Supervised and Unsupervised Machine Learning Algorithms for Forecasting the Fracture Location in Dissimilar Friction-Stir-Welded Joints

Abstract

Artificial-intelligence-based algorithms are used in manufacturing to automate difficult activities and discover workflow or process patterns that had never been noticed before. Recent studies deal with the forecasting of the fracture location in dissimilar friction-stir-welded AA5754–C11000 alloys. Four types of supervised machine-learning-based classification algorithms i.e., decision tree, logistic classification, random forest, and AdaBoost were implemented. Additionally, in the present work, for the first time, a neurobiological-based unsupervised machine learning algorithm, i.e., self-organizing map (SOM) neural network, is implemented for determining the fracture location in dissimilar friction-stir-welded AA5754–C11000 alloys. Tool shoulder diameter (mm), tool rotational speed (RPM), and tool traverse speed (mm/min) are input parameters, while the fracture location, i.e., whether the specimen’s fracture is in the thermo-mechanically affected zone (TMAZ) of copper, or if it fractures in the TMAZ of aluminium. The results show that out of all implemented algorithms, the SOM algorithm is able to predict the fracture location with the highest accuracy of 96.92%.

1. Introduction

Information processing carried out by networks of neurons is referred to as neural computing. The philosophical movement known as computational mind theory, or computationalism, which promotes the idea that neural computation accounts for cognition, has ties to neural computation [1,2,3,4]. Nowadays, these types of algorithms are used in the manufacturing and materials sectors for the determination of mechanical and microstructure properties of fabricated alloys or specimens [5,6]. An artificial neural network (ANN) was used by Shiau et al. [7] to model Taiwan’s industrial energy demand in relation to subsector industrial output and climate change. It was the first investigation to measure the relationship between industrial energy use, manufacturing output, and climate change using the ANN technique. A multilayer perceptron (MLP) with a feedforward backpropagation neural network was used as the ANN model in this investigation. In order to improve the implementation of natural fibers in green bio-composites, Jarrah et al. [8] used doubly interconnected artificial neural networks to make unique classifications and predictions of the inherent mechanical properties of natural fibers. Whether convolutional neural networks (CNNs) are effective for identifying internal weld faults in addition to surface defects was determined by Hartl et al. [9]. Ultrasonic testing was used to create 120 welds for this purpose, and those data were used to determine if it was “good” or “defective.” Different artificial neural network models were examined for their ability to anticipate where the welds would fall within the designated classes. The method used to label the data was found to be important for the level of precision that could be attained. A revolving tool generates frictional heat during friction stir welding (FSW), which is a solid-state joining technique that is used to fuse materials. The non-consumable tool is turned and inserted into the joint between two work parts. It has a contoured probe and shoulder. The substance then heats up and softens as it moves along the joint line. This plasticized substance, which is dynamically combined to form a solid-phase weld, is likewise contained by the shoulder. FSW is applied in a wide range of fields, from electronics to shipbuilding, rail, and aerospace, incorporating EV battery trays. Friction stir welding is shown to produce aluminum alloys with greater mechanical properties than other welding techniques, such arc welding. A weld nugget, a thermo-mechanically affected zone (TMAZ), and a heat-affected zone (HAZ) are typically the three primary microstructural regions of FSW related to its mechanical qualities. The microstructural properties of the weld nugget and the TMAZ are taken into account independently, even though they are both “thermo-mechanically affected zones”. This is due to the fact that the TMAZ does not undergo dynamic recrystallization, whereas the weld nugget does. However, the type of material and the processing circumstances have an impact on the precise composition and range of the microstructural structure in these zones. These, for instance, may change based on variables such as the welding conditions and the architecture of the FSW equipment being utilized. Using a Bayesian neural network and a decision tree algorithm, Du et al. [10] looked at the circumstances that lead to void development. They looked at three different types of input datasets, such as raw welding parameters and computed parameters using an analytic and a numerical friction stir welding model. The void generation for the friction stir welding of three aluminum alloys, AA2024, AA2219, and AA6061, was studied in 128 different sets of experimental data. With process parameters, sample and tool designs, and properties of the material as input, the neural-network-based methodology accurately predicts void formation with an accuracy of 83.3%. In order to assess the sequence of causative factors for tool failure, Du et al. [11] examined 114 sets of test data for three widely used alloys. Six significant friction stir welding factors are ranked according to their relative impact on tool failure using three decision-tree-based techniques. The biggest factor causing tool failure is found to be the maximum shear stress. The flow stress, which impacts how plasticized material flows around the tool pin, is the second-most significant element. All other factors are discovered to be considerably less relevant. Additionally, three algorithms produce the same outcomes, and have a 98% accuracy rate in predicting tool failure. By applying an appropriate orthogonal decomposition, Cao et al. [12] proposed a reduced basis technique to solve the generalized unified framework of heat and Navier–Stokes equations (POD). They also used a machine learning approach centered on an artificial neural network (ANN) to understand roughly the relationship between pertinent parameters and POD coefficients. The computational studies show that a significant speed-up is possible while still retaining an adequate level of accuracy. Using machine learning (ML) techniques, Anandan et al. [13] investigated the prediction of peak temperature using a variety of regression analysis techniques, including polynomial regression (PR), random forest regression (RFR), linear regression (LR), decision tree regression (DTR), and support vector regression (SVR). The peak temperature in the FSW process can, therefore, be accurately predicted using the RFR analysis. A peak temperature of less than 300 °C, good appearance, adequate material mixing, and the lack of flaws are all guaranteed by a tool rotating at a speed of 1000 rpm. The increased use of FSW processes necessitates online monitoring systems for early defect identification and control. A technique for the classification and detection of faulty welds employing weld surface images was developed by Sudhagar et al. [14]. By adjusting the tool rotating speed, welding speed, tool shoulder diameter, and pin diameter, welding joints are created under various welding conditions. Using a digital camera, the weld surfaces created under various welding conditions are collected to extract features. The maximum stable extremal region technique was utilized to extract the features from the weld surface picture, which are then used as input for the classification of the weld joint. The classification of welds using surface image features was performed using support vector machines. The use of machine learning techniques in assessing and forecasting the tensile performance of friction-stir-welded AA6082 was examined by Verma et al. [15]. Ultimate tensile strength (UTS) was measured as a response parameter, and rotational speed and feed rate were used as input factors. The experimental findings were validated using random forest regression, artificial neural network (ANN), and M5P tree regression. These models, which are based on machine learning, are used to analyze absurdity in both current and anticipated data. In terms of machine learning, it is found that random forest regression performs the best in estimating the tensile performance of FSW joints. Rotational speed is found to have the greatest influence on ultimate tensile strength (UTS). The future scope of the application of machine learning algorithms can be in the semiconductors and composite manufacturing industries [16,17,18,19,20].

