Mode Recognition of Lamb Wave Detecting Signals in Metal Plate Using the Hilbert-Huang Transform Method

The dispersion and multiple modes characteristics which exist in the propagation of Lamb waves (LW) in metal plates make it extremely hard to analyze and recognize the detection echo signals of defects. As a newly developed time-frequency analysis method in recent years, Hilbert-Huang transform (HHT) is one of the powerful tools to analyze non-stationary signals. The experimental LW detecting system for single aluminum plate is setup in this work, and the LW detecting signals are analyzed by HHT. The overlapped LW detecting signals of different modes are recognized by the means of extracting flight time of intrinsic mode functions (IMFs) after Hilbert transform (HT). The experiment results, agreeing well with the theoretical analysis, indicate that the HHT method can clearly recognize overlapped LW detecting signals of different modes in metal plates, but could hardly recognize that of the same mode. HHT can be an effective method to recognize LW detecting signals of different modes in metal plates.

Analysis of the characteristics of gastrointestinal motility based on Hilbert-Huang transform method

Pressure activity data as an important index of gastrointestinal(GI)motility can be obtained from thewireless radiotelemetry capsule.The Hilbert-Huang transform(HHT)method,whieh is more effective toprocess non-stationary signal,is proposed to identify the characteristics of GI motility.We decompose thepressure activity data into intrinsic mode functions(IMFs),calculate the Hilbert marginal spectrum andattain the peristalsis characteristics of GI tract.The IMFs represent the peristalses modes of GI tract activ-ity embedded in the pressure data.The time-varying characteristic of the method suggests that the HI-IT issuitable to aeeommodate other non-stationary biomedical data analysis.

Application of Elzaki Transform Method to Market Volatility Using the Black-Scholes Model

Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.

基于残差U-Net和自注意力Transformer编码器的磁场预测方法

利用有限元方法对几何结构复杂的电机和变压器进行磁场分析,存在仿真时间长且无法复用的问题。因此,该文提出一种基于残差U-Net和自注意力Transformer编码器的磁场预测方法。首先建立永磁同步电机(PMSM)和非晶合金变压器(AMT)有限元模型,得到深度学习训练所需的数据集;然后将Transformer模块与U-Net模型结合,并引入短残差机制建立ResUnet-Transformer模型,通过预测图像的像素实现磁场预测;最后通过Targeted Dropout算法和动态学习率调整策略对模型进行优化,解决拟合问题并提高预测精度。计算实例证明,ResUnet-Transformer模型在PMSM和AMT数据集上测试集的平均绝对百分比误差(MAPE)均小于1%,且仅需500组样本。该文提出的磁场预测方法能减少实际工况和多工况下精细模拟和拓扑优化的时间和资源消耗,亦是虚拟传感器乃至数字孪生的关键实现方法之一。

On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods

Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analyticalmeans.Thus,we need numerical inversionmethods to convert the obtained solution fromLaplace domain to a real domain.In this paper,we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main steps.First,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo sense.Secondly,we transformthe fractional differential equation in Caputo sense to an equivalent equation in Laplace space.Then the solution of the transformed equation is obtained in Laplace domain.Finally,the solution is converted into the real domain using numerical inversion of Laplace transform.Three inversion methods are evaluated in this paper,and their convergence is also discussed.Three test problems are used to validate the inversion methods.We demonstrate our results with the help of tables and figures.The obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method.

On Time Fractional Partial Differential Equations and Their Solution by Certain Formable Transform Decomposition Method

This paper aims to investigate a new efficient method for solving time fractional partial differential equations.In this orientation,a reliable formable transform decomposition method has been designed and developed,which is a novel combination of the formable integral transform and the decomposition method.Basically,certain accurate solutions for time-fractional partial differential equations have been presented.Themethod under concern demandsmore simple calculations and fewer efforts compared to the existingmethods.Besides,the posed formable transformdecompositionmethod has been utilized to yield a series solution for given fractional partial differential equations.Moreover,several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing theory.Furthermore,the formable transform decomposition method has been employed for finding a series solution to a time-fractional Klein-Gordon equation.Over and above,some numerical simulations are also provided to ensure reliability and accuracy of the new approach.

The Natural Transform Decomposition Method for Solving Fractional Klein-Gordon Equation

In this paper, a coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Klein-Gordan equation. The (NTDM), is introduced to derive the approximate solutions in series form for this equation. Solutions have been drawn for several values of the time power. To identify the strength of the method, three examples are presented.

