Restarted Full Orthogonalization Method with Deflation for Shifted Linear Systems

In this paper,we study shifted restated full orthogonalization method with deflation for simultaneously solving a number of shifted systems of linear equations.Theoretical analysis shows that with the deflation technique,the new residual of shifted restarted FOM is still collinear with each other.Hence,the new approach can solve the shifted systems simultaneously based on the same Krylov subspace.Numerical experiments show that the deflation technique can significantly improve the convergence performance of shifted restarted FOM.

Selecting the Technology of Sodium Silicate Modified Poplar with the Highest Performance by Fuzzy Orthogonal Method

Sodium silicate modification can improve the overall performance of wood.The modification process has a great influence on the properties of modified wood.In this study,a new method was introduced to analyze the wood modification process,and the properties of modified wood were studied.Poplar wood was modified with sodium silicate by vacuum-pressure impregnation.After screening using single-factor experiments,an orthogonal experiment was carried out with solution concentration,impregnation time,impregnation pressure,and the cycle times as experimental factors.The modified poplar with the best properties was selected by fuzzy mathematics and characterized by SEM,FT-IR,XRD and TG.The results showed that some lignin and hemicellulose were removed from the wood due to the alkaline action of sodium silicate,and the orderly crystal area of poplar became disorderly,resulting in the reduction of crystallinity of the modified poplar wood.FT-IR analysis showed that sodium silicate was hydrolyzed to form polysilicic acid in wood,and structural analysis revealed the formation of Si-O-Si and Si-O-C,indicating that sodium silicate reacted with fibers on the wood cell wall.TG-DTG curves showed that the final residual mass of modified poplar wood increased from 25%to 67%,and the temperature of the maximum loss rate decreased from 343℃ to 276℃.The heat release and smoke release of modified poplar wood decreased obviously.This kind of material with high strength and fire resistance can be used in the outdoor building and indoor furniture.

A REDUCED-ORDER MFE FORMULATION BASED ON POD METHOD FOR PARABOLIC EQUATIONS

In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis- tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.

Modified OMP method for multi-target parameter estimation in frequency-agile distributed MIMO radar

Introducing frequency agility into a distributed multipleinput multiple-output(MIMO)radar can significantly enhance its anti-jamming ability.However,it would cause the sidelobe pedestal problem in multi-target parameter estimation.Sparse recovery is an effective way to address this problem,but it cannot be directly utilized for multi-target parameter estimation in frequency-agile distributed MIMO radars due to spatial diversity.In this paper,we propose an algorithm for multi-target parameter estimation according to the signal model of frequency-agile distributed MIMO radars,by modifying the orthogonal matching pursuit(OMP)algorithm.The effectiveness of the proposed method is then verified by simulation results.

Warm Compaction Process of P/M Steels by Orthogonal Testing Method

In order to achieve higher density of P/M steels using the die wall lubrication compacting method or powder lubricant in warm compaction process, the influence of different process parameters on the green density of warm compacted samples was studied. According to the orthogonal test method, the authors systematically study the influence of the different compaction pressure, condition of lubrication and compaction temperature on the green density of the sample in the warm compaction process, and put forward the optimal process parameter of warm compaction experiment. It is found that, a high compaction pressure （≥700 MPa）, die wall lubrication combined with a small amount of internal lubricants, and fitting compaction temperature by different condition of lubrication, are the optimal parameters in warm compaction process.

Mathematical Description of Acousto-Optic Tunable Filter Orthogonal Polarizing Method

The transfer function of the optical splitting system of the acousto-optic tunable filter （AOTF） is deduced to be a reference to optical design. The characteristic matrix （ transfer function） of AOTF is used to describe quantitatively the characters of polarization elements in the orthogonal polarizing system. According to the characteristic matrix, the included angle of polarizer＇s transmission direction and polarization analyzer＇s transmission direction should be 90°. As a result the signal to noise ratio increased about 20 times though the light intensity was reduced to 54.3%,because both the transmittances of polarizer and polarization analyzer are 0. 74, which is an intrinsic character. The orthogonal polarizing method is an effective method to get rid of the influence of zero order light and improve the spectrum resolution and signal-to-noise ratio.

