Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems

This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.

Intelligent Small Sample Defect Detection of Concrete Surface Using Novel Deep Learning Integrating Improved YOLOv5

Dear Editor,This letter presents an intelligent small sample defect detection of concrete surface using novel deep learning integrating the improved YOLOv5 based on the Wasserstein GAN(WGAN)enhancement algorithm.The proposed method is capable of producing top-notch data sets to address the issues of insufficient samples and substandard quality.

Stability of an explicit time-integration algorithm for hybrid tests, considering stiffness hardening behavior

An explicit unconditionally stable algorithm for hybrid tests,which is developed from the traditional HHT-α algorithm,is proposed.The unconditional stability is first proven by the spectral radius method for a linear system.If the value of α is selected within [-0.5,0],then the algorithm is shown to be unconditionally stable.Next,the root locus method for a discrete dynamic system is applied to analyze the stability of a nonlinear system.The results show that the proposed method is conditionally stable for dynamic systems with stiffness hardening.To improve the stability of the proposed method,the structure stiffness is then identified and updated.Both numerical and pseudo-dynamic tests on a structure with the collision effect prove that the stiffness updating method can effectively improve stability.

CHARACTERISTIC GALERKIN METHOD FOR CONVECTION-DIFFUSION EQUATIONS AND IMPLICIT ALGORITHM USING PRECISE INTEGRATION

This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.

Integrated classification method of tight sandstone reservoir based on principal component analysise simulated annealing genetic algorithmefuzzy cluster means

In this research,an integrated classification method based on principal component analysis-simulated annealing genetic algorithm-fuzzy cluster means(PCA-SAGA-FCM)was proposed for the unsupervised classification of tight sandstone reservoirs which lack the prior information and core experiments.A variety of evaluation parameters were selected,including lithology characteristic parameters,poro-permeability quality characteristic parameters,engineering quality characteristic parameters,and pore structure characteristic parameters.The PCA was used to reduce the dimension of the evaluation pa-rameters,and the low-dimensional data was used as input.The unsupervised reservoir classification of tight sandstone reservoir was carried out by the SAGA-FCM,the characteristics of reservoir at different categories were analyzed and compared with the lithological profiles.The analysis results of numerical simulation and actual logging data show that:1)compared with FCM algorithm,SAGA-FCM has stronger stability and higher accuracy;2)the proposed method can cluster the reservoir flexibly and effectively according to the degree of membership;3)the results of reservoir integrated classification match well with the lithologic profle,which demonstrates the reliability of the classification method.

Test Case Prioritization in Unit and Integration Testing:A Shuffled-Frog-Leaping Approach

Both unit and integration testing are incredibly crucial for almost any software application because each of them operates a distinct process to examine the product.Due to resource constraints,when software is subjected to modifications,the drastic increase in the count of test cases forces the testers to opt for a test optimization strategy.One such strategy is test case prioritization(TCP).Existing works have propounded various methodologies that re-order the system-level test cases intending to boost either the fault detection capabilities or the coverage efficacy at the earliest.Nonetheless,singularity in objective functions and the lack of dissimilitude among the re-ordered test sequences have degraded the cogency of their approaches.Considering such gaps and scenarios when the meteoric and continuous updations in the software make the intensive unit and integration testing process more fragile,this study has introduced a memetics-inspired methodology for TCP.The proposed structure is first embedded with diverse parameters,and then traditional steps of the shuffled-frog-leaping approach(SFLA)are followed to prioritize the test cases at unit and integration levels.On 5 standard test functions,a comparative analysis is conducted between the established algorithms and the proposed approach,where the latter enhances the coverage rate and fault detection of re-ordered test sets.Investigation results related to the mean average percentage of fault detection(APFD)confirmed that the proposed approach exceeds the memetic,basic multi-walk,PSO,and optimized multi-walk by 21.7%,13.99%,12.24%,and 11.51%,respectively.

