Using internal temperature measurements from inside a solid to determine the initial or boundary conditions or material properties is a common inverse heat conduction problem. These problems are ill-posed in nature and a robust mathematical solution is not available for them. Stochastical search algorithms like Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) have been found to be very effective in dealing with some of the challenges in solving inverse problems, such as time step size limit and sensitivity to the measurement errors. However, these methods normally require large population size and do not use the gradient information and, therefore, their computational costs are generally higher than their gradient based alternatives. This is especially true when using a computationally expensive high-fidelity method like finite element analysis as the direct solver in the core of the inverse algorithm. The inherent inefficiency of this procedure is even more obvious when we notice that an algorithm like PSO is rank-based, i.e. the actual magnitude of cost function is not important, and only their relative ordering is used. In a typical implementation of PSO, most of the objective function evaluations are discarded, unless when it is improving the local memory of the particle. A computationally cheaper substitute for full analysis methods is using metamodels also known as surrogate models. They construct an approximation to the direct problem using a set of available data and the underlying physics of the problem. In this research, an inexact pre-evaluation of the boundary heat flux components using a simplified physics and data fitting is used to find the more promising solutions, and then an accurate but computationally expensive three-dimensional finite element discretization of the heat conduction problem is applied only to these elite members of the population. The result is an inverse heat conduction analysis method that has the stability and effectiveness of PSO, and at the same time has a much lower computational cost. In this research, we use a sequential implementation of PSO in dealing with the transient boundary heat flux, and a future time step regularization method is used to create a more stable algorithm. The focus of the test cases in this research paper will be the inverse heat conduction problem in the controlled cooling of steel strips on a run-out table, but the algorithm is readily applicable to other applications of inverse heat conduction analysis.
Application of the Finite Element Method to the Nonlinear Inverse Heat Conduction Problem Using Beck’s Second Method
