Asymmetric Wavelet Kernel for Nonlinear System Identification
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Solution Overview
Problem
Identifying the parallel model of a nonlinear dynamical system is complex and challenging due to feedback involvement, with existing approaches being less effective compared to series-parallel models, especially when system output state data is unreliable or unavailable.
Innovation Solution
A novel asymmetric wavelet kernel function, derived from a raised-cosine wavelet, is used in conjunction with a linear programming algorithm (LP-SVM-ARMA2K) to identify and model nonlinear dynamical systems, allowing for training in a series-parallel configuration and operation in a parallel configuration, which stabilizes model prediction and reduces error.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a parallel model configuration is used for nonlinear dynamical system identification, then flexibility and practical applicability are improved (model can operate without system output data), but model stability deteriorates (outputs rapidly diverge from actual system values)
Solution Approach 1:
The patent applies asymmetry by using different kernel functions for the two components of the parallel model: an asymmetric wavelet kernel for the nonlinear function approximation and a symmetric ARMA kernel for the linear dynamic filtering. This asymmetric kernel configuration stabilizes the parallel model by separating the handling of nonlinearities and linear dynamics, preventing the rapid divergence while maintaining the flexibility of parallel operation without requiring system output data
2Measurement precision
If an asymmetric wavelet kernel is used in support vector regression, then transient signal capture ability is improved, but model complexity increases
Solution Approach 1:
The patent segments the complex modeling task into two distinct components handled by separate kernels: the asymmetric wavelet kernel specifically targets transient signal capture and nonlinear features, while the ARMA kernel handles linear dynamic relationships. This segmentation allows each kernel to be optimized for its specific function, improving transient capture without requiring the entire model to be overly complex
3Reliability
If linear programming algorithm is used with asymmetric wavelet kernel, then parallel model identification reliability is improved, but computational complexity increases
Solution Approach 1:
The patent employs linear programming as a feedback optimization mechanism that iteratively adjusts the support vector coefficients to minimize prediction error while satisfying constraints. The linear programming algorithm provides systematic feedback loops that converge to reliable solutions for parallel model identification, managing computational complexity through efficient optimization rather than brute-force methods
Data Source
AI summary
Example methods of modeling a nonlinear dynamical system such as a vehicle engine include providing a model using linear programming support vector regression (LP-SVR) having an asymmetric wavelet kernel, such as derived from a raised-cosine wavelet function. The model may be trained to determine parallel model parameters while in a series-parallel configuration, and operated in the parallel configuration allowing improved and more flexible model performance. An improved engine control unit may use an LP-SVR with an asymmetric wavelet kernel.