A comprehensive scheme for reduction of nonlinear dynamical systems
- 26 Downloads
Model order reduction (MOR) also known as dimension reduction is a computational tool to obtain cost-effective lower order approximations of large scale dynamical systems. This paper presents a detailed yet simplified MOR approach using nonlinear moment matching (NLMM) in conjuncture with the Discrete Empirical Interpolation Method (DEIM). NLMM avoids the expensive simulation of the underlying nonlinear Sylvester partial differential equation by reducing it to a system of nonlinear algebraic equations using proper step-by-step simplifications. This reduces the offline computational cost of generating the orthonormal projection basis substantially. This is followed by the DEIM algorithm, resulting in comprehensive savings in computational resources. The proposed algorithms are tested on two benchmark problems and the results so obtained are compared with proper orthogonal decomposition for different test inputs.
KeywordsModel order reduction Nonlinear moment matching Steady state response
Compliance with ethical standards
Conflict of Interest
The authors declare that they have no conflict of interest regarding the publication of this paper.
- 5.Rewienski M, White J (2002) Improving trajectory piecewise-linear approach to nonlinear model order reduction for micromachined devices using an aggregated projection basisGoogle Scholar
- 9.Beattie CA, Gugercin S (2014) Model reduction by rational interpolation. In: Benner P, Cohen A, Ohlberger M, Willcox K (eds) Model reduction and algorithms: theory and applications. Computational science and engineering, vol 15. SIAM, Philadelphia, pp 297–334 Google Scholar
- 11.Astolfi A (2010) Model reduction by moment matching, steady-state response and projections. In: 49th IEEE conference on decision and control (CDC). IEEE, pp 5344–5349Google Scholar
- 12.Ionescu TC, Astolfi A (2013) Families of reduced order models that achieve nonlinear moment matching. In: 2013 American control conference. IEEE, pp 5518–5523Google Scholar
- 19.Cruz Verona L, Gebhart R Practical simulation-free model order reduction by nonlinear moment matching. arXiv:1901.10750
- 21.Grimme E (1997) Krylov projection methods for model reduction. Ph.D. dissertation, University of Illinois at Urbana ChampaignGoogle Scholar