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dr hab., prof. AGH
Szeliga, Danuta
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Wydział Inżynierii Metali i Informatyki PrzemysłowejJednostki organizacyjne (rel.)
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- KsiążkaOtwarty dostępIdentification problems in metal forming : a comprehensive study(Wydawnictwa AGH, 2013) Szeliga, DanutaThe work presents an identification problem of the parameters of models applied in the numerical simulation of metal forming processes. The main thesis of the work is a supposition that it is possible to obtain optimal solutions to ill-posed inverse problems of identification with the application of sensitivity analysis methods combined with optimization procedures. The objectives defined and executed in the work, as well as the application of the developed methods to solve practical identification problems of metal forming, prove the work thesis. Identification problems are inverse problems transformed into optimization tasks for which a minimum is searched. These problems are ill-posed, thus, the main objective of the work was to develop a method based on the sensitivity analysis algorithms coupled with optimization procedures which would constitute a robust tool to solve inverse problems and which would allow to obtain solutions close to the exact ones. The application of sensitivity algorithms to decrease computational costs of identification is presented. The application was the next objective of the work. The methods of reducing the space dimension of decision variables dedicated to the identification of parameters of the highest importance, based on sensitivity analysis algorithms, are provided in the work. This problem is particularly important for numerical models of metal forming, which are computationally expensive due to non-stationary nature of these problems and due to solvers of finite element method with hp-adaptation to improve the quality of the solution. Another advantage of this application of sensitivity analysis is the constraint of a possible number of solutions. The application of sensitivity analysis as a preliminary step of optimization to bound or extend the parameters domain, to generate starting points for optimization or to investigate behavior of the functional defined in optimization is presented in the work. Another provided application of sensitivity analysis is a hybrid optimization procedure, such as a combination of nondeterministic optimization methods and local sensitivity analysis algorithms for exploring local minima. The thesis was proved with the solution of practical problems presented in the work. The following problems were solved: identification of mechanical boundary condition (friction coefficient), identification of parameters of rheological models, identification of fracture criteria parameters, identification of parameters of multiscale models, parameters of the phase transformation model and identification of production cycle control parameters. All the listed problems were solved with the developed software and they are presented in the monograph. The presentation starts with the state of the art of identification problems investigated in metal forming. The identification achievements are summarized and weaknesses of theoretical research are pointed out. The conclusions from this part were basis to formulate the thesis of the work. Next general equilibrium equations used in the modeling of metal forming processes and the formulation of inverse problems for these equations are provided. The mathematical background of inverse operators and an attempt to apply mathematical formalism to construct the inverse operator for metal forming equations is included. Then, a description of sensitivity analysis methods and the ability to apply sensitivity analysis algorithms to inverse calculations as a supporting tool is presented. The performed investigations allowed to develop an algorithm dedicated to the parameters identification of models with the application of sensitivity analysis methods described in the work. The algorithm was implemented and all the calculations of identification problems presented in the work were computed with the designed software. The monograph ends with conclusions which summarize the work achievements and which prove the formulated thesis that it is possible to effectively solve ill-posed identification problems of metal forming with the developed application of identification strategy algorithm, based on sensitivity analysis methods coupled with optimization procedures.