Integrated multi-scale approach combining global homogenization and local refinement for multi-field analysis of high-temperature superconducting composite magnets

Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting applications.With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components,the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic fields.Traditional numerical models include homogenized orthotropic models,which simplify overall field calculation but miss detailed multi-physics aspects,and full refinement(FR)ones that are thorough but computationally demanding.Herein,we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils.This approach combines a global homogenization(GH)scheme based on the homogenized electromagnetic T-A model,a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A,and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale.We then identify“dangerous regions”at the macroscopic scale and obtain finer details using a local refinement(LR)scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale.The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature,indicating that the present approach is accurate and efficient.The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.

Multi-scale Incremental Analysis Update Scheme and Its Application to Typhoon Mangkhut(2018)Prediction

In the traditional incremental analysis update(IAU)process,all analysis increments are treated as constant forcing in a model’s prognostic equations over a certain time window.This approach effectively reduces high-frequency oscillations introduced by data assimilation.However,as different scales of increments have unique evolutionary speeds and life histories in a numerical model,the traditional IAU scheme cannot fully meet the requirements of short-term forecasting for the damping of high-frequency noise and may even cause systematic drifts.Therefore,a multi-scale IAU scheme is proposed in this paper.Analysis increments were divided into different scale parts using a spatial filtering technique.For each scale increment,the optimal relaxation time in the IAU scheme was determined by the skill of the forecasting results.Finally,different scales of analysis increments were added to the model integration during their optimal relaxation time.The multi-scale IAU scheme can effectively reduce the noise and further improve the balance between large-scale and small-scale increments in the model initialization stage.To evaluate its performance,several numerical experiments were conducted to simulate the path and intensity of Typhoon Mangkhut(2018)and showed that:(1)the multi-scale IAU scheme had an obvious effect on noise control at the initial stage of data assimilation;(2)the optimal relaxation time for large-scale and small-scale increments was estimated as 6 h and 3 h,respectively;(3)the forecast performance of the multi-scale IAU scheme in the prediction of Typhoon Mangkhut(2018)was better than that of the traditional IAU scheme.The results demonstrate the superiority of the multi-scale IAU scheme.

Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field

Self-oscillating systems abound in the natural world and offer substantial potential for applications in controllers,micro-motors,medical equipments,and so on.Currently,numerical methods have been widely utilized for obtaining the characteristics of self-oscillation including amplitude and frequency.However,numerical methods are burdened by intricate computations and limited precision,hindering comprehensive investigations into self-oscillating systems.In this paper,the stability of a liquid crystal elastomer fiber self-oscillating system under a linear temperature field is studied,and analytical solutions for the amplitude and frequency are determined.Initially,we establish the governing equations of self-oscillation,elucidate two motion regimes,and reveal the underlying mechanism.Subsequently,we conduct a stability analysis and employ a multi-scale method to obtain the analytical solutions for the amplitude and frequency.The results show agreement between the multi-scale and numerical methods.This research contributes to the examination of diverse self-oscillating systems and advances the theoretical analysis of self-oscillating systems rooted in active materials.

Melt Index Prediction by Neural Soft-Sensor Based on Multi-Scale Analysis and Principal Component Analysis

Prediction of melt index （MI）, the most important parameter in determining the product＇s grade and quality control of polypropylene produced in practical industrial processes, is studied. A novel soft-sensor model with principal component analysis （PCA）, radial basis function （RBF） networks, and multi-scale analysis （MSA） is proposed to infer the MI of manufactured products from real process variables, where PCA is carried out to select the most relevant process features and to eliminate the correlations of the input variables, MSA is introduced to a^quire much more information and to reduce the uncertainty of the system, and RBF networks are used to characterize the nonlinearity of the process. The research results show that the proposed method provides promising prediction reliability and accuracy, and supposed to have extensive application prospects in propylene polymerization processes.