Nonlinear Oscillation Analysis by an Orthogonal Function Method

In this paper an orthogonal function method is presented based on the idea to suppose perioche sohuion with the method of harmonie balance The displaeement is expressed in the form of trigonometric fumctions a group of simplified digenequationsare obtained by the use of orthogonarity of trigonometric fumetions and linear mondes The method overcomes the diffieulty of a drifi term existing in systems with quadratic nonlinearities .The ealeulation examples show that the method has thd advantages of high caleulation preeision high convergenee speed and littld ealeulation work

ON THE METHOD OF ORTHOGONALITY CONDITIONS FOR SOLVING THE PROBLEM OF LARGE DEFLECTION OF CIRCULAR PLATE

In this paper, we reexamine the method of successive approximation presented by Prof. Chien Wei-zangfor solving the problem of large deflection of a circular plate, and find that the method could be regarded as the method of strained parameters in the singular perturbation theory. In terms of the parameter representing the ratio of the center deflection to the thickness of the plate, we make the asymptotic expansions of the deflection, membrane stress and the parameter of load as in Ref. [1], and then give the orthogonality conditions (i.e. the solvability conditions) for the resulting equations, by which the stiffness characteristics of the plate could be determined. It is pointed out that with the solutions for the small deflection problem of the circular plate and the orthogonality conditions, we can derive the third order approximate relations between the parameter of load and the center deflection and the first-term approximation of membrane stresses at the center and edge of the plate without solving the differential equations. For some special cases (i.e. under uniform load, under compound toad, with different boundary conditiors), we deduce the specific expressions and obtain the results in agreement with the previous ones given by Chien Wei-zang, Yeh kai-yuan and Hwang Chien in Refs. [1 - 4J.

Finite Element Orthogonal Collocation Approach for Time Fractional Telegraph Equation with Mamadu-Njoseh Polynomials

Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It is one of the most general methods when compared to other numerical techniques. PDEs posed in a variational form over a given space, say a Hilbert space, are better numerically handled with the FEM. The FEM algorithm is used in various applications which includes fluid flow, heat transfer, acoustics, structural mechanics and dynamics, electric and magnetic field, etc. Thus, in this paper, the Finite Element Orthogonal Collocation Approach (FEOCA) is established for the approximate solution of Time Fractional Telegraph Equation (TFTE) with Mamadu-Njoseh polynomials as grid points corresponding to new basis functions constructed in the finite element space. The FEOCA is an elegant mixture of the Finite Element Method (FEM) and the Orthogonal Collocation Method (OCM). Two numerical examples are experimented on to verify the accuracy and rate of convergence of the method as compared with the theoretical results, and other methods in literature.

Simulation and analysis of soil homogenization drills based on discrete element method and response surface methodology

Currently,rotary drilling is one of the main pieces of equipment used for in-situ remediation of contaminated soil.However,this equipment has problems such as uneven mixing and low utilization efficiency,which affect the efficiency of in-situ soil remediation.To improve the efficiency of in-situ soil remediation,this paper takes contaminated black soil as the research object,and the structural design of the new three-stage soil remediation auger is carried out based on SolidWorks.The mixing process of soil and heavy metal passivator under different motion and structural parameters was investigated by the discrete element method(DEM)and response surface methodology.The experimental design was based on rotational speed,homogenizing mixing time,crushing section pitch,and homogenizing section pitch as factors,and soil fragmentation ratio,the coefficient of dispersion,and torque as optimization indices.The kinematic and structural parameters of the three-stage auger drill bit were then optimized using the one-factor method,the orthogonal test,and the response surface methodology,respectively.The test method uses a one-way test to determine the central level value of the orthogonal test and a comprehensive balance method to determine the best combination of parameters for the orthogonal test,which is then used as the central value of the response surface test for parameter optimization.The optimal combinations of kinematic and structural parameters of the three-stage auger drill bit are determined and validated using response surface methodology.The optimum combination of parameters was found to be a speed of 129 rpm,a homogenizing mixing time of 24 s,a pitch of 165 mm in the crushing section,and a pitch of 132 mm in the homogenizing section.The error between the optimal value of the predicted model using the response surface method and the actual simulated value under the optimal parameters is 4.2%,4.9%,and 5.3%,respectively.The optimized factor parameters provide a reference for the design of the structural and kinematic parameters of the in-situ homogenization equipment.

