Analýza nejistot inverzního problému vedení tepla ve dvou prostorových souřadnicích

Abstract

This dissertation examines an inverse heat conduction problem (IHCP) approach to approximate the transient heat transfer coefficient (HTC) distribution on the cooling surface of a high-pressure die casting (HPDC) die insert. We design a synthetic numerical experiment to produce internal temperature data, which is used as input for the inverse analysis. A derivative-free technique of optimization, BOBYQA which is applied via the the NLOPT library is employed to reconstruct the HTC. The HTC are spatially discretized at the thermocouple projection points by the inverse model and linear interpolation is used to approximate the continuous distribution. A strong agreement of viability is manifested against reference data which confirms the accuract of the method. An investigation of sensitivity revealed that even small perturbations in the positions of thermocouples heavily impact the reconstructed HTC. This highlights the significance of the placement of sensors. The robustness of the method is further supported by the analysis of pointwise relative error where local errors are very low. Even though regularization was not performed, it potential to improve stability is discussed as a further enhancement. Altogether, this work provides a practical and efficient inverse method for thermal diagnostics in HPDC, resulting in an enhanced process modeling and experimental design.This dissertation examines an inverse heat conduction problem (IHCP) approach to approximate the transient heat transfer coefficient (HTC) distribution on the cooling surface of a high-pressure die casting (HPDC) die insert. We design a synthetic numerical experiment to produce internal temperature data, which is used as input for the inverse analysis. A derivative-free technique of optimization, BOBYQA which is applied via the the NLOPT library is employed to reconstruct the HTC. The HTC are spatially discretized at the thermocouple projection points by the inverse model and linear interpolation is used to approximate the continuous distribution. A strong agreement of viability is manifested against reference data which confirms the accuract of the method. An investigation of sensitivity revealed that even small perturbations in the positions of thermocouples heavily impact the reconstructed HTC. This highlights the significance of the placement of sensors. The robustness of the method is further supported by the analysis of pointwise relative error where local errors are very low. Even though regularization was not performed, it potential to improve stability is discussed as a further enhancement. Altogether, this work provides a practical and efficient inverse method for thermal diagnostics in HPDC, resulting in an enhanced process modeling and experimental design.