Artificial Intelligence Model Used for Optimizing Abrasive Water Jet Machining Parameters to Minimize Delamination in Carbon Fiber-Reinforced Polymer
Abstract
:1. Introduction
2. Materials and Methods
2.1. Design of Experiments
2.2. Materials
2.3. Experimental Procedure and Results
2.4. Artificial Neural Network (ANN) Model
- Data input. The first step in the modeling process involves feeding the process parameters into the neural network. The dataset consists of predictors (input data) and responses (target data). A double array with 51 samples and 4 features representing the process parameters (water jet pressure P, standoff distance SOD, material thickness t, and abrasive start synchronization ASS) comprises the predictors. The response consists of a double array with 51 samples and 4 features representing the delamination extent (Dext). Each feature in the predictor array is represented as a neuron in the input layer of the network, which serves as the starting point for data processing. The data input (51 samples) was split, with 70% used for ANN model training, 15% for model validation, and 15% for model testing.
- Hidden layer processing. After the input data enter the network, they are processed by the hidden layer, which contains 10 neurons. These neurons use a sigmoid activation function to introduce non-linearity into the model. Each hidden neuron calculates a weighted sum of the input values, adding a bias term to this sum. The sigmoid function is then applied to this weighted sum, which helps the network learn complex patterns and relationships between the input parameters and the desired output.
- Output layer processing. The processed data from the hidden layer are then passed to the output layer. The neurons in the output layer use a linear activation function suitable for producing continuous output values. Each output neuron calculates a weighted sum of the outputs from the hidden layer neurons, including a bias term. The linear function is then applied to this weighted sum to produce the final output, which in this case is a prediction of delamination.
- Loss calculation. The network’s predicted output is compared with the actual measurements of delamination. The difference between these values is quantified using the mean squared error (MSE) loss function, which measures how well the network’s predictions match the real data. This loss value indicates the network’s performance and guides further adjustments.
- Backward propagation. To improve the network’s performance, backpropagation is used; this calculates how much each weight and bias contributes to the total error. The error at the output layer is determined by comparing the predicted and actual values. It is then used to calculate the error for each neuron in the hidden layer, considering how the output of each hidden neuron influences the final prediction.
- Parameter update. Using the errors calculated during backpropagation, the network updates its weights and biases to reduce the loss. This is accomplished using a technique called gradient descent, which adjusts each parameter slightly in the direction that will decrease the error. The learning rate determines the size of these adjustments. In this study, the Levenberg–Marquardt algorithm is used for training, which is known for its efficiency in handling non-linear least squares problems.
- Iteration. The entire process of forward propagation, loss calculation, backward propagation, and parameter update is repeated for many iterations, known as epochs. This iterative process continues until the network’s performance stabilizes and the loss converges to a minimum value, indicating that the network has been effectively trained.
3. Results and Discussions
3.1. Performance of the ANN Model in Predicting Delamination
3.2. The Morphology of the Machined Surfaces Investigation
3.3. ANN Model Validation
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
- function [y1] = myNeuralNetworkFunction(x1)
- %MYNEURALNETWORKFUNCTION neural network simulation function.
- % Auto-generated by MATLAB, 23-Jul-2024 13:01:05.
- % [y1] = myNeuralNetworkFunction(x1) takes these arguments:
- % x = Qx4 matrix, input #1
- % and returns:
- % y = Qx1 matrix, output #1
- % where Q is the number of samples.
