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Novel technique to investigate the convergence analysis of the tempered fractional natural transform method applied to diffusion equations

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Journal of Ocean Engineering and Science 2023年第6期8卷 636-646页

作者： Nazek A.Obeidat Daniel E.Bentil Department of Mathematics and Statistics University of VermontBurlingtonVermont 05405USA

In this research work,we present proof of the existence and uniqueness of solution for a novel method called tempered fractional natural transforms(TFNT)and give error estimates.This efficient method is applied to models,such as the time-space tempered fractional convection-diffusion equation(FCDE)and tempered fractional Black-Scholes equation(FBSE).We obtain exact solutions for these models using our methodology,which is very important for knowing the wave behavior in ocean engineering models and for the studies related to marine science and engineering.Finding exact solutions to tempered fractional differential equations(TFDEs)is far from trivial.Therefore,the proposed method is an excellent addition to the myriad of techniques for solving TFDE problems.

关键词： Tempered fractional calculus Diffusion equation Caputo derivative Riemann-Liouville derivative integral transforms

Hypersonic Vehicle Trajectory Prediction Algorithm Based on Hough Transform

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Chinese Journal of Electronics 2021年第5期30卷 918-930页

作者： LI Fan XIONG Jiajun LAN Xuhui BI Hongkui TAN Xiansi Air Force Early Warning Academy Unit 95980 of the PLA

Trajectory prediction is a prerequisite for missile and high-speed vehicle guidance interception. To address the trajectory problem for the near space hypersonic unpowered gliding vehicle. Firstly, the trajectory prediction mechanism is analyzed. Based on the existing NSHV trajectory prediction method, the key techniques of trajectory prediction are discussed from the perspectives of prediction parameter selection and prediction parameter description. Then, a trajectory prediction method based on Hough transform is proposed. The core of the method is to select the longitude latitude, and high direction positions as prediction parameters, and use the Hough transform to fit the prior basis functions. In the latitude and longitude direction, the rationality of predicting parameters is discussed from two aspects: position extreme point and lateral maneuverability. In the height direction,for the NSHV oscillation drop characteristic, two Hough transforms are used to separate the periodic term from the linear term. In addition, we give the approximate interval of the parameter values of the method, and design a parameter adaptive scheme. Finally, trajectory prediction is performed on two different control patterns. The error of the prediction time of 100 s is within 25 km, and the results show the effectiveness of the proposed method.

关键词： Neural nets (theory) Spatial variables control Aerospace control integral transforms Control system analysis and synthesis methods Near space hypersonic vehicle trajectory prediction Hough transform

材料特性对输送脉动流体的粘弹性轴向功能梯度管非线性动力行为的影响

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哈尔滨工程大学学报（英文版） 2023年第2期22卷 247-259页

作者：付光明庹宇航张贺恩苏健孙宝江王锴娄敏 Key Laboratory of Unconventional Oil&Gas Development(China University of Petroleum(East China)) Ministry of EducationQingdao 266580China China Petroleum Pipeline Engineering Co. Ltd.Langfang 065201China CNPC Offshore Engineering Company Limited Beijing 100028China Nuclear Engineering Department COPPEFederal University of Rio de JaneiroRio de Janeiro 21941-972Brazil

The nonlinear dynamic behaviors of viscoelastic axially functionally graded material(AFG)pipes conveying pulsating internal flow are very complex.And the dynamic behavior will induce the failure of the pipes,and research of vibration and stability of pipes becomes a major concern.Considering that the elastic modulus,density,and coefficient of viscoelastic damping of the pipe material vary along the axial direction,the transverse vibration equation of the viscoelastic AFG pipe conveying pulsating fluid is established based on the Euler-Bernoulli beam theory.The generalized integral transform technique(GITT)is used to transform the governing fourth-order partial differential equation into a nonlinear system of fourth-order ordinary differential equations in time.The time domain diagram,phase portraits,Poincarémap and power spectra diagram at different dimensionless pulsation frequencies,are discussed in detail,showing the characteristics of chaotic,periodic,and quasi-periodic motion.The results show that the distributions of the elastic modulus,density,and coefficient of viscoelastic damping have significant effects on the nonlinear dynamic behavior of the viscoelastic AFG pipes.With the increase of the material property coefficient k,the transition between chaotic,periodic,and quasi-periodic motion occurs,especially in the high-frequency region of the flow pulsation.