A HYBRID GRANULARITY PARALLEL ALGORITHM FOR PRECISE INTEGRATION OF STRUCTURAL DYNAMIC RESPONSES

Precise integration methods to solve structural dynamic responses and the corresponding time integration formula are composed of two parts： the multiplication of an exponential matrix with a vector and the integration term. The second term can be solved by the series solution. Two hybrid granularity parallel algorithms are designed, that is, the exponential matrix and the first term are computed by the fine-grained parallel algorithra and the second term is computed by the coarse-grained parallel algorithm. Numerical examples show that these two hybrid granularity parallel algorithms obtain higher speedup and parallel efficiency than two existing parallel algorithms.

A new integration algorithm for finite deformation of thermo-elasto-viscoplastic single crystals

An algorithm for integrating the constitutive equations in thermal framework is presented, in which the plastic deformation gradient is chosen as the integration variable. Compared with the classic algorithm, a key feature of this new approach is that it can describe the finite deformation of crystals under thermal conditions. The obtained plastic deformation gradient contains not only plastic defor- mation but also thermal effects. The governing equation for the plastic deformation gradient is obtained based on ther- mal multiplicative decomposition of the total deformation gradient. An implicit method is used to integrate this evo- lution equation to ensure stability. Single crystal 1 100 aluminum is investigated to demonstrate practical applications of the model. The effects of anisotropic properties, time step, strain rate and temperature are calculated using this integration model.

COORDINATION OF THE MOTION PARAMETERS WITHIN STEP-BY-STEP INTEGRATION FOR DYNAMIC EQUATION

A method is presented that coordinates the calculation of the displacement, velocity and acceleration of structures within the time-steps of different types of step-by-step integration. The dynamic equation is solved using an energy equation and the calculating data of the original method. The method presented is better than the original method in terms of calculating postulations and is in better conformity with the system's movement. Take the Wilson-θ method as an example. By using the coordination process, the calculation precision has been greatly im proved (reducing the errors by approximately 90% ), and the greater part of overshooting of the calculation result has been eliminated. The study suggests that the mal-coordination of the motion parameters within the time-step is the major factor that contributes to the result errors of step-by-step integration for the dynamic equation.

A CLASS OF EBE TIME INTEGRATION ALGORITHMS FOR TRANSIENT FINITE ELEMENT STRUCTURAL DYNAMICAL ANALYSIS

A new class of algorithms for trails lent finite element structural dynamical analysis which is amenable to all efficient implementation inl parallel computers (especially Massively Parallel Computers) is proposed. The suitability of the method for parallel computation stems from the fact that, gived an arbitrary partition of the finite element mesh, each element in the partition can be processed over a time step independently and simultaneously with the rest, and no global equation solving effort is involved. Although the Proposed EBE time integration algorithms are shown to have the structure of an explicit scheme, they are unconditionally stable over a certain range of the algorithmic parameter.

The Integration of Cooperation Model and Genetic Algorithm

In the photogrammetry,some researchers have applied genetic algorithms in aerial image texture classification and reducing hyper_spectrum remote sensing data.Genetic algorithm can rapidly find the solutions which are close to the optimal solution.But it is not easy to find the optimal solution.In order to solve the problem,a cooperative evolution idea integrating genetic algorithm and ant colony algorithm is presented in this paper.On the basis of the advantages of ant colony algorithm,this paper proposes the method integrating genetic algorithms and ant colony algorithm to overcome the drawback of genetic algorithms.Moreover,the paper takes designing texture classification masks of aerial images as an example to illustrate the integration theory and procedures.

