Accelerated Modal Frequency Response Calculation
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Solution Overview
Problem
Current methods for calculating modal frequency responses in simulation engineering systems are computationally costly due to the need to solve complex equations at numerous frequencies, especially when dealing with large-scale engineering structures like automobiles, buildings, and aircraft, where direct or iterative solutions are not feasible due to high computational demands.
Innovation Solution
The approach involves dividing excitation frequencies into subsets, performing preparatory calculations, and storing data to efficiently calculate modal frequency responses by transforming the modal frequency response problem into forms that require less computational power, such as diagonal plus low-rank matrices or using eigenvalue problems, allowing for faster processing and reduced computational costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If direct or iterative solutions are used to calculate modal frequency responses at numerous frequencies, then calculation accuracy is maintained, but computational cost and processing time increase significantly
Solution Approach 1:
The patent segments the frequency range into multiple subsets and processes each subset independently using the accelerated algorithm. This allows parallel computation of frequency responses across different frequency ranges, reducing total processing time while maintaining accuracy through systematic coverage of the entire frequency spectrum
Solution Approach 2:
The patent performs preliminary calculations of system matrices (mass, damping, stiffness) and eigenvalue decompositions before the actual frequency response calculation. These pre-computed components are stored and reused across multiple frequency points, eliminating redundant computations and significantly reducing processing time for each frequency point
2Measurement precision
If direct or iterative solutions are used to calculate modal frequency responses, then accurate results are obtained, but computational power requirements become prohibitive for large-scale structures
Solution Approach 1:
The patent transforms the frequency response calculation from solving the full system of equations at each frequency point to using eigenvalue decomposition and mode superposition. This parameter transformation reduces the computational complexity from O(n³) per frequency point to O(n²) or better, significantly reducing computational power requirements while maintaining accuracy
Solution Approach 2:
The patent extracts and utilizes the eigenvalues and eigenvectors of the system matrices to construct the frequency response. By separating the system characteristics (eigenmodes) from the frequency-dependent response, the method computes only the essential system properties once and reuses them across all frequency points, reducing overall computational power consumption
3Reliability
If modal frequency responses are calculated for all excitation frequencies, then complete simulation accuracy is achieved, but computational cost becomes prohibitive
Solution Approach 1:
The patent divides the excitation frequencies into multiple subsets and applies the accelerated algorithm to each subset. This segmentation enables parallel processing of frequency subsets, improving calculation efficiency through concurrent computation while ensuring complete coverage of all frequencies for maintaining simulation accuracy
Solution Approach 2:
The patent performs preliminary eigenvalue decomposition and mode shape calculation before processing each frequency subset. These pre-computed system characteristics are stored in memory and reused across all frequency subsets, eliminating redundant computations and significantly improving calculation efficiency while maintaining complete accuracy for all frequencies
Data Source
AI summary
A computer-implemented method is provided for simulating a modal frequency response of a real-world object. The computer-implemented method includes dividing a plurality of excitation frequencies into a plurality of excitation frequency subsets, calculating modal frequency responses for at least a portion of the excitation frequencies in a given excitation frequency subset, and generating a simulation of the real-world object based at least in part on the modal frequency responses.