关键词： Axially functionally graded pipe Pipe conveying pulsating flow integral transforms Nonlinear dynamics Chaotic motion Quasi-periodic motion

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Myocardial Infarction Detection and Localization with Electrocardiogram Based on Convolutional Neural Network

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Chinese Journal of Electronics 2021年第5期30卷 833-842页

作者： LIU Jikui WANG Ruxin WEN Bo LIU Zengding MIAO Fen LI Ye Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences Shenzhen College of Advanced Technology University of Chinese Academy of Sciences

Electrocardiogram(ECG) is widely used in Myocardial infarction(MI) diagnosis. The automatic diagnosis of MI based on the 12-lead ECG needs to consider not only the waveform change features in multi-resolution time series, but also the spatial correlation information between the leads. To this end, this work proposed multiscale spatiotemporal feature extraction method based on Convolutional neural network(CNN) for MI automatic diagnosis. First, the 12-lead ECG is first transformed into an ECG image through wavelet decomposition and 3-dimensional space reconstruction. The MI-CNN model is then constructed to identify MI using 41368 ECG images.Finally, we develop the LL-CNN model, which is utilized only after the ECG signal is identified as an MI event by the MI-CNN model, to localize MI by employing transfer learning to overcome the limited data problem. The proposed method has achieved an accuracy of 99.51% on MI detection, and a macro-F1 of 99.14% on MI localization.Moreover, the features visualization shows that U-wave has significant diagnostic value for MI. The proposed method significantly improves the performance of MI detection and localization compared with other methods. It is promising to be used for MI monitoring and diagnosis.

关键词： Function theory, analysis Electrical activity in neurophysiological processes Signal detection Bioelectric signals Digital signal processing integral transforms integral transforms Electrodiagnostics and other electrical measurement techniques Biology and medical computing Machine learning (artificial intelligence) Electrocardiogram Myocardial infarction Spatiotemporal information Convolutional neural network Transfer learning

Chaotic Signal Denoising Algorithm Based on Self-Similarity

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Chinese Journal of Electronics 2021年第3期30卷 482-488页

作者： HUANG Jinwang LYU Shanxiang CHEN Yue School of Cyberspace Science Dongguan University of Technology College of Cyber Security Jinan University School of Robotics The Open University of Guangdong

Inspired by the self-similar fractal properties of chaotic attractors and the heuristics of similarity filtering of images, a novel chaotic signal denoising algorithm is proposed. By grouping the chaotic signal with similar segments, the denoising of one-dimensional input is transformed into a two-dimensional joint filtering problem. Singular value decomposition is performed on the grouped signal segments and the transform coefficients are processed by thresholding to attenuate noise and finally undergo inverse transformation to recover the signal.Because the similar segments in the grouping have good correlation, the two-dimensional transformation of the grouping can obtain a more sparse representation of the original signal compared with the threshold value denoising in the direct one-dimensional transform domain, thereby having better noise suppression effect. Simulation results show that the algorithm can improve the reconstruction accuracy and has better signal-to-noise ratio than existing chaotic signal denoising algorithms.

关键词： Optical, image and video signal processing Signal processing and detection Filtering methods in signal processing Computer vision and image processing techniques integral transforms Other topics in statistics integral transforms Self-similarity Noise reduction Singular value decomposition Chaotic signal

JACOBI POLYNOMIALS USED TO INVERT THE LAPLACE TRANSFORM

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Analysis in Theory and Applications 2004年第1期20卷 28-34页

作者： A.Al-Shuaibi F.Al-Rawjih King Fahd University of Petroleum and Minerals Dhahran Saudi ArabiaCollege For Girls Dammam Saudi Arabia

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find on approximation to f(t) by the use of the dassical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series ex-pansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.

关键词： Inverse Laplace transform Jacobi polynomials integral transforms Ill-posed problems

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