Low-Order Model Identification of Distributed Parameter Systems by a Combination of Singular Value Decomposition and the Karhunen−Loève Expansion

Abstract

In this work, a new system identification method that combines the characteristics of singular value decomposition (SVD) and the Karhunen-Loève (KL) expansion for distributed parameter systems is presented. This method is then demonstrated on two nonlinear reactor systems that can be described by systems of partial differential equations (PDEs). The results indicate that this new method provides satisfactory low-order models when compared to models developed using either the SVD approach or the KL expansion in a Galerkin method. In particular, it has the advantage of not requiring an exact PDE model, which is necessary for the KL solution and it captures the dynamics of the process in contrast to the SVD solution. This has important implications especially for applications such as control that require low-order models for implementable solutions.

Spectral analysis and text processing over the computer science literature

“…Technique SVD is a matrix factorization method widely used in applications such as signal processing and statistics [8]. Given an An×m matrix, let U be an nxr matrix whose columns are the singular vectors orthogonal to Λ, and V T be the rxm matrix whose columns are the singular vectors orthogonal to Λ; then A can be defined by equality 1.…”

State-shared model for multiple-input multiple-output systems

“…One way of reducing the order of the controller is to generate a reduced-order approximation of the plant before designing the controller [ 6,7 ].…”

A fuzzy-based spatio-temporal multi-modeling for nonlinear distributed parameter processes

“…A time-invariant Green's function model can be estimated using singular value decomposition (SVD) method [12]. For linear time-varying DPS, a time-varying Green's function model can be obtained from the singular function and Karhunen-Loève (KL) basis function expansion using SVD-KL method [13][14][15]. The least-squares method can also be used [16].…”