Aluminum (Al) and copper (Cu) dissimilar welding has several uses in the electrical power, electronic, and pipeline industries. These applications place a high priority on the weldments because of their ability to conduct heat, electricity, and corrosion. In the present work, a self-organizing map neural network model, which is an unsupervised machine-learning-based algorithm, is used in addition with other supervised machine learning classification-based algorithms for the first time for forecasting the fracture location in friction-stir-welded dissimilar joints [21]. This work is different from previous published works, because in the previous work, we only used supervised machine learning in algorithms without comparing their performance on the basis of AUC score [22,23,24]. However, in this work, we compared the performance on the basis of AUC score, as well as using unsupervised machine learning for the first time.

2. Materials and Methods

Technically speaking, the weld nugget and TMAZ are both “thermo-mechanically affected zones,” but they are regarded independently, since they have different microstructural characteristics. In contrast to the TMAZ, the weld nugget dynamically recrystallizes. These zones depend on the material and testing procedures for their extent and microstructural makeup. Figure 1 and Figure 2 show the process flow chart of the methodology implemented in the present research work. Firstly, the data were obtained from the experimental test [16] and further prepared in the form of a CSV file, where input parameters and output parameters were entered in column-wise format. In the present study, the tensile specimen, tool traverse speed (mm/min), tool shoulder diameter (mm), and tool rotational speed (RPM) were the input parameters, while the fracture location was an output parameter. Tensile specimens were classified on the basis of extracting the samples from the different location of the weld line. If the tensile specimen fractures in the TMAZ Cu zone, then its value is assigned as ‘0’, and if the tensile specimen fractures in the TMAZ Al zone, then its value is assigned as ‘1’.