Improved calibration method for displacement transformation coefficient in optical and visual measurements

Optical and visual measurement technology is used widely in fields that involve geometric measurements,and among such technology are laser and vision-based displacement measuring modules(LVDMMs).The displacement transformation coefficient(DTC)of an LVDMM changes with the coordinates in the camera image coordinate system during the displacement measuring process,and these changes affect the displacement measurement accuracy of LVDMMs in the full field of view(FFOV).To give LVDMMs higher accuracy in the FFOV and make them adaptable to widely varying measurement demands,a new calibration method is proposed to improve the displacement measurement accuracy of LVDMMs in the FFOV.First,an image coordinate system,a pixel measurement coordinate system,and a displacement measurement coordinate system are established on the laser receiving screen of the LVDMM.In addition,marker spots in the FFOV are selected,and the DTCs at the marker spots are obtained from calibration experiments.Also,a fitting method based on locally weighted scatterplot smoothing(LOWESS)is selected,and with this fitting method the distribution functions of the DTCs in the FFOV are obtained based on the DTCs at the marker spots.Finally,the calibrated distribution functions of the DTCs are applied to the LVDMM,and experiments conducted to verify the displacement measurement accuracies are reported.The results show that the FFOV measurement accuracies for horizontal and vertical displacements are better than±15μm and±19μm,respectively,and that for oblique displacement is better than±24μm.Compared with the traditional calibration method,the displacement measurement error in the FFOV is now 90%smaller.This research on an improved calibration method has certain significance for improving the measurement accuracy of LVDMMs in the FFOV,and it provides a new method and idea for other vision-based fields in which camera parameters must be calibrated.

集成卷积神经网络和视觉Transformer的隧道掌子面岩性判识研究

为研究综合高效的隧道掌子面岩性智能分类方法,首先,通过收集高铁沿线施工隧道高清掌子面照片、地质素描图及工程地质说明,筛选并统计出灰岩、泥岩、砂岩、玄武岩4种岩性,在此基础上,采用图像增强扩充样本数量并构建岩性样本集;然后,基于上述样本集分别构建ResNet50V2岩性分类迁移模型及VIT岩性分类模型,对比二者岩性分类效果,并采用Stacking方法集成2种模型的分类特点;最后,通过对比3种元学习器(逻辑回归、支持向量机、决策树)对2种模型的集成融合效果来选取最适用的元学习器。结果表明:采用逻辑回归集成ResNet50V2及VIT所构建的集成模型对岩性的分类效果最好,能充分融合掌子面岩性的全、局部特征来进行分类,模型准确率达到93.8%。

基于CNN-Swin Transformer Network的LPI雷达信号识别

针对在低信噪比(SNR)条件下,低截获概率雷达信号调制方式识别准确率低的问题,提出一种基于Transformer和卷积神经网络(CNN)的雷达信号识别方法。首先,引入Swin Transformer模型并在模型前端设计CNN特征提取层构建了CNN+Swin Transformer网络(CSTN),然后利用时频分析获取雷达信号的时频特征,对图像进行预处理后输入CSTN模型进行训练,由网络的底部到顶部不断提取图像更丰富的语义信息,最后通过Softmax分类器对六类不同调制方式信号进行分类识别。仿真实验表明:在SNR为-18 dB时,该方法对六类典型雷达信号的平均识别率达到了94.26%,证明了所提方法的可行性。

Research on the Digital Transformation of English Teaching in Vocational Education

With the advancement of technology,exploring the impact of digital transformation on vocational education English teaching has become crucial.This study aims to investigate the effectiveness of digital transformation in English teaching in vocational education in China by exploring students’and teachers’attitudes,views,and experiences on the use of digital technology in English teaching.This study employed a mixed method of qualitative and quantitative analysis.The research results indicate that digital transformation has had a positive impact on vocational education English teaching,as it enhances the teaching process,promotes communication and collaboration,and increases students’enthusiasm and participation.However,implementing digital transformation in vocational education English teaching also poses challenges,including a lack of resources,infrastructure,and training.This study provides an in-depth understanding of the advantages and challenges of digital transformation in vocational education English teaching and proposes strategies to improve the implementation of digital technology in this context.

Structural modal parameter identifi cation and damage diagnosis based on Hilbert-Huang transform

Traditional modal parameter identifi cation methods have many disadvantages,especially when used for processing nonlinear and non-stationary signals.In addition,they are usually not able to accurately identify the damping ratio and damage.In this study,methods based on the Hilbert-Huang transform(HHT) are investigated for structural modal parameter identifi cation and damage diagnosis.First,mirror extension and prediction via a radial basis function(RBF) neural network are used to restrain the troublesome end-effect issue in empirical mode decomposition(EMD),which is a crucial part of HHT.Then,the approaches based on HHT combined with other techniques,such as the random decrement technique(RDT),natural excitation technique(NExT) and stochastic subspace identifi cation(SSI),are proposed to identify modal parameters of structures.Furthermore,a damage diagnosis method based on the HHT is also proposed.Time-varying instantaneous frequency and instantaneous energy are used to identify the damage evolution of the structure.The relative amplitude of the Hilbert marginal spectrum is used to identify the damage location of the structure.Finally,acceleration records at gauge points from shaking table testing of a 12-story reinforced concrete frame model are taken to validate the proposed approaches.The results show that the proposed approaches based on HHT for modal parameter identifi cation and damage diagnosis are reliable and practical.

