VMD Parameter Optimization for Bearing Vibration Signals
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Solution Overview
Problem
Current signal decomposition methods for bearing vibration signals, such as VMD, face challenges in optimizing bandwidth parameter α and number of modes K, often considering only one parameter at a time, ignoring their interaction and the distance between reconstructed modes and original signals, leading to suboptimal mode components that hinder feature extraction and failure mode identification.
Innovation Solution
An optimization algorithm that automatically determines optimal VMD parameters (αopt and Kopt) by establishing bandwidth, energy loss, and mode mean position distance optimization sub-models, using self-power spectral density and genetic algorithms to ensure accurate decomposition and feature extraction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If only one parameter (α or K) is optimized alone in VMD, then the optimization process is simpler, but the decomposition performance is suboptimal due to ignoring parameter interactions
Solution Approach 1:
The patent merges the optimization of bandwidth parameter α and mode number K into a unified optimization framework. By establishing an objective function that simultaneously considers both parameters and their interactions, the method avoids the suboptimal results of sequential or independent optimization while maintaining computational tractability through the proposed objective function formulation.
Solution Approach 2:
The patent transforms the parameter optimization problem by introducing a comprehensive objective function that evaluates decomposition quality based on multiple criteria (energy concentration, mode separation, reconstruction accuracy). This parameter change approach allows simultaneous optimization of α and K by searching their joint parameter space rather than treating them independently.
2Reliability
If the bandwidth parameter α is increased to reduce mode aliasing, then mode separation improves, but the bandwidth of each mode becomes too narrow causing information loss
Solution Approach 1:
The patent implements feedback mechanisms through the objective function that evaluates decomposition quality and guides parameter adjustment. The objective function incorporates terms that measure both mode separation quality and information preservation, creating a feedback loop that automatically balances α selection to achieve optimal separation without excessive bandwidth restriction.
Solution Approach 2:
The patent makes the bandwidth parameter α dynamic by optimizing it adaptively based on the specific characteristics of the input signal. Rather than using fixed or manually selected values, the optimization process dynamically determines the appropriate α for each decomposition task, allowing the bandwidth to adjust according to signal properties while maintaining the balance between separation and information preservation.
3Measurement precision
If the number of modes K is increased to capture more signal features, then decomposition completeness improves, but computational complexity and error accumulation increase
Solution Approach 1:
The patent applies the principle of partial action by optimizing K to the minimum necessary value that captures the essential signal features. Rather than using excessive numbers of modes that would increase computational burden, the objective function guides the selection of an optimal K that provides sufficient decomposition completeness while avoiding unnecessary computational complexity and error accumulation.
Solution Approach 2:
The patent performs preliminary optimization of K before actual signal decomposition. By establishing the optimal number of modes through the objective function evaluation in advance, the method avoids the computational waste of performing decompositions with insufficient or excessive K values, thereby reducing overall computational complexity while ensuring decomposition completeness.
4Productivity
If traditional VMD decomposition is used without parameter optimization, then the process is faster and simpler, but the mode components have negative effects on subsequent feature extraction and failure mode identification
Solution Approach 1:
The patent performs preliminary optimization of VMD parameters α and K before actual decomposition. By pre-determining the optimal parameter values through the objective function, the method ensures that subsequent decompositions use optimized parameters, thereby improving feature extraction quality and failure mode identification accuracy without significantly impacting overall processing time.
Solution Approach 2:
The patent transforms the fixed-parameter VMD approach into a variable-parameter optimization framework. By changing from manual or fixed parameter selection to automated optimization based on signal characteristics, the method improves decomposition quality and subsequent analysis reliability while maintaining computational efficiency through the proposed objective function and optimization strategy.
Data Source
AI summary
The present invention provides an optimization algorithm for automatically determining variational mode decomposition parameters based on bearing vibration signals. First, mode energy is used to reflect bandwidth, a bandwidth optimization sub-model is established to automatically obtain optimal bandwidth parameter αopt. Secondly, energy loss optimization sub-model is established to avoid under-decomposition. Thirdly, a mode mean position distance optimization sub-model is established to prevent the generation of too much K and avoid the phenomenon of over-decomposition. Finally, considering the interaction between the bandwidth parameter α and the total number of modes K, the interaction between mode components and the integrity of reconstruction information, nonlinear transformation is performed by a logarithmic function, so as to make the values of three optimization sub-models form similar scales, obtain an optimization model that can automatically determine optimal VMD parameters αopt and Kopt, and establish a quantitative evaluation index for the decomposition performance of a VMD algorithm.