Abstract
This paper studies parametric reduced-order modeling via the interpolation of linear multiple-input multiple-output reduced-order, or, more general, surrogate models in the frequency domain. It shows that realization plays a central role and two methods based on different realizations are proposed. Interpolation of reduced-order models in the Loewner representation is equivalent to interpolating the corresponding frequency response functions. Interpolation of reduced-order models in the (real) pole-residue representation is equivalent to interpolating the positions and residues of the poles. The latter pole-matching approach proves to be more natural in approximating system dynamics. Numerical results demonstrate the high efficiency and wide applicability of the pole-matching method. It is shown to be efficient in interpolating surrogate models built by several different methods, including the balanced truncation method, the Krylov method, the Loewner framework, and a system identification method. It is even capable of interpolating a reduced-order model built by a projection-based method and a reduced-order model built by a data-driven method. Its other merits include low computational cost, small size of the parametric reduced-order model, relative insensitivity to the dimension of the parameter space, and capability of dealing with complicated parameter dependence.
Highlights
Model order reduction (MOR), as a flourishing computational technique to accelerate simulation-based system analysis in the last decades, has been applied successfully to high-dimensional models arising from various fields such as circuit simulations [1,2,3], acoustics [4], design of microelectromechanical systems [5], and chromatography in chemical engineering [6]
This paper studies parametric reduced-order modeling via the interpolation of linear multiple-input multiple-output reduced-order, or, more general, surrogate models in the frequency domain
Interpolatory parametric MOR (PMOR) in the Loewner realization we propose a method that interpolates reduced-order model (ROM) built by the Loewner framework to approximate the dynamical system described by the frequency response function (FRF) H(s, p)
Summary
Model order reduction (MOR), as a flourishing computational technique to accelerate simulation-based system analysis in the last decades, has been applied successfully to high-dimensional models arising from various fields such as circuit simulations [1,2,3], (vibro) acoustics [4], design of microelectromechanical systems [5], and chromatography in chemical engineering [6]. Though we do not explicitly use any of these methods in our approach, we will frequently refer to them and will use them for comparison purposes in the numerical examples section. We include this brief review for better readability. A projection-based PMOR method [7,18] first builds two bases Q, U ∈ Rn×k (normally, k n), and approximates X(s, p) ≈ Ux(s, p) (x(s, p) ∈ Rk ) in the range of U , and forces the residual to be orthogonal to the range of Q to obtain the pROM: sE(p) − A(p) x(s, p) = B(p)u(s), y(s, p) = C(s, p)x(s, p), (2). We discuss some subcategories under the general framework presented above:
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