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including wire pieces, aluminum scraps and tin dregs were prepared. The weight
of particle ranges from 0.5 mg to 10 mg, and the shape is close to sphere. Accord-
ing to GJB-65B-99 and MIL-STD-883E standards and device-level mechanical
environmental routine test conditions, the vibration frequency was set as 40 Hz,
and acceleration 5 g (1 g =9 . 8 m/s 2 ).
3 Feature Extraction Based on PCA
In traditional methods, the features directly obtained from different material
particle collision signals could lead to overlapping patterns. In order to reduce
the redundant information, PCA was performed for further feature extraction.
3.1 Basis of PCA
As a widely used statistical technique, PCA has been employed to reduce the
dimensionality of problems and to transform interdependent coordinates into sig-
nificant and independent ones [9]. PCA is to convert a set of correlated variables
into a set of values of linearly uncorrelated variables called principal components.
This transformation is defined in such a way that the first principal component
has the largest possible variance, and each succeeding component in turn has
the highest variance possible under the constraint that it be orthogonal to the
preceding components.
In this work, the PCA is performed with the following eigenvector algorithm:
(1) normalizing the original data X and calculating the covariance matrix C x ;
(2) by eigenvector decomposition of the C x , the eigenvectors U i ( i =1, 2,
···
,
K ) and corresponding eigenvalues λ i are sorted in descending order;
(3) obtaining the principle components(PCs) PC i (i=1, 2,
···
, K ) by project-
ing X onto the resulting eigenvectors U i ;
(4) to ensure the integrity and dimension reduction of the information, select-
ing the first N principal components according to the eigenvalues λ i in descend-
ing order.
Define R N as the accumulative contribution rate of the first N principal com-
ponents with respect to the whole principal components, and according to the
threshold of R N , the first N principal components are chosen as feature vectors.
3.2 Feature Extraction
The identification accuracy depends on the features that are sensitive to the
fault. There are overlapping and noise for different features, and some features
may even weaken the detection ability. A variety of time domain and frequency
domain features have been proposed including acoustic waveform parameters
and power spectrum.
In this paper, pulse duration time, energy, zero-crossing rate (ZCR), amplitude
divided by duration time and rise time divided duration time are used as the
features in time domain. Pulse duration time and energy measurements can be
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