An Improved Higher-Order Time Integration Algorithm for Structural Dynamics

Based on the weighted residual method,a single-step time integration algorithm with higher-order accuracy and unconditional stability has been proposed,which is superior to the second-order accurate algorithms in tracking long-term dynamics.For improving such a higher-order accurate algorithm,this paper proposes a two sub-step higher-order algorithm with unconditional stability and controllable dissipation.In the proposed algorithm,a time step interval[t_(k),t_(k)+h]where h stands for the size of a time step is divided into two sub-steps[t_(k),t_(k)+γh]and[t_(k)+γh,t_(k)+h].A non-dissipative fourth-order algorithm is used in the rst sub-step to ensure low-frequency accuracy and a dissipative third-order algorithm is employed in the second sub-step to lter out the contribution of high-frequency modes.Besides,two approaches are used to design the algorithm parameterγ.The rst approach determinesγby maximizing low-frequency accuracy and the other determinesγfor quickly damping out highfrequency modes.The present algorithm usesρ_(∞)to exactly control the degree of numerical dissipation,and it is third-order accurate when 0≤ρ_(∞)<1 and fourth-order accurate whenρ_(∞)=1.Furthermore,the proposed algorithm is self-starting and easy to implement.Some illustrative linear and nonlinear examples are solved to check the performances of the proposed two sub-step higher-order algorithm.

Simple Program for Step-by-Step Time Integration in Chemical Kinetics, Applied to Simple Model for Hydrogen Combustion

A simple algorithm is proposed for step-by-step time integration of stiff ODEs in Chemical Kinetics. No predictor-corrector technique is used within each step of the algorithm. It is assumed that species concentrations less than 10-6 mol·L-1 do not activate any chemical reaction. So, within each step, the time steplength Δt of the algorithm is determined from the fastest reaction rate maxR by the formula Δt = 10-6mol·L-1/max R. All the reversible elementary reactions occur simultaneously;however, by a simple book-keeping technique, the updating of species concentrations, within each step of the algorithm, is performed within each elementary reaction separately. The above proposed simple algorithm for Chemical Kinetics is applied to a simple model for hydrogen combustion with only five reversible elementary reactions (Initiation, Propagation, First and Second Branching, Termination by wall destruction) with six species (H2, O2, H, O, HO, H2O). These five reversible reactions are recommended in the literature as the most significant elementary reactions of hydrogen combustion [1] [2]. Based on the proposed here simple algorithm for Chemical Kinetics, applied to the global mechanism of proposed five reversible elementary reactions for hydrogen combustion, a simple and short computer program has been developed with only about 120 Fortran instructions. By this proposed program, the following are obtained: 1) The total species concentration of hydrogen combustion, starting from the sum of initial reactants concentrations [H2] + [O2], gradually diminishes, due to termination reaction by wall destruction, and tends to the final concentration of the product [H2O], that is to the 2/3 of its initial value, in accordance to the established overall stoichiometric reaction of hydrogen combustion 2H2 + O2 → 2H2O. 2) Time-histories for concentrations of main species H2, O2, H, H2O of hydrogen combustion, in explosion and equilibrium regions, obtained by the proposed program, are compared to corresponding ones obtained by accurate computational studies of [3]. 3) In the first step of the algorithm, the only nonzero species concentrations are those of reactants [H2], [O2]. So, the maximum reaction rate is that of the forward initiation reaction max R = Rif = kif[H2] [O2], where the rate constant kif is very slow. Thus, the first time steplength Δt1 = 10-6mol·L-1/max R results long in sec. After the first step, the sequences of all the following Δt’s are very short, in μsec. So, the first time steplength Δt1 can be considered as ignition delay time. 4) It is assumed that explosion corresponds to ignition delay time Δt1 t1 = 10 sec., can be considered as explosion limit curve. This curve is compared to the corresponding one obtained by the accurate computational studies of [2].

INTEGRATED OPERATOR GENETIC ALGORITHM FOR SOLVING MULTI-OBJECTIVE FLEXIBLE JOB-SHOP SCHEDULING

In the flexible job-shop scheduling problem （FJSP）, each operation has to be assigned to a machine from a set of capable machines before alocating the assigned operations on all machines. To solve the multi-objective FJSP, the Grantt graph oriented string representation （GOSR） and the basic manipulation of the genetic algorithm operator are presented. An integrated operator genetic algorithm （IOGA） and its process are described. Comparison between computational results and the latest research shows that the proposed algorithm is effective in reducing the total workload of all machines, the makespan and the critical machine workload.