Strength of copolymer grouting material based on orthogonal experiment

Using the orthogonal experimental design method involving three factors and three levels, the flexural strength and the compressive strength of copolymer grouting material were studied with different compositions of water-cement ratio （mass fraction of water to cement）, epoxy resin content, and waterborne epoxy curing agent content. By orthogonal range and variance analysis, the orders of three factors to influence the strength, the significance levels of different factors, and the optimized compound ratio scheme of copolymer grouting material mixture at different curing ages were determined. An empirical relationship among the strength of copolymer grouting material, the water-cement ratio, the epoxy resin content, and the waterborne epoxy curing agent content was established by multivariate regression analysis. The results indicate that water-cement ratio is the most principal and significant influencing factor on the strength. Epoxy resin content and waterbome epoxy curing agent content also have a significant influence on the strength. But epoxy resin content has a greater influence on the 7-day and 28-day flexural strength, and waterborne epoxy curing agent content has a greater influence on the 3-day flexural strength and the compressive strength. The copolymer grouting material with water-cement ratio of 0.4, epoxy resin content of 8% （mass fraction） and waterbome epoxy curing agent content of 2% （mass fraction） is the best one for repairing of cement concrete pavement. The flexural strength and the compressive strength have good correlation, and the ratio of compressive strength to flexural strength is between 1.0 and 3.3.

Sensitivity analyses of cables to suspen-dome structural system

The construction of the cables is a key step for erecting suspen-dome structures. In practical engineering, it is difficult to ensure that the designed pre-stresses of cables have been exactly introduced into the structures in the site; so it is necessary to evaluate the influence of the variation of the pre-stresses on the structural behavior. In the present work, an orthogonal design method was employed to investigate the pre-stressed cables' sensitivity to the suspen-dome system. The investigation was concentrated on a Kiewitt suspen-dome. Parametric studies were carried out to study the sensitivity of the structure's static behavior, dynamic behavior, and buckling loads when the pre-stresses in the cables varied. The investigation indicated that suspen-dome structures are sensitive to the pre-stresses in all cables; and that the sensitivity depended on the location of the cables and the kind of structural behavior. Useful suggestions are given at the end of the paper.

Tuning PID Parameters Based on a Combination of the Expert System and the Improved Genetic Algorithms

a new strategy combining an expert system and improved genetic algorithms is presented for tuning proportional-integral-derivative （PID） parameters for petrochemical processes. This retains the advantages of genetic algorithms, namely rapid convergence and attainment of the global optimum. Utilization of an orthogonal experiment method solves the determination of the genetic factors. Combination with an expert system can make best use of the actual experience of the plant operators. Simulation results of typical process systems examples show a good control performance and robustness.

CNC FLEXIBLE GENERATING SPECIFIC GEAR TOOTH PROFILE BASED ON STANDARD INVOLUTE GEAR HOB

A new method named orthogonal two-way link-shift here has been proposed.Based on the method and a standard involute gear hob, a specific gear tooth profile (including anarbitrary gear tooth profile and a modified involute gear tooth profile) can be generated on aCNC(computer numerical control) bobbing machine. Computer simulation has been carried out, and theresults prove that the method is right and practicable. So, the fabrication costs can be greatlydecreased than before. The new method has momentous significance to realize gear's optimizedmodification under different work conditions.

Mesoscopic-Scale Numerical Investigation Including the Influence of Process Parameters on LPBF Multi-Layer Multi-Path Formation

As a typical laser additive manufacturing technology,laser powder bed fusion(LPBF)has achieved demonstration applications in aerospace,biomedical and other fields.However,how to select process parameters quickly and reasonably is still themain concern of LPBF production.In order to quantitatively analyze the influence of different process parameters(laser power,scanning speed,hatch space and layer thickness)on the LPBF process,the multilayer and multi-path forming process of LPBF was predicted based on the open-source discrete element method framework Yade and the open-source finite volume method framework OpenFOAM.Based on the design of experiments method,a four-factor three-level orthogonal test scheme was designed,and the porosity and surface roughness data of each calculation scheme were extracted.By analyzing the orthogonal test data,it was found that as the laser power increased,the porosity decreased,and as the scanning speed,hatch space,and layer thickness increased,the porosity increased.In addition,the influence of laser power and scanning speed on surface roughness showed a trend of decreasing first and then increasing,while the influence of scanning distance and layer thickness on surface roughness showed amonotonous increasing trend.The order of the influence of each process parameter on porosity was:scanning speed>laying thickness>laser power>hatch space,and the order of the influence of each process parameter on surface roughness was:hatch space>layer thickness>laser power>scanning speed.So the porosity of the part is most sensitive to scanning speed,and the surface roughness is the most sensitive to hatch space.The above conclusions are expected to provide process control basis for actual LPBF production of the 316L stainless steel alloy.

