Variable Differential Method Research Articles

СИСТЕМА АВТОМАТИЧНОГО РОЗПОДІЛУ ГАРЯЧОГО ДУТТЯ ПО ФУРМАХ ДОМЕННОЇ ПЕЧІ

The article considers the current issue of automatic control of the distribution of the blast through the blast furnace tuyeres. Ensuring a uniform distribution of blast over the furnace hearth allows you to even out the heating around its circumference, improve the distribution of gas flows in the column of charge materials and the full use of chemical and thermal energy of gases. Studies of existing blast distribution systems have shown the reasons for their inoperability. This was because the measuring equipment, the control devices and the actuators do not withstand high temperatures. As a solution to this problem, it was proposed to add carbon fiber in the development of the actuators that will significantly reduce the abrasive wear and increase the resistance to high temperatures. A system of automatic control of the blast distribution for each tuyere separately was also developed. The airflow in the system is measured with Venturi tubes using a variable differential method. Regulation in the system is carried out by means of a carbon fiber-reinforced butterfly valve installed in the fixed knee of the tuyere device befind Venturi tube. In the environment of object-oriented programming, special software for controlling the process of the blast distribution through the tuyeres, its uniform distribution and redistribution between all tuyeres, with the option to set the total flow rate and the flow rate for a single tuyere was developed. Using the developed system of automatic distribution of blast by tuyeres will ensure a uniform supply of blast to the furnace of the blast furnace through separate tuyeres, which will increase the productivity of the furnace itself while reducing coke consumption

Simultaneous estimation of hydro-dipersive parameters using a new modified levenberg-marquardt algorithm

Determination of soil hydrodynamic parameters at field scale is of great importance for modeling soil water dynamics and for agricultural water management. The direct estimation of those parameters is time-consuming and afflicted with serious uncertainties. Inverse modeling is known to get efficient technique for solving non-linear problems in hydrology. Levenberg–Marquardt (LM) algorithm is a gradient-based method, which has been widely used for solving inverse soil water flow problems. In the LM algorithm, sensitivity coefficients are mainly evaluated by numerical differentiation methods. However, sensitivity coefficients are difficult to be precisely calculated by numerical differentiation methods, if transient states and non-linearities are involved. In this paper, a new approach is proposed for sensitivity analysis using the complex variabledifferentiation method (CVDM) to estimate simultaneously the hydraulic and dispersive properties of unsaturated soil from in-situ experiments. In this approach, the sensitivity coefficients can be determined in a more accurate way than the traditional finite difference method. The results show that the new inverse analysis method in the present work has high accuracy, validity, uniqueness and higher inversion efficiency, compared with the previous least-squares method. The simulated and measured water contents and tracer concentration were generally close. Overall, it was concluded that the CVDM is a promising method to estimate hydro-dispersive parameters in the unsaturated zone.

A new approach to speed up the conjugate gradient method by applying the complex variable differentiation method

ABSTRACTThis study represents a novel approach to speed up the solution of nonlinear inverse heat conduction problems (IHCPs) by the implementation of the complex variable differentiation method (CVDM). A difficulty appeared in the solution of nonlinear problems is the great amount of computational time. To handle this problem, a new scheme is introduced to improve the conjugate gradient method (CGM). The main contribution in the improvement of conventional CGM is the simultaneous solution of direct and sensitivity problems by applying the complex variable method. The derivation of sensitivity problem by utilizing the analytic derivative is difficult or impossible, since the direct problem is complicated mathematically in many cases. By this approach, the analytic derivation of sensitivity problem is circumvented, while the Jacobian matrix components are obtained accompanied by the solution of the direct problem. Therefore, the developed scheme results in the reduction of mathematical manipulations. Due to the high nonlinearity of moving boundary inverse problems, the ablation problem is considered as the benchmark to examine the accuracy and effectiveness of the proposed scheme. The simulated results illustrate that the developed scheme has the potential to significantly reducing of the computational expenses while maintaining the quality of numerical solution.

