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| Laguerre-Based Model Reduction Using Balanced Truncation for Large-Scale Dynamical Systems: Application to Cardiac Electrical Signal Modeling |
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| KeyWord:Model order reduction, balanced truncation, transfer function, laguerre function, lyapunov equations |
| Author Name | Affiliation | | Md. Shafiqul Islam | Department of Mathematics, International University of Business Agriculture and Technology, Dhaka-1230, Bangladesh | | Md. Saiduzzaman | Department of Mathematics, International University of Business Agriculture and Technology, Dhaka-1230, Bangladesh | | M. Monir Uddin | Department of Mathematics and Physics, North South University, Dhaka-1229, Bangladesh | | M. Osman Gani | Department of Mathematics, Jahangirnagar University, Savar-1236, Bangladesh |
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| Abstract: |
| Cardiac electrical signal modeling is governed by complex nonlinear dynamics that require large-scale computations. To make these simulations feasible, model order reduction (MOR) techniques are employed to capture the essential dynamics in a reduced framework. For large-scale dynamical systems, the balanced truncation (BT) method cannot be applied directly because solving the associated Lyapunov equations becomes computationally infeasible. In this work, we introduce the Laguerre function expansion method for continuous-time systems for the first time. Furthermore, we propose a novel approach that incorporates Laguerre functions within the BT framework. This combined method yields improved results compared to the conventional Laguerre function expansion technique. The reduction process for both approaches is performed within specified frequency bands to preserve the systemâs behavior in relevant spectral regions. We also utilize the COMSOL Multiphysics package to simulate and capture the system's behavior across various phases accurately. For computational analysis, MATLAB software is used to display the reduction results. To validate our approach, we examine the transfer function and perform an error comparison between the full and the reduced models. Finally, we provide the stability graph of the system matrix in reduced dimensions for different frequency limits. |
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