#
Visual-Acoustic Sensor-Aided Sorting Efficiency Optimization of Automotive Shredder Polymer Residues Using Circularity Determination^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Tested ASR Plastics

#### 2.2. Scraps’ Regularity Analysis by Using RRSB Distribution

_{1}, y

_{1}), (x

_{2}, y

_{2}), …, (x

_{n}, y

_{n})] can be computed easily with experimental data. The values of n and m in equation (5) can be determined by putting the known coordinate points into a linear regression calculation.

_{er}is the residual sum of squares, S is the total sum of squares, ȳ

_{i}is the mean value of y

_{n}, and ŷ

_{i}is the associated modeled value of y

_{n}. R

^{2}is a value that ranges from 0 to 1.0: R

^{2}approaching 1.0 means that the data fit well to each other. According to the mechanism of RRSB distribution analysis, if there are certain amount of scraps with irregular shape, the mass variations between different sieving fraction would be relatively high, which leads to the passing rate distribution on x to be far from fitted line y, which were introduced in Equation (5), and this kind of deviation would result in the low value of R

^{2}of passing rates. Therefore, if R

^{2}is close to 1.0, it means that the particle sizes or masses are regularly distributed.

#### 2.3. Impact Acoustic Sorting Theories

_{m,n}is a dimensionless coefficient associated with the corresponding flexural vibration mode (m, n), which depends on different modes of impact, i.e., the impact position and shape of impact bodies. By impact tests and fitting analysis, the specific impact frequency coefficient k

_{c}of each material can be determined, which can then be used as a sorting criterion of different kinds of plastics.

#### 2.4. Image Processing

_{ij}is the grayscale value of pixels, a grayscale value of 0 means the pixel is totally black, and a grayscale value of 1 means that it is totally white; T* is the automatic threshold level calculated by using the filter function proposed by Otsu [32], which was used for its simple and convenient processing. The binary image is shown in Figure 5a.

#### 2.5. Circularity Determination

#### 2.5.1. Methods for Circularity Determination

_{P}is the area of a circle with the same perimeter as the object, and P is the perimeter of the object.

_{dmax}is the area of a circle with the maximum diameter of the object, and d

_{max}is the maximum distance between two random border points of the object. The greatest advantage of this method is that it avoids calculating the perimeter, thus eliminating a source of unnecessary errors.

_{bmin}is the minimum radius from the border to the center point of the object and r

_{bmax}is the maximum radius.

_{j}is the corresponding radius from the border point j to the center point, and r

_{b}is the mean radius from the border points to the center point of the object.

#### 2.5.2. Calculation of Scrap Shape Parameters

_{j}and b

_{j}

_{+1}are the adjacent border pixels and D equals 0.948 when b

_{j}and b

_{j}

_{+1}are on a straight line; otherwise, D equals 1.343, which has been confirmed by Niehaus [41].

_{x}, c

_{y}) define the centroid of the object, (x

_{i}, y

_{i}) are the pixels of the object, and A

_{s}is the signed area of the object, which can be obtained by [42]:

_{actual}is the actual width of the scanning area with a unit of mm, d

_{pixel}is the number of pixels occupied by the horizontal direction of the image with a unit of pixel, and the unit of k is mm/pixel.

## 3. Results and Discussion

#### 3.1. Results of Regularity Analysis

^{2}equals 0.9924. The RRSB distribution analysis of ABS/PC scraps shows that d’ = 20.587 mm and the passing rate is 63.2%, which means that 63.2% of the tested ABS/PC scraps have an equivalent particle size under 20.587 mm. The slope n of the fitting line equals 8.8396, and R

^{2}equals 0.9937. The RRSB distribution analysis of the PP samples shows that d’ = 19.829 mm and the passing rate is 63.2%, which means that 63.2% of the tested PP scraps have an equivalent particle size under 19.829 mm. The slope n of the fitting line equals 8.7075 and R

^{2}equals 0.9886. The RRSB distribution analysis of the tested PP/EPDM scraps shows that d’ = 20.014 mm and the passing rate is 63.2%, which means that 63.2% of PP/EPDM samples have an equivalent particle size under 20.014 mm. The slope n of the fitting line equals 7.9348, and R

^{2}equals 0.9830.

