An efficient approach for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations

An efficient approach is proposed for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations.The concentrated plastic hinges,described by the Bouc-Wen model,are assumed to occur at the two ends of a linear-elastic beam element.The auxiliary differential equations governing the plastic rotational displacements and their corresponding hysteretic displacements are replaced with linearized differential equations.Then,the two sets of equations of motion for the original nonlinear system can be reduced to an expanded-order equivalent linearized equation of motion for equivalent linear systems.To solve the equation of motion for equivalent linear systems,the nonstationary random vibration analysis is carried out based on the explicit time-domain method with high efficiency.Finally,the proposed treatment method for initial values of equivalent parameters is investigated in conjunction with parallel computing technology,which provides a new way of obtaining the equivalent linear systems at different time instants.Based on the explicit time-domain method,the key responses of interest of the converged equivalent linear system can be calculated through dimension reduction analysis with high efficiency.Numerical examples indicate that the proposed approach has high computational efficiency,and shows good applicability to weak nonlinear and medium-intensity nonlinear systems.

Stability and Time-Step Constraints of Implicit-Explicit Runge-Kutta Methods for the Linearized Korteweg-de Vries Equation

This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.

Linearization Learning Method of BP Neural Networks

Feedforward multi layer neural networks have very strong mapping capability that is based on the non linearity of the activation function, however, the non linearity of the activation function can cause the multiple local minima on the learning error surfaces, which affect the learning rate and solving optimal weights. This paper proposes a learning method linearizing non linearity of the activation function and discusses its merits and demerits theoretically.

MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method

This paper investigates the magnetohydrodynamic （MHD） boundary layer flow of an incompressible upper-convected Maxwell （UCM） fluid over a porous stretching surface. Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations. The nonlinear prob- lem is solved by using the successive Taylor series linearization method （STSLM）. The computations for velocity components are carried out for the emerging parameters. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.

A symplectic finite element method based on Galerkin discretization for solving linear systems

We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.

THE LINEAR SAMPLING METHOD FOR RECONSTRUCTING A PENETRABLE CAVITY WITH UNKNOWN EXTERNAL OBSTACLES

We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the first part,we obtain the well-posedness of the direct scattering problem by the variational method.In the second part,we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity,and the shape of the external obstacle,however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.

Development of a Quantitative Prediction Support System Using the Linear Regression Method

The development of prediction supports is a critical step in information systems engineering in this era defined by the knowledge economy, the hub of which is big data. Currently, the lack of a predictive model, whether qualitative or quantitative, depending on a company’s areas of intervention can handicap or weaken its competitive capacities, endangering its survival. In terms of quantitative prediction, depending on the efficacy criteria, a variety of methods and/or tools are available. The multiple linear regression method is one of the methods used for this purpose. A linear regression model is a regression model of an explained variable on one or more explanatory variables in which the function that links the explanatory variables to the explained variable has linear parameters. The purpose of this work is to demonstrate how to use multiple linear regressions, which is one aspect of decisional mathematics. The use of multiple linear regressions on random data, which can be replaced by real data collected by or from organizations, provides decision makers with reliable data knowledge. As a result, machine learning methods can provide decision makers with relevant and trustworthy data. The main goal of this article is therefore to define the objective function on which the influencing factors for its optimization will be defined using the linear regression method.

Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method

A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.

A new two-step variational model for multiplicative noise removal with applications to texture images

Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motivated by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper.In the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing.Once the isophote directions are constructed,an image is restored to fit the constructed directions in the second step.The existence and uniqueness of the solution to the variational problems are proved.In these two steps,we use the gradient descent method and construct finite difference schemes to solve the problems.Especially,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation.Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.

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.

Hierarchical Controller Synthesis Under Linear Temporal Logic Specifications Using Dynamic Quantization

Linear temporal logic(LTL)is an intuitive and expressive language to specify complex control tasks,and how to design an efficient control strategy for LTL specification is still a challenge.In this paper,we implement the dynamic quantization technique to propose a novel hierarchical control strategy for nonlinear control systems under LTL specifications.Based on the regions of interest involved in the LTL formula,an accepting path is derived first to provide a high-level solution for the controller synthesis problem.Second,we develop a dynamic quantization based approach to verify the realization of the accepting path.The realization verification results in the necessity of the controller design and a sequence of quantization regions for the controller design.Third,the techniques of dynamic quantization and abstraction-based control are combined together to establish the local-to-global control strategy.Both abstraction construction and controller design are local and dynamic,thereby resulting in the potential reduction of the computational complexity.Since each quantization region can be considered locally and individually,the proposed hierarchical mechanism is more efficient and can solve much larger problems than many existing methods.Finally,the proposed control strategy is illustrated via two examples from the path planning and tracking problems of mobile robots.

Underdetermined direction of arrival estimation with nonuniform linear motion sampling based on a small unmanned aerial vehicle platform

Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.

