Papers by Keyword: Inverse Problems

Abstract: An inverse problem involves determining unknown physical quantities denoted as u = (u₁, ..., u_np), which cannot be directly measured but need to be evaluated based on accessible measurements, represented as y = M(u), where M is a mathematical model. Solving such problems often requires mathematical techniques like differential equations or optimization methods such as least squares. Inverse problems can be well-posed (stable, unique solutions) or ill-posed (unstable or non-unique), with ill-posedness often resulting from poor experimental setups or measurement errors. This study addresses the identification of thermophysical parameters - specifically thermal conductivity and heat transfer coefficients—in a 2D steady-state diffusive medium. The proposed method uses a boundary element approach and an iterative descent algorithm to minimize a functional and identify the unknown parameters, validated through simulated thermograms. As a result, the use of sensitivity functions to weight the functional to be minimized makes it possible to avoid selection of the sensors according to the parameter to be identified.

Abstract: Fly ash, a by-product of burning pulverized coal in electrical generating stations, is used as a supplementary pozzolanic material in the production of Portland cement concrete. It improves, e.g., workability of a concrete mixture, suppresses bleeding, reduces the rate of production of hydration heat and delays finishing operations. Consequently experimental research, theoretical analysis, incorporating available microstructural data, and efficient numerical simulations are needed to understand the influence of early-age curing on later macroscopic mechanical, thermal, etc. material properties. This paper presents a proper experimental and computational approach to the evaluation of time-variable thermal characteristics of a hardening mixture, based on the weak formulation of the evolution problem and on the least squares optimization. Results of such types are necessary for reliable prediction of behaviour, performance and durability of buildings and engineering structures.

Abstract: Utilization of advanced materials in civil engineering motivates research in both experimental and computational methods of reliable identification of their material characteristics, as e.g. the thermal conductivity and diffusivity in semilinear evolutionary equations of heat conduction, coming from the energy balance in classical thermodynamics, or the capillary transfer coefficient in similar equations, coming from the mass balance. The paper presents mathematical preliminaries of such inverse analysis and an overview of computational approaches with references to practical applications.

Abstract: Inverse eddy current problem using Artificial Neural Networks (ANN) approach for the localization and the classification shape of defects is considered. The task of reconstructing the cracks and damage in the plate profile of an inspected specimen in order to estimate its material properties can be described in this research work. This is accomplished by inverting eddy current probe impedance measurements that are recorded as a function of probe position, excitation frequency or both. In eddy current nondestructive evaluation, this is widely recognized as a complex theoretical problem whose solution is likely to have a significant impact on the characterization of cracks in materials .

Abstract: In the paper the selected problems related to the modeling of microscale heat transfer are presented. In particular, thermal processes occurring in thin metal films exposed to short-pulse laser are described by two-temperature hyperbolic model supplemented by appropriate boundary and initial conditions. Sensitivity analysis of electrons and phonons temperatures with respect to the microscopic parameters is discussed and also the inverse problems connected with the identification of relaxation times and coupling factor are presented. In the final part of the paper the examples of computations are shown.

Abstract: Thermokinetic constants for the drying process of different steppe fuels are determined using the developed method for solving inverse kinetic problems on the basis of obtained experimental data. The anatomical structure of the investigated fuels is found to be a dominant parameter influencing on evaporation. The basic conductor of combustion is proposed for prediction of fire hazard for the investigated area.

Abstract: We propose an novel computational method for solving dynamic loads identification problems. The algorithm considered here is detailedly given. The present method is applied to the identification of the multi-source dynamic loads on a surface of plate. Numerical simulations validate the stability and effectivity of the proposed method.

Abstract: Surface-wave dispersion analysis is widely used in civil engineering to infer a shear wave velocity model of the subsoil for a wide variety of applications. Combining with a example, multi-channel analysis of surface waves method (MASW) was discussed in this paper. The entire MASW's procedure of three steps: acquiring ground roll data in the field, processing the data to determine dispersion curve, and back calculation of the geologic parameters for different depths. Based upon all the research results by far, MASW method is an efficient methods because of its high accuracy that is achieved by both special field technique and data processing technique.

Abstract: The inverse problems of measurement are investigated in this paper. The main hypothesis was suggested for evaluation of exact solutions of such problems. For obtaining the steady evaluations of exact solutions of measurement's inverse problem the regularization method was used. Two practical inverse problems have been considered as examples: Krylov's inverse problem, identification of moment of technological resistance on rolling mill.