Add Smooth Orthogonal Decomposition (SOD) implementation#141
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ChrisRackauckas-Claude wants to merge 1 commit intoSciML:mainfrom
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Add Smooth Orthogonal Decomposition (SOD) implementation#141ChrisRackauckas-Claude wants to merge 1 commit intoSciML:mainfrom
ChrisRackauckas-Claude wants to merge 1 commit intoSciML:mainfrom
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Implements the Smooth Orthogonal Decomposition (SOD) algorithm for extracting linear normal modes and natural frequencies from time-series data, as proposed by Chelidze and Zhou (2006). SOD extends POD by considering temporal smoothness in addition to spatial variance. It uses the covariance matrices of displacement and velocity responses to form a generalized eigenvalue problem (Σ_xx Ψ = λ Σ_vv Ψ), which yields smooth orthogonal modes and values without requiring knowledge of the system's mass matrix. Key features: - SOD type following the same pattern as POD - Automatic velocity computation from displacement data using finite differences - Support for user-provided velocity data - Energy-based truncation for automatic mode selection - Natural frequency estimation from smooth orthogonal values (SOVs) - Support for both matrix and vector-of-vectors input formats References: - Chelidze D, Zhou W. Smooth orthogonal decomposition-based vibration mode identification. J Sound Vib. 2006; 292(3-5): 461-473. Closes SciML#9 Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
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Summary
Key Features
SODtype following the same pattern as existingPODTest plan
References
Closes #9
cc @ChrisRackauckas
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