- %#ok<*RPMT0>
- % ===== NEURAL NETWORK CONSTANTS =====
- % Input 1
- x1_step1.xoffset = [100;1;0;2];
- x1_step1.gain = [0.00666666666666667;0.222222222222222;2;0.666666666666667];
- x1_step1.ymin = −1;
- % Layer 1
- b1 = [3.0942814848929001137;−1.6412631940412265585;−1.7357019482919628928;0.0046341803092739136671;−0.12092182611574373019;0.0017721478219405242815;−0.73329001720699682476;0.89508232533568099498;1.871406632027108774;−2.2806622933958196064];
- IW1_1 = [−1.3180624629005928128 −1.3806326862996611826 0.80956172730409159399 0.24635899622397591791;1.1998835046210121202 −0.76280403929718321177 1.9324656114513456551 0.80216733375313908905;0.40939565241548864227 −2.3991523673818146989 −0.97839919126131558169 −0.29980263631366899091;3.0237925270406353917 −0.1146067506786898893 0.38968148073836933465 −0.25453631251896452481;0.85283782903481264448 −0.47911720974742144641 −1.2273801839673017522 2.1822395897464237358;−0.44452333762914120197 0.046225899173519845176 0.31531716693307315635 −2.6451698302159476484;−2.082201349833978643 −0.76346898345159097676 0.80987596832556574267 −0.26354987734844792513;0.23328632180445929567 1.9398593712767222552 −2.1170295819115390046 −0.95572595759438017105;1.2950325142995149363 −0.40655955776770902332 −1.3348898800375803564 1.9412701409376558193;0.2620678477346494728 1.4222211061809311161 −1.0819256332215649863 −1.8734496430651590426];
- % Layer 2
- b2 = 0.037914970571524556076;
- LW2_1 = [−0.3338122113448129813 −0.062787018149683293533 −0.023067778401084607087 0.30886252071691638887 0.11947332736834551103 0.25517375503750572285 −0.46461748677279546271 0.073666775477091439583 0.15553036075489234946 −0.23597420977667460384];
- % Output 1
- y1_step1.ymin = −1;
- y1_step1.gain = 0.08;
- y1_step1.xoffset = 0;
- % ===== SIMULATION ========
- % Dimensions
- Q = size(x1,1); % samples
- % Input 1
- x1 = x1’;
- xp1 = mapminmax_apply(x1,x1_step1);
- % Layer 1
- a1 = tansig_apply(repmat(b1,1,Q) + IW1_1*xp1);
- % Layer 2
- a2 = repmat(b2,1,Q) + LW2_1*a1;
- % Output 1
- y1 = mapminmax_reverse(a2,y1_step1);
- y1 = y1’;
- end
- % ===== MODULE FUNCTIONS ========
- % Map Minimum and Maximum Input Processing Function
- function y = mapminmax_apply(x,settings)
- y = bsxfun(@minus,x,settings.xoffset);
- y = bsxfun(@times,y,settings.gain);
- y = bsxfun(@plus,y,settings.ymin);
- end
- % Sigmoid Symmetric Transfer Function
- function a = tansig_apply(n,~)
- a = 2 ./(1 + exp(−2*n)) − 1;
- end
- % Map Minimum and Maximum Output Reverse-Processing Function
- function x = mapminmax_reverse(y,settings)
- x = bsxfun(@minus,y,settings.ymin);
- x = bsxfun(@rdivide,x,settings.gain);
- x = bsxfun(@plus,x,settings.xoffset);
- end
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Parameters | Value |
---|---|
Water jet pressure (P) | 100, 143.93, 250, 356.07, 400 MPa |
Standoff distance (SOD) | 1, 2.32, 5.5, 8.68, 10 mm |
Material thickness (t) | 2, 5 mm |
Abrasive start synchronization (ASS) | On/Off |
Abrasive mass flow (ma) | 0.45 kg/min |
Abrasive size | 80 mesh |
Focusing tube diameter | 0.76 mm |
Orifice diameter | 0.35 mm |
Parameters | Value |
---|---|
Cutting head | Carat 3.0 Gardella |
Abrasive inlet angle | Ψ = 40 deg. |
Orifice | Diamond, do = 0.35 mm |
Focusing tube | Ceratizit WJNS (df = 0.76 mm/lf = 101.6 mm) |
Run | P | SOD | ASS | t | Dext | Run | P | SOD | ASS | t | Dext |
---|---|---|---|---|---|---|---|---|---|---|---|
MPa | mm | On/Off | mm | mm | MPa | mm | On/Off | mm | mm | ||
