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.

Geometrical-Analysis-Based Algorithm for Stereo Matching of Single-Lens Binocular and Multi-Ocular Stereovision System

A geometrical analysis based algorithm is proposed to achieve the stereo matching of a single-lens prism based stereovision system. By setting the multi- face prism in frontal position of the static CCD （CM-140MCL） camera, equivalent stereo images with different orientations are captured synchronously by virtual cameras which are defined by two boundary lines： the optical axis and CCD camera field of view boundary. Subsequently, the geometrical relationship between the 2D stereo images and corresponding 3D scene is established by employing two fundamentals： ray sketching in which all the pertinent points, lines, and planes are expressed in the 3D camera coordinates and the rule of refraction. Landing on this relationship, the epipolar geometry is thus obtained by fitting a set of corresponding candidate points and thereafter, stereo matching of the prism based stereovision system is obtained. Moreover, the unique geometrical properties of the imaging system allow the proposed method free from the complicated camera calibration procedures and to be easily generalized from binocular and tri-oeular to multi-ocular stereovision systems. The performance of the algorithm is presented through the experiments on the binocular imaging system and the comparison with a conventional projection method demonstrates the efficient assessment of our novel contributions.

Global Geometric Analysis of Ship Rolling and Capsizing in Random Waves

The nonlinear biased ship rolling motion and capsizing in randoro waves are studied by utilizing a global geometric method. Thompson＇ s α-parameterized family of restoring functions is adopted in the vessel equation of motion for the representation of bias. To take into account the presence of randomness in the excitation and the response, a stochastic Melnikov method is developed and a mean-square criterion is obtained to provide an upper bound on the domain of the potential chaotic rolling motion. This criterion can be used to predict the qualitative nature of the invariant manifolds which represent the boundary botween safe and unsafe initial conditions, and how these depend on system parameters of the specific ship model. Phase space transport theory and lobe dynamics are used to demonstrate how motions starting from initial conditions inside the regions bounded by the intersected manifolds will evolve and how unexpected capsizing can occur.

PERTURBATION ANALYSIS FOR MAGNETO-PLASTIC INSTABILITY OF FERROMAGNETIC BEAM-PLATES WITH GEOMETRIC IMPERFECTION

The magneto-plastic instability of a ferromagnetic beam-type plate with simple supports and small initial imperfection is analytically investigated in this paper for that the plastic deformation of the plate with a linear-strain hardening relation is considered when the plate is located in a strong uniformly distributed magnetic ?eld. After the distribution of magnetic ?elds related to the de?ected con?guration of plate is imaginably divided into two parts, i.e., one is related to the ?at plate and the other dependent on the perturbation of magnetic ?elds for which the plate con?guration changes from the ?at into the deformed state, the perturbation technique is employed to analyze the distribution of the perturbation magnetic ?elds in and out-of the magnetic medium of the ferromagnetic structure in a transverse magnetic ?eld, which leads to some analytical formulae/solutions for the magnetic ?elds and the resulting magnetic force exerted on the plate. Based on them, the magneto-plastic buckling and snapping of the plate in a transverse magnetic ?eld is discussed, and the critical magnetic ?eld is analytically formulated in terms of the parameters of geometry and material of the plate employed by solving the governing equation of the magneto-plastic plate in the applied magnetic ?eld. Further, the sensitivity of the initial imperfection on the magneto-plastic instability, expressed by an ampli?cation function, is obtained by solving the dynamic equation of de?ection of the plate after the inertial force in the transverse direction is taken into account. The results obtained show that the critical magnetic ?eld is sensitive to the plastic characteristic, e.g., hardening coe?cient, and the instability mode and de?ection of the plate are dependent on the geometrical imperfection as well.

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.

Geometric Covariance Modeling for Surface Variation of Compliant Parts Based on Hybrid Polynomial Approximation and Spectrum Analysis

Part variation characterization is essential to analyze the variation propagation in flexible assemblies. Aiming at two governing types of surface variation,warping and waviness,a comprehensive approach of geometric covariance modeling based on hybrid polynomial approximation and spectrum analysis is proposed,which can formulate the level and the correlation of surface variations accurately. Firstly,the form error data of compliant part is acquired by CMM. Thereafter,a Fourier-Legendre polynomial decomposition is conducted and the error data are approximated by a Legendre polynomial series. The weighting coefficient of each component is decided by least square method for extracting the warping from the surface variation. Consequently,a geometrical covariance expression for warping deformation is established. Secondly,a Fourier-sinusoidal decomposition is utilized to approximate the waviness from the residual error data. The spectrum is analyzed is to identify the frequency and the amplitude of error data. Thus,a geometrical covariance expression for the waviness is deduced. Thirdly,a comprehensive geometric covariance model for surface variation is developed by the combination the Legendre polynomials with the sinusoidal polynomials. Finally,a group of L-shape sheet metals is measured along a specific contour,and the covariance of the profile errors is modeled by the proposed method. Thereafter,the result is compared with the covariance from two other methods and the real data. The result shows that the proposed covariance model can match the real surface error effectively and represents a tighter approximation error compared with the referred methods.

