The Use of Neural Networks and Genetic Algorithms to Control Low Rigidity Shafts Machining
<p>Work-holding method for securing the low-rigidity shaft specimen in the turning machine. Notation: <span class="html-italic">F<sub>be</sub></span>—bending force exerted by the cutting tool bit, <span class="html-italic">F<sub>x</sub></span>—tensile force along the x axis. <span class="html-italic">x<sub>2</sub>, y<sub>1</sub>, y<sub>2</sub></span>—current coordinates at each section of the workpiece, <span class="html-italic">a</span>—distance from spindle to the tip of the cutting tool bit, <span class="html-italic">L</span>—length of shaft, <span class="html-italic">M<sub>0</sub>, Q<sub>0</sub></span>—initial parameters: moment and transverse force at the holding point, respectively, <span class="html-italic">M<sub>1</sub></span>—moment generated by the axial component of cutting force, <span class="html-italic">M<sub>2</sub></span>—moment generated at the holding point at which the part is secured to the tailstock of the turning machine.</p> "> Figure 2
<p>(<b>a</b>) Roughness measuring instrument; tailstock collet assembly for machining elastic-deformable shafts: (<b>b</b>) idle position, tensile force of 2 kN; (<b>c</b>) view of the test stand with the shaft secured in the lathe (Ø6, L = 300 mm); (<b>d</b>) specimens.</p> "> Figure 3
<p>Curves of objective function y, tensile force <span class="html-italic">Fx<sub>1</sub></span><sub>,</sub> and eccentricity <span class="html-italic">e</span> for <span class="html-italic">d</span> = 6 mm, <span class="html-italic">F<sub>be</sub></span> = 49 N, <span class="html-italic">Fx<sub>1</sub></span> = 980 N, <span class="html-italic">L</span> = 300 mm, <span class="html-italic">F<sub>f</sub></span> = 30 N.</p> "> Figure 4
<p>Curves of objective function y, tensile force <span class="html-italic">Fx<sub>1</sub></span>, and eccentricity <span class="html-italic">e</span> for <span class="html-italic">d</span> = 6 mm, <span class="html-italic">F<sub>be</sub></span> = 70 N, <span class="html-italic">F<sub>x10</sub></span> = 980 N, <span class="html-italic">L</span> = 300 mm, <span class="html-italic">F<sub>f</sub></span> = 40 N.</p> "> Figure 5
<p>Curves of objective function y, tensile force <span class="html-italic">Fx<sub>1</sub></span>, and eccentric <span class="html-italic">e</span> for <span class="html-italic">d</span> = 8 mm, <span class="html-italic">F<sub>be</sub></span> = 147 N, <span class="html-italic">Fx<sub>10</sub></span> = 980 N, <span class="html-italic">L</span> = 300 mm, <span class="html-italic">F<sub>f</sub></span> = 196 N.</p> "> Figure 6
<p>Curves of objective function y, tensile force <span class="html-italic">Fx<sub>1</sub></span>, and eccentric <span class="html-italic">e</span> for <span class="html-italic">d</span> = 8 mm, <span class="html-italic">F<sub>be</sub></span> = 147 N, <span class="html-italic">Fx<sub>10</sub></span> = 980 N, <span class="html-italic">L</span> = 300 mm, <span class="html-italic">F<sub>f</sub></span> = 196 N.</p> "> Figure 7
<p>Structure of the shallow neural network.</p> "> Figure 8
<p>Best validation performance is 1.5775 × 10<sup>−5</sup> at epoch 20: (<b>a</b>) general view, (<b>b</b>) enlarged view of the terminal part of the curve.</p> "> Figure 9
