Abstract: In the present work steady inviscid hypersonic flows
are calculated by approximate Method. Maslens' inverse method is the chosen approximate method. For the inverse problem, parabolic
shock shape is chosen for the two-dimensional flow, and the body shape and flow field are calculated using Maslen's method. For the axisymmetric inverse problem paraboloidal shock is chosen and the
surface distribution of pressure is obtained.
Abstract: In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP): Given X ∈ Rn×p and a diagonal matrix Λ ∈ Rp×p, find nontrivial real-valued symmetric arrow-head matrices A and B such that AXΛ = BX. We then consider an optimal approximation problem: Given real-valued symmetric arrow-head matrices A, ˜ B˜ ∈ Rn×n, find (A, ˆ Bˆ) ∈ SE such that Aˆ − A˜2 + Bˆ − B˜2 = min(A,B)∈SE (A−A˜2 +B −B˜2), where SE is the solution set of IEP. We show that the optimal approximation solution (A, ˆ Bˆ) is unique and derive an explicit formula for it.
Abstract: This paper presents an approach which is based on the
use of supervised feed forward neural network, namely multilayer
perceptron (MLP) neural network and finite element method (FEM)
to solve the inverse problem of parameters identification. The
approach is used to identify unknown parameters of ferromagnetic
materials. The methodology used in this study consists in the
simulation of a large number of parameters in a material under test,
using the finite element method (FEM). Both variations in relative
magnetic permeability and electrical conductivity of the material
under test are considered. Then, the obtained results are used to
generate a set of vectors for the training of MLP neural network.
Finally, the obtained neural network is used to evaluate a group of
new materials, simulated by the FEM, but not belonging to the
original dataset. Noisy data, added to the probe measurements is used
to enhance the robustness of the method. The reached results
demonstrate the efficiency of the proposed approach, and encourage
future works on this subject.
Abstract: Nondestructive testing in engineering is an inverse
Cauchy problem for Laplace equation. In this paper the problem
of nondestructive testing is expressed by a Laplace-s equation with
third-kind boundary conditions. In order to find unknown values on
the boundary, the method of fundamental solution is introduced and
realized. Because of the ill-posedness of studied problems, the TSVD
regularization technique in combination with L-curve criteria and
Generalized Cross Validation criteria is employed. Numerical results
are shown that the TSVD method combined with L-curve criteria is
more efficient than the TSVD method combined with GCV criteria.
The abstract goes here.
Abstract: This paper presents the identification of the impact
force acting on a simply supported beam. The force identification is
an inverse problem in which the measured response of the structure is
used to determine the applied force. The identification problem is
formulated as an optimization problem and the genetic algorithm is
utilized to solve the optimization problem. The objective function is
calculated on the difference between analytical and measured
responses and the decision variables are the location and magnitude
of the applied force. The results from simulation show the
effectiveness of the approach and its robustness vs. the measurement
noise and sensor location.
Abstract: The nonlinear damping behavior is usually ignored in
the design of a miniature moving-coil loudspeaker. But when the
loudspeaker operated in air, the damping parameter varies with the
voice-coil displacement corresponding due to viscous air flow. The
present paper presents an identification model as inverse problem to
identify the nonlinear damping parameter in the lumped parameter
model for the loudspeaker. Theoretical results for the nonlinear
damping are verified by using laser displacement measurement
scanner. These results indicate that the damping parameter has the
greatly different nonlinearity between in air and vacuum. It is believed
that the results of the present work can be applied in diagnosis and
sound quality improvement of a miniature loudspeaker.
Abstract: The paper discusses a 3D numerical solution of the inverse boundary problem for a continuous casting process of alloy. The main goal of the analysis presented within the paper was to estimate heat fluxes along the external surface of the ingot. The verified information on these fluxes was crucial for a good design of a mould, effective cooling system and generally the whole caster. In the study an enthalpy-porosity technique implemented in Fluent package was used for modeling the solidification process. In this method, the phase change interface was determined on the basis of the liquid fraction approach. In inverse procedure the sensitivity analysis was applied for retrieving boundary conditions. A comparison of the measured and retrieved values showed a high accuracy of the computations. Additionally, the influence of the accuracy of measurements on the estimated heat fluxes was also investigated.
Abstract: In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw
Abstract: The current practice of determination of moisture diffusivity of building materials under laboratory conditions is predominantly aimed at the absorption phase. The main reason is the simplicity of the inverse analysis of measured moisture profiles. However, the liquid moisture transport may exhibit significant hysteresis. Thus, the moisture diffusivity should be different in the absorption (wetting) and desorption (drying) phase. In order to bring computer simulations of hygrothermal performance of building materials closer to the reality, it is then necessary to find new methods for inverse analysis which could be used in the desorption phase as well. In this paper we present genetic algorithm as a possible method of solution of the inverse problem of moisture transport in desorption phase. Its application is demonstrated for AAC as a typical building material.
Abstract: This paper investigates the inverse problem of determining
the unknown time-dependent leading coefficient in the parabolic
equation using the usual conditions of the direct problem and an additional
condition. An algorithm is developed for solving numerically
the inverse problem using the technique of space decomposition in a
reproducing kernel space. The leading coefficients can be solved by a
lower triangular linear system. Numerical experiments are presented
to show the efficiency of the proposed methods.