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Fig. 2. Layer-wise unsupervised pre-training of hidden layers weights for the DNN depicted in Figure 1. At each step, a hidden layer is trained using the output of its predecessor hidden layer by tuning a pair of encoder and decoder functions, (f;,9;). At each step, the norm of reconstruction error, \|fi(v?-+) — gi(fi(v?—1))||2 is minimized for i = 1, 2,3.

Figure 2 Layer-wise unsupervised pre-training of hidden layers weights for the DNN depicted in Figure 1. At each step, a hidden layer is trained using the output of its predecessor hidden layer by tuning a pair of encoder and decoder functions, (f;,9;). At each step, the norm of reconstruction error, \|fi(v?-+) — gi(fi(v?—1))||2 is minimized for i = 1, 2,3.

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Fig. 1. A DNN with three hidden layers (L=3). Input and output layers are counted separately. Each layer’s output is obtained by applying a nonlinear map, f;(-), to its predecessor layer’s output.
Fig. 1. A DNN with three hidden layers (L=3). Input and output layers are counted separately. Each layer’s output is obtained by applying a nonlinear map, f;(-), to its predecessor layer’s output.
Fig. 3. Dropped out regularization in training. The randomly omitted neuron’s output replaced by zero during training. They are shown as white nodes with a cross.
Fig. 3. Dropped out regularization in training. The randomly omitted neuron’s output replaced by zero during training. They are shown as white nodes with a cross.
Fig. 4. Two levels of DWT decomposition of x(t) second, as mentioned in Subsection II-C, there are some basis functions for a wavelet system. However, the right choice of basis function, or equivalently the filter bank, in a particular application is very crucial for having a useful representation of signal and it is usually done by some sort of art. Authors in [24] addressed this problem by introducing an adaptive Morlet to make a balance in time and scale localization to find a good basis function. This method enabled authors to detect mechanical faults in early stages. However, applying this technique requires a deep understanding of the wavelet transform and applying it requires a certain circumstances.
Fig. 4. Two levels of DWT decomposition of x(t) second, as mentioned in Subsection II-C, there are some basis functions for a wavelet system. However, the right choice of basis function, or equivalently the filter bank, in a particular application is very crucial for having a useful representation of signal and it is usually done by some sort of art. Authors in [24] addressed this problem by introducing an adaptive Morlet to make a balance in time and scale localization to find a good basis function. This method enabled authors to detect mechanical faults in early stages. However, applying this technique requires a deep understanding of the wavelet transform and applying it requires a certain circumstances.
Fig. 5. |The proposed fault diagnosis algorithm. The DWT coefficients corresponding to a sliding window of time are fed directly to DNN.
Fig. 5. |The proposed fault diagnosis algorithm. The DWT coefficients corresponding to a sliding window of time are fed directly to DNN.
Fig. 6. The customized test rig for gathering sensory data with different modalities. Several experiments have been done in faulty and fault- free conditions at five levels of load. Each test is repeated 10 times to validate repeatability of the experiment. Faults
Fig. 6. The customized test rig for gathering sensory data with different modalities. Several experiments have been done in faulty and fault- free conditions at five levels of load. Each test is repeated 10 times to validate repeatability of the experiment. Faults
Fig. 7. (a) Pinion-wheel contact at tooth surface damage point. (b) Wheel tooth surface damage fault. (c) Pinion tooth surface damage fault.
Fig. 7. (a) Pinion-wheel contact at tooth surface damage point. (b) Wheel tooth surface damage fault. (c) Pinion tooth surface damage fault.
Fig. 8. Nvidia Jetson TX1 embedded board with dimension of an ATM card.
Fig. 8. Nvidia Jetson TX1 embedded board with dimension of an ATM card.
Fig. 9. ROC of 5 classifiers for different measurements obtained by plot true positive rate (TPR) versus false positive rate (FPR). As can seen, all classes have a ROC near ideal for all datasets. But this is not the case for synchronous fault. It means classifying samples of this fault is associated with a higher degree of uncertainty. { The evaluation latency is measured as the total wall clock time of evaluation of network output for entire of each dataset divided by number of its windows. § The training time is measured as the wall clock time of training the network for each dataset divided by number of windows in each dataset per epoch.
Fig. 9. ROC of 5 classifiers for different measurements obtained by plot true positive rate (TPR) versus false positive rate (FPR). As can seen, all classes have a ROC near ideal for all datasets. But this is not the case for synchronous fault. It means classifying samples of this fault is associated with a higher degree of uncertainty. { The evaluation latency is measured as the total wall clock time of evaluation of network output for entire of each dataset divided by number of its windows. § The training time is measured as the wall clock time of training the network for each dataset divided by number of windows in each dataset per epoch.
Related topics:
AcousticsMachine LearningGPU ComputingCondition monitoring and fault diagnosis of electric machineryFault diagnosisEmbedded System
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