Koopman Operator Estimation for Multi-Element Phase Models
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Solution Overview
Problem
Existing methods struggle to estimate a phase model for multiple elements using the Koopman operator, as they are primarily designed for single-element systems.
Innovation Solution
An estimation device that includes an operator estimation unit to estimate the Koopman operator from time-series data of multiple elements and a phase model estimation unit to represent collective vibration and interactions between elements using the Koopman operator.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Koopman operator method is used to estimate the phase model, then the measurement precision of the phase model is improved, but the device complexity increases because the method requires only one element while the patent needs to handle multiple elements
Solution Approach 1:
The patent segments the estimation problem by processing each element's time-series data independently to estimate individual Koopman operators, then combines these operators to form the complete phase model for multiple elements. This segmentation allows the method to handle multiple elements while maintaining the accuracy benefits of the Koopman operator approach.
Solution Approach 2:
The patent merges the individually estimated Koopman operators for multiple elements into a unified phase model that captures both individual dynamics and interactions between elements. This combining step enables the system to achieve accurate phase model estimation while properly handling multiple elements.
2Ease of operation
If the Fourier series or Hilbert transform method is used to estimate the phase model, then the ease of operation is improved, but the measurement precision deteriorates because the entire phase function cannot be accurately estimated
Solution Approach 1:
The patent replaces the traditional mechanical approach of using Fourier series or Hilbert transforms with a Koopman operator-based method. This substitution enables accurate estimation of the entire phase function while maintaining operational feasibility through a systematic estimation procedure that processes time-series data to derive both phase functions and interaction models.
3Adaptability or versatility
If the Koopman operator method is extended to multiple elements, then the adaptability of the method is improved, but the device complexity increases due to the need to process multiple time-series data
Solution Approach 1:
The patent applies segmentation by estimating Koopman operators for each element separately from their individual time-series data, then combining these operators to form a comprehensive phase model. This segmented approach enables the method to adapt to multiple elements while managing complexity through modular processing of each element's dynamics.
Solution Approach 2:
The patent achieves universality by developing a Koopman operator-based framework that can handle both single-element and multi-element systems through a unified approach. The method universally estimates phase functions and interaction models from time-series data regardless of the number of elements, thereby improving adaptability while controlling complexity through systematic procedures.
Data Source
AI summary
An estimation apparatus according to an embodiment includes an operator estimation unit configured to estimate a Koopman operator from time-series data composed of a plurality of elements by using the time-series data as an input, and a phase model estimation unit configured to estimate a phase model representing collective vibration of the plurality of elements and an interaction between the elements using the Koopman operator.