# A New Deep Learning Model for Fault Diagnosis with Good Anti-Noise and Domain Adaptation Ability on Raw Vibration Signals

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- We propose a novel and simple learning framework, which works directly on raw temporal signals. A comparison with traditional methods that require extra feature extraction is shown in Figure 1.
- (2)
- This algorithm itself has strong domain adaptation capacity, and the performance can be easily improved by a simple domain adaptation method named AdaBN.
- (3)
- This algorithm performs well under noisy environment conditions, when working directly on raw noisy signals with no pre-denoising methods.
- (4)
- We try to explore the inner mechanism of WDCNN model in mechanical feature learning and classification by visualizing the feature maps learned by WDCNN.

## 2. A Brief Introduction to CNN

#### 2.1. Convolutional Layer

#### 2.2. Activation Layer

#### 2.3. Pooling Layer

#### 2.4. Batch Normalization

## 3. Proposed WDCNN Intelligent Diagnosis Method

#### 3.1. Architecture of the Proposed WDCNN Model

**z**

_{j}denotes the logits of the j-th output neuron.

#### 3.2. Training of the WDCNN

**H**, where (

**W,b**) are the parameters. Then the error for the l layer is computed as:

^{l}is the input to the l-th layer. The operation “$*$” computes the valid convolution between i-th input in the l-th layer and the error of the k-th kernel. The flip results from derivation of delta error in Convolution Neural Network.

#### 3.3. Domain Adaptation Framework for WDCNN

Algorithm 1 AdaBN for WDCNN | |

Input: | Input of neuron i in BN layers of WDCNN for unlabeled target signal p, ${x}_{t}^{\left(i\right)}\left(p\right)\in {x}_{t}^{\left(i\right)}$,where ${x}_{t}^{\left(i\right)}=\{{x}_{t}^{\left(i\right)}\left(1\right),\dots ,{x}_{t}^{\left(i\right)}\left(n\right)\}$ The trained scale and shift parameters ${\gamma}_{s}^{\left(i\right)}$ and ${\beta}_{s}^{\left(i\right)}$ for neuron i using the labeled source signals. |

output: | Adjusted structure of WDCNN |

For | Each neuron i and each signal p in target domain Calculate the mean and variance of all the samples in target domain: ${\mu}_{t}^{\left(i\right)}\leftarrow E[{x}_{t}^{\left(i\right)}]$ ${\sigma}_{t}^{\left(i\right)}\leftarrow Var[{x}_{t}^{\left(i\right)}]$ Calculate the BN output by: ${\hat{x}}_{t}^{\left(i\right)}\left(p\right)=\frac{{x}_{t}^{\left(i\right)}\left(p\right)-{\mu}_{t}^{\left(i\right)}}{{\sigma}_{t}^{\left(i\right)}}$ ${\hat{y}}_{t}^{\left(i\right)}\left(p\right)={\gamma}^{\left(i\right)}{\hat{x}}_{t}^{\left(i\right)}\left(p\right){\beta}^{\left(i\right)}$ |

End for |

#### 3.4. Data Augumentation

## 4. Validation of the Proposed WDCNN Model

#### 4.1. Data Description

#### 4.2. Experimental Setup

#### 4.2.1. Baseline System

#### 4.2.2. Parameters of the Proposed CNN

^{(l)}= 1, P

^{(l)}= 2, W

^{(l)}= 3, therefore R

^{(l+1)}= 2R

^{(l)}+ 2, where R

^{(n+1)}= 1, and n is the number of convolutional layers. Solving the iterative equation gives us:

^{(0)}of the receptive field that each neuron in fully connected layer has on the input signal is:

^{(0)}and the input signal should satisfy T ≤ R

^{(0)}≤ L, where T is the size of signal sampled in one rotating period, L is the size of the whole signal, in this paper, T ≈ 400, L = 2048. Besides, L must be divisible by S

^{(1)}. According to the rules above, we can easy find the stride for the first convolutional kernel is 8 or 16 when the number of convolutional layers is 5. When configuring parameters, it’s also worth noticing that with the increase of the number of convolutional kernels, width of kernels, depth of layers, and the decrease of stride, the number of neurons will increase, which improves the capacity of the model, but also makes it easier to overfit. Therefore, we need to enlarge the overlapping size between training signals to increase the number of training samples and vice versa.

#### 4.3. Effect of the Data Number for Training

#### 4.4. Performance under Different Working Environment

#### 4.4.1. Case Study I: Performance across Different Load Domains

#### 4.4.2. Case Study II: Performance under Noise Environment

_{signal}and P

_{noise}are the power of the signal and the noise, respectively.