An Extended Numerical Method by Stancu Polynomials for Solution of Integro-Differential Equations Arising in Oscillating Magnetic Fields

In this study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled by a class of linear integro-differential equations. As the method has been improved, the Stancu polynomials that are generalization of the Bernstein polynomials have been used. The method has been tested on a physical problem how the method can be applied. Moreover, numerical results of the method have been compared with the numerical results of the other methods to indicate the efficiency of the method.

Low-complexity signal detection for massive MIMO systems via trace iterative method

Linear minimum mean square error(MMSE)detection has been shown to achieve near-optimal performance for massive multiple-input multiple-output(MIMO)systems but inevitably involves complicated matrix inversion,which entails high complexity.To avoid the exact matrix inversion,a considerable number of implicit and explicit approximate matrix inversion based detection methods is proposed.By combining the advantages of both the explicit and the implicit matrix inversion,this paper introduces a new low-complexity signal detection algorithm.Firstly,the relationship between implicit and explicit techniques is analyzed.Then,an enhanced Newton iteration method is introduced to realize an approximate MMSE detection for massive MIMO uplink systems.The proposed improved Newton iteration significantly reduces the complexity of conventional Newton iteration.However,its complexity is still high for higher iterations.Thus,it is applied only for first two iterations.For subsequent iterations,we propose a novel trace iterative method(TIM)based low-complexity algorithm,which has significantly lower complexity than higher Newton iterations.Convergence guarantees of the proposed detector are also provided.Numerical simulations verify that the proposed detector exhibits significant performance enhancement over recently reported iterative detectors and achieves close-to-MMSE performance while retaining the low-complexity advantage for systems with hundreds of antennas.

Revealing the Hidden Mathematical Beauties of the Cayley-Hamilton Method

The inversion of a non-singular square matrix applying a Computer Algebra System (CAS) is straightforward. The CASs make the numeric computation efficient but mock the mathematical characteristics. The algorithms conducive to the output are sealed and inaccessible. In practice, other than the CPU timing, the applied inversion method is irrelevant. This research-oriented article discusses one such process, the Cayley-Hamilton (C.H.) [1]. Pursuing the process symbolically reveals its unpublished hidden mathematical characteristics even in the original article [1]. This article expands the general vision of the original named method without altering its practical applications. We have used the famous CAS Mathematica [2]. We have briefed the theory behind the method and applied it to different-sized symbolic and numeric matrices. The results are compared to the named CAS’s sealed, packaged library commands. The codes are given, and the algorithms are unsealed.

A Study of EM Algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

Solution of Nonlinear Integro Differential Equations by Two-Step Adomian Decomposition Method (TSAM)

The Adomian decomposition method (ADM) can be used to solve a wide range of problems and usually gets the solution in a series form. In this paper, we propose two-step Adomian Decomposition Method (TSAM) for nonlinear integro-differential equations that will facilitate the calculations. In this modification, compared to the standard Adomian decomposition method, the size of calculations was reduced. This modification also avoids computing Adomian polynomials. Numerical results are given to show the efficiency and performance of this method.

Internal residual stress measurement on linear friction welding of titanium alloy plates with contour method

The internal residual stress within a TC 17 titanium alloy joint welded by linear friction welding （LFW） was measured by the contour method, which is a relatively new and destructive technique to obtain a full map of internal residual stress. The specimen was first cut into two parts; the out-of-plane displacement contour formed by the release of the residual stress was then measured; finally, taking the measured contour of the cut plane as the boundary conditions, a linear elastic finite element analysis was carried out to calculate the corresponding distribution of residual stress normal to the cut plane. The internal stress distribution of the TC 17 titanium alloy LFWjoint was also analyzed. The results show that the tensile residual stress in the TC17 LFW weld is mainly present within a region about 12 mm from the weld centerline; the peak tensile residual stress occurs at the weld centerline and reaches 360 MPa （about one third of the yield strength of TC17 alloy）; within the weld zone of the TC17 LFW weld, the through-thickness stress is not uniform, and the internal stress is larger than that near the top or bottom surface.

Improved absorbing boundary condition based on linear interpolation for ADI-FDTD method

With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.

ANALYSIS OF NONLINEAR PIEZOELECTRIC CIRCULAR SHALLOW SPHERICAL SHELLS BY DIFFERENTIAL QUADRATURE ELEMENT METHOD

The static behavior of piezoelectric circular spherical shallow shells under both electrical and mechanical loads is studied by using the differential quadrature element method (DQEM). Geometrical nonlinearity effect is considered. Detailed formulations and procedures are given for the first time. Several examples are analyzed and accurate results are obtained by the DQEM. Based on the results in this paper, one may conclude that the DQEM is a useful tool for obtaining solutions of structural elements. It can be seen that the shell shape may be theore tically controlled and snap through may occur when the applied voltage reaches a critical value even without mechanical load for certain geometric configurations.