SIMULATION OF CRACK DIAGNOSIS OF ROTOR BASED ON MULTI-SCALE SINGUUR-SPECTRUM ANALYSIS

In the diagnosis of rotor crack based on wavelet analysis, it is a painful task to find out an adaptive mother wavelet as many of them can be chosen and the analytic results of different mother wavelets are yet not the same. For this limitation of wavelet analysis, a novel diagnostic approach of rotor crack based on multi-scale singular-spectrum analysis （MS-SSA） is proposed. Firstly, a Jeffcott model of a cracked rotor is developed and the forth-order Runge-Kutta method is used to solve the motion equations of this rotor to obtain its time response （signals）. Secondly, a comparatively simple approach of MS-SSA is presented and the empirical orthogonal functions of different orders in various scales are regarded as analyzing functions. At last, the signals of the cracked rotor and an uncracked rotor are analyzed using the proposed approach of MS-SSA, and the simulative results are compared. The results show that, the data-adaptive analyzing functions can capture many features of signals and the rotor crack can be identified and diagnosed effectively by comparing the analytic results of signals of the cracked rotor with those of the uncracked rotor using the analyzing functions of different orders.

Multi-Scale Analysis of Fretting Fatigue in Heterogeneous Materials Using Computational Homogenization

This paper deals with modeling of the phenomenon of fretting fatigue in heterogeneous materials using the multi-scale computational homogenization technique and finite element analysis(FEA).The heterogeneous material for the specimens consists of a single hole model(25% void/cell,16% void/cell and 10% void/cell)and a four-hole model(25%void/cell).Using a representative volume element(RVE),we try to produce the equivalent homogenized properties and work on a homogeneous specimen for the study of fretting fatigue.Next,the fretting fatigue contact problem is performed for 3 new cases of models that consist of a homogeneous and a heterogeneous part(single hole cell)in the contact area.The aim is to analyze the normal and shear stresses of these models and compare them with the results of the corresponding heterogeneous models based on the Direct Numerical Simulation(DNS)method.Finally,by comparing the computational time and%deviations,we draw conclusions about the reliability and effectiveness of the proposed method.

Multi-scale analysis of earthquake activity in Chinese mainland

Identifying the active and inactive period of earthquakes in Chinese mainland is of great importance for guiding mid-short term, especially short term, earthquake forecast.……

Multi-scale and multi-fractal analysis of pressure fluctuation in slurry bubble column bed reactor

The Daubechies second order wavelet was applied to decompose pressure fluctuation signals with the gas flux varying from 0.18 to 0.90 m3/h and the solid mass fraction from 0 to 20% and scales 1?9 detail signals and the 9th scale approximation signals. The pressure signals were studied by multi-scale and R/S analysis method. Hurst analysis method was applied to analyze multi-fractal characteristics of different scale signals. The results show that the characteristics of mono-fractal under scale 1 and scale 2, and bi-fractal under scale 3?9 are effective in deducing the hydrodynamics in slurry bubbling flow system. The measured pressure signals are decomposed to micro-scale signals, meso-scale signals and macro-scale signals. Micro-scale and macro-scale signals are of mono-fractal characteristics, and meso-scale signals are of bi-fractal characteristics. By analyzing energy distribution of different scale signals,it is shown that pressure fluctuations mainly reflects meso-scale interaction between the particles and the bubble.

Feature Extraction by Multi-Scale Principal Component Analysis and Classification in Spectral Domain

Feature extraction of signals plays an important role in classification problems because of data dimension reduction property and potential improvement of a classification accuracy rate. Principal component analysis (PCA), wavelets transform or Fourier transform methods are often used for feature extraction. In this paper, we propose a multi-scale PCA, which combines discrete wavelet transform, and PCA for feature extraction of signals in both the spatial and temporal domains. Our study shows that the multi-scale PCA combined with the proposed new classification methods leads to high classification accuracy for the considered signals.

Multivariate Image Analysis in Gaussian Multi-Scale Space for Defect Detection

Inspired by the coarse-to-fine visual perception process of human vision system,a new approach based on Gaussian multi-scale space for defect detection of industrial products was proposed.By selecting different scale parameters of the Gaussian kernel,the multi-scale representation of the original image data could be obtained and used to constitute the multi- variate image,in which each channel could represent a perceptual observation of the original image from different scales.The Multivariate Image Analysis (MIA) techniques were used to extract defect features information.The MIA combined Principal Component Analysis (PCA) to obtain the principal component scores of the multivariate test image.The Q-statistic image, derived from the residuals after the extraction of the first principal component score and noise,could be used to efficiently reveal the surface defects with an appropriate threshold value decided by training images.Experimental results show that the proposed method performs better than the gray histogram-based method.It has less sensitivity to the inhomogeneous of illumination,and has more robustness and reliability of defect detection with lower pseudo reject rate.

