PREDICTION OF MAGNETOCRYSTALLINE ANISOTROPY OF POLYCRYSTALLINE MATERIALS WITH GENERALIZED VECTOR METHOD

The crystallite orientation distribution functions(ODFs)were determined for the surface, 1/4 depth and 1/2 depth layers of a cold-rolled W20 non-oriented silicon steel sheet.By extending the theory of magnetic anisotropy to textured materials with no sample symmetry, the variation of magnetic torque versus directions in the plane of the sheet was further calcu- lated quantitatively,which fits well with the measured torque curve.

THE SOLUTION FOR TRANSIENT TWO-PHASE FLOW BY SPLIT FLUX VECTOR METHOD

In this paper the transient two-phase flow equations and their eigenvalues are first introduced. The flux vector is then split into subvectors which just contain a specially signed eigenvalue. Using one-sided spatial difference operators finite difference equations and their solutions are obtained. Finally comparison with experiment shows the predicted results produce good agreement with experimental data.

Dynamic Stability Analysis of Wedge in Rock Slope Based on Kinetic Vector Method

A new method （kinetic vector method, KVM） is presented for analyzing the dynamic stability of wedge in rock slope. The dynamic analysis is carried out based on three dimensional distinct element code （3DEC）, and the kinetic inertial force of the wedge under seismic loading can be obtained via calculating the net vectorial nodal force of the finite difference grid. Then, the factor of safety （FOS） of the wedge can be calculated based on limit equilibrium method （LEM） at each dynamic analysis step, therefore time series of the FOS for whole earthquake process can be obtained. For the purpose of evaluating the entire dynamic stability of the wedge, dynamic factor of safety （DFOS） is proposed and defined as a numerical value corresponding with a given rate of probability guarantee based on reliability theory. Consequently, the KVM inherits the merits of the LEM and also has fully nonlinear dynamic analysis capabilities, and the feasibility and correctness of the KVM are tested by an example given by Hoek and Bray （1981）. Finally, a rock slope case in Wenchuan Earthquake regions of China is presented to verify the engineering practicability of the KVM, and the results matched the actual situation well.

Fully Distributed Learning for Deep Random Vector Functional-Link Networks

In the contemporary era, the proliferation of information technology has led to an unprecedented surge in data generation, with this data being dispersed across a multitude of mobile devices. Facing these situations and the training of deep learning model that needs great computing power support, the distributed algorithm that can carry out multi-party joint modeling has attracted everyone’s attention. The distributed training mode relieves the huge pressure of centralized model on computer computing power and communication. However, most distributed algorithms currently work in a master-slave mode, often including a central server for coordination, which to some extent will cause communication pressure, data leakage, privacy violations and other issues. To solve these problems, a decentralized fully distributed algorithm based on deep random weight neural network is proposed. The algorithm decomposes the original objective function into several sub-problems under consistency constraints, combines the decentralized average consensus (DAC) and alternating direction method of multipliers (ADMM), and achieves the goal of joint modeling and training through local calculation and communication of each node. Finally, we compare the proposed decentralized algorithm with several centralized deep neural networks with random weights, and experimental results demonstrate the effectiveness of the proposed algorithm.

Slope stability analysis under seismic load by vector sum analysis method

The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method （DFEM）. Combining with the DFEM, the vector sum analysis method （VSAM） is employed in seismic stability analysis of a slope in this paper. Different from other conventional methods, the VSAM is proposed based on the vector characteristic of force and current stress state of the slope. The dynamic stress state of the slope at any moment under seismic load can he obtained by the DFEM, thus the factor of safety of the slope at any moment during earthquake can be easily obtained with the VSAM in consideration of the DFEM. Then, the global stability of the slope can be estimated on the basis of time-history curve of factor of safety and reliability theory. The VSAM is applied to a homogeneous slope under seismic load. The factor of safety of the slope is 1.30 under gravity only and the dynamic factor of safety under seismic load is 1.21. The calculating results show that the dynamic characteristics and stability state of the slope with input ground motion can be actually analyzed. It is believed that the VSAM is a feasible and practical approach to estimate the dynamic stability of slopes under seismic load.

Casing life prediction using Borda and support vector machine methods

Eight casing failure modes and 32 risk factors in oil and gas wells are given in this paper. According to the quantitative analysis of the influence degree and occurrence probability of risk factors, the Borda counts for failure modes are obtained with the Borda method. The risk indexes of failure modes are derived from the Borda matrix. Based on the support vector machine （SVM）, a casing life prediction model is established. In the prediction model, eight risk indexes are defined as input vectors and casing life is defined as the output vector. The ideal model parameters are determined with the training set from 19 wells with casing failure. The casing life prediction software is developed with the SVM model as a predictor. The residual life of 60 wells with casing failure is predicted with the software, and then compared with the actual casing life. The comparison results show that the casing life prediction software with the SVM model has high accuracy.