A new method for identifying flow pattern of spouted fluidized bed by coupling Hilbert-Huang transform characteristics of differential pressure signals in different zones

On a cold spouted fluidized bed,this study compares the characteristic differences in intrinsic mode function(IMF)energy and Hilbert–Huang spectrum between the spout zone and annulus zone under different combinations of spouted gas and fluidized gas flow rates for five typical flow patterns.The energy distribution characteristics under different flow patterns are also analyzed.The Hilbert–Huang spectrum and IMF energy of pressure difference signals exhibit distinct variations in different zones as the flow pattern changes.Moreover,there exists a correlation between the energy in the middle-frequency range and the flow pattern.Leveraging the K-means algorithm,the middle-frequency range energy of IMFs in the spout zone and annulus zone is subjected to clustering analysis,leading to the identification of partition boundaries for each flow pattern.Based on this,a flow pattern identification method of spouted fluidized bed coupled with middle-frequency range energy in spout zone and annulus zone is proposed,which has very high identification accuracy.

Practical implementation of Hilbert-Huang Transform algorithm

Hilbert-Huang Transform (HHT) is a newly developed powerful method for nonlinear and non-stationary time series analysis. The empirical mode decomposition is the key part of HHT, while its algorithm was protected by NASA as a US patent, which limits the wide application among the scientific community. Two approaches, mirror periodic and extrema extending methods, have been developed for handling the end effects of empirical mode decomposition. The implementation of the HHT is realized in detail to widen the application. The detailed comparison of the results from two methods with that from Huang et al. (1998, 1999), and the comparison between two methods are presented. Generally, both methods reproduce faithful results as those of Huang et al. For mirror periodic method (MPM), the data are extended once forever. Ideally, it is a way for handling the end effects of the HHT, especially for the signal that has symmetric waveform. The extrema extending method (EEM) behaves as good as MPM, and it is better than MPM for the signal that has strong asymmetric waveform. However, it has to perform extrema envelope extending in every shifting process.

A technique to improve the empirical mode decomposition in the Hilbert-Huang transform

The Hilbert-based time-frequency analysis has promising capacity to reveal the time-variant behaviors of a sys- tem.To admit well-behaved Hilbert transforms,component decomposition of signals must be performed beforehand.This was first systematically implemented by the empirical mode decomposition(EMD)in the Hilbert-Huang transform,which can provide a time-frequency representation of the signals.The EMD,however,has limitations in distinguishing different components in narrowband signals commonly found in free-decay vibration signals.In this study,a technique for decompo- sing components in narrowband signals based on waves' beating phenomena is proposed to improve the EMD,in which the time scale structure of the signal is unveiled by the Hilbert transform as a result of wave beating,the order of component ex- traction is reversed from that in the EMD and the end effect is confined.The proposed technique is verified by performing the component decomposition of a simulated signal and a free decay signal actually measured in an instrumented bridge structure.In addition,the adaptability of the technique to time-variant dynamic systems is demonstrated with a simulated time-variant MDOF system.

New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology

We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method （HAM）. This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.

Differential transformation method for studying flow and heat transfer due to stretching sheet embedded in porous medium with variable thickness, variable thermal conductivity,and thermal radiation

This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations （PDEs） are transformed into a system of coupled non-linear ordinary differential equations （ODEs） with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method （DTM）. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.

NONLINEAR TIME TRANSFORMATION METHOD FOR STRONG NONLINEAR OSCILLATION SYSTEMS

In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.

Application of Hilbert-Huang Transform to the Analysis of the Landslides Triggered by the Wenchuan Earthquake

A steep rock hill with two side slopes located at DK30+256 of National Road 213 was used as a prototype for analysis. The full process from initial deformation to sliding of the slope during ground shaking was simulated by using a new Continuum-based Discrete Element Method. During the earthquake, when shaking amplitudes were lower,the stress concentration points firstly appeared at the top of the slip mass, and then some tension failure points appeared, followed by shear failure points. At the same time, both the instantaneous frequencies of accelerations in the bedrock and that in the slip mass basically stayed in two different ranges. The energy transmittance coefficients of the sliding surface also stayed in a high range. As the ground shaking lasted,the number of failure points gradually increased until landslide occurrence. The instantaneous frequencies of accelerations in the slip mass and the energy transmittance coefficients of sliding surface gradually decreased, and both finally converged to a lower range. And then, the reasons triggering landslides are analysis in the joint time-frequency domain using Hilbert-Huang Transform, as follows: the differences of distribution and dissipation of the earthquake energy and the inconsistency of movements between the slip mass and the bedrock were the two major influence factors.

Extracting Power Transformer Vibration Features by a Time-Scale-Frequency Analysis Method

In order to take advantage of the merits of WPT and HHT in feature extraction from vibration signals of power transformer, a time-scale-frequency analysis method is developed based on the combination of these two techniques. This method consists of two steps. First, the desirable wavelet packet nodes corresponding to characteristic frequency bands of power transformer are selected through a Correlation Degree Threshold Screening (CDTS) technique for reconstructing a time-domain signal that contains useful information of power transformer. Second, the HHT is then conducted on the reconstructed signal to track the instantaneous frequencies corresponding to natural characteristics of power transformer. Experimental results are provided by analyzing a real power transformer vibration signal. Compared with the features extracted by directly using HHT, the features obtained by the proposed method reveal clearer condition pattern of the transformer, which shows the potential of this method in condition monitoring of power transformer.