Damage identification method for cantilever beam based on multifractal spectrum of multi-scale reconstructed attractor

Patent metadata

Field	Value
Publication number	US-12498291-B2
Application number	US-202318144868-A
Country	US
Kind code	B2
Filing date	May 9, 2023
Priority date	May 9, 2022
Publication date	Dec 16, 2025
Grant date	Dec 16, 2025

Abstract

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.

First claim

What is claimed is:

1 . A damage identification method for a cantilever beam based on a multifractal spectrum of a multi-scale reconstructed attractor, comprising:
acquiring an original acceleration signal of the cantilever beam by a dynamic measurement system, and performing smooth filter preprocessing on the original acceleration signal to obtain a preprocessed acceleration signal; performing stationary wavelet decomposition on the preprocessed acceleration signal to obtain multi-scale sub-signals having the same data length; selecting a multi-scale sub-signal representing vibration characteristics of the cantilever beam for phase space reconstruction and normalization to obtain the multi-scale reconstructed attractor; forming the multifractal spectrum according to the multi-scale reconstructed attractor; obtaining a damage index according to a singularity index of the multifractal spectrum; and locating a damage position in the cantilever beam according to a relative numerical value of the damage index; wherein the step of selecting the multi-scale sub-signal representing the vibration characteristics of the cantilever beam for phase space reconstruction and normalization comprises: transforming a stationary wavelet containing a main frequency range of structural vibration into an approximate coefficient to be taken as the multi-scale sub-signal representing main vibration characteristics of a structure, and performing boundary truncation on the multi-scale sub-signal to obtain a multi-scale sub-signal s; performing phase space reconstruction on the multi-scale sub-signal s after the boundary truncation to obtain the multi-scale reconstructed attractor; and normalizing the multi-scale reconstructed attractor to make a value range of phase space dimensions being [0,1].

2 . The damage identification method according to claim 1 , wherein when stationary wavelet decomposition is performed on the preprocessed acceleration signal, a wavelet basis function is rbio2.4, and the wavelet decomposition level is 3.

3 . The damage identification method according to claim 1 , wherein in the boundary truncation of the multi-scale sub-signal, a boundary truncation length of left and right sides of the multi-scale sub-signal is 1% of a total length of the multi-scale sub-signal.

4 . The damage identification method according to claim 1 , wherein the phase space reconstruction of the multi-scale sub-signal s comprises:
calculating phase point coordinates in the reconstructed attractor Y according to the following formulation:
y k =( s k ,s k +τ, . . . s k +( m− 1)τ)

wherein, y k represents the k th phase point in the reconstructed attractor Y, s k represents amplitude of the k th signal of the multi-scale sub-signal after truncation, and m and τ are embedding dimension and delay time of embedding parameters; calculating a covariance matrix C of the reconstructed attractor Y:
C=Y τ Y;
performing eigenvalue decomposition on the covariance matrix C:
C=Φ∧Φ −1
wherein, Φ is a square matrix listed as a characteristic vector, and ∧ is a diagonal matrix whose principal diagonal elements are eigenvalues; and obtaining the reconstructed attractor Y by being projected along the first principal direction:
Z=YΦ
wherein Z is the multi-scale reconstructed attractor obtained by phase space reconstruction.

5 . The damage identification method according to claim 4 , wherein the embedding parameters of phase space reconstruction are m=2 and τ=1.

6 . The damage identification method according to claim 1 , wherein construction of the multifractal spectrum comprises:
counting the total number of phase points of the multi-scale reconstructed attractor Z, and denoted as M; presetting a weight factor sequence qV and a grid size sequence sV; for each grid size sV m , dividing the multi-scale reconstructed attractor Z into grids having a size of G m ×G m , counting the number of phase points in each grid, and denoted as g m,ij , where SV m represents the m-th element of sV, and G m represents the number of grids when the grid size is sV m ; calculating the percentage of the number of phase points in each grid to the total number of phase points:
p m,ij =g m,ij /M× 100%
calculating intermediate variables as follows:

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Ma mt =Σ i Σ j [μ mt,ij ·log 10 ( p m,ij )]

Mf mt =Σ i Σ j [μ mt,ij ·log 10 (μ mt,ij )]

Msc =−log 10 ( sV )

wherein, q t represents the t th element of qV; and
according to linear regression coefficients of Ma mt and Mf mt with Msc separately, determining variable matrices α q and f q of the singularity index; and obtaining the multifractal spectrum of the multi-scale reconstructed attractor represented by f−α.

7 . The damage identification method according to claim 6 , wherein the preset weight factor sequence qV and the grid size sequence sV are: qV=−2:0.2:2, and sV=2:1:8 separately.

8 . The damage identification method according to claim 1 , wherein calculating the damage index comprises:
λ = ( Δ ⁢ α r + Δ ⁢ α l ) ⁢ Δ ⁢ α r Δ ⁢ α l κ = ( Δ ⁢ f r - Δ ⁢ f l ) ⁢ Δ ⁢ f r Δ ⁢ f l wherein, Δα r =α max −α q=0
Δα l =α q=0 −α min
Δ f r =f max −f min,r
Δ f l =f max −f min,r
wherein, α max , α min , α q=0 , f max , f min,r , f min,l correspond to values of α and f at endpoints and vertices separately in the multifractal spectrum repres

Assignees

• Univ Hohai
• Univ Jiangxi Sci & Technology
• Jsti Group

Inventors

• Cao Maosen
• Li Dayang
• Deng Tongfa
• Sumarac Dragoslav
• Sha Ganggang
• Zhang Yufeng
• Manoach Emil
• Wang Zeyu

Classifications

• G01M5/0066

  by exciting or detecting vibration or acceleration (vibration testing of structures G01M7/00) · CPC title

• G01M5/0025

  of elongated objects, e.g. pipes, masts, towers or railways (G01M5/0058 takes precedence) · CPC title

• Y02T90/00

  Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation · CPC title

• G06F2218/06

  by applying a scale-space analysis, e.g. using wavelet analysis · CPC title

• G01N2291/0289

  Internal structure, e.g. defects, grain size, texture · CPC title