Abstract
This work presents a technique called Time Traveling Regularization (TTR) applied to an optimization technique in order to solve ill-posed problems. This new methodology does not interfere in the minimization technique process. The Golden Section method together with TTR are applied only to the objective function which will be minimized. It consists of finding an ideal timeline that minimizes an objective function in a defined future time step. In order to apply the proposed methodology, inverse heat conduction problems were studied. Controlled experiments were performed on 5052 aluminum and AISI 304 stainless steel samples to validate the proposed technique. One-dimensional and three-dimensional heat input experiments were carried out for the 5052 aluminum and AISI 304 stainless steel samples, respectively. The Sequential Function Specification Method (SFSM) was also used to be compared with the results of heat flux obtained by TTR. The estimated heat flux presented a good agreement when compared with experimental values and those estimated by SFSM. Moreover, TTR presented lower residuals than the SFSM.
Highlights
In mathematical physics, solving a direct problem usually means finding a mathematical function that describes a phenomenon or a process of a given domain at any time instant
The Sequential Function Specification Method (SFSM) was used to be compared with the results of heat flux obtained by Time Traveling Regularization (TTR)
The estimated heat flux presented a good agreement when compared with experimental values and those estimated by SFSM
Summary
In mathematical physics, solving a direct problem usually means finding a mathematical function that describes a phenomenon or a process of a given domain at any time instant. Many transient and non-linear problems do not have a direct solution for their governing equations. In those cases, the development of new approaches and techniques to solve those problems is necessary. There are the techniques based on the solution of inverse problems. The inverse model aims to find a cause from an effect or observation. This particular situation is often called ill-posed problems [1]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
