State-Space Model Generation Using Cholesky Factorization
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Solution Overview
Problem
Existing methods for generating state-space models from large port-count S-parameter data are inefficient due to the computational burden of singular value decomposition, especially when dealing with structures having a high number of ports, which leads to slow simulation times and potential passivity violations.
Innovation Solution
The approach involves generating a passive model by approximating the number of significant basis functions needed, avoiding the computation of singular value decomposition, and using Cholesky factorization to enforce passivity, thereby improving simulation efficiency and reducing model fitting errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If singular value decomposition is performed on the wide X matrix to generate basis functions for state-space modeling, then the model fitting accuracy is improved, but the computational time increases significantly
Solution Approach 1:
The patent extracts only the essential information needed for modeling without performing the complete singular value decomposition. Instead of computing all basis functions through full SVD, the method identifies and uses only the critical components required for accurate state-space modeling, thereby reducing computational burden while maintaining model fidelity
Solution Approach 2:
The patent applies partial action by performing an incomplete or truncated version of the singular value decomposition process. Rather than computing the full decomposition of the wide X matrix, the method uses a reduced set of computations that capture the dominant modes of the system, achieving sufficient accuracy without the complete computational expense
2Reliability
If the complete singular value decomposition is performed on large port-count S-parameter data, then comprehensive basis functions are obtained, but the simulation efficiency decreases
Solution Approach 1:
The method extracts only the necessary subset of information from the S-parameter data required for effective simulation. By identifying and removing redundant computations in the basis function generation process, the patent achieves simulation-ready models without the overhead of complete singular value decomposition
Solution Approach 2:
The patent performs preliminary processing of the S-parameter data to identify the essential characteristics needed for simulation before committing to full decomposition. This preliminary analysis allows the method to prepare sufficient modeling information in advance without performing the complete computationally intensive SVD operation
3Device complexity
If standard model generation methods are used without passivity enforcement, then the computational process is simpler, but passivity violations occur in the generated model
Solution Approach 1:
The patent implements feedback mechanisms to detect and correct passivity violations in the generated state-space model. By continuously monitoring the passivity properties during model generation and adjusting the parameters accordingly, the method ensures that the final model satisfies passivity requirements without requiring overly complex generation procedures
Solution Approach 2:
The method adjusts specific parameters of the state-space model to enforce passivity constraints. By modifying certain model parameters within acceptable ranges, the patent achieves passivity compliance while maintaining the overall simplicity of the model generation process
Data Source
AI summary
A model synthesizer generates a state-space model of a structure from frequency domain parameters of the structure using a selected number of significant eigenvalues of a matrix derived from the frequency-domain parameters such that the quality of the fit of the model is improved. A matrix of the frequency-domain parameters is reshaped so as to improve performance of determination of the fit quality. Passivity violations in the model can be removed via regularization and error control such that the fit quality of the model after removal of the passivity violations is within a specified tolerance. Cholesky factorization can improve the performance of passivity violation detection. This Abstract is provided for the sole purpose of complying with the Abstract requirement rules. This Abstract is submitted with the explicit understanding that it will not be used to interpret or to limit the scope or the meaning of the claims.