Study on spline wavelet finite-element method in multi-scale analysis for foundation

A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.

Analysis of Multi-Scale Fractal Dimension for Image Interpolation

This article presents a novel image interpolation based on rational fractal fimction. The rational function has a simple and explicit expression. At the same time, the fi＇actal interpolation surface can be defined by proper parameters. In this paper, we used the method of ＇covering blanket＇ combined with multi-scale analysis; the threshold is selected based on the multi-scale analysis. Selecting different parameters in the rational function model, the texture regions and smooth regions are interpolated by rational fractal interpolation and rational interpolation respectively. Experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance compared with the state-of-the-art interpolation algorithms, especially in image details and texture features.

Response of the North Pacific Storm Track Activity in the Cold Season to Multi-scale Oceanic Variations of Kuroshio Extension System: A Statistical Assessment

In this paper,a statistical method called Generalized Equilibrium Feedback Analysis(GEFA)is used to investigate the responses of the North Pacific Storm Track(NPST)in the cold season to the multi-scale oceanic variations of the Kuroshio Extension(KE)system,including its large-scale variation,oceanic front meridional shift,and mesoscale eddy activity.Results show that in the cold season from the lower to the upper troposphere,the KE large-scale variation significantly weakens the storm track activity over the central North Pacific south of 30°N.The northward shift of the KE front significantly strengthens the storm track activity over the western and central North Pacific south of 40°N,resulting in a southward shift of the NPST.In contrast,the NPST response to KE mesoscale eddy activity is not so significant and relatively shallow,which only shows some significant positive signals near the dateline in the lower and middle troposphere.Furthermore,it is found that baroclinicity and baroclinic energy conversion play an important role in the formation of the NPST response to the KE multi-scale oceanic variations.

Study on Multi-Scale Blending Initial Condition Perturbations for a Regional Ensemble Prediction System

An initial conditions （ICs） perturbation method was developed with the aim to improve an operational regional ensemble prediction system （REPS）. Three issues were identified and investigated： （1） the impacts of perturbation scale on the ensemble spread and forecast skill of the REPS; （2） the scale characteristic of the IC perturbations of the REPS; and （3） whether the REPS＇s skill could be improved by adding large-scale information to the IC perturbations. Numerical experiments were conducted to reveal the impact of perturbation scale on the ensemble spread and forecast skill. The scales of IC perturbations from the REPS and an operational global ensemble prediction system （GEPS） were analyzed. A ＂multi-scale blending＂ （MSB） IC perturbation scheme was developed, and the main findings can be summarized as follows： The growth rates of the ensemble spread of the REPS are sensitive to the scale of the IC perturbations; the ensemble forecast skills can benefit from large-scale perturbations; the global ensemble IC perturbations exhibit more power at larger scales, while the regional ensemble IC perturbations contain more power at smaller scales; the MSB method can generate IC perturbations by combining the small-scale component from the REPS and the large-scale component from the GEPS; the energy norm growth of the MSB-generated perturbations can be appropriate at all forecast lead times; and the MSB-based REPS shows higher skill than the original system, as determined by ensemble forecast verification.

Scale-Dependent Representations of Relief Based on Wavelet Analysis

Automatic generalization of geographic information is the core of multi_scale representation of spatial data,but the scale_dependent generalization methods are far from abundant because of its extreme complicacy.This paper puts forward a new consistency model about scale_dependent representations of relief based on wavelet analysis,and discusses the thresholds in the model so as to acquire the continual representations of relief with different details between scales.The model not only meets the need of automatic generalization but also is scale-dependent completely.Some practical examples are given.

