# The Quality Control of the Automatic Manipulating Process of a Flexible Container When Bulk Materials are Packaged

^{*}

## Abstract

**:**

## 1. Introduction

- the dispersion and distribution of nanoparticles in the polymer matrix;
- interaction between polymer chains and nanoparticles.

_{i}. This coefficient is called the weight of the A–R link.

## 2. The Proposed System of Machine Vision for Diagnostics of FC Gripping and Opening Accuracy

#### 2.1. The Mathematical Model of the Flexible Container Neck Sagging Curve

^{3}) of the FC cloth length unit.

_{1}and C

_{2}are arbitrary integration constants, the values of which are determined by the boundary conditions for the concrete quantities Lg and a by solution of the set of equations for the FC suspension points at the length of sagged part (Lg – a).

_{1}. We find it by solving this equation by one of the known ways.

_{2}by substituting C

_{1}into Equation (11).

_{1}, C

_{2}, and λ for the particular case of FC holding, represented in Figure 2, when the planes of the grippers are located on one horizontal line is given by

_{1}, C

_{2}, and λ by solving Equation (14) and using graphico-analytical methods. As a result, we obtain

_{1}is determined from the transcendental equation

_{1}is presented in Figure 4. Here, the intersection of the Z

_{1}and Z

_{2}function plots for the left and right parts of Equation (16) is presented, located in the right half of the coordinate plane. The point of their intersection gives the solution of the transcendental equation—value C

_{1}. The solution of the equation is in the left half of the coordinate plane, too, but as sh(x) is an odd function, i.e., sh(−x) = −sh(x), both values coincide.

#### 2.2. Development of the Algorithm for the Machine Vision System

- A1, Forming of the image in the area of the FC gripping—getting a picture of the FC gripped by the gripping device;
- A2, Preliminary processing of the image—transformation of the image into black and white, smoothing of shades of grey, partitioning of the image into clusters;
- A3, Diagnostics of the accuracy of the FC gripping—comparison of clusters of the obtained image with clusters of the reference one, recording of comparison results, calculation of probabilities, transmission of calculations on the output neurons of the neural network;
- A4, Forming of the report—forming descriptions of deviations which were revealed in the diagnostics process of the FC gripping accuracy of packaged bulk materials.

#### 2.3. Synthesis of the Neural Network Algorithm for Image Processing

_{i}is a numerical value of weight and b is the weight of the element of displacement at 1.

_{1}w

_{1}.

def f(x): |

return 1 / (1 + np.exp(−x)) |

def f_deriv(x): |

return f(x) * (1 − f(x)) |

^{(l)}for each layer. Then, Δw and Δb are assigned, the initial values of which are zero. The step of gradient descent is α for instances from 1 to m. A feedforward process is activated through all nl layers. The output of the activation function is saved in h

^{(l)}. Value δ

^{(nl}) of the output layer is searched. ΔW

^{(l)}and Δb

^{(l)}are refreshed for all layers. The process of gradient descent is then activated:

import numpy.random as r |

def setup_and_init_weights(nn_structure): |

W = {} |

b = {} |

for l in range(1, len(nn_structure)): |

W[l] = r.random_sample((nn_structure[l], nn_structure[l-1])) |

b[l] = r.random_sample((nn_structure[l],)) |

return W, b |

Further, zero initial values were assigned to two variables Δw and Δb. |

def init_tri_values(nn_structure): |

tri_W = {} |

tri_b = {} |

for l in range(1, len(nn_structure)): |

tri_W[l] = np.zeros((nn_structure[l], nn_structure[l-1])) |

tri_b[l] = np.zeros((nn_structure[l],)) |

return tri_W, tri_b |

Further, a feedforward process was activated: |

def feed_forward(x, W, b): |

h = {1: x} |

z = {} |

for l in range(1, len(W) + 1): |

if l == 1: |

node_in = x |

else: |

node_in = h[l] |

z[l+1] = W[l].dot(node_in) + b[l] # z^(l+1) = W^(l)*h^(l) + b^(l) |

h[l+1] = f(z[l+1]) # h^(l) = f(z^(l)) |

return h, z |

^{(nl)}and value δ

^{(l)}in hidden layers were found for the activation of back propagation:

