# SDD-CNN: Small Data-Driven Convolution Neural Networks for Subtle Roller Defect Inspection

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Materials and Methods

#### 3.1. Overview of Proposed Method

_{x}, C

_{y}) denote the center of the roller; R and R

_{0}denote the outer radius and inner radius of the roller, respectively; and (P

_{x}, P

_{y}) and (D

_{w}, D

_{r}) represent the coordinates of the corresponding points before and after the transformation, respectively. Then, the P2C transformation can be described as

#### 3.2. Small Data Preprocessing

#### 3.2.1. Label Dilation

#### 3.2.2. Semi-Supervised Data Augmentation

#### 3.3. CNN Architectures

#### 3.3.1. SqueezeNet v1.1

#### 3.3.2. Inception v3

_{i}represents the logits or unnormalized log-probabilities. Considering the ground-truth distribution over labels q(k|x) for this training example, the loss can be defined as the cross entropy:

_{k}and the gradient has a simple form:

_{k,y}, where δ

_{k,y}is Dirac delta, which equals 1 for k = y and 0 otherwise. This maximum is not achievable for finite z

_{k}, but is approached if z

_{y}>> z

_{k}for all k ≠ y. This, however, can cause over-fitting and encourage the differences between the largest logit and all others to become large, which reduces the ability of the model to adapt. In order to encourage the model to be less confident about its predictions, a distribution over labels u(k), independent of the training example x, and a smoothing parameter ϵ are introduced to replace the q(k|x) with

#### 3.3.3. VGG-16

#### 3.3.4. ResNet-18

**×**3 filters in series, and the other uses 1

**×**1, 3

**×**3, and 1

**×**1 filters in series.

## 4. Experiments and Results

#### 4.1. Experimental Setup

- CPU: Intel E3-1230 V2*2 (3.30 GHz);
- Memory: 16 GB DDR3;
- GPU: NVIDIA GTX-1080Ti.
- The software platform used is the following:
- Ubuntu 16.04 LTS;
- Visual Studio Code with Python 2.7.

#### 4.2. Network Training and Performance Metrics

**×**3 strategies) use the same hyperparameter values (momentum 0.9, weight decay 0.0005, learning rate 0.005, and batch size 32).

#### 4.3. Model Visualizations

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Framework and flowchart of proposed small data-driven convolution neural network (SDD-CNN) for roller defect inspection.

**Figure 2.**Examples of different roller samples: (

**a**) CQ: chamfer qualified; (

**b**) CC: chamfer cracks; (

**c**) CI: chamfer indentations; (

**d**) CSc: chamfer scratches; (

**e**) CSt: chamfer stains; (

**f**) EFQ: end-face qualified; (

**g**) EFC: end-face cracks; (

**h**) EFI: end-face indentations; (

**i**) EFSc: end-face scratches; (

**j**) EFSt: end-face stains; (

**k**) EFSF: end-face serious fracture.

**Figure 11.**Confusion matrixes for different models: (

**a**) deep SDD-Inception v3; (

**b**) SDD-SqueezeNet v1.1; (

**c**) deep SDD-ResNet18; (

**d**) deep SDD-VGG16.

**Figure 12.**Comparison of t-SNE across the four networks at the end of training: (

**a**) Deep SDD-Inception v3; (

**b**) Deep SDD-SqueezeNet v1.1; (

**c**) Deep SDD-VGG16; (

**d**) Deep SDD-ResNet18.

**Figure 13.**Occlusion experiments on a couple of roller surface defect images: (

**a**) CC; (

**b**) CSc; (

**c**) CSt; (

**d**) CSt; (

**e**) EFC; (

**f**) EFSF.

Surface Type | EFQ | EFC | EFI | EFSc | EFSt | EFSF |
---|---|---|---|---|---|---|

Number of samples | 300 | 94 | 14 | 32 | 18 | 44 |

Surface type | CQ | CC | CI | CSc | CSt | |

Number of samples | 200 | 70 | 31 | 6 | 21 |

Input:k categories of target samples: {C _{1}, C_{2}, …, C_{k}}, each of which has a number of {N _{1}, N_{2}, …, N_{k}}; Process: For the most numerous category C _{m}, the sample size is N_{m}, and the sample order is P _{m0} = {1, 2, …, N_{m}}. Randomly scramble the sample order to P _{m-rand} = {p_{1}, p_{2}, …, p_{Nm}}. Output: For any other categories C _{i} (i = 1, 2, …, k, i ≠ m), the original sample order is P _{i0} = {1, 2, …, N_{i}}, and the expanded sample order is P _{i-LD} = {p_{1} mod N_{i}, p_{2} mod N_{i}, …, p_{Nm} mod N_{i}}. |

Type | EFQ/EFC/EFI/EFSc/EFSt/EFSF | CQ/CC/CI/CSc/CSt |
---|---|---|

Training set | 1440 | 960 |

Validation set | 480 | 320 |

Test set | 480 | 320 |

Total number | 2400 | 1600 |

Model Name. | Training Type | Number of Layers | Number of Parameters |
---|---|---|---|

SqueezeNet v1.1 | From scratch | 18 | 728,139 |

SDD-SqueezeNet v1.1 | From scratch | ||

SDD-SqueezeNet v1.1 | Deep transfer | ||

Inception v3 | From scratch | 18 | 24,734,048 |

SDD-Inception v3 | From scratch | ||

SDD-Inception v3 | Deep transfer | ||

VGG16 | From scratch | 16 | 134,305,611 |

SDD-VGG16 | From scratch | ||

SDD-VGG16 | Deep transfer | ||

ResNet18 | From scratch | 18 | 11,196,107 |

SDD-ResNet18 | From scratch | ||

SDD-ResNet18 | Deep transfer |

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**MDPI and ACS Style**

Xu, X.; Zheng, H.; Guo, Z.; Wu, X.; Zheng, Z.
SDD-CNN: Small Data-Driven Convolution Neural Networks for Subtle Roller Defect Inspection. *Appl. Sci.* **2019**, *9*, 1364.
https://doi.org/10.3390/app9071364

**AMA Style**

Xu X, Zheng H, Guo Z, Wu X, Zheng Z.
SDD-CNN: Small Data-Driven Convolution Neural Networks for Subtle Roller Defect Inspection. *Applied Sciences*. 2019; 9(7):1364.
https://doi.org/10.3390/app9071364

**Chicago/Turabian Style**

Xu, Xiaohang, Hong Zheng, Zhongyuan Guo, Xiongbin Wu, and Zhaohui Zheng.
2019. "SDD-CNN: Small Data-Driven Convolution Neural Networks for Subtle Roller Defect Inspection" *Applied Sciences* 9, no. 7: 1364.
https://doi.org/10.3390/app9071364