<p>(<b>a</b>) Error histogram with 20 bins, (<b>b</b>) gradient curve, (<b>c</b>) Mu curve.</p> "> Figure 10
<p>Structure of nonlinear autoregressive network with exogenous input (NARX) neural network: (<b>a</b>) open-loop architecture; (<b>b</b>) closed-loop architecture.</p> "> Figure 11
<p>Best validation performance is 3.9897 × 10<sup>−8</sup> at epoch 20: (<b>a</b>) general view, (<b>b</b>) enlarged view of the terminal part of the curve.</p> "> Figure 12
<p>(<b>a</b>) Error histogram with 20 bins, (<b>b</b>) gradient curve, (<b>c</b>) Mu curve.</p> "> Figure 13
<p>Regression statistics for closed-loop step-ahead NARX: (<b>a</b>) R ≈ 1 for whole set of 5980 cases, (<b>b</b>) R = 0.99946 for the subset of 16 cases.</p> "> Figure 14
<p>Structure of a long short-term memory (LSTM) layer [<a href="#B26-sensors-20-04683" class="html-bibr">26</a>].</p> "> Figure 15
<p>Training performance for LSTM.</p> "> Figure 16
<p>Training loss for LSTM.</p> "> Figure 17
<p>Neural-genetic controller.</p> "> Figure 18
<p>Genetic algorithm—the best fitness plot.</p> "> Figure 19
<p>Machining quality prediction using MLP ANN.</p> "> Figure 20
<p>Machining quality prediction using MLP ANN—detail of the process for L = 154 ÷ 165 mm in <a href="#sensors-20-04683-f019" class="html-fig">Figure 19</a>.</p> "> Figure 21
<p>Machining quality prediction using NARX.</p> "> Figure 22
<p>Machining quality prediction using NARX—detail of the process for L = 154 ÷ 165 mm in <a href="#sensors-20-04683-f021" class="html-fig">Figure 21</a>.</p> "> Figure 23
<p>Machining quality prediction using LSTM.</p> "> Figure 24
<p>Machining quality prediction using LSTM—detail of the process for L = 154 ÷ 165 mm in <a href="#sensors-20-04683-f022" class="html-fig">Figure 22</a>.</p> "> Figure 25
<p>Neural-genetic controller for a = 100 mm and a = 200 mm.</p> "> Figure 26
<p>Neural-genetic controller for a = 250 mm.</p> ">
Abstract
:1. Introduction
1.1. The Problem of Low-Rigidity Shaft Machining
1.2. Automation of the Low-Rigidity Shaft Turning Process
1.3. The Application of Artificial Intelligence in the Machining of Parts
1.4. Innovative Aspects of the Proposed Approach
2. Materials and Methods
2.1. Data Preparation
Algorithm 1 Two-dimensional gradient descent search algorithm |
|
2.2. Shallow Neural Network
2.3. NARX Neural Network
2.4. Deep Network LSTM
2.5. GA-Based Controller
3. Results and Discussion
3.1. Shallow MLP Network
3.2. NARX Neural Network
3.3. Deep LSTM Network
3.4. Neural-Genetic Controller
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviation
Symbol or Abbreviation | Explanation |
a | distance from spindle to the tip of the cutting tool bit |
e | eccentricity of tensile force under tension |
Fbe | bending force exerted by the cutting tool bit |
Fr | reaction along the x axis |
Fx | tensile force along the x axis |
Fx1 | moving tensile force |
L | length of shaft |
M0, Q0 | initial parameters: moment and transverse force at the holding point, respectively |
M1 | moment generated by the axial component of cutting force |
M2 | moment generated at the holding point at which the part is secured to the tailstock of the turning machine |
R | regression coefficient |
x1, x2, y1, y2 | current coordinates at each section of the workpiece |
reference value for the i-th shaft section; | |
predicted value for the i-th shaft section | |
