Production of the unit of capacitance

Conclusion The perfection of the complex of measuring means that are presently a state primary standard of the farad of the USSR have as their purpose a further decrease in the error of reproducing the farad, which must be decreased and brought to between 1·10^–7 and 2·10^–7. An important role, namely the perfection of indirect methods and an increase in the precision of reproducing still other electromagnetic units, was assigned to the primary standard of the unit of capacitance in the course of perfecting the system of standards of units of electrical magnitudes [4], These units include resistance, inductance, magnetic flux, and magnetic induction, whose reproduction error in the new system of standards will be decreased to between one-third and one-half.Translated from Izmeritel'naya Tekhnika, No. 4, pp. 76–78, April, 1976.     

Determining the heat conduction of anisotropic media on the basis of the scanning method. Theoretical basis of the method

The solution of the heat-conduction equation is obtained for an anisotropic semiinfinite medium heated by a mobile heat source. The temperature fields of various types of mobile source are analyzed, with a view to developing a method of determining the heat conduction of anisotropic media.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 2, pp. 273–279, February, 1988.     

Numerical simulation of forward problem for electrical capacitance tomography using element-free Galerkin method

Electrical capacitance tomography (ECT) is a new measurement technology, which is often used to identify two-phase/multi-phase flow regime and investigate the solid distribution in circulating fluidized bed. It is composed of forward problem and inverse problem. Usually, forward problem is solved using finite element method (FEM). Element-free Galerkin method (EFGM) is one of the meshless methods developed recently. In order to obtain the numerical solution using EFGM, a shape function is constructed by moving least-squares (MLS) approximation, a variational equation weak form of the studied problem is used to deduce the discrete equation, and Lagrange multipliers are used to satisfy essential boundary conditions. In EFGM, only nodal data are necessary compared with FEM. In this paper, EFGM was used to solve forward problem and simulation results showed EFGM has high accuracy and its post-processing is easy.     

Errors in reproducing the planar-angle unit with a ring laser

Translated from Izmeritel'naya Tekhnika, No. 12, pp. 11–12, December, 1989.     

Quasi-convex reproducing kernel meshfree method

A quasi-convex reproducing kernel approximation is presented for Galerkin meshfree analysis. In the proposed meshfree scheme, the monomial reproducing conditions are relaxed to maximizing the positivity of the meshfree shape functions and the resulting shape functions are referred as the quasi-convex reproducing kernel shape functions. These quasi-convex meshfree shape functions are still established within the framework of the classical reproducing or consistency conditions, namely the shape functions have similar form as that of the conventional reproducing kernel shape functions. Thus this approach can be conveniently implemented in the standard reproducing kernel meshfree formulation without an overmuch increase of computational effort. Meanwhile, the present formulation enables a straightforward construction of arbitrary higher order shape functions. It is shown that the proposed method yields nearly positive shape functions in the interior problem domain, while in the boundary region the negative effect of the shape functions are also reduced compared with the original meshfree shape functions. Subsequently a Galerkin meshfree analysis is carried out by employing the proposed quasi-convex reproducing kernel shape functions. Numerical results reveal that the proposed method has more favorable accuracy than the conventional reproducing kernel meshfree method, especially for structural vibration analysis.     

Simulation design of electrical capacitance tomography sensors

The resolution and sensing field of electrical capacitance tomography sensors depends upon the configuration of their electrodes and guards, so optimum design is essential in order to provide improved response. Simulations in 2D and 3D are performed based on the finite element method to study the influence of the electrode, guard size and screen arrangement on the sensor characteristics and the reconstructed image     

Image reconstruction algorithm based on the extended regularised total least squares method for electrical capacitance tomography

Electrical capacitance tomography (ECT) is a non-invasive imaging technology that aims at the visualisation of the cross-sectional permittivity distribution of a dielectric object based on the measured capacitance data. Successful applications of ECT depend greatly on the precision and speed of the image reconstruction algorithms. ECT image reconstruction is a typical ill-posed problem, and its solution is unstable, that is, the solution is sensitive to noises in the input data. Methods that ensure the stability of a solution while enhancing the quality of the reconstructed images should be used to obtain a meaningful reconstruction result. An image reconstruction algorithm based on the regularised total least squares (TLS) method that considers the errors in both the sensitivity field matrix and the capacitance data for ECT is presented. The regularised TLS method is extended using a combination robust estimation technique and an extended stabilising functional according to the ill-posed characteristics of ECT, which transforms the image reconstruction problem into an optimisation problem. In addition, the Newton algorithm is employed to solve the objective functional. Numerical simulations indicate that the algorithm is feasible and overcomes the numerical instability of ECT image reconstruction; for the cases of the reconstructed objects considered here, the spatial resolution of the reconstructed images obtained using the algorithm is enhanced; as a result, an efficient method for ECT image reconstruction is introduced.     

Treatment of discontinuity in the reproducing kernel element method

A discontinuous reproducing kernel element approximation is proposed in the case where weak discontinuity exists over an interface in the physical domain. The proposed method can effectively take care of the discontinuity of the derivative by truncating the window function and global partition polynomials. This new approximation keeps the advantage of both finite element methods and meshfree methods as in the reproducing kernel element method. The approximation has the interpolation property if the support of the window function is contained in the union of the elements associated with the corresponding node; therefore, the continuity of the primitive variables at nodes on the interface is ensured. Furthermore, it is smooth on each subregion (or each material) separated by the interface. The major advantage of the method is its simplicity in implementation and it is computationally efficient compared to other methods treating discontinuity. The convergence of the numerical solution is validated through calculations of some material discontinuity problems. Copyright © 2005 John Wiley & Sons, Ltd.     

Matrix properties of data from electrical capacitance tomography

Some properties of the matrix of capacitance-data collected by the electrical capacitance tomography (ECT) technique are studied. These data are used to extract information in various industrial process applications and, in particular, about flows in pipelines. The features in the eigenvalue distribution of normalized capacitance matrices for three practical classes of permittivity distributions, namely core flows, annular flows, and stratified flows, are investigated and compared by numerical solution. It is shown that the leading eigenvalue is strongly related to the area ratio of permittivity contrast in the cross-section of the flow, while the next two eigenvalues provide a basis for distinguishing among these three classes of flows. In particular, for core and annular flows, the difference between the second and third eigenvalues is shown to be related to the eccentricity of permittivity profile. Numerical examples are presented to illustrate how the area ratio for some permittivities that do not belong to these classes can be effectively estimated.     

Theoretical basis of the finite element iterative method for the eigenvalue problem in stationary cracks

In a recently published paper a finite element based iterative method was introduced for the solution of the eigenvalue problem of stationary cracks.¹ In this paper we give the theoretical basis of this iterative method and we show why it converges and how it could be extended to more complex fracture problems. The cases of cracks at interfaces are illustrated.