1 | 250 | 5.5 | Off | 2 | 17.5 | 26 | 356.07 | 2.32 | Off | 2 | 25 |
2 | 250 | 5.5 | On | 2 | 12.5 | 27 | 250 | 5.5 | On | 2 | 12.5 |
3 | 250 | 5.5 | Off | 5 | 17.5 | 28 | 250 | 10 | Off | 5 | 17.8 |
4 | 143.93 | 2.32 | Off | 5 | 8.6 | 29 | 250 | 5.5 | Off | 2 | 16.1 |
5 | 250 | 1 | Off | 5 | 15.5 | 30 | 250 | 5.5 | On | 5 | 11.2 |
6 | 143.93 | 8.68 | Off | 5 | 8.3 | 31 | 356.07 | 8.68 | On | 5 | 20.5 |
7 | 356.07 | 8.68 | Off | 5 | 25 | 32 | 356.07 | 8.68 | On | 2 | 20.5 |
8 | 100 | 5.5 | On | 2 | 0 | 33 | 250 | 10 | On | 2 | 15.5 |
9 | 250 | 1 | On | 5 | 8.2 | 34 | 356.07 | 8.68 | Off | 2 | 25.2 |
10 | 356.07 | 2.32 | Off | 5 | 25 | 35 | 100 | 5.5 | Off | 5 | 5.5 |
11 | 250 | 5.5 | Off | 2 | 17.5 | 36 | 143.93 | 2.32 | On | 5 | 2.8 |
12 | 250 | 5.5 | Off | 2 | 17.5 | 37 | 250 | 5.5 | On | 5 | 12.5 |
13 | 356.07 | 2.32 | On | 2 | 18.5 | 38 | 100 | 5.5 | On | 5 | 0 |
14 | 143.93 | 8.68 | On | 5 | 2.3 | 39 | 250 | 10 | On | 5 | 15.5 |
15 | 400 | 5.5 | Off | 5 | 25 | 40 | 250 | 5.5 | On | 2 | 11 |
16 | 250 | 5.5 | Off | 5 | 17.5 | 41 | 400 | 5.5 | On | 5 | 19 |
17 | 250 | 1 | On | 2 | 8.2 | 42 | 250 | 5.5 | On | 5 | 12.5 |
18 | 143.93 | 2.32 | On | 2 | 2.1 | 43 | 250 | 5.5 | Off | 5 | 17.1 |
19 | 250 | 5.5 | Off | 5 | 17.2 | 44 | 250 | 5.5 | On | 2 | 11.5 |
20 | 250 | 1 | Off | 2 | 15.5 | 45 | 250 | 5.5 | Off | 5 | 17.1 |
21 | 250 | 10 | Off | 2 | 17.5 | 46 | 250 | 5.5 | On | 5 | 12.2 |
22 | 400 | 5.5 | On | 2 | 19 | 47 | 143.93 | 8.68 | Off | 2 | 8.3 |
23 | 250 | 5.5 | Off | 2 | 17.1 | 48 | 143.93 | 2.32 | Off | 2 | 7.2 |
24 | 400 | 5.5 | Off | 2 | 25 | 49 | 100 | 5.5 | Off | 2 | 3.5 |
25 | 250 | 5.5 | On | 2 | 12.5 | 50 | 143.93 | 8.68 | On | 2 | 3.5 |
Run | P | SOD | ASS | t | Predicted Dext | Measured Dext |
---|---|---|---|---|---|---|
MPa | mm | On/Off | mm | mm | mm | |
1 | 350 | 8 | Off | 2 | 24.1 | 25 |
2 | 100 | 8 | Off | 2 | 3.6 | 8 |
3 | 350 | 8 | On | 2 | 21 | 17.8 |
4 | 100 | 8 | On | 2 | 1.9 | 0 |
5 | 350 | 1 | Off | 5 | 21.9 | 18 |
6 | 100 | 1 | Off | 5 | 4.1 | 0 |
7 | 350 | 5 | Off | 5 | 23 | 25 |
8 | 100 | 5 | Off | 5 | 8.1 | 11.5 |
9 | 350 | 0.5 | On | 5 | 17.5 | 15.5 |
10 | 100 | 0.5 | On | 5 | 0.38 | 0 |
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Popan, I.A.; Bocăneț, V.I.; Softic, S.; Popan, A.I.; Panc, N.; Balc, N. Artificial Intelligence Model Used for Optimizing Abrasive Water Jet Machining Parameters to Minimize Delamination in Carbon Fiber-Reinforced Polymer. Appl. Sci. 2024, 14, 8512. https://doi.org/10.3390/app14188512
Popan IA, Bocăneț VI, Softic S, Popan AI, Panc N, Balc N. Artificial Intelligence Model Used for Optimizing Abrasive Water Jet Machining Parameters to Minimize Delamination in Carbon Fiber-Reinforced Polymer. Applied Sciences. 2024; 14(18):8512. https://doi.org/10.3390/app14188512
Chicago/Turabian StylePopan, Ioan Alexandru, Vlad I. Bocăneț, Selver Softic, Alina Ioana Popan, Nicolae Panc, and Nicolae Balc. 2024. "Artificial Intelligence Model Used for Optimizing Abrasive Water Jet Machining Parameters to Minimize Delamination in Carbon Fiber-Reinforced Polymer" Applied Sciences 14, no. 18: 8512. https://doi.org/10.3390/app14188512
APA StylePopan, I. A., Bocăneț, V. I., Softic, S., Popan, A. I., Panc, N., & Balc, N. (2024). Artificial Intelligence Model Used for Optimizing Abrasive Water Jet Machining Parameters to Minimize Delamination in Carbon Fiber-Reinforced Polymer. Applied Sciences, 14(18), 8512. https://doi.org/10.3390/app14188512