(s):  
Flow Field ◽  
Time Domain ◽  
Reduced Order Model ◽  
Navier Stokes ◽  
Computational Time ◽  
Order Model ◽  
Navier Stokes Equation ◽  
Reduced Order ◽  
Non Linear ◽  
The Time Domain

ABSTRACTThe aeroelastic phenomenon of limit-cycle oscillations (LCOs) is analysed using a projection-based reduced-order model (PROM) and Navier–Stokes computational fluid dynamics (CFD) in the time domain. The proposed approach employs incompressible Navier–Stokes CFD to construct the full-order model flow field. A proper orthogonal decomposition (POD) of the snapshot matrix is conducted to extract the POD modes and corresponding temporal coefficients. The POD modes are directly projected to the incompressible Navier–Stokes equation to reconstruct the flow field efficiently. The methodology is applied to a plunging cylinder and an aerofoil undergoing LCOs. This scheme decreases the computational time while preserving the capability to predict the flow field accurately. The ROM is capable of reducing the computational time by at least 70% while maintaining the discrepancy within 0.1%. The causes of LCOs are also investigated. The scheme can be used to analyse non-linear aeroelastic phenomena in the time domain with reduced computational time.

Time-Domain Approach for Acoustic Scattering of Rotorcraft Noise

2012 ◽  
Vol 57 (4) ◽  
pp. 1-12 ◽  
Author(s):  
Seongkyu Lee ◽  
Kenneth S. Brentner ◽  
Philip J. Morris
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Impulsive Noise ◽  
Near Field ◽  
Acoustic Scattering ◽  
Frequency Domain Analysis ◽  
Computational Time ◽  
Computationally Efficient ◽  
Time Saving ◽  
The Time Domain

This paper addresses acoustic scattering of rotorcraft noise in the time domain. A time-domain equivalent source method is used since it is considered to be a computationally efficient method to solve acoustic scattering. In addition, the time-domain method provides a solution for all frequencies of interest in a single computation and is able to predict the acoustic scattering of aperiodic signals. The prediction is validated against exact solutions for a monopole source. The numerical method is then used to predict acoustic scattering of noise from a BO105 tail rotor by a representative fuselage. Complex directivity patterns are seen in the near field, and a large scattering effect is observed in the far field to the side of the fuselage. The time-domain code results of sound pressure level are validated against the results obtained by a frequency-domain analysis. Finally, acoustic scattering for an impulsive noise source is investigated to simulate main rotor blade–vortex interaction noise. The scattered pressure has a comparable amplitude as that of the incident pressure so that the total pressure is dramatically changed compared to the incident pressure. For the impulsive noise, a large computational time saving is achieved compared to the frequency-domain approach, in which the computation must be repeated for each frequency.

A recursive method for the separation of upgoing and downgoing waves of vertical seismic profiling data

Geophysics ◽  
1986 ◽  
Vol 51 (12) ◽  
pp. 2206-2218 ◽  
Author(s):  
F. Aminzadeh
Keyword(s):  
Time Domain ◽  
Fourier Transforms ◽  
A Priori ◽  
Computational Time ◽  
Linear Filter ◽  
Seismic Profiling ◽  
Vertical Seismic Profiling ◽  
Starting Point ◽  
Vsp Data ◽  
The Time Domain

An important part of the processing of vertical seismic profiling (VSP) data is the separation of upgoing and downgoing waves. I introduce a new method for separation based on a time‐domain recursive linear filter. The separation method uses an approximation to an optimal, frequency‐domain, nonlinear filter solution as the starting point. The time‐domain recursive linear (approximate) filter converges to the optimal (exact) solution. Since the computation is in the time domain and since this filter is linear, some of the temporal aliasing and other problems resulting from the forward and inverse Fourier transforms are avoided. Specifically, instability for some frequencies (spectral singularities) is not experienced here. This method uses a priori information of the opposite stepouts of the upgoing and downgoing waves. Equal spacing between borehole measurement points is not required. Further, the computational time may be controlled according to the desired accuracy. An important feature of this method is that it locates the reflecting boundaries of the subsurface. Having located the homogeneous layers, it allows variable‐length windows of traces for separation, which eliminates the undesirable effects of smearing and extending wave fields beyond their origins. Also, knowledge of acoustic impedances for accurate implementation of the optimum filter is no longer required.

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