Average vector field methods for the coupled Schrdinger KdV equations

The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.

A new method for orbit determination: Unit vector method

In this paper, a method of orbit determination is presented according to the principle of unit vector method (UVM). The model and arithmetic are improved and it not only suits initial orbit determination with short arc data, it also suits orbit improvement with data longer. It is also suitable for orbit of any eccentricity and any inclination. It omits most partial derivatives of all the elements which must be calculated in classical differential orbit improvement (DOI), so, it is more efficient than DOI, and the accuracy of orbit determination and convergence of algorithm are also improved appreciably.

A combination of damage locating vector method （DLV） and differential evolution algorithm （DE） for structural damage assessment

在这研究，一个二阶段的方法为识别多重损坏情形被介绍。在第一个阶段，定位向量(DLV ) 的损坏用规范的累积精力(nce ) 的方法在结构为损坏本地化被采用。在第二个阶段，微分进化算法(DE ) 被用于结构的损坏严厉。在第二个阶段，另外，可得到的客观功能的修正为传递对称的结构的问题被做。验证现在的技术的有效性，一个 72 酒吧空格的数字例子捆绑并且一个一个跨度钢门框架被考虑。另外，鉴定结果的表演上的噪音的效果也被调查。数字结果证明建议联合为多重结构的损坏案例给对损坏地点和程度的好评价。

WAVE SUPERPOSITION METHOD BASED ON VIRTUAL SOURCE BOUNDARY WITH COMPLEX RADIUS VECTOR FOR SOLVING ACOUSTIC RADIATION PROBLEMS

By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.

THE GENERALIZED VECTOR METHOD OF QUANTITATIVE TEXTURE ANALYSIS

The vector method (VM) of quantitative texture analysis has been entirely reconstructedin the Euler space using Roe’s notation. The reconstructed VM, called the generalized vectormethod (GVM), has got rid of the limitations arising from the original form of orientationrepresentation of the VM, such as the inconvenience in searching the relation between tex-tures and physical properties of materials, and conserves all the advantages of VM. The investigation on a cubic crystal system indicates that the texture vector of a samplemay be quantitatively determined with the GVM, using a complete or even an incompletepole figure. Also, the series expansion coefficients of the crystallite orientation distributionfunction (ODF) needed in calculating macroscopic anisotropies of the sample can be easilyevaluated.

Vibration reliability analysis for aeroengine compressor blade based on support vector machine response surface method

To ameliorate reliability analysis efficiency for aeroengine components, such as compressor blade, support vector machine response surface method(SRSM) is proposed. SRSM integrates the advantages of support vector machine(SVM) and traditional response surface method(RSM), and utilizes experimental samples to construct a suitable response surface function(RSF) to replace the complicated and abstract finite element model. Moreover, the randomness of material parameters, structural dimension and operating condition are considered during extracting data so that the response surface function is more agreeable to the practical model. The results indicate that based on the same experimental data, SRSM has come closer than RSM reliability to approximating Monte Carlo method(MCM); while SRSM(17.296 s) needs far less running time than MCM(10958 s) and RSM(9840 s). Therefore,under the same simulation conditions, SRSM has the largest analysis efficiency, and can be considered a feasible and valid method to analyze structural reliability.

A new magneto-cardiogram study using a vector model with a virtual heart and the boundary element method

A cardiac vector model is presented and verified, and then the forward problem for cardiac magnetic fields and electric potential are discussed based on this model and the realistic human torso volume conductor model, including lungs. A torso-cardiac vector model is used for a 12-lead electrocardiographic （ECG） and magneto-cardiogram （MCG） simulation study by using the boundary element method （BEM）. Also, we obtain the MCG wave picture using a compound four-channel HTc.SQUID system in a magnetically shielded room. By comparing the simulated results and experimental results, we verify the cardiac vector model and then do a preliminary study of the forward problem of MCG and ECG. Therefore, the results show that the vector model is reasonable in cardiac electrophysiology.

