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Explicit model reduction for nonlinear systems with no prior information about the type of nonlinearity involved is difficult and challenging. It is easier to reduce nonlinear systems which nonlinearity is known. In this paper we introduce two nonlinear model reduction techniques for quadratic nonlinear systems. The first technique is nonlinear balanced(More)
For a vast variety of fluid flows the dynamics are governed by the Navier-Stokes equations which are highly nonlinear. In particular, the corresponding Galerkin models involve a quadratic type nonlinear-ity. The latter incudes the Burgers' equation as well. In this paper, a computational algorithm for nonlin-ear balanced truncation of the Galerkin models is(More)
This paper presents two approaches to locate the source of a chemical plume; Nonlinear Least Squares and Stochastic Approximation (SA) algorithms. Concentration levels of the chemical measured by special sensors are used to locate this source. Non-linear Least Squares technique is applied at different noise levels and compared with the localization using(More)
The building sector consumes a large part of the energy used in the United States and is responsible for nearly 40% of greenhouse gas emissions. It is therefore economically and environmentally important to reduce the building energy consumption to realize massive energy savings. In this paper, a method to control room temperature in buildings is proposed.(More)
Spectral imaging typically generates a large amount of high-dimensional data that are acquired in different sub-bands for each spatial location of interest. The high dimensionality of spectral data imposes limitations on numerical analysis. As such, there is an emerging demand for robust data compression techniques with loss of less relevant information to(More)
— In this paper, we investigate new methods that make the Proper Orthogonal Decomposition (POD) more accurate in reducing the order of large scale nonlinear systems. The general framework is to apply POD locally to clusters instead of applying it to the global system. Each cluster contains relatively close in distance behavior within itself, and(More)
Nonlinear PDEs domain discretization yields finite but high dimensional nonlinear systems. Proper Orthogonal Decomposition (POD) is widely used to reduce the order of such systems but it assumes that data belongs to a linear space and therefore fails to capture the nonlinear degrees of freedom. To overcome this problem, we develop a Space Vector Clustering(More)