Phase Space Prediction for Chaotic Systems
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Solution Overview
Problem
Existing prediction methodologies for nonlinearly deterministic systems, such as wind turbines, often misclassify or inefficiently predict chaotic behavior due to the failure to account for exponential divergence/convergence of trajectories, leading to inaccurate and inefficient control and prediction.
Innovation Solution
The method involves embedding time series data into a reconstructed phase space and predicting future states based on the rate of separation of trajectories within this space, using a phase space embedding module and prediction module executed by a processor, which considers the maximum Lyapunov exponent to accurately forecast system behavior.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If stochastic analysis and prediction methodologies are used for nonlinearly deterministic systems, then the systems can be analyzed with available tools, but the prediction accuracy deteriorates due to misclassification of chaotic behavior
Solution Approach 1:
The patent transforms the approach by changing the parameter of analysis from stochastic assumptions to deterministic chaotic system parameters. By identifying and analyzing the Lyapunov exponent and embedding dimension, the system transitions from misclassified stochastic analysis to accurate deterministic prediction, resolving the contradiction between tool availability and prediction accuracy.
2Adaptability or versatility
If deterministic prediction algorithms are designed to smooth nonlinearities, then the algorithms can be applied to complex systems, but the prediction accuracy deteriorates due to loss of chaotic behavior details
Solution Approach 1:
The patent applies dynamics by using the embedding dimension and time delay to dynamically reconstruct the phase space, allowing the algorithm to adapt to the inherent chaotic behavior rather than smoothing it. This dynamic approach preserves the nonlinearities while achieving accurate prediction through proper phase space reconstruction.
3Measurement precision
If phase space embedding with proper time delay and embedding dimension is used, then prediction accuracy is improved by capturing chaotic behavior, but the computational complexity increases
Solution Approach 1:
The patent applies preliminary action by pre-calculating the embedding dimension and optimal time delay from the time series data before performing the actual prediction. This preliminary phase space reconstruction prepares the data structure in advance, making the subsequent prediction process more efficient and reducing overall computational complexity while maintaining high accuracy.
Data Source
AI summary
A method of predicting at least one future state of a system is provided. The method comprises embedding, using a phase space embedding module, time series data relating to the system within a reconstructed phase space. The phase space embedding module comprises instructions stored on a non-transitory computer-readable medium that are executable by a processor. The method further comprises predicting, using a prediction module, the at least one future state of the system based on a rate of separation of trajectories of the embedded data within the reconstructed phase space. The prediction module comprises instructions stored on the non-transitory computer-readable medium that are executable by the processor.