#### 4.5. Networks Visualizations

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

CNN | Convolutional Neural Network |

WDCNN | Deep Convolutional Neural Networks with Wide First-layer Kernels |

AdaBN | Adaptive Batch Normalization |

DNN | Deep Neural Network |

SVM | Support Vector Machine |

MLP | Multi-Layer Perceptron |

ReLU | Rectified Linear Unit |

BN | Batch Normalization |

FFT | Fast Fourier Transformation |

t-SNE | T-distributed Stochastic Neighbor Embedding |

SNR | Signal-to-Noise Ratio |

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**Figure 1.**Three intelligent fault diagnosis frameworks: (

**a**) traditional method; (

**b**) features extracted by unsupervised learning [27]; (

**c**) the proposed method.

**Figure 8.**Feature visualization via t-SNE: last hidden fully-connected layer representation for the test samples in WDCNN trained by different numbers of training samples: (

**a**) 90 training samples; (

**b**) 300 training samples; (

**c**) 3000 training samples and (

**d**) 19,800 training samples.

**Figure 9.**Results of the proposed WDCNN and WDCNN (AdaBN) of six domain shifts on the Datasets A, B and C, compared with FFT-SVM, FFT-MLP and FFT-DNN.

**Figure 10.**Feature visualization via t-SNE: last hidden fully-connected layer representation of WDCNN for (

**a**) test set C and B before AdaBN, and (

**b**) test C and B after AdaBN.

**Figure 11.**Figures for original signal of inner race fault, the additive white Gaussian noise, and the composite noisy signal with SNR = 0 dB respectively.

**Figure 13.**Visualization of convolutional kernels learned by (

**a**) WDCNN and their (

**b**) frequency-domain representation.

**Figure 14.**Visualization of the activations from the first convolutional layer with 10 kinds of fault signals as input. Red represents an activation of maximum, while blue means the neuron is not activated.

**Figure 15.**Visualization of all convolutional neuron activations in WDCNN for (

**a**) a segment of normal vibration signal and (

**b**) a segment of fault signal (inner race fault with 0.014-inch fault diameter). Red represents an activation of maximum, while blue means the neuron is not activated.

**Figure 16.**Visualization of the feature distribution of all the test samples with no noise extracted from each convolutional layers and the last fully-connected layer via t-SNE method.

Fault Location | None | Ball | Inner Race | Outer Race | Load | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Category Labels | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||

Fault diameter (inch) | 0 | 0.007 | 0.014 | 0.021 | 0.007 | 0.014 | 0.021 | 0.007 | 0.014 | 0.021 | ||

Dataset A no. | Train | 660 | 660 | 660 | 660 | 660 | 660 | 660 | 660 | 660 | 660 | 1 |

Test | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | ||

Dataset B no. | Train | 660 | 660 | 660 | 660 | 660 | 660 | 660 | 660 | 660 | 660 | 2 |

test | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | ||

Dataset C no. | train | 660 | 660 | 660 | 660 | 660 | 660 | 660 | 660 | 660 | 660 | 3 |

test | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | ||

Dataset D no. | Train | 1980 | 1980 | 1980 | 1980 | 1980 | 1980 | 1980 | 1980 | 1980 | 1980 | 1,2,3 |

Test | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 |

No. | Layer Type | Kernel Size/Stride | Kernel Number | Output Size (Width × Depth) | Padding |
---|---|---|---|---|---|

1 | Convolution1 | 64 × 1/16 × 1 | 16 | 128 × 16 | Yes |

2 | Pooling1 | 2 × 1/2 × 1 | 16 | 64 × 16 | No |

3 | Convolution2 | 3 × 1/1 × 1 | 32 | 64 × 32 | Yes |

4 | Pooling2 | 2 × 1/2 × 1 | 32 | 32 × 32 | No |

5 | Convolution3 | 3 × 1/1 × 1 | 64 | 32 × 64 | Yes |

6 | Pooling3 | 2 × 1/2 × 1 | 64 | 16 × 64 | No |

7 | Convolution4 | 3 × 1/1 × 1 | 64 | 16 × 64 | Yes |

8 | Pooling4 | 2 × 1/2 × 1 | 64 | 8 × 64 | No |

9 | Convolution5 | 3 × 1/1 × 1 | 64 | 6 × 64 | No |

10 | Pooling5 | 2 × 1/2 × 1 | 64 | 3 × 64 | No |

11 | Fully-connected | 100 | 1 | 100 × 1 | |

12 | Softmax | 10 | 1 | 10 |

Scenario Settings for Domain Adaptation | |||
---|---|---|---|

Domain types | Source domain | Target domain | |

Description | labeled signals under one single load | unlabeled signals under another load | |