The third step was to import the Python libraries such as pandas, NumPy, Matplotlib, SciPy, and sklearn for computation purposes. One of the most popular tools for data cleaning and analysis in machine learning and data science is called pandas. Pandas is the ideal tool to deal with this chaotic real-world data in this situation. In addition, one of the accessible Python packages constructed on top of NumPy is pandas. Numerous mathematical operations can be carried out on arrays with NumPy. It provides a vast library of high-level arithmetic operations that work on these arrays and matrices, as well as strong data structures that facilitate optimal computation with arrays and matrices. A well-liked Python library for visualization techniques is Matplotlib. It is not primarily linked with machine learning, similar to Pandas. It is especially helpful when a coder needs to see the data patterns. It is a library for 2D charting used to produce 2D graphs and maps. The given data are subjected to mathematical processes using the SciPy special functions. A module for SciPy’s special functions is included in the SciPy package. The most practical Platform for machine learning is definitely scikit-learn. Numerous effective methods for machine learning and statistical modeling, such as classification, regression, clustering, and dimensionality reduction, are included in the sklearn package. The fourth step was to split the dataset into testing and training sets, i.e., 80% of data are used for training purposes and 20% of data are used for testing purposes. The last step was to subject the self-organizing maps neural network and other supervised machine learning algorithms, and further evaluate the accuracy score on the used dataset.

3. Results

Table 1. Statistical Analysis.

	Tensile Sample	Rotational Speed (RPM)	Traverse Speed (mm/min)	Shoulder Diameter (mm)	Fracture Location
Count	81	81	81	81	81
Mean	2.000	916.666	166.666	19.333	0.320
Std	0.821	247.613	103.380	4.216	0.469
Min	1.000	600.000	50.000	15.000	0.000
25%	1.000	600.000	50.000	15.000	0.000
75%	3.000	1200.000	300.000	25.000	1.000
Max	3.000	1200.000	300.000	25.000	1.000

shows the result obtained from the statistical data analysis on the experimental dataset. With the use of statistical analysis, we can quickly spot patterns in any set of data, efficiently evaluate it, and draw more reliable conclusions. In machine learning (ML), statistical knowledge enables us to properly comprehend the efficacy of our models based on evaluation. Figure 3 shows the exploratory data analysis (EDA) results obtained for the given experimental dataset. EDA’s primary goal is to keep data “clean,” which implies that it needs to be free of redundancies. It makes it easier to spot false datasets so that they can be quickly eliminated, and the data processed. Additionally, it helps us understand the connection between the variables, giving us a wider perspective of the data, and enabling us to build on it by utilizing the connection between the variables. It also helps in the analysis of the statistical measurements in the dataset.

Figure 4 shows the plot of heat map obtained for the experimental dataset. These coefficients are displayed as a heat map to show the degree of association between various factors. It assists in identifying traits that are ideal for creating machine learning models. The correlation matrix is converted into color labeling via the heat map.

Figure 5 shows the graph of the feature importance results. Feature importance is used to find the input parameter that affects or contribute towards the output most. It is observed that the tensile sample parameter contributes towards the output most, while rotational speed (RPM) has a negligible impact on the output parameter.

While evaluating the performance of classification-based algorithms, the F1 score and AUC scores of each algorithm are evaluated. An evaluation metric for a classification that is defined as the harmonic mean of recall and precision is the F1 score or F-measure. It is a metric used in statistics to assess how accurate a test or model is. The capacity of a classifier to differentiate between classes is measured by the area under the curve (AUC), which is used as a description of the ROC curve. The model performs better at differentiating between both the positive and negative classes the higher the AUC. Equation (1) is used for the calculation of the F1 score value.

$$F1-Score=2\times \frac{precision\times recall}{precision+recall}$$

(1)

Table 2. Results obtained from supervised machine learning classification-based algorithms.