standard deviation of reference values | |
standard deviation of predicted values | |
ADAM | adaptive moment estimation optimization method |
ANN | artificial neural network |
BiLSTM | bidirectional LSTM layer |
DBN | deep belief network |
GA | genetic algorithms |
LMA | Levenberg-Marquardt optimization algorithm |
LSTM | long short-term memory neural network, which is a recurrent deep learning network |
MLP | multilayer perceptron |
MSE | mean square error |
NARX | flat nonlinear autoregressive network with exogenous input designed for the prediction of multidimensional time series and signals |
RBM | restricted Boltzmann machine |
RMSE | rooted MSE |
SVM | support vector machine |
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Data Subset | Number of Cases in Set | Mean Square Error (MSE) | Regression (R) |
---|---|---|---|
Training set (70%) | 4187 | 1.5059 × 10−5 | 0.99886 |
Validation set (15%) | 897 | 1.5775 × 10−5 | 0.99880 |
Testing set (15%) | 897 | 1.4976 × 10−5 | 0.99878 |
Data Subset | Number of Cases in Set | Mean Square Error (MSE) | Regression (R) |
---|---|---|---|
Training set (70%) | 4187 | 3.7450 × 10−8 | 0.999 |
Validation set (15%) | 897 | 3.9897 × 10−8 | 0.999 |
Testing set (15%) | 897 | 3.8548 × 10−8 | 0.999 |
Closed-Loop NARX | Mean Square Error (MSE) | Regression (R) |
---|---|---|
step-ahead prediction | 3.7982 × 10−8 | 0.9999 |
whole sequence prediction | 9.7246 × 10−3 | 0.5506 |
# | Layer Description | Activations | Learnable Parameters (Weights and Biases) |
---|---|---|---|
1 | Sequence input with 3 dimensions | 3 | – |
2 | BiLSTM with 200 hidden units | 200 | Input weights: 800 × 2; Recurrent Weights: 800 × 200; Bias: 800 × 1. |
3 | One fully connected layer | 1 | Weights: 6 × 200; Bias: 1 × 1. |
4 | Regression output | – | – |
Epoch | Iteration | RMSE Mini-Batch | Mini-Batch Loss | Base Learning Rate |
---|---|---|---|---|
1 | 1 | 1.06 | 0.6 | 0.05 |
1 | 50 | 0.07 | 2.1 × 10−3 | 0.05 |
2 | 100 | 0.01 | 1.0 × 10−4 | 0.05 |
2 | 150 | 0.01 | 8.9 × 10−5 | 0.05 |
3 | 200 | 0.01 | 7.9 × 10−5 | 0.05 |
3 | 250 | 0.01 | 1.1 × 10−4 | 0.05 |
4 | 300 | 0.01 | 8.7 × 10−5 | 0.05 |
4 | 350 | 0.01 | 8.7 × 10−5 | 0.05 |
5 | 400 | 0.02 | 1.1 × 10−4 | 0.05 |
5 | 450 | 0.01 | 7.0 × 10−5 | 0.05 |
Closed-Loop LSTM | Mean Square Error (MSE) | Regression (R) |
---|---|---|
step-ahead prediction | 1.4067 × 10−4 | 0.9999 |
whole sequence prediction | 2.6045 × 10−2 | 0.5506 |
Neural Network Type | MSE | R |
---|---|---|
Deep LSTM (step-ahead prediction) | 1.5456 × 10−5 | 0.9999 |
Shallow MLP ANN | 2.3984 × 10−4 | 0.9997 |
NARX (step-ahead prediction) | 1.8819 × 10−5 | 0.9999 |
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Share and Cite
Świć, A.; Wołos, D.; Gola, A.; Kłosowski, G. The Use of Neural Networks and Genetic Algorithms to Control Low Rigidity Shafts Machining. Sensors 2020, 20, 4683. https://doi.org/10.3390/s20174683
Świć A, Wołos D, Gola A, Kłosowski G. The Use of Neural Networks and Genetic Algorithms to Control Low Rigidity Shafts Machining. Sensors. 2020; 20(17):4683. https://doi.org/10.3390/s20174683
Chicago/Turabian StyleŚwić, Antoni, Dariusz Wołos, Arkadiusz Gola, and Grzegorz Kłosowski. 2020. "The Use of Neural Networks and Genetic Algorithms to Control Low Rigidity Shafts Machining" Sensors 20, no. 17: 4683. https://doi.org/10.3390/s20174683