Domain details | Training set A | Test set B | Test set C |

Training set B | Test set C | Test set A | |

Training set C | Test set A | Test set B | |

Target | Diagnose unlabeled vibration signals in target domain |

Kernel Size | SNR (dB) | |||||||
---|---|---|---|---|---|---|---|---|

−4 | −2 | 0 | 2 | 4 | 6 | 8 | 10 | |

16 | 27.14% | 40.89% | 55.37% | 72.03% | 85.71% | 94.58% | 98.41% | 99.35% |

24 | 35.32% | 52.72% | 70.15% | 84.75% | 94.37% | 98.50% | 99.64% | 99.82% |

32 | 42.00% | 57.66% | 72.76% | 86.53% | 95.47% | 98.40% | 99.52% | 99.69% |

40 | 46.84% | 63.03% | 77.55% | 90.20% | 97.07% | 99.21% | 99.71% | 99.82% |

48 | 50.15% | 66.16% | 80.21% | 92.08% | 97.69% | 99.35% | 99.73% | 99.87% |

56 | 51.67% | 66.83% | 80.85% | 92.32% | 97.84% | 99.21% | 99.73% | 99.79% |

64 | 51.75% | 67.15% | 82.03% | 93.06% | 98.07% | 99.29% | 99.79% | 99.81% |

72 | 53.69% | 68.53% | 82.23% | 92.93% | 97.91% | 99.35% | 99.71% | 99.82% |

80 | 56.07% | 69.39% | 84.24% | 94.84% | 98.69% | 99.44% | 99.83% | 99.85% |

88 | 56.05% | 71.62% | 85.33% | 95.04% | 98.46% | 99.37% | 99.74% | 99.83% |

96 | 64.29% | 78.80% | 89.91% | 96.97% | 99.03% | 99.62% | 99.81% | 99.85% |

104 | 62.91% | 79.21% | 90.36% | 97.52% | 99.23% | 99.77% | 99.81% | 99.84% |

112 | 66.95% | 80.81% | 90.51% | 97.01% | 98.88% | 99.54% | 99.83% | 99.81% |

120 | 61.84% | 77.60% | 90.47% | 97.40% | 99.08% | 99.67% | 99.81% | 99.87% |

128 | 60.88% | 77.49% | 89.79% | 97.28% | 99.13% | 99.59% | 99.83% | 99.83% |

Max | 66.95% | 80.81% | 90.51% | 97.52% | 99.23% | 99.77% | 99.83% | 99.87% |

Kernel Size | SNR (dB) | |||||||
---|---|---|---|---|---|---|---|---|

−4 | −2 | 0 | 2 | 4 | 6 | 8 | 10 | |

16 | 81.84% | 90.38% | 95.66% | 98.45% | 99.01% | 99.54% | 99.75% | 99.77% |

24 | 87.24% | 93.99% | 97.34% | 99.03% | 99.61% | 99.81% | 99.87% | 99.89% |

32 | 89.81% | 95.16% | 97.93% | 99.29% | 99.55% | 99.76% | 99.77% | 99.86% |

40 | 90.96% | 95.99% | 98.32% | 99.33% | 99.59% | 99.75% | 99.83% | 99.89% |

48 | 91.69% | 96.29% | 98.33% | 99.39% | 99.67% | 99.80% | 99.81% | 99.88% |

56 | 92.65% | 96.59% | 98.61% | 99.47% | 99.70% | 99.77% | 99.86% | 99.87% |

64 | 92.56% | 96.79% | 98.77% | 99.49% | 99.67% | 99.83% | 99.87% | 99.93% |

72 | 92.36% | 96.39% | 98.51% | 99.35% | 99.61% | 99.76% | 99.79% | 99.84% |

80 | 92.31% | 96.70% | 98.67% | 99.40% | 99.62% | 99.76% | 99.87% | 99.86% |

88 | 92.61% | 97.02% | 98.77% | 99.45% | 99.63% | 99.75% | 99.81% | 99.83% |

96 | 92.65% | 97.04% | 98.77% | 99.57% | 99.67% | 99.80% | 99.83% | 99.84% |

104 | 92.45% | 96.57% | 98.63% | 99.51% | 99.67% | 99.79% | 99.81% | 99.91% |

112 | 91.70% | 96.31% | 98.68% | 99.43% | 99.67% | 99.79% | 99.89% | 99.91% |

120 | 92.11% | 96.46% | 98.75% | 99.47% | 99.66% | 99.77% | 99.83% | 99.89% |

128 | 91.92% | 96.53% | 98.67% | 99.38% | 99.63% | 99.73% | 99.82% | 99.87% |

Max | 92.65% | 97.04% | 98.77% | 99.57% | 99.70% | 99.83% | 99.89% | 99.93% |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, W.; Peng, G.; Li, C.; Chen, Y.; Zhang, Z.
A New Deep Learning Model for Fault Diagnosis with Good Anti-Noise and Domain Adaptation Ability on Raw Vibration Signals. *Sensors* **2017**, *17*, 425.
https://doi.org/10.3390/s17020425

**AMA Style**

Zhang W, Peng G, Li C, Chen Y, Zhang Z.
A New Deep Learning Model for Fault Diagnosis with Good Anti-Noise and Domain Adaptation Ability on Raw Vibration Signals. *Sensors*. 2017; 17(2):425.
https://doi.org/10.3390/s17020425

**Chicago/Turabian Style**

Zhang, Wei, Gaoliang Peng, Chuanhao Li, Yuanhang Chen, and Zhujun Zhang.
2017. "A New Deep Learning Model for Fault Diagnosis with Good Anti-Noise and Domain Adaptation Ability on Raw Vibration Signals" *Sensors* 17, no. 2: 425.
https://doi.org/10.3390/s17020425