To accurately model or predict future operating conditions of a system in engineering or applied mechanics, it is necessary to understand its fundamental principles. These may be the material parameters, defining dimensional characteristics, or the boundary conditions. However, there are instances when there is little to no prior knowledge of the system properties or conditions, and consequently, the problem cannot be modeled accurately. It is therefore critical to define a method that can identify the desired characteristics of the current system without accumulating extensive computation time. This thesis formulates an inverse approach using proper orthogonal decomposition (POD) with an accompanying radial basis function (RBF) interpolation network. This method is capable of predicting the desired characteristics of a specimen even with little prior knowledge of the system. This thesis first develops a conductive heat transfer problem, and by using the truncated POD – RBF interpolation network, temperature values are predicted given a varying Biot number. Then, a simple bifurcation problem is modeled and solved for velocity profiles while changing the mass flow rate. This bifurcation problem provides the data and foundation for future research into the left ventricular assist device (LVAD) and implementation of POD – RBF. The trained POD – RBF inverse approach defined in this thesis can be implemented in several applications of engineering and mechanics. It provides model reduction, error filtration, regularization and an improvement over previous analysis utilizing computational fluid dynamics (CFD).
Bachelor of Science in Mechanical Engineering (B.S.M.E.)
College of Engineering and Computer Science
Mechanical and Aerospace Engineering
Orlando (Main) Campus
Ashley, Rebecca A., "Application of Trained POD-RBF to Interpolation in Heat Transfer and Fluid Mechanics" (2018). Honors Undergraduate Theses. 279.