A new scheme for model order reduction of large-scale second-order systems in time-limited intervals is presented. Time-limited Gramians that are solutions of continuous-time algebraic Lyapunov equations for second-order form systems are introduced. Time-limited second-order balanced truncation procedures with provision of balancing position and velocity Gramians are formulated. Stability conditions for reduced-order models are stated and algorithms that preserve stability in reduced-order models are discussed. Numerical examples are presented to validate the superiority of the proposed scheme compared with the infinite-time Gramians technique for time-limited applications.
A new structure preserving model order reduction technique for second order systems in limited frequency interval is presented. Frequency limited Gramians (FLGs) and corresponding continuous time algebraic lyapunov equations (CALEs) are developed. For solution of CALEs and Cholesky factorization of FLGs, computationally efficient approximation scheme is proposed. Multiple transformations based on balancing of frequency limited position or velocity Gramians are defined in order to compute Hankel singular values (HSVs). Frequency limited second order balanced truncation based on magnitudes of HSVs is performed for order reduction. Moreover, stability conditions for reduced order models (ROMs) are stated and algorithms for achieving stability in ROMs are proposed. Results are compared with existing technique to certify the usefulness of the proposed technique.
In this work, comprehensive analysis on single and dual mode, uniform and apodized Fiber Bragg Grating (FBG) based gas concentration measurement sensor performance in the presence of noise and temperature variations is presented. Different scenarios are formulated. Firstly, the indirect sensing method for gas concentration measurement is presented, followed by the discussion on single and dual mode uniform FBG sensor design. Thereafter single and dual mode Gaussian apodized FBG sensor design and its pros and cons are discussed. The effect of temperature variations and noise on FBG sensor is also discussed. Afterwards as per referred literature the simulation results for uniform and apodized FBG in the presence or absence of noise, temperature variations and strain applications are validated. The quantitative analysis shows that the single mode apodized FBG has highest side lobes suppression ratio which is 88.21%. In terms of FWHM single mode apodized FBG has narrowest bandwidth of amplitude 0.18. While dual mode apodized FBG has highest reflectivity, that is, −0.20571. It is observed that reflection spectrum of uniform FBG sensor contains large strength of side lobes at adjacent wavelength. Moreover, the dual mode FBG sensor performance is more affected by variation in temperature and noise but dual mode FBG sensor works better as compared to single mode FBG sensor in context of minimum side lobes, high absorption depth and enhanced reflectivity. The presented investigation will be helpful to prescribe the correct amount of dosage for biomedical application. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.
The first half of this manuscript deals with a review of different variants for second-order balanced truncation techniques for stable second-order form systems. Later, multiple nonexisting extensions of model order reduction techniques for stable and unstable second-order form systems are proposed. The framework for gramians based frequency or time (or both) limited model order reduction is presented. Comments on the preservation of large order system properties in the reduced-order model (ROM) that include structure and stability are discussed, and consequent conditions for the preservation of these properties in ROM are stated. The proposed techniques are tested on multiple benchmark/self-generated examples for successful validation of presented developments. The superiority of proposed extensions over existing techniques is also validated. The presented study can be utilized as a resource for infinite and finite interval model order reduction applications of continuous or discrete, stable, or unstable second-order form systems.INDEX TERMS Second-order systems, model order reduction, frequency-limited gramians, time-limited gramians, unstable systems, Hankel singular values.
In the present work, multiple non existing model order reduction (MOR) techniques for unstable second‐order form systems (SOSs) are proposed. For unstable SOSs, continuous‐time algebraic Lyapunov equations get unsolvable that halt the reduction process. To avoid this problem, unstable SOS is first decomposed into stable and unstable portions and balanced truncation is applied to the stable part. The obtained reduced order model (ROM) for the stable portion is augmented with the unstable portion to obtain the overall reduced system. It is observed that the second‐order structure in ROM for the first technique gets lost as well as augmented unstable dynamics degrade the ROM performance. To cater to these constraints, two structure‐preserving second‐order balanced truncation techniques for unstable SOSs are proposed in second part. System is first stabilized using the Bernoulli feedback stabilization procedure and then gramians are computed for the stabilized system. Further, gramians are partitioned into position and velocity portions to achieve structure preservation in ROM and balanced truncation is applied. As second technique retains second‐order structure as well as involves stabilized system dynamics, this technique far closely approximates original system behavior. Proposed techniques are tested on multiple systems and results certify the correct development of proposed techniques that can be utilized for MOR applications of unstable SOSs. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.
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