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.

INVESTIGATION OF FLIGHT DYNAMICS OF THRUST VECTORING AIRCRAFT USING EXTENDED CONTINUATION METHODS

This paper presents the flight dynamical behavior of the thrust vectoring aircraft with extended bifurcation and continuation methods. In contrast to the standard bifurcation and continuation methods, the extended methods are capable of calculating the continuation curves of the equilibrium points for the particular type of trimming flight. Therefore, these methods can not only give the performance measures of aircraft, but also determine the stability of trimming points. In this paper, the methods are used to verify the effectiveness of the thrust vectoring control law, to define the flight envelope boundary, to analyze the stability and controllability of trimming flight, and to predict the departures of the instable flight. The result shows that the extended methods provide more flight dynamic information and are useful in preliminary design of the thrust vectoring aircraft.

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 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.

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 Morgenstem-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 andfon reliability index of slopes was taken into discussion and the changing trend was observed.

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.

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.

New regularization method and iteratively reweighted algorithm for sparse vector recovery

Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design an iterative algorithm,namely the iteratively reweighted algorithm(IR-algorithm),for efficiently computing the sparse solutions to the proposed regularization model.The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length.Finally,we present numerical examples to illustrate the features of the new regularization and algorithm.

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.

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.

SVD-MPE: An SVD-Based Vector Extrapolation Method of Polynomial Type

An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors , where , N being very large. Such sequences arise, for example, in the solution of systems of linear or nonlinear equations by fixed-point iterative methods, and are simply the required solutions. In most cases of interest, however, these sequences converge to their limits extremely slowly. One practical way to make the sequences converge more quickly is to apply to them vector extrapolation methods. Two types of methods exist in the literature: polynomial type methods and epsilon algorithms. In most applications, the polynomial type methods have proved to be superior convergence accelerators. Three polynomial type methods are known, and these are the minimal polynomial extrapolation (MPE), the reduced rank extrapolation (RRE), and the modified minimal polynomial extrapolation (MMPE). In this work, we develop yet another polynomial type method, which is based on the singular value decomposition, as well as the ideas that lead to MPE. We denote this new method by SVD-MPE. We also design a numerically stable algorithm for its implementation, whose computational cost and storage requirements are minimal. Finally, we illustrate the use of SVD-MPE with numerical examples.

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.

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.

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.

Multi-coupled single scattering method of solving vector radiative transfer equations

A new method of multi-coupled single scattering （MCSS） for solving a vector radiative transfer equation is de- veloped and made public on Internet. Recent solutions from Chandrasekhar＇s X-Y method is used to validate the MCSS＇s result, which shows high precision. The MCSS method is theoretically simple and clear, so it can be easily and credibly extended to the simulation of aerosol/cloud atmosphere＇s radiative properties, which provides effective support for research into polarized remote sensing.

Analysis method and algorithm design of biological sequence problem based on generalized k-mer vector

K-mer can be used for the description of biological sequences and k-mer distribution is a tool for solving sequences analysis problems in bioinformatics.We can use k-mer vector as a representation method of the k-mer distribution of the biological sequence.Problems,such as similarity calculations or sequence assembly,can be described in the k-mer vector space.It helps us to identify new features of an old sequence-based problem in bioinformatics and develop new algorithms using the concepts and methods from linear space theory.In this study,we defined the k-mer vector space for the generalized biological sequences.The meaning of corresponding vector operations is explained in the biological context.We presented the vector/matrix form of several widely seen sequence-based problems,including read quantification,sequence assembly,and pattern detection problem.Its advantages and disadvantages are discussed.Also,we implement a tool for the sequence assembly problem based on the concepts of k-mer vector methods.It shows the practicability and convenience of this algorithm design strategy.

Krylov Iterative Methods for Support Vector Machines to Classify Galaxy Morphologies

Large catalogues of classified galaxy images have been useful in many studies of the universe in astronomy. There are too many objects to classify manually in the Sloan Digital Sky Survey, one of the premier data sources in astronomy. Therefore, efficient machine learning and classification algorithms are required to automate the classifying process. We propose to apply the Support Vector Machine (SVM) algorithm to classify galaxy morphologies and Krylov iterative methods to improve runtime of the classification. The accuracy of the classification is measured on various categories of galaxies from the survey. A three-class algorithm is presented that makes use of multiple SVMs. This algorithm is used to assign the categories of spiral, elliptical, and irregular galaxies. A selection of Krylov iterative solvers are compared based on their efficiency and accuracy of the resulting classification. The experimental results demonstrate that runtime can be significantly improved by utilizing Krylov iterative methods without impacting classification accuracy. The generalized minimal residual method (GMRES) is shown to be the most efficient solver to classify galaxy morphologies.

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.