Application of orthogonal experimental design and Tikhonov regularization method for the identification of parameters in the casting solidification process

The inverse heat conduction method is one of methods to identify the casting simulation parameters. A new inverse method was presented according to the Tikhonov regularization theory. One appropriate regularized functional was established, and the functional was solved by the sensitivity coefficient and Newtonaphson iteration method. Moreover, the orthogonal experimental design was used to estimate the appropriate initial value and variation domain of each variable to decrease the number of iteration and improve the identification accuracy and efficiency. It illustrated a detailed case of AlSiTMg sand mold casting and the temperature measurement experiment was done. The physical properties of sand mold and the interracial heat transfer coefficient were identified at the meantime. The results indicated that the new regularization method was efficient in overcoming the ill-posedness of the inverse heat conduction problem and improving the stability and accuracy of the solutions.

The proper orthogonal decomposition method for the Navier-Stokes equations

The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.

Optimizing casting parameters of steel ingot based on orthogonal method

The influence and signification of casting parameters on the solidification process of steel ingot were discussed based on the finite element method (FEM) results by orthogonal experiment method. The range analysis, analysis of variance (ANOVA) and optimization project were used to investigate the FEM results. In order to decrease the ingot riser head and improve the utilization ratio of ingot, the casting parameters involved casting temperature, pouring velocity and interface heat transfer were optimized to decrease shrinkage pore and microporosity. The results show that the heat transfer coefficient between melt and heated board is a more sensitive factor. It is favor to decrease the shrinkage pore and microporosity under the conditions of low temperature, high pouring velocity and high heat transfer between melt and mold. If heat transfer in the ingot body is quicker than that in the riser, the position of shrinkage pore and microporosity will be closer to riser top. The results of optimization project show that few of shrinkage pore and microporosity reach into ingot body with the rational parameters, so the riser size can be reduced.

Influence of radial forging process on strain inhomogeneity of hollow gear shaft using finite element method and orthogonal design

Due to the current trend towards lightweight design in automotive industry,hollow stepped gear shafts for automobile and its radial forging process are widely investigated.Utilizing coupled finite element thermo-mechanical model,radial forging process of a hollow stepped gear shaft for automobile was simulated.The optimal combination of three process parameters including initial temperature,rotation rate and radial reduction was also selected using orthogonal design method.To examine the strain inhomogeneity of the forging workpiece,the strain inhomogeneity factor was introduced.The results reveal that the maximum effective strain and the minimum effective strain appeared in the outermost and innermost zones of different cross sections for the hollow stepped gear shaft,respectively.Optimal forging parameters are determined as a combination of initial temperature of 780°C,rotation rate of 21°/stroke and radial reduction of 3 mm.

STRESS INTENSITY FACTORS CALCULATION IN ANTI-PLANE FRACTURE PROBLEM BY ORTHOGONAL INTEGRAL EXTRACTION METHOD BASED ON FEMOL

For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions （or between the derivatives of eigenfunctions） of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors （SIFs）, so any order SIF can be extracted based on a certain known solution of displacement （an analytic result or a numerical result）. Many numerical examples based on the finite element method of lines （FEMOL） show that the present method is very powerful and efficient.

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.

Numerical Solutions of Volterra Equations Using Galerkin Method with Certain Orthogonal Polynomials

This work is aim at providing a numerical technique for the Volterra integral equations using Galerkin method. For this purpose, an effective matrix formulation is proposed to solve linear Volterra integral equations of the first and second kind respectively using orthogonal polynomials as trial functions which are constructed in the interval [-1,1] with respect to the weight function w(x)=1+x2. The efficiency of the proposed method is tested on several numerical examples and compared with the analytic solutions available in the literature.

Factors influencing HPAM solution viscosity prepared by produced water using orthogonal method

The effect of temperature and metal ion components on the viscosity of HPAM solution was studied by means of orthogonal method.Five factors and 4 levels were considered for the orthogonal design.The five factors included temperature,contents of Na+,Mg2+,Ca2+ and S2-,and the four levels mainly considered the level of produced water components in main oilfields in China.The experiment results show that temperature is the most important factor to control HPAM solution viscosity prepared by produced water.The effect of ions was in order of Na+>S2->Mg2+>Ca2+.The mechanism of each factor influencing viscosity was also discussed.Based on the actual condition of Nanyang oilfield,the desulfurization was used to improve the solution viscosity,and satisfactory result was obtained.

Plasma shape optimization for EAST tokamak using orthogonal method

It is necessary to reduce the currents of poloidal field(PF) coils as small as possible, during the static equilibrium design procedure of Experimental Advanced Superconductive Tokamak(EAST). The quasi-snowflake(QSF) divertor configuration is studied in this paper. Starting from a standard QSF plasma equilibrium, a new QSF equilibrium with 300 kA total plasma current is designed. In order to reduce the currents of PF6 and PF14, the influence of plasma shape on PF coil current distribution is analyzed. A fixed boundary equilibrium solver based on a non-rigid plasma model is used to calculate the flux distribution and PF coil current distribution. Then the plasma shape parameters are studied by the orthogonal method. According to the result, the plasma shape is redefined, and the calculated equilibrium shows that the currents of PF6 and PF14 are reduced by 3.592 kA and 2.773 kA, respectively.

CVD Method for Carbon Nanotubes Preparation Based on Orthogonal Experiment Using C_3H_6

Carbon nanotubes (CNTs) have potential applications in many fields, chemical vapor deposition (CVD) is an effective method for CNTs preparation. By CVD, the catalytic pyrolysis temperature, pyrolysis time and the size of the raw gas flow have a great influence on yield rate of CNTs and their form. In this paper, the orthogonal experiment analysis method is used for studying the influence factors of yield rate of CNTs. Research results show that, in the suitable temperature range of preparing CNTs, there is relatively more CNTs with excellent morphology, otherwise, if the temperature is too low, the growth of CNTs will not be sufficient; if the temperature is too high, then CNTs will be generated with excessive defects; with longer growth time of suitable pyrolysis of CNTs, higher yield of CNTs will be obtained; CNTs morphology with reaction time is not proportional; too low or too high raw gas flow rate is not conducive to the growth of CNTs. We have found the optimum conditions for the CNTs preparation: pyrolysis temperature 68 degrees C, pyrolysis time 35 min, propylene flow rate of 180 mL/min. The results have a reference value for the preparation of CNTS and their composites.

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.

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.

Fully Discrete Orthogonal Collocation Method of Sobolev Equations

In this paper, the fully discrete orthogonal collocation method for Sobolev equations is considered, and the equivalence for discrete Garlerkin method is proved. Optimal order error estimate is obtained.

Development of Efficient Fermentation Process at Bioreactor Level by Taguchi's Orthogonal Array Methodology for Enhanced Dextransucrase Production from <i>Weissella confusa</i>Cab3

The influence of medium ingredients on extracellular dextransucrase production by a new bacterial strain Weissella confusa Cab3 (Genbank Accession Number JX649223) was evaluated using fractional factorial design of Taguchi's orthogonal array. Four metabolism influencing factors viz. sucrose, yeast extract, K2HPO4 and Tween80 were selected to optimize dextransucrase production by W. confusa Cab3 using fractional factorial design of Taguchi methodology. Based on the influence of interaction components of fermentation, least significant factors of individual level have higher interaction severity index and vice versa for enzyme production from Weissella confusa Cab3. Sucrose and yeast extract were found to be the most significant factors which positively influenced the dextransucrase production. The optimized medium composition consisted of sucrose—5%;yeast extract—2%;K2HPO4—1.0%;Tween80—0.5%, based on Taguchi orthogonal array method. The optimized composition gave an experimental value of dextransucrase activity of 17.9 U/ml at shake flask level which corresponded well with the predicted value of 17.54 U/ml by the model. The optimized medium by Taguchi method gave significant (3 fold) enhancement of dextransucrase activity as compared to unoptimised enzyme activity of 6.0 U/ml. The dextransucrase production was scaled up in lab scale bioreactor resulting in further enhancement of enzyme activity (22.0 U/ml).

Solution of Electrohydrodynamic Flow Equation Using an Orthogonal Collocation Method Based on Mixed Interpolation

In this Paper, we have proposed a new weighted residual method known as orthogonal collocation-based on mixed interpolation (OCMI). Mixed interpolation uses the classical polynomial approximation with two correction terms given in the form of sine and cosine function. By these correction terms, we can control the error in the solution. We have applied this approach to a non-linear boundary value problem (BVP) in ODE which governs the electrohydrodynamic flow in a cylindrical conduit. The solution profiles shown in the figures are in good agreement with the work of Paullet (1999) and Ghasemi et al. (2014). Our solution is monotonic decreasing and satisfies , where, α governs the strength of non-linearity and for large values of α solutions are . The residual errors are given in Table 1 and Table 2 which are significantly small. Comparison of residual errors between our proposed method, Least square method and Homotopy analysis method is also given and shown via the Table 3 where as the profiles of the residual error are depicted in Figures 4-8. Table and graphs show that efficiency of the proposed method. The error bound and its L2-norm with relevant theorems for mixed interpolation are also given.

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

Jacobi-Sobolev Orthogonal Polynomialsand Spectral Methods for Elliptic Boundary Value Problems

Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized Jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the Jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy.

Galerkin Method for Numerical Solution of Volterra Integro-Differential Equations with Certain Orthogonal Basis Function

This paper concerns the implementation of the orthogonal polynomials using the Galerkin method for solving Volterra integro-differential and Fredholm integro-differential equations. The constructed orthogonal polynomials are used as basis functions in the assumed solution employed. Numerical examples for some selected problems are provided and the results obtained show that the Galerkin method with orthogonal polynomials as basis functions performed creditably well in terms of absolute errors obtained.

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.