Fast precise integration method for hyperbolic heat conduction problems

A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.

Dynamic and Integrated Load-Balancing Scheduling Algorithm for Cloud Data Centers

One of the challenging scheduling problems in Cloud data centers is to take the allocation and migration of reconfigurable virtual machines as well as the integrated features of hosting physical machines into consideration. We introduce a Dynamic and Integrated Resource Scheduling algorithm (DAIRS) for Cloud data centers. Unlike traditional load-balance scheduling algorithms which often consider only one factor such as the CPU load in physical servers, DAIRS treats CPU, memory and network bandwidth integrated for both physical machines and virtual machines. We develop integrated measurement for the total imbalance level of a Cloud datacenter as well as the average imbalance level of each server. Simulation results show that DAIRS has good performance with regard to total imbalance level, average imbalance level of each server, as well as overall running time.

Integrity Monitoring in Navigation Systems: Fault Detection and Exclusion RAIM Algorithm Implementation

The use of GPS is becoming increasingly popular for real-time navigation systems. To ensure that satellite failures are detected and excluded at the receiver is of high importance for the integrity of the satellite navigation system. The focus of this paper is to implement a fault detection and exclusion algorithm in a software GPS receiver in order to provide timely warnings to the user when it is not advisable to use the GPS system for navigation. The GPS system currently provides some basic integrity information to users via the navigation message, but it is not timely enough for safety-critical applications. RAIM is a means of providing integrity with the capability of detecting when a satellite failure or a measurement error has occurred. It is the simplest and most cost effective technique for integrity monitoring. After applying the iterative fault detection and the exclusion algorithm, a significant improvement in positioning accuracy is achieved.

ITERATIVE ALGORITHM FOR AXIALLY ACCELERATING STRINGS WITH INTEGRAL CONSTITUTIVE LAW

A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is applied to discretize the state variables, and the Runge- Kutta method is applied to solve the resulting differential-integral equation system. A linear iterative process is designed to compute the integral terms at each time step, which makes the numerical method more efficient and accurate. As examples, nonlinear parametric vibrations of an axially moving viscoelastic string are analyzed.

Dosimetric Comparison of Integral Radiation Dose: Anisotropic Analytical Algorithm and Acuros XB in Breast Radiotherapy

The impact of the difference between Anisotropic Analytical Algorithm (AAA) and Acuros XB (AXB) in breast radiotherapy is not clearly due to different uses and further research is required to explain this effect. The aim of this study is to investigate the contribution of calculation differences between AAA and AXB to the integral radiation dose (ID) on critical organs. Seven field intensity modulated radiotherapy (IMRT) plans were generated using with AAA and AXB algorithms for twenty patients with early stage left breast cancer after breast conserving surgery. Volumetric and dosimetric differences, as well as, the Dmean, V5, V20 doses of the left and right-sided lung, the Dmean, V10, V20, V30 doses of heart and the Dmean, V5, V10 doses of the contralateral breast were investigated. The mean dose (Dmean), V5, V20 doses of the left-sided lung, the Dmean, V5, V10 doses of right-sided lung, the Dmean, V10, V20, V30 doses of heart and the Dmean, V5, V10 doses of the contralateral breast were found to be significantly higher with AAA. In this research integral dose was also higher in the AAA recalculated plan and the AXB plan with the average dose as follows left lung 2%, heart 2%, contralateral breast 8%, contralateral lung 4% respectively. Our study revealed that the calculation differences between Acuros XB (AXB) and Anisotropic Analytical Algorithm (AAA) in breast radiotherapy caused serious differences on the stored integral doses on critical organs. In addition, AXB plans showed significantly dosimetric improvements in multiple dosimetric parameters.