Algorithms	Precision Value of ‘0′	Precision Value of ‘1′	Recall Value of ‘0′	Recall Value of ‘1′	F1-Score
Logistic Classification	0.83	0.80	0.91	0.67	0.82
Decision tree	0.65	0.00	1.00	0.00	0.65
Random forest	0.73	1.00	1.00	0.33	0.76
AdaBoost	0.65	0.00	1.00	0.00	0.65

shows the obtained results for supervised machine-learning-based classification algorithms. In the decision tree classification-based algorithm, entropy is used as a criterion, which is calculated by Equation (2). Entropy is a unit of measurement for information that depicts the unpredictability of the target’s features. The feature with the lowest entropy selects the optimal split, just as the Gini index does. A node is pure when the entropy has its lowest value, which is zero, and it reaches its largest value when the probabilities of the two classes are equal.

$$Entropy=-{\displaystyle \sum }_j{p}_j·lo{g}_2·p_j$$

(2)

where $p_j$ stands for class j probability.

Figure 6 and Figure 7 shows the confusion matrix and AUC curve plot of each supervised machine learning classification-based algorithms. To determine where inaccuracies in the model are produced in classification issues, confusion matrix tables are employed. The rows correspond to the actual courses for which the results were intended. The predictions we have made are represented by the columns. This table makes it simple to identify those predictions that are incorrect.

The blue line in the AUC Curve indicates to a condition where True Positive Rate is equal to False Positive Rate.

A self-organizing map is an unsupervised machine learning algorithm that works on the principle of competitive learning. There is a special organization in the distribution of neurons. Here, we are basically talking in terms of the lattice of the output neurons, which can be arranged as a one-dimensional lattice, two-dimensional lattice, or even a higher dimensional lattice space where the neurons are organized. Higher dimensional lattice space involves a lot of complexity, so because of this reason, from a practical point of view, we use one-dimensional and dimensional lattice space. If those neurons are connected to the inputs in some manner, the input patterns are fed and act as a stimulus to the neurons that are present at outputs. When the stimulus is present, then out of different neurons that are existing in the lattice, one of them is the winner and the synaptic connections from the input layer to the output layer are adjusted, then weight updating takes place in such a way that the Euclidian distance between the input vector and the weight vector is minimized. The minimization of the Euclidian distance means the maximization of the w^Tx, which is the output (w is the weight matrix). It is noted that one of the neurons emerges as a winner, and the different patterns are fed through the input space to the given system. Input distribution is basically a non-uniform distribution, but if we start with a regular lattice structure, depending on the input statistics, then the ultimate organization of the lattice structure is slightly different, and these results are indicative of the statistics of the input patterns that are applied as stimuli. It should be noted that the neurons that are present at the output act in a competitive manner; this means that they inhibit the responses from each other. From a neurobiological point of view, it is observed that the neurons that are closer to the winning neurons have an excitatory response. On the other hand, an inhibitor response is created by the neurons that are far from the winning neurons. This means that the self-organizing maps network exhibits short-range excitation and long-range inhibition. A self-organizing map is a neurobiologically motivated algorithm. There are two models of self-organizing maps, i.e., the von der Malsburg model and the other, more general, model is the Kohnen model. In our recent study, we use the Kohnen model. In the Kohnen model, we generally take an output model where the output layer is organized in a lattice. The input does not need to be connected in the form of lattice, and this input is connected to all the outputs, which constitute a bundle of synaptic connections, as shown in Figure 8. Half of the data compression is possible in this case because the number of inputs is less than those the outputs. The Kohnen model is based on a vector-coding algorithm that optimally places a fixed number of vectors into a higher dimension input space.

The accuracy score obtained as a result is 0.9692. This is due to the fact that competitive learning is at the heart of SOM. In competitive learning, the distance between input data and neuron weight influences neuron activity. The most learning occurs in an excited neuron, and as a result, its weights change. The dataset we used for this study is clean, with a relatively small number of features and observations. The data scientists encounter far more complex problems in the real world, and the labeled dataset is not entirely available. If they are offered, their quality might not be trustworthy.

