Papers by Keyword: Inverse Problem

Abstract: The temperature dependence of the thermal conductivity of plasma‑sprayed ZrO₂-5 wt.% CaO, (ZrO₂-5 wt.% CaO)-10 wt.% Ni, and (ZrO₂-5 wt.% CaO)-30 wt.% Ni coatings was investigated. A combined experimental and numerical approach was employed, comprising specimen heating with a propane–oxygen torch with in situ temperature field measurements and numerical simulation using COMSOL Multiphysics®. Thermal conductivity was calculated via an iterative solution of the inverse heat conduction problem. It was found that thermal conductivity increases with increasing Ni content: for the ZrO₂/CaO ceramic coating, thermal conductivity in the temperature range 20–1100°C ranged from 0.76 to 1.22 W·m⁻¹·K⁻¹, whereas for the metal–ceramic coatings containing 10% and 30% Ni, the values were 1.11–1.87 W·m⁻¹·K⁻¹ and 1.71–4.18 W·m⁻¹·K⁻¹, respectively. These results provide valuable insights for the design and optimization of thermal barrier coatings.

Abstract: The aim of this study is to identify simultaneously the thermal conductivity tensor and the volume heat coefficient of a bimaterial (checkerboard) whose heat conduction obeys Fourier's law. This approach is validated by numerical simulation. The simulated temperature fields are obtained by the direct resolution heat conduction solved numerically by the finite element method formulation. To identify parameters, an inverse method is developed by using the finite element temperature approach (FEU-T) model fitting method based on the Levemberg-Marquardt algorithm. We validated the numerical procedure by using noiseless temperature fields at different time and space steps. The influence of the noise on the temperature fields is also studied and shows the efficiency of the inverse method. The results show that this procedure is not very sensitive to the number of elements (or space steps) and the number of time steps.

Abstract: The article considers the influence of the surface geometry of a detail on the deposition of coating thickness in the simulation of electroplating processes. The methods for obtaining sets of points describing the surface of a detail are analyzed. Solving the inverse problem (recovering the 3D surface of a detail according to its 2D drawings) is the most promising method. The inverse problem solution is decomposed into simpler geometric problems: input data processing; obtaining primitives; obtaining the desired surface of a detail by applying logical operations to primitives. Mathematical statements are formulated and solution algorithms are proposed for solving these problems. The inverse problem solution is implemented through software. The distribution of the nickel coating thickness is shown for a detail, the surface of which is obtained by solving the inverse problem.

Abstract: This study demonstrates application of mathematical techniques such as modeling, inverse analysis, and numerical simulation to biodegradation of xenobiotic polymer. In particular, this paper presents results of numerical simulation based on experimental results. Numerical results and experimental results show the behavior of microbial population in exogenous type depolymerization processes.

Abstract: This paper presents a quick calculation procedure to solve the heat transfer problem in some specific experimental arrangements. A brief overview of our previous efforts related to this topic is found in [1][2]. The goal of our effort is to quantify the thermal properties of insulation coatings applied to concrete material. We mostly deal with the computational aspects of thermal properties’ determination process. The proposed calculation approach is based on restricting the calculation to the first four members of the Fourier decomposition of the heat transfer partial differential equation’s solution. The reason for such a level of restrictions is given. The approach to the problem of deciding on the sufficient number of Fourier series’ members is indicated [3]. The effecting speedup is of three order of magnitude. Simplified formulas allowing the quick calculation of estimated values of material parameters are derived. The outline of an even quicker calculation procedure is described in a simplified manner.

Abstract: The paper presents a method for obtaining the power of thermal source, based on finite element approach, when the temperature distribution is known from an infrared image. The method is solving for the load vector, and extracts the power at element level from this vector.

Abstract: The continuation inverse problem for a solution to an elliptic equation in cylindrical layer for a model of stationary diffusion process is considered. Cauchy data are given on the outer boundary of the cylindrical layer; need to recover a field at the inner boundary of the cylinder. The problem is reduced to three different Cauchy problems for a second order ordinary differential equation. On the base of necessary minimization conditions of the residual functional analytical formulas for a regularized quasisolution to the inverse problem are derived.

Abstract: Calculation technique in order to reconstruct the 3D temperature field and predict the microstructure and mechanical properties of the weld metal in hybrid laser-arc welding is developed. The technique is based on the solution of the direct 3D temperature problem by a function-analytical method, the numerical solution of the inverse problem for the unknown parameters of a volume heat source, the employment of the known models for prediction of the microstructure and mechanical properties. The proposed calculation technique makes it possible to reduce considerably the total time for data input and solution. It is demonstrated with an example of butt hybrid laser-arc welding.

Abstract: In present work we develop the stable methods for technical and technological diagnostics of unsteady objects and/or processes by means of the L.A. Urban GPA (Gas Path Analysis) method: the dynamic system classes, which are suitable to be applied by technical and technological diagnostics by means of the L.A. Urban GPA method, are allocated; regularizing algorithms for construction of a stable diagnostic matrix are developed; methods for finding the optimal regularization parameter are proposed; development of methods for optimal regularizing parameter choice.

Abstract: This paper presents a general mathematical model for NC-machining an APT-LIKE rotating cutter. The design model of cutting-edge and helical groove are also developed by using the principles of differential geometry and kinematics. The analytical solution for the resolution profile of helical groove has also been developed. The results of numerical experiment indicate that the proposed systematic design method by using 2-axis NC machine setup are feasible and reliable.