We present a parallel GPU solution of the Caputo fractional reaction-diffusion equation in one spatial dimension with explicit finite difference approximation. The parallel solution, which is implemented with CUDA programming model, consists of three procedures: preprocessing, parallel solver, and postprocessing. The parallel solver involves the parallel tridiagonal matrix vector multiplication, vector-vector addition, and constant vector multiplication. The most time consuming loop of vector-vector addition and constant vector multiplication is optimized and impressive performance improvement is got. The experimental results show that the GPU solution compares well with the exact solution. The optimized GPU solution on NVIDIA Quadro FX 5800 is 2.26 times faster than the optimized parallel CPU solution on multicore Intel Xeon E5540 CPU.
Jie Liu;Chunye Gong;为民 包;Guojian Tang;Yuewen Jiang
Discrete Dynamics in Nature and Society
A novel robust adaptive gliding guidance strategy based on multi-constrained analytical optimal guidance and online identification of aerodynamic coefficients for hypersonic vehicles is proposed. The guidance models are constructed in both longitudinal and lateral directions and optimal guidance law, namely required load factor, is designed with minimum energy consumption to satisfy terminal position, altitude and flight-path angle constraints. Considering aerodynamic coefficients are the core factors in the angle-of-attack calculation, it constructs the aerodynamic models in the form of quadratic polynomial function and employs extended Kalman filter to estimate the unknown parameters. Using the optimal guidance law based on current flight states and terminal constraints and the identified outputs to calculate angle-of-attack, then the gliding guidance mission can be achieved adaptively and robustly. Finally, the simulation experiments of high performance of the common aerothermodynamics-shell vehicle (CAV-H) are carried out to validate the guidance performance.
Jianwen Zhu;Luhua Liu;Guojian Tang;为民 包
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering
In terms of the terminal guidance of intercepting the endoatmospheric maneuvering targets, an adaptive integral sliding-mode guidance law is presented. Based on the principle of suppressing the rotation of the line of sight from a missile to a target, a tracking profile is designed where the convergence rate of the line of sight can be regulated. The tracking error and its integral are selected as the state variables. An integral sliding-mode surface of the states converging to zero in finite time and a rapid reaching law are used to derive an integral sliding-mode guidance law. To deal with an unknown target maneuver, an adaptive algorithm is proposed to estimate the square of the upper bound of the target maneuver, and then the adaptive integral sliding-mode guidance law is constructed. The finite-time convergence characteristic of the law is proven, and the convergence regions are given of the state variables.Finally, the guldance law is converted into the corresponding form suitable for the endoatmosphenc interception. The simulation results indicate that the proposed guidance law can precisely intercept the maneuvering targets and the convergence rate is rapid of the tracking error. The overload distribution is reasonable, and less energy is consumed. Furthermore, the law possesses good profile noise characteristics and is easy to be implemented in practice.
Jing Shuai Huang;Hong Bo Zhang;Guo Jian Tang;为民 包
Yuhang Xuebao/Journal of Astronautics
In the numerical approximation of fractional order derivatives, the crucial point is to balance the computing complexity and the computing accuracy. We proposed a piecewise memory principle for fractional derivatives, in which the past history is divided into several segments instead of discarded. The piecewise approximation is performed on each segment. Error estimation of piecewise memory principle is analyzed also. Numerical examples show that the contradiction of computing accuracy and complexity is effectively relaxed and the piecewise memory principle is superior to the existing short, variable and equal-weight memory principles. The impacts of the memory length, step size and segment size are also discussed.
Chunye Gong;为民 包;Jie Liu
Fractional Calculus and Applied Analysis
No restrictions are imposed on the motion states of missile and target and the line of sight rotation coordinate system is introduced into the derivation of differential geometric guidance law. Then, the extended differential geometric guidance law is achieved whose scope of application is largely extended. In order to realize the derived law, instead of the complex computation of torsion command, a novel and simple algebraic approach is proposed to directly determining the applied direction of commanded missile acceleration. Furthermore, the target acceleration is estimated on basis of the extended state observer theory, which makes the derived law more applicable to intercepting maneuvering targets in practical engagement scenarios. Simulation results demonstrate that the obtained laws are effective and can fill up the drawback that pure proportional navigation cannot cope with high-speed maneuvering targets inside the atmosphere.