Quantitative Analysis of Flabellophyton from the Ediacaran Lantian Biota, South China: Application of Geometric Morphometrics in Precambrian Fossil Research

As a more efficient quantitative method for morphological analysis, geometric morphometrics is applied to the flabellate fossils Flabellophyton including Flabellophyton lantianensis and Flabellophyton strigata from Neoproterozoic Ediacaran Lantian biota, South China. Both traditional morphometric analysis （including diverging angle, length, and width distribution） and geometric morphometric analysis [including superposition of normalized area analysis, non-metric multidimensional scaling （n-MDS）, Bray-Curtis similarity cluster analysis （CLUSTER） and analysis of similarities （ANOSIM）[ were performed. The results indicate there are great interspecific morphological differences between F. lantianensis and F. strigata, in addition to some intraspecific variations within each species. Here we preliminarily suggest that the previously defined Flabellophyton should be subdivided into 2 genera at least： one marked by the dark transverse striated structure, and the other without. This recharacterization and reclassification work still needs further careful observation and comprehensive analysis with large number of flabeilate fossils combining morphology, structure, population, and community-ecology study.

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.……

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.

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.

Geometric Scaling Analysis of Deep Inelastic Scattering Data Including Heavy Quarks

An analytic massive total cross section of photon proton scattering is derived, which has geometric scaling. A geometric scaling is used to perform a global analysis of the deep inelastic scattering data on inclusive structure function F2 measured in lepton-hadron scattering experiments at small values of Bjorken x. It is shown that the descriptions of the inclusive structure function F2 and longitudinal structure function FL are improved with the massive analytic structure function, which may imply the gluon saturation effect dominating the parton evolution process at HERA. The inclusion of the heavy quarks prevent the divergence of the lepton-hadron cross section, which plays a significant role in the description of the photoproduction region.

Development of analysis model for geometric error in turning processes

A finite element model was established for analyzing the geometric errors in turning operations and a two-step analyzing process was proposed.In the first analyzing step,the cutting force and the cutting heat for the cutting conditions were obtained using the AdvantEdge.Also,the deformation of a workpiece was estimated in the second step using the ANSYS.The deformation was analyzed for a 150 mm-long workpiece at three different measuring points,such as 10,70 and 130 mm from a reference point,and the amounts of the deformation were compared through experiments.In the results of the comparison and analysis,the values obtained from these comparison and analysis represent similar tendencies.Also,it is verified that their geometric errors increase with the increase in temperature.In addition,regarding the factors that affect the deformation of a workpiece,it can be seen that the geometric error in the lathe is about 15%,the error caused by the cutting force is about 10%,and the deformation caused by the heat is about 75%.

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.

Geometrically Nonlinear Analysis of Structures Using Various Higher Order Solution Methods: A Comparative Analysis for Large Deformation

The suitability of six higher order root solvers is examined for solving the nonlinear equilibrium equations in large deformation analysis of structures.The applied methods have a better convergence rate than the quadratic Newton-Raphson method.These six methods do not require higher order derivatives to achieve a higher convergence rate.Six algorithms are developed to use the higher order methods in place of the Newton-Raphson method to solve the nonlinear equilibrium equations in geometrically nonlinear analysis of structures.The higher order methods are applied to both continuum and discrete problems(spherical shell and dome truss).The computational cost and the sensitivity of the higher order solution methods and the Newton-Raphson method with respect to the load increment size are comparatively investigated.The numerical results reveal that the higher order methods require a lower number of iterations that the Newton-Raphson method to converge.It is also shown that these methods are less sensitive to the variation of the load increment size.As it is indicated in numerical results,the average residual reduces in a lower number of iterations by the application of the higher order methods in the nonlinear analysis of structures.

Computational Geometric Analysis for <i>C. elegans</i>Trajectories on Thermal and Salinity Gradient

Elegans are one of the best model organisms in neural researches, and tropism movement is a typical learning and memorizing activity. Based on one imaging technique called Fast Track-Capturing Microscope (FTCM), we investigated the movement regulation. Two movement patterns are extracted from various trajectories through analysis on turning angle. Then we applied this classification on trajectory regulation on the compound gradient field, and theoretical results corresponded with experiments well, which can initially verify the conclusion. Our breakthrough is performed computational geometric analysis on trajectories. Several independent features were combined to describe movement properties by principal composition analysis (PCA) and support vector machine (SVM). After normalizing all data sets, no-supervising machine learning was processed along with some training under certain supervision. The final classification results performed perfectly, which indicates the further application of such computational analysis in biology researches combining with machine learning.

Relationships between femoral strength evaluated by nonlinear finite element analysis and BMD,material distribution and geometric morphology

Precisely quantifying the strength of the proximal femur and accurately assessing hip fracture risk would enable those at high risk to be identified so that preventive interventions could be taken.Development of better measures of femoral strength using the clinically

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.