Active Depths of Main Faults in the Ying-Qiong Basin Investigated by Multi-Scale Wavelet Decomposition of Bouguer Gravity Anomalies and Power Spectral Methods

The Ying-Qiong Basin is located on the northwestern margin of the South China Sea and at the junction of the South China Block and the Indochina Block.It is characterized by complex geological structures.The existing seismic data in the study area is sparse due to the lack of earthquake activities.Because of the limited source energy and poor coverage of seismic data,the knowledge of deep structures in the area,including the spatial distribution of deep faults,is incomplete.Contrarily,satellite gravity data cover the entire study area and can reveal the spatial distribution of faults.Based on the wavelet multi-scale decomposition method,the Bouguer gravity field in the Ying-Qiong Basin was decomposed and reconstructed to obtain the detailed images of the first-to sixth-order gravitational fields.By incorporating the known geological features,the gravitational field responses of the main faults in the Ying-Qiong Basin were identified in the detailed fields,and the power spectrum analysis yielded the depths of 1.4,8,15,26.5,and 39 km for the average burial depths of the bottom surfaces from the first-to fifth-order detailed fields,respectively.The four main faults in the Yinggehai Basin all have a large active depth range:fault A(No.1)is between 5 and 39 km,fault B is between 26.5 and 39 km,and faults C and D are between 15 and 39 km.However,the depth of active faults in the Qiongdongnan Basin is relatively shallow,mainly between 8 and 26.5 km.

A MULTI-SCALE MORPHOLOGICAL APPROACH TO SAR IMAGE EDGE DETECTION

This paper introduces a multi-scale morphological edge detection algorithm to extract SAR image edge which suffers seriously from noise. Combining the basic theme of morphology with that of multi-scale analysis, the algorithm presents the outstanding characteristics of accuracy and robustness. Comparative Experiments reveal its fine performance.

An Automated Brain Image Analysis System for Brain Cancer using Shearlets

In this paper,an Automated Brain Image Analysis(ABIA)system that classifies the Magnetic Resonance Imaging(MRI)of human brain is presented.The classification of MRI images into normal or low grade or high grade plays a vital role for the early diagnosis.The Non-Subsampled Shearlet Transform(NSST)that captures more visual information than conventional wavelet transforms is employed for feature extraction.As the feature space of NSST is very high,a statistical t-test is applied to select the dominant directional sub-bands at each level of NSST decomposition based on sub-band energies.A combination of features that includes Gray Level Co-occurrence Matrix(GLCM)based features,Histograms of Positive Shearlet Coefficients(HPSC),and Histograms of Negative Shearlet Coefficients(HNSC)are estimated.The combined feature set is utilized in the classification phase where a hybrid approach is designed with three classifiers;k-Nearest Neighbor(kNN),Naive Bayes(NB)and Support Vector Machine(SVM)classifiers.The output of individual trained classifiers for a testing input is hybridized to take a final decision.The quantitative results of ABIA system on Repository of Molecular Brain Neoplasia Data(REMBRANDT)database show the overall improved performance in comparison with a single classifier model with accuracy of 99% for normal/abnormal classification and 98% for low and high risk classification.

Multi-scale wavelet separation of aeromag-netic anomaly and study of faults in Beijing area

In this paper, through a multi-scale separation of the aeromagnetic anomaly by wavelet transform technique, we reprocessed the aeromagnetic data collected 20 years ago in Beijing area and analyzed the aeromagnetic anomaly qualitatively, integrating geological structure features in the area. In particular, we studied the spatial distributions of the two main faults called Shunyi-Liangxiang fault and Banqiao-Babaoshan-Tongxian fault, which have cut and gone through the central Beijing area striking in NE and EW directions, respectively. The influences of these two faults on the earthquakes have also been discussed briefly.

Medical Image Segmentation Based on Wavelet Analysis and Gradient Vector Flow

Medical image segmentation is one of the key technologies in computer aided diagnosis. Due to the complexity and diversity of medical images, the wavelet multi-scale analysis is introduced into GVF (gradient vector flow) snake model. The modulus values of each scale and phase angle values are calculated using wavelet transform, and the local maximum points of modulus values, which are the contours of the object edges, are obtained along phase angle direction at each scale. Then, location of the edges of the object and segmentation is implemented by GVF snake model. The experiments on some medical images show that the improved algorithm has small amount of computation, fast convergence and good robustness to noise.