Antenna Design by an Adaptive Variable Differential Artificial Bee Colony Algorithm

Optimal design of antennas is very useful to attain narrow beam and low sidelobe, while keeping a low manufacturing cost. Artificial bee colony (ABC) algorithm has shown good performance in solving electromagnetic inverse problems. However, the ABC algorithm costs too much number of iterations and converges slowly in the antenna design. This paper proposes an adaptive variable differential method for ABC (AVDABC). This method adaptively decides the number of decision variables to be mutated. Existing modified ABC algorithms employ the same search equation in one iteration. The proposed adaptive variable method assigns different search equations to chosen decision variables in one iteration. The proposed AVDABC algorithm is more diverse than the existing ABC algorithms. Through numerical simulation on mathematical functions, AVDABC converges faster than three compared algorithms. Moreover, demonstrated by the design of sparse nonuniform antenna array and Yagi-Uda antenna, the AVDABC algorithm achieves promising performance. Thus, the proposed algorithm is helpful to solve antenna array design problems.

Efficient hypersingular line and surface integrals direct evaluation by complex variable differentiation method

We present an efficient numerical scheme to evaluate hypersingular integrals appeared in boundary element methods. The hypersingular integrals are first separated into regular and singular parts, in which the singular integrals are defined as limits around the singularity and their values are determined analytically by taking the finite part values. The remaining regular integrals can be evaluated using rational interpolatory quadrature or complex variable differentiation (CVDM) for the regular function when machine precision like accuracy is required. The proposed method is then generalised for evaluating hypersingular surface integrals, in which the inner integral is treated as the hypersingular line integral via coordinate transformations. The procedure is implemented into 8-node rectangular boundary element and 6-node triangular element for numerical evaluation. Finally, several numerical examples are presented to demonstrate the efficiency of the present method. To the best of our knowledge, the proposed method is more accurate, faster and more generalised than other methods available in the literature to evaluate hypersingular integrals.

Inverse analysis of thermal conductivities in transient non-homogeneous and non-linear heat conductions using BEM based on complex variable differentiation method

This paper presents a new inverse analysis approach to sensitivity analysis and material property identification in transient non-homogeneous and non-linear heat conduction Boundary Element Method (BEM) analysis based on Complex Variable Differentiation Method (CVDM). In this approach, the material properties are taken as the optimization variables, and the sensitivity coefficients are computed by CVDM. The advantages of using CVDM are that the computation of partial derivatives of an implicit function is reduced to function calculation in a complex domain, and the parameter sensitivity coefficients can be determined in a more accurate way than the traditional Finite Difference Method (FDM). Based on BEM and CVDM in evaluation of the sensitivity matrix of heat flux, the parameter such as thermal conductivity can be accurately identified. Six numerical examples are given to demonstrate the potential of the proposed approach. The results indicate that the presented method is efficient for identifying the thermal conductivity with single or multiple parameters.

Application of the Complex Variable Differential Method in the Back Analysis of Geotechnical Engineering

On the stability analysis of complex slope, the determination of rock-soil masses shear strength parameters is very important. It’s very necessary to use the back analysis method to verify experiment result of rock-soil masses parameters for the important slope engineering. Because the sensitivity of shear strength parameters to displacement parameters is very poor, so that we couldn’t get the satisfactory shear strength parameters result by traditional back analysis method. Aiming at the problems of traditional back analysis method, this paper puts forward a totally new method of back analysis, which is applicable to the shear strength parameters of rock-soil masses through the integration of complex variable differentiation method, optimization method and elastic-plasticity finite-element method. The method mathematically back calculates shear strength parameters of rock-soil masses on the basis of displacement of measuring point. The sample calculation result indicates that the method possesses high accuracy and searching efficiency, and is a method of back analysis of displacement deserving popularizing.

Explicit formulations for evaluation of velocity gradients using boundary‐domain integral equations in 2D and 3D viscous flows

AbstractIn this paper, explicit boundary‐domain integral equations for evaluating velocity gradients are derived from the basic velocity integral equations. A free term is produced in the new strongly singular integral equation, which is not included in recent formulations using the complex variable differentiation method (CVDM) to compute velocity gradients (Int. J. Numer. Meth. Fluids 2004; 45:463–484; Int. J. Numer. Meth. Fluids 2005; 47:19–43). The strongly singular domain integrals involved in the new integral equations are accurately evaluated using the radial integration method (RIM). Considerable computational time for evaluating integrals of velocity gradients can be saved by using present formulation than using CVDM. The formulation derived in this paper together with those presented in reference (Int. J. Numer. Meth. Fluids 2004; 45:463–484) for 2D and in (Int. J. Numer. Meth. Fluids 2005; 47:19–43) for 3D problems constitutes a complete boundary‐domain integral equation system for solving full Navier–Stokes equations using primitive variables. Three numerical examples for steady incompressible viscous flow are given to validate the derived formulations. Copyright © 2007 John Wiley & Sons, Ltd.