Cantilever Beam Damage Detection Using Multifractal Attractors
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Solution Overview
Problem
Traditional dynamic nondestructive testing methods for cantilever beams are limited by low accuracy and insufficient noise immunity due to the inability to effectively separate damage information from interference noise and neglecting nonlinear dynamic motions, leading to inadequate damage detection.
Innovation Solution
A damage identification method using a multifractal spectrum of a multi-scale reconstructed attractor, involving multi-scale analysis to separate damage and noise, and establishing a damage index based on multifractal characteristics for accurate damage evaluation and localization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional linear theory-based dynamic nondestructive testing method is used, then the testing process is simple, but the ability to extract nonlinear features sensitive to damage is insufficient
Solution Approach 1:
The patent transforms the acceleration signal through multiple parameter transformations: wavelet decomposition to obtain multi-scale sub-signals, phase space reconstruction to create attractor trajectories, and multifractal analysis to extract singularity parameters. These parameter changes enable the system to capture nonlinear damage features that linear methods miss, resolving the contradiction between detection accuracy and analysis complexity.
Solution Approach 2:
The patent introduces several intermediary transformations between the raw signal and damage detection: wavelet coefficients as intermediaries to separate noise scales, phase space coordinates as intermediaries to reveal dynamic behavior, and multifractal spectra as intermediaries to quantify nonlinear characteristics. These intermediaries bridge the gap between simple measurement and accurate damage identification.
2Measurement precision
If phase space reconstruction is performed directly on structural dynamic response, then the reconstruction process is straightforward, but damage information and interference noise are not effectively separated
Solution Approach 1:
The patent segments the acceleration signal through wavelet decomposition into multiple scale sub-signals, separating different frequency components and noise levels. This segmentation allows selective processing of relevant vibration information while filtering out interference, directly improving damage identification accuracy without overwhelming complexity.
Solution Approach 2:
The patent performs preliminary wavelet decomposition and signal separation before phase space reconstruction. By pre-processing the signal to extract meaningful components and remove noise at earlier stages, the subsequent reconstruction and analysis become more effective and less complex, resolving the contradiction between accuracy and difficulty.
3Measurement precision
If existing damage detection methods focusing on topological differences of reconstructed attractor are used, then the method is relatively simple, but attention to nonlinear dynamic motions of complex systems is insufficient
Solution Approach 1:
The patent combines multiple analytical approaches into a composite methodology: wavelet transform for multi-scale analysis, phase space reconstruction for dynamic behavior representation, and multifractal analysis for nonlinear characteristic quantification. This composite approach captures complex nonlinear dynamics while maintaining a systematic and manageable analysis framework.
Solution Approach 2:
The patent transitions from analyzing simple topological differences in 2D phase space to examining multifractal spectra that characterize the entire distribution of singularities across different scales. This dimensional expansion from geometric topology to spectral analysis enables deeper insight into nonlinear dynamics while preserving analytical tractability.
4Reliability
If curvature mode method is used for damage location, then the method is straightforward, but the anti-noise ability of the acquired damage index is greatly reduced
Solution Approach 1:
The patent replaces the mechanical curvature-based damage location method with a dynamics-based approach using phase space reconstruction and multifractal analysis. Instead of relying on spatial derivatives of modal shapes that amplify noise, the method uses temporal dynamics and scale-dependent fractal characteristics that are inherently more robust to measurement noise, achieving both reliability and reasonable complexity.
Data Source
AI summary
A damage identification method for a cantilever beam based on a multifractal spectrum of a multi-scale reconstructed attractor includes: acquiring an original acceleration signal of the cantilever beam by a dynamic measurement system, performing stationary wavelet decomposition on a pretreated acceleration signal to obtain multi-scale sub-signals, selecting the multi-scale sub-signal that can represent main vibration characteristics of the cantilever beam for phase space reconstruction and normalization to obtain a normalized multi-scale reconstructed attractor, constructing the multifractal spectrum of the multi-scale reconstructed attractor, establishing a damage index based on a singularity index of the multifractal spectrum, and identifying and locating damage of the cantilever beam according to a relative numerical value of the damage index. The method can quantify structural damage characteristics in multi-scale phase space domain from the perspective of multifractal, and provide the simple, rapid and accurate damage identification method for cantilever beam.