The available data for the problem at hand is in the form of in-situ thermal profiles of AFP-manufactured composites which have been obtained using an experimentally validated FEA model of the AFP process for different combinations of process parameters. The different steps followed in the study are shown in Figure 2.
Step 1: Thermal history data generation using an FEA model
An experimentally validated full-scale 3-D finite element thermo-mechanics model of the hot gas torch-based AFP manufacturing process developed in Abaqus incorporating the effects of transient heat and pressure was used to generate in-situ thermal profiles of the AFP process [21]. The thermal profiles predicted by the model have been previously validated against manufacturing trials conducted using FBG sensors embedded inside the laminate for temperature assessment. Boundary conditions and loads for the FEA AFP process model are shown in Figure 3.
The generation of in-situ thermal profiles for various combinations of input AFP process parameters is carefully planned by varying the AFP process parameters at different levels as shown in Table 1. A full factorial design of experiments approach is used to get a test matrix of 27 different combinations of AFP process parameters.
Table 1: Different AFP process parameters and their levels used for the in-situ thermal profile data generation
Factors →
|
Material Deposition Velocity
|
Consolidation Force
|
HGT Temperature
|
Level ↓
|
(mm/sec)
|
(N)
|
(0C)
|
1
|
76
|
180
|
850
|
2
|
100
|
230
|
900
|
3
|
124
|
300
|
950
|
The FEA model of the AFP process is simulated for the 27 different combinations of the AFP process parameters to generate the data required for training, testing and validation of the ML-based predictive models.
Step 2: Parametrization of thermal profiles
A typical thermal profile at the interface of two prepreg tows obtained from the FEA model with various heating and cooling cycles is shown in Figure 4. The attributes of thermal profiles are marked in the sequence of their relative importance for the development of interlaminar strength in Figure 4. The most important attribute is the first peak temperature (marked as 1) followed by the cooling profile (marked as 2), heating rate (marked as 3) and second peak temperature (marked as 4).
The parameterization process starts by identifying a suitable function for the best statistical representation of the cooling profile (marked as 2 in Figure 4) as it is the most complex parameter of the thermal profile to identify. A curve fitting tool in MATLAB was utilized to fit various functions on the data for the cooling profile. Three different types of functions were used: exponential, power and rational. The objective of this curve-fitting process was to minimize the number of parameters (to simplify the training of machine learning models) and maximize the correlation coefficient (to ensure the best possible curve fit). Following this, the thermal profile for each of the 27 FEA simulations is parametrized using a parametrization algorithm developed in MATLAB. This algorithm extracts the parameters of a thermal profile from FEA results and defines the thermal profile using piece-wise functions.
Step 3: Developing the machine learning-based predictive models
The prediction accuracy of a machine learning-based predictive model depends on the size of the training data, the underlying features of the data and the selection of the ML algorithm [22]. Simpler ML algorithms such as multivariate linear regression (MLR) and multivariate polynomial regression (MPR) provide a cost-effective way to develop predictive models for data following a linear or full polynomial behaviour thus providing a good starting point to estimate the behaviour of the data [23] [24]. However, non-linear data features require the implementation of more sophisticated and computationally expensive algorithms such as support vector machines (SVM), artificial neural networks (ANN) or random forest (RF) allowing the mapping of highly non-linear data features and thus enhancing the accuracy of such predictive models [25] [26]. Multivariate Linear Regression (MLR), Multivariate Polynomial Regression (MPR), Support Vector Machines (SVM), Artificial Neural Network (ANN) and Random Forest (RF) machine learning algorithms are trained, tested and validated using parametrized thermal profiles data of FEA model of the AFP process.
The FEA simulations data set is small (27 samples) and the test matrix for the AFP FEA model is sparse as shown in Table 3. In order to have a well-distributed representation of each class in the cross-validation data set, the data is split manually rather than randomly. This careful manual split of data is performed ensuring each class of FEA data has at least one sample in the cross-validation set. 70% of the data is used for training machine learning algorithms and 30% of the data is utilized as cross-validation data set. The AFP process parameters (deposition velocity, consolidation force, HGT temperature) are used as inputs for machine learning algorithms while the seven parameters of parametrized thermal profiles are outputs for the ML algorithms.
The MPR algorithm is optimized for the degree of polynomial and regularization parameters to avoid overfitting the data. The sensitivity of the training and cross-validation mean squared error (MSE) is studied against the regularization parameter and degree of the polynomial. The regularization parameter and degree of polynomial minimizing cross-validation MSE are selected as the optimized parameters for MPR training. The SVM model is optimized for all the hyperparameters (epsilon, kernel function, kernel scale and box constraints) using a built-in MATLAB function utilizing Bayesian Optimization. Artificial Neural Network (ANN) optimization requires the definition of optimal neural network architecture and smart choice of performance parameters (as the inputs are of different ranges). The number of hidden layers is selected to be equal to 01 to avoid overfitting as the data set is very small. The number of hidden units defines the number of unknown weights in the backpropagation algorithm. As a general rule, the number of weights (unknowns) is kept small as compared to the number of training equations. Therefore, the hidden layer units are varied from 01 to 10 to select the best-performing neural network architecture. MATLAB functions are used to train ANN using the Levenberg-Marquardt optimization method for weight and bias value updates in backpropagation. The hyperbolic tangent sigmoid transfer function (tansig) is used as an activation function for the hidden layer while no activation (linear activation) is applied to outputs for regression analysis. Mean Squared Error (MSE) normalized to ‘percentage’ (which normalizes outputs and targets to [-0.5, 0.5] and errors to [-1, 1]) is used as a performance parameter for network diagnosis. Each configuration of ANN is trained 20 times to minimize the errors due to random initializations of weights and to select the best-performing neural network. The neural network configuration providing the best performance on the training and testing data set is chosen as the optimized ANN for the problem at hand. The Random Forest algorithm is optimized for a number of learning cycles, learning rate and minimum leaf size of each decision tree to find the optimal performing RF.
Step 4: Thermal profile prediction
The machine learning-based predictive models provide predictions for thermal profile parameters. Replotting thermal profiles from these parameters require information regarding time scale. The time scale is only a function of deposition velocity and is simply extracted by fitting a curve on the time versus deposition velocity data. The quadratic curve fits the velocity-time data accurately by mapping the FEA points exactly as a unique quadratic curve can be defined using 3 points. Such curves are fitted on data for base temperature-1, peak temperature-1, base temperature-2 and peak temperature-2 for extraction of their respective timescale information. The predicted thermal profile parameters along with the timescale information are used to replot the thermal profiles.
Step 5: GUI-based tool for thermal profile prediction
The trained artificial neural network (ANN) for the prediction of thermal profile parameters is utilized to develop a graphical user interface (GUI) based thermal profile prediction application. The application is packaged using MATLAB Compiler Runtime (MCR) as a standalone as well as MATLAB application. The application uses trained ANN to predict thermal profile parameters, extracts the timescale information of parameters from fitted curve parameters, plots the thermal profile, and labels the base and peak temperatures of the profiles.