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J. Kim and J.-M. Kim
methods have been developed [3, 4]. Although the performance of the DNN-based
methods achieved high classification accuracy, the result is uninterpretable due to the
black box-like approach of DNN. This problem makes DNN unreliable and unvalidated for applications. Gradient-weighted class activation mapping (Grad-CAM) is
a promising method to provide visual explanations of the classification result with
DNN, which has been validated for object detection and recognition [5]. This paper
applies Grad-CAM for bearing fault diagnosis method and validate the performance
by visualizing important regions in the envelope spectrum of AE signal.
46.2 Proposed Method
The proposed method consists of the following steps. (Step 1) Envelope spectrums
are calculated from pre-acquired AE signals containing healthy and faulty condition. (Step 2) frequency magnitudes in the characteristic frequency range of bearing
are extracted as features. (Step 3) DNN is trained using the extracted features. The
envelope spectrums of new AE signals are classified into healthy or faulty condition
using the trained DNN. (Step 4) A importance weights with frequency are generated including important regions in the envelope spectrum using Grad-CAM for the
acquired AE signals.
46.2.1 Step 1: Envelope Spectrum Calculation
Since the burst signals from bearing failures is amplitude-modulated, AE signals
are demodulated to extract pure burst signals. In this paper, Hilbert transform-based
envelope analysis is used for demodulation of the AE signal [6]. Firstly, Hilbert
transform is applied to the AE signal as follows:
x(t) =
1
π
∞
∫
−∞
x(τ )
t − τ
dτ,
(46.1)
where t is the time, x(τ ) is a sample of input signal at τ , and
x(t) is a sample of
Hilbert transformed signal at time t.
To obtain the analytical signal, z(t), Hilbert transformed signal,
x(t), and input
signal, x(t) are combined as complex numbers:
z(t) = x(t) + i
x(t), i =
√ −1.
(46.2)
Then, the envelope signal, e(t) is computed as |z(t)|. Finally, envelope spectrum
is calculated as the root-square of the fast Fourier transform of e(t).
J. Kim and J.-M. Kim
methods have been developed [3, 4]. Although the performance of the DNN-based
methods achieved high classification accuracy, the result is uninterpretable due to the
black box-like approach of DNN. This problem makes DNN unreliable and unvalidated for applications. Gradient-weighted class activation mapping (Grad-CAM) is
a promising method to provide visual explanations of the classification result with
DNN, which has been validated for object detection and recognition [5]. This paper
applies Grad-CAM for bearing fault diagnosis method and validate the performance
by visualizing important regions in the envelope spectrum of AE signal.
46.2 Proposed Method
The proposed method consists of the following steps. (Step 1) Envelope spectrums
are calculated from pre-acquired AE signals containing healthy and faulty condition. (Step 2) frequency magnitudes in the characteristic frequency range of bearing
are extracted as features. (Step 3) DNN is trained using the extracted features. The
envelope spectrums of new AE signals are classified into healthy or faulty condition
using the trained DNN. (Step 4) A importance weights with frequency are generated including important regions in the envelope spectrum using Grad-CAM for the
acquired AE signals.
46.2.1 Step 1: Envelope Spectrum Calculation
Since the burst signals from bearing failures is amplitude-modulated, AE signals
are demodulated to extract pure burst signals. In this paper, Hilbert transform-based
envelope analysis is used for demodulation of the AE signal [6]. Firstly, Hilbert
transform is applied to the AE signal as follows:
x(t) =
1
π
∞
∫
−∞
x(τ )
t − τ
dτ,
(46.1)
where t is the time, x(τ ) is a sample of input signal at τ , and
x(t) is a sample of
Hilbert transformed signal at time t.
To obtain the analytical signal, z(t), Hilbert transformed signal,
x(t), and input
signal, x(t) are combined as complex numbers:
z(t) = x(t) + i
x(t), i =
√ −1.
(46.2)
Then, the envelope signal, e(t) is computed as |z(t)|. Finally, envelope spectrum
is calculated as the root-square of the fast Fourier transform of e(t).