def calculate_out_layer_delta(y, h_out, z_out): |

# delta^(nl) = -(y_i - h_i^(nl)) * f’(z_i^(nl)) |

return -(y-h_out) * f_deriv(z_out) |

def calculate_hidden_delta(delta_plus_1, w_l, z_l): |

# delta^(l) = (transpose(W^(l)) * delta^(l+1)) * f’(z^(l)) |

return np.dot(np.transpose(w_l), delta_plus_1) * f_deriv(z_l) |

All stages are united into one function: |

def train_nn(nn_structure, X, y, iter_num=3000, alpha=0.25): |

W, b = setup_and_init_weights(nn_structure) |

cnt = 0 |

m = len(y) |

avg_cost_func = [[] |

print(’Beginning of gradient descent for {} iterations’.format(iter_num)) |

while cnt 1: |

delta[l] = calculate_hidden_delta(delta[l+1], W[l], z[l]) |

# triW^(l) = triW^(l) + delta^(l+1) * transpose(h^(l)) |

tri_W[l]+=np.dot(delta[l+1][:,np.newaxis], np.transpose(h[l][:,np.newaxis])) |

# trib^(l) = trib^(l) + delta^(l+1) |

tri_b[l] += delta[l+1] |

# activates gradient descent for weights in each layer |

for l in range(len(nn_structure) - 1, 0, -1): |

W[l] += -alpha * (1.0/m * tri_W[l]) |

b[l] += -alpha * (1.0/m * tri_b[l]) |

# completes calculations of overall evaluation |

avg_cost = 1.0/m * avg_cost |

avg_cost_func.append(avg_cost) |

cnt += 1 |

return W, b, avg_cost_func |

#### 2.4. Development of the Automated System for FC Gripping and Opening Control

- sensor level, which is represented by a Raspberry Pi Camera Board v2.1; photographing of the FC gripping area was carried out using this camera;
- controller level, the architecture of which includes a single-board Raspberry Pi 3 computer and 5V power supply;
- supervisory level, which is represented by the automated workstation (AWS) of the operator, linked with the microcontroller via Ethernet protocol.

## 3. Materials and Methods

- flexible container dimensions: length, 1050 mm; width, 550 mm;
- stroke of the pneumatic cylinder piston with the upper VGD, 145 mm;
- diameter of the upper VGD vacuum chambers, 10 mm; distance between centers of the end side chambers, 470 mm.

## 4. Results and Discussion

## 5. Conclusions

## 6. Patents

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**The functional model of diagnostics of the FC gripping accuracy (diagram of decomposition).

**Figure 6.**The diagram of second-level decomposition of the functional block A3 in diagnostics of the FC gripping accuracy.

**Figure 9.**A sigmoid function which describes the variation of slope depending on the displacement weight.

**Figure 14.**General view of the laboratory unit: 1, Raspberry Pi camera; 2, Raspberry Pi minicomputer; 3, laptop computer; 4, 5, vacuum gripping devices (VGDs); 6, flexible container; 7, table; 8, pneumatic cylinder; 9, control board.

Photograph | Classification | Photograph | Classification |
---|---|---|---|

Correct opening | Correct opening | ||

Incorrect opening | Has not gripped | ||

Has not opened | Has gripped not by all VGDs |

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## Share and Cite

**MDPI and ACS Style**

Makarov, A.M.; Mushkin, O.V.; Lapikov, M.A.; Kukhtik, M.P.; Serdobintsev, Y.P. The Quality Control of the Automatic Manipulating Process of a Flexible Container When Bulk Materials are Packaged. *Machines* **2019**, *7*, 62.
https://doi.org/10.3390/machines7040062

**AMA Style**

Makarov AM, Mushkin OV, Lapikov MA, Kukhtik MP, Serdobintsev YP. The Quality Control of the Automatic Manipulating Process of a Flexible Container When Bulk Materials are Packaged. *Machines*. 2019; 7(4):62.
https://doi.org/10.3390/machines7040062

**Chicago/Turabian Style**

Makarov, Aleksey M., Oleg V. Mushkin, Maksim A. Lapikov, Mikhail P. Kukhtik, and Yuriy P. Serdobintsev. 2019. "The Quality Control of the Automatic Manipulating Process of a Flexible Container When Bulk Materials are Packaged" *Machines* 7, no. 4: 62.
https://doi.org/10.3390/machines7040062