^{2}) that are very close to 1.0, which means that the PSD of these four scrap materials had adequate homogeneity and regularity. The occurrence of irregular scraps was very low, which fulfills the requirements for circularity determination.

#### 3.2. Determination of Scrap Circularity

_{max}in Equation (10). The final results are shown in Table 1.

#### 3.3. Results of Sorting Efficiency Optimization

_{C}was fitted with high accuracy.

_{C}of ABS is 530.25 m/s, and the fitting coefficient is 0.9874; the k

_{C}of ABS/PC is 661.74 m/s, and the fitting coefficient is 0.9874; the k

_{C}of PP is 231.47 m/s, and the fitting coefficient is 0.9952; the k

_{C}of PP/EPDM is 211.77 m/s, and the fitting coefficient is 0.9830. From Figure 16, it can be observed that the fitting curves of ABS-based materials are far from those of PP-based materials, meaning that, theoretically, they could be completely sorted. The k

_{C}values of ABS and ABS/PC are very close, which means that they have similar impact frequency response properties; PP and PP/EPDM are in a similar situation. Therefore, the coefficient kc of ABS-based and PP-based materials are similar, which limits their recognition accuracy and sorting efficiency. In our previous study, the actual sorting efficiency for the scrap materials with diameters ranging from 14 to 23 mm was 39.2% for PP and 41.4% for PP/EPDM scraps; similarly, it was 62.4% for ABS and 70.8% for ABS/PC scraps [18].

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Image processing: (

**a**) binary image; (

**b**) image with border lines; and, (

**c**) scraps with minimum rectangle bounding box.

**Figure 6.**Diagrams of four circularity determination methods: (

**a**) Form Factor; (

**b**) Roundness Factor; (

**c**) Radius Ratio; and, (

**d**) Mean Roundness.

**Figure 8.**Rosin–Rammler–Sperling–Bennet (RRSB) distribution of acrylonitrile-butadiene-styrene (ABS) scraps.

**Figure 13.**Bar plots of measurement results: (

**a**) Form Factor; (

**b**) Roundness Factor; (

**c**) Radius Ratio; and, (

**d**) Mean Roundness.

**Figure 17.**The 90% confidence level of the ABS and ABS/PC mixture by using circularity measurements.

**Figure 18.**The 70% confidence level of the PP and PP/EPDM mixture by using circularity measurements.

**Figure 19.**Confidence intervals of ABS and ABS/PC at the 75% confidence level by using fine sieving diameter determination.

**Figure 20.**Confidence intervals of PP and PP/EPDM at the 50% confidence level by using fine sieving diameter determination.

No. | Circularity | No. | Circularity | No. | Circularity |
---|---|---|---|---|---|

1 | 0.8561 | 8 | 0.4621 | 15 | 0.5837 |

2 | 0.8361 | 9 | 0.5048 | 16 | 0.6321 |

3 | 0.8964 | 10 | 0.5540 | 17 | 0.6349 |

4 | 0.8311 | 11 | 0.6018 | 18 | 0.4252 |

5 | 0.4796 | 12 | 0.4376 | 19 | 0.4263 |

6 | 0.4464 | 13 | 0.5925 | ||

7 | 0.6840 | 14 | 0.6592 |

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**MDPI and ACS Style**

Huang, J.; Xu, C.; Zhu, Z.; Xing, L.
Visual-Acoustic Sensor-Aided Sorting Efficiency Optimization of Automotive Shredder Polymer Residues Using Circularity Determination. *Sensors* **2019**, *19*, 284.
https://doi.org/10.3390/s19020284

**AMA Style**

Huang J, Xu C, Zhu Z, Xing L.
Visual-Acoustic Sensor-Aided Sorting Efficiency Optimization of Automotive Shredder Polymer Residues Using Circularity Determination. *Sensors*. 2019; 19(2):284.
https://doi.org/10.3390/s19020284

**Chicago/Turabian Style**

Huang, Jiu, Chaorong Xu, Zhuangzhuang Zhu, and Longfei Xing.
2019. "Visual-Acoustic Sensor-Aided Sorting Efficiency Optimization of Automotive Shredder Polymer Residues Using Circularity Determination" *Sensors* 19, no. 2: 284.
https://doi.org/10.3390/s19020284