Novel Real-Time Seam Tracking Algorithm Based on Vector Angle and Least Square Method

Real-time seam tracking can improve welding quality and enhance welding efficiency during the welding process in automobile manufacturing.However,the teaching-playing welding process,an off-line seam tracking method,is still dominant in automobile industry,which is less flexible when welding objects or situation change.A novel real-time algorithm consisting of seam detection and generation is proposed to track seam.Using captured 3D points,space vectors were created between two adjacent points along each laser line and then a vector angle based algorithm was developed to detect target points on the seam.Least square method was used to fit target points to a welding trajectory for seam tracking.Furthermore,the real-time seam tracking process was simulated in MATLAB/Simulink.The trend of joint angles vs.time was logged and a comparison between the off-line and the proposed seam tracking algorithm was conducted.Results show that the proposed real-time seam tracking algorithm can work in a real-time scenario and have high accuracy in welding point positioning.

Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method

Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.

Fast Tensor Principal Component Analysis via Proximal Alternating Direction Method with Vectorized Technique

This paper studies the problem of tensor principal component analysis (PCA). Usually the tensor PCA is viewed as a low-rank matrix completion problem via matrix factorization technique, and nuclear norm is used as a convex approximation of the rank operator under mild condition. However, most nuclear norm minimization approaches are based on SVD operations. Given a matrix , the time complexity of SVD operation is O(mn2), which brings prohibitive computational complexity in large-scale problems. In this paper, an efficient and scalable algorithm for tensor principal component analysis is proposed which is called Linearized Alternating Direction Method with Vectorized technique for Tensor Principal Component Analysis (LADMVTPCA). Different from traditional matrix factorization methods, LADMVTPCA utilizes the vectorized technique to formulate the tensor as an outer product of vectors, which greatly improves the computational efficacy compared to matrix factorization method. In the experiment part, synthetic tensor data with different orders are used to empirically evaluate the proposed algorithm LADMVTPCA. Results have shown that LADMVTPCA outperforms matrix factorization based method.

DIAGONALIZATION METHOD FOR A SINGULARLY PERTURBED VECTOR ROBIN PROBLEM

In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type.

Time-variant reliability analysis of three-dimensional slopes based on Support Vector Machine method

In the reliability analysis of slope, the performance functions derived from the most available stability analysis procedures of slopes are usually implicit and cannot be solved by first-order second-moment approach. A new reliability analysis approach was presented based on three-dimensional Morgenstern-Price method to investigate three-dimensional effect of landslide in stability analyses. To obtain the reliability index, Support Vector Machine (SVM) was applied to approximate the performance function. The time-consuming of this approach is only 0.028% of that using Monte-Carlo method at the same computation accuracy. Also, the influence of time effect of shearing strength parameters of slope soils on the long-term reliability of three-dimensional slopes was investigated by this new approach. It is found that the reliability index of the slope would decrease by 52.54% and the failure probability would increase from 0.000 705% to 1.966%. In the end, the impact of variation coefficients of c and f on reliability index of slopes was taken into discussion and the changing trend was observed.

A New Class of Vector PadéApproximants in the Asymptotic Numerical Method: Application in Nonlinear 2D Elasticity

The Asymptotic Numerical Method (ANM) is a family of algorithms for path following problems, where each step is based on the computation of truncated vector series [1]. The Vector Padé approximants were introduced in the ANM to improve the domain of validity of vector series and to reduce the number of steps needed to obtain the entire solution path [1,2]. In this paper and in the framework of the ANM, we define and build a new type of Vector Padé approximant from a truncated vector series by extending the definition of the Padé approximant of a scalar series without any orthonormalization procedure. By this way, we define a new class of Vector Padé approximants which can be used to extend the domain of validity in the ANM algorithms. There is a connection between this type of Vector Padé approximant and Vector Padé type approximant introduced in [3, 4]. We show also that the Vector Padé approximants introduced in the previous works [1,2], are special cases of this class. Applications in 2D nonlinear elasticity are presented.

Method for Measuring Self-noise of Vector Hydrophones

The Vector Hydrophone(VH) is widely used to remotely detect underwater targets. Accurately measuring the self-noise of the VH provides an important basis for evaluating the performance of the detection system in which it is utilized, since the ability to acquire weak signals is determined by the VH self-noise level. To accurately measure the VH self-noise level in actual working conditions, the Dual-channel Transfer Function Method(DTFM) is proposed to reduce ambient background noise interference. In this paper, the underlying principles of DTFM in reducing ambient background noise is analyzed. The numerical simulations to determine the influence of ambient background noise, and the sensitivity difference of the two VHs on the measurement results are studied. The results of measuring the VH self-noise level in a small laboratory water tank by using DTMF indicate that ambient background noise interference can be reduced effectively by employing DTMF, more accurate self-noise level can be obtained as well. The DTMF provides an effective method for accurately measuring the self-noise level of VHs and also provides technical support for the practical application of the VH in underwater acoustics.