Jingshuai Huang;Hongbo Zhang;Guojian Tang;为民 包
When flight vehicles (e.g., aerospace vehicles, Low Earth Orbit (LEO) satellites, near-space aircrafts, Unmanned Aerial Vehicles (UAVs) and drones) fly at high speed, their surfaces suffer the micro-pressure from high-altitude thin air. The long-term effect of this pressure causes the surface components of flight vehicle to deform or fall off, which can lead to a serious accident. To solve this problem, this paper proposes a sensitivity-compensated micro-pressure flexible sensor based on hyper-elastic plastic material and plate parallel capacitance. The sensor is able to measure a range of 0–6 kPa micro-pressure suffered by the flight vehicle’s surface with high sensitivity and flexible devices. In this paper, we propose the principle, structure design and fabrication of the sensitivity-compensated micro-pressure flexible sensor. We carried out experiments to obtain the static characteristic curve between micro-pressure and the output capacitance of the sensor devices, and investigated the relationship between sensitivity and geometric parameters. We also compared the performance of the flexible sensor before and after sensitivity compensation. The result shows that the sensor can measure a range of 0–2 kPa and 2–6 kPa with a sensitivity of 0.27 kPa−1 and 0.021 kPa−1, which are 80% and 141.38% higher than the sensor before compensation; a linearity of 1.39% and 2.88%, which are 51.7% and 13.1% higher than the sensor before compensation; and a hysteresis and repeatability of 4.95% and 2.38%, respectively. The sensor has potential applications in flight vehicles to measure the micro-pressure with high sensitivity and flexibility.
Xiaozhou Lü;Jianan Jiang;辉 王;Qiaobo Gao;Shaobo Zhao;Ning Li;Jiayi Yang;松林 王;为民 包;人杰 陈
It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O (M x M y N 2). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16-4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.
Chunye Gong;为民 包;Guojian Tang;Yuewen Jiang;Jie Liu
The Scientific World Journal
In this paper, fractional-order calculus (FC) is applied in the sliding mode control of a generic hypersonic vehicle (GHV). In the design of the controller, dynamic inversion is applied to deal with strong couplings among pitch angle, yaw angle and roll angle. The effect of FC is evaluated in a sliding mode controller. Simulation results demonstrate that sliding mode controller becomes more robust and damping characteristic is strengthened by use of FC.
Haidong Liu;为民 包;Huifeng Li;Chunye Gong;Yuxin Liao
This correspondence paper aims at addressing the estimation of carrier frequency offset (CFO) for the uplink orthogonal frequency-division multiple access systems. Since the CFOs of the signals from different active users are sparsely distributed in the frequency domain, a sparse Bayesian learning (SBL) is tailored to determine the CFO in this paper, ending up with the SBL assisted CFO (SBL-CFO) estimator. In particular, the CFO estimation problem is first formulated as a sparse nonnegative least squares (S-NNLS) problem. Meanwhile, background noise and sampling errors are mitigated utilizing a selection matrix and a whitening filter, respectively. This enables us to exploit the SBL with nonnegative Laplace prior (SBL-NLP) to solve the S-NNLS problem. Furthermore, in order to make the convergence of the SBL-NLP algorithm faster and its estimation more accurate, the hyperprior inherent in the SBL-NLP algorithm is initialized by the traditional SBL with nonnegative Gaussian prior. Simulation results show that our proposed SBL-CFO estimator significantly outperforms the state-of-The-Art estimators in terms of estimation accuracy, especially when the CFOs and the number of active users are large.
Min Huang;Lei Huang;Weize Sun;为民 包;Jihong Zhang
IEEE Transactions on Vehicular Technology
It is time consuming to numerically solve fractional differential equations. The fractional ordinary differential equations may produce Toeplitz-plus-band triangular systems. An efficient iteration method for Toeplitz-plus-band triangular systems is presented with O M l o g M computational complexity and O M memory complexity in this paper, compared with the regular solution with O M 2 computational complexity and O M 2 memory complexity. M is the discrete grid points. Some methods such as matrix splitting, FFT, compress memory storage and adjustable matrix bandwidth are used in the presented solution. The experimental results show that the presented method compares well with the exact solution and is 4.25 times faster than the regular solution.
Chunye Gong;为民 包;Guojian Tang;Changwan Min;Jie Liu
Mathematical Problems in Engineering