PDF Publication Title:
Text from PDF Page: 119
where εP OD (M ) is the normalized error in projection. A value of M is chosen such that norm εPOD(M) ≤ λ∗ for a desired threshold error tolerance λ∗. In other words, the normalized norm projection error should be less than the tolerance level λ∗ [175, 65, 27]. It is also known as an M -rank approximation since the rank of the matrix U after truncation, and that of the solution matrix obtained after solving the POD-based reduced-order model, is always M ≤ Nx. It is commonly observed that the first few singular values are significantly larger than the subsequent ones, thus representing most of the captured projection of the system. Therefore, based on the aforementioned criterion, basis functions corresponding to those smaller singular values are dropped, which eventually leads to a much smaller subspace spanned by a very few basis functions. Hence, a significant model reduction is achieved since generally the value of M is much smaller compared to the value of Nx. For instance, M can be less than 10, whereas N can be on the order of 100s, and the error εPOD(M) can still be only 1-3%. x norm 6.3 Reduced-order Modeling 6.3.1 Methodology After computing POD basis functions, a reduced-order model (ROM) is derived by projecting the underlying PDEs of the system onto the corresponding POD subspace. We use a Galerkin- type projection scheme to project our set of PDEs in this work. Let the set of hyperbolic/parabolic PDEs be given as ∂y ∂y∂2y ∂t = f y, ∂x, ∂x2 In terms of the new set of POD basis functions, the state variable y(x, t) is written as M (6.11) (6.12) y(x, t) = ai(t)φi(x) i=1 where {ai}Mi=1 are the unknown temporal coefficients in the expansion. We solve this system of Chapter 6. Reduced-order Modeling for Optimization 105 6.3 Reduced-order ModelingPDF Image | Design and Operation of Pressure Swing Adsorption Processes
PDF Search Title:
Design and Operation of Pressure Swing Adsorption ProcessesOriginal File Name Searched:
anshul_thesis.pdfDIY PDF Search: Google It | Yahoo | Bing
CO2 Organic Rankine Cycle Experimenter Platform The supercritical CO2 phase change system is both a heat pump and organic rankine cycle which can be used for those purposes and as a supercritical extractor for advanced subcritical and supercritical extraction technology. Uses include producing nanoparticles, precious metal CO2 extraction, lithium battery recycling, and other applications... More Info
Heat Pumps CO2 ORC Heat Pump System Platform More Info
CONTACT TEL: 608-238-6001 Email: greg@infinityturbine.com (Standard Web Page)