4. Discussion

From Table 2, it is observed that the logistic classification algorithm results in the highest F1 score of 0.82 in comparison to the results of other algorithms. From Figure 8, it is also observed that the logistic classification algorithm results in the highest AUC score of 0.88. It is observed that logistic regression is simpler to use, more understandable, and extremely effective to train. It classifies unfamiliar records fairly quickly. When the dataset can be linearly separated, it works well. It can use model coefficients to determine the significance of a characteristic.

There are some essential processes that need to be fulfilled for self-organizing maps. The first process is called competition, which means that for each input pattern, the neurons present in the output layer determine a discriminant function that provides a basis for the competition. The particular neuron with the largest discriminant function emerges as the winner. The second process is cooperation, in which the winning neurons determine the topological neighborhood of the excited neuron. The excitation process is the cooperation that not only strengthens the winning neuron, but also strengthens the neurons that are closer to the winning neurons. It should be noted that competition refers to the long-range inhibition process, while cooperation refers to the short-range excitation process. The third process is called the step of synaptic adaptation, which enables the excited neurons to increase their discriminant function in response to the stimulus that causes the winning of the neuron.

In the competitive process, we considered m dimensional input, so that the input $\underset{x}{\to }$ is given by Equation (3).

$$\underset{x}{\to }={\left[x_1 x_{2 \dots \dots \dots \dots \dots }{x}_n\right]}^T$$

(3)

The weight is given by Equation (4).

$${\underset{w}{\to }}_j={\left[w_{j1} w_{j2}\dots \dots w_{jm}\right]}^T,\mathrm{j}=1,2,3\dots \mathrm{l}$$

(4)

where l is the number of output neurons. It should be noted that every output is connected to the inputs. The main objective is to determine the best match between $\underset{x}{\to }$ and ${\underset{w}{\to }}_j$. There is competition between l, number of output neurons, in which $\underset{x}{\to }$ finds the best match with ${\underset{w}{\to }}_j$, which then emerges as the winner. In this case, the winning index is j, and the corresponding weight is the winning weight vector. The maximization process is represented in Equation (5), which leads to the minimization of Euclidean distance, as shown in Equation (6).

$$Max \left|\underset{w_j{}^T}{\to }·\underset{X}{\to }\right|$$

(5)

$$Min ||\underset{x}{\to }-\underset{w_j}{\to }||$$

(6)

Index of the winning neuron can be processed by using Equation (7).

$$i\left(\underset{x}{\to }\right)=\arg {}_j{}^{min}||\underset{x}{\to }-\underset{w_j}{\to }||$$

(7)

We use majority voting to allocate a single label per each neuron on the map, in order to create a label map. If a neuron is chosen without a best matching unit (BMU), the final iteration’s label map is shown in Figure 9. A large number of neurons are neither 0 or 1 at the beginning, and the class labels seem to be dispersed haphazardly. The last iteration clearly separates the class 0 and 1 region; however, we still notice a few cells that are not in the final iteration.

5. Conclusions

The implementation of supervised machine-learning-based classification algorithms and an unsupervised self-organizing map neural network algorithm for a classification problem is shown in the current paper. For an unsupervised learning algorithm, we used data without labels to train the map, and we projected the labels onto the map to verify the training’s outcome. The results show that the unsupervised learning algorithm forecasts the fracture location with the highest accuracy of 96.92%. As anticipated, we see that each class has distinct regions, with neurons with related characteristics clustered closer together. Finally, we evaluated the map’s prediction accuracy using an unanticipated test dataset. Implementing the self-organizing map neural network to a real-world situation presents certain difficulties for us. First, without a tagged dataset, we are unable to calculate the loss. We have no way to verify the dependability of the trained map. The features of the data themselves have a significant impact on the map’s quality. The distance-based approach requires the normalization of the data as a pre-processing step. Understanding the distribution of the data points necessitates an initial analysis of the dataset. We may employ other dimensionality reduction techniques, such as PCA and singular value decomposition, especially for