Damage evolution analysis of cast steel GS-20Mn5V based on modified GTN model

A modified Gurson-Tvergaard-Needleman （GTN） model that accounts for the mixed （isotropic and kinematic） hardening of cast steel GS-20Mn5V was developed and implemented in the finite dement program ABAQUS/Standard via a user-defined material subroutine UMAT. This model couples the stress state and damage evolution （pore volume fraction increase） by a classic method that assumes that the total void volume fraction is divided into a nucleation and a growth part. A parametric study was conducted to assess the effect of modified GTN model parameters on mechanical properties such as the nucleation, growth and coalescence of voids and to obtain the optimal parameter combination by the orthogonal test method. The predicted load-displacement curves of notched specimens with the optimal parameters are favorably compared to the experimental curves. Therefore, the modified GTN model can be used to predict the damage evaluation and fracture behavior of GS-20Mn5V.

Predictive Modeling and Parameter Optimization of Cutting Forces During Orbital Drilling

To optimize cutting control parameters and provide scientific evidence for controlling cutting forces,cutting force modeling and cutting control parameter optimization are researched with one tool adopted to orbital drill holes in aluminum alloy 6061.Firstly,four cutting control parameters(tool rotation speed,tool revolution speed,axial feeding pitch and tool revolution radius)and affecting cutting forces are identified after orbital drilling kinematics analysis.Secondly,hybrid level orthogonal experiment method is utilized in modeling experiment.By nonlinear regression analysis,two quadratic prediction models for axial and radial forces are established,where the above four control parameters are used as input variables.Then,model accuracy and cutting control parameters are analyzed.Upon axial and radial forces models,two optimal combinations of cutting control parameters are obtained for processing a13mm hole,corresponding to the minimum axial force and the radial force respectively.Finally,each optimal combination is applied in verification experiment.The verification experiment results of cutting force are in good agreement with prediction model,which confirms accracy of the research method in practical production.

Sensitivity Analysis and Optimization of Geometric Parameters of a New Fluid Bag Buffer Mechanism on Buffering Performance

A new fluid bag buffer mechanism,which can provide large axial stiffness under the small displacement,is designed.The dynamic change laws of the mechanism stiffness and the internal pressure of the fluid bag are studied when it is subjected to impact load.According to the protection performance for the flexible joint and the pressure change in the fluid bag during the impact process,the sensitivity of the geometric parameters of the fluid bag to the axial stiffness is analyzed by using the orthogonal experimental method,and the optimal parameter combination of the geometric parameters of the fluid bag under impact is obtained,leading to the displacement of the inner shell reduce by 41.4%.The results show that the internal pressure of the fluid bag is a rising process of oscillation and fluctuation.The sensitivity of the geometric parameters of the fluid bag to the displacement of the inner shell from high to low is as follows:Height H,radius r,wall thickness t,chamfer A.The correlation between the geometric parameters of the fluid bag and its internal pressure is:H is negatively correlated with the internal pressure,while the r,t,and A are positively correlated with the internal pressure.

Bifurcation analysis for nonlinear multi-degree-of-freedom rotor system with liquid-film lubricated bearings

The oil-film oscillation in dimensional nonlinear problem. In this a large rotating machinery is a complex high- paper, a high pressure rotor of an aero engine with a pair of liquid-film lubricated bearings is modeled as a twenty-two-degree-of-freedom nonlinear system by the Lagrange method. This high-dimensional nonlinear system can be reduced to a two-degree-of-freedom system preserving the oil-film oscillation property by introducing the modified proper orthogonal decomposition （POD） method. The effi- ciency of the method is shown by numerical simulations for both the original and reduced systems. The Chen-Longford （C-L） method is introduced to get the dynamical behaviors of the reduced system that reflect the natural property of the oil-film oscillation.

VIRTUAL EXPERIMENTAL ANALYSIS ON CLEANING ELEMENT OF SUGARCANE HARVESTER

The laws of influence of different factors have been analyzed in order to enhance the working efficiency and fatigue life of the cleaning element in brush shape of the sugarcane harvester. Based on the principle of orthogonal experiment design, the virtual-orthogonal-experimental analysis for the cleaning element is carried out on the finite element analysis （FEA） software-ANSYS after analyzing the nonlinear structural behavior in the working procedure. The results are analyzed with the overall balancing method, and then the optimal combination is got, which is made up of different levels of different factors. Also the optimal combination of design parameters of the cleaning element received fiom the virtual experimental analysis is conducted an experiment to confirm that the virtual analysis model and results are right, and the effect of factors on the function of the cleaning element is obtained by more analysis and further optimizing.