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.

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.

Optimizing Average Electric Power During the Charging of Lithium-Ion Batteries Through the Taguchi Method

In recent times, lithium-ion batteries have been widely used owing to their high energy density, extended cycle lifespan, and minimal self-discharge rate. The design of high-speed rechargeable lithium-ion batteries faces a significant challenge owing to the need to increase average electric power during charging. This challenge results from the direct influence of the power level on the rate of chemical reactions occurring in the battery electrodes. In this study, the Taguchi optimization method was used to enhance the average electric power during the charging process of lithium-ion batteries. The Taguchi technique is a statistical strategy that facilitates the systematic and efficient evaluation of numerous experimental variables. The proposed method involved varying seven input factors, including positive electrode thickness, positive electrode material, positive electrode active material volume fraction, negative electrode active material volume fraction, separator thickness, positive current collector thickness, and negative current collector thickness. Three levels were assigned to each control factor to identify the optimal conditions and maximize the average electric power during charging. Moreover, a variance assessment analysis was conducted to validate the results obtained from the Taguchi analysis. The results revealed that the Taguchi method was an eff ective approach for optimizing the average electric power during the charging of lithium-ion batteries. This indicates that the positive electrode material, followed by the separator thickness and the negative electrode active material volume fraction, was key factors significantly infl uencing the average electric power during the charging of lithium-ion batteries response. The identification of optimal conditions resulted in the improved performance of lithium-ion batteries, extending their potential in various applications. Particularly, lithium-ion batteries with average electric power of 16 W and 17 W during charging were designed and simulated in the range of 0-12000 s using COMSOL Multiphysics software. This study efficiently employs the Taguchi optimization technique to develop lithium-ion batteries capable of storing a predetermined average electric power during the charging phase. Therefore, this method enables the battery to achieve complete charging within a specific timeframe tailored to a specificapplication. The implementation of this method can save costs, time, and materials compared with other alternative methods, such as the trial-and-error approach.

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.

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.

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.

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 simu- lation 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 coeffcient and Newton-Raphson iteration method. Moreover, the orthogonal experimental design was used to estimate the ap- propriate initial value and variation domain of each variable to decrease the number of iteration and improve the identification accuracy and effciency. It illustrated a detailed case of AlSi7Mg sand mold casting and the temperature measurement ex- periment was done. The physical properties of sand mold and the interfacial heat transfer coeffcient were identified at the meantime. The results indicated that the new regularization method was effcient in overcoming the ill-posedness of the inverse heat conduction problem and improving the stability and accuracy of the solutions.

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.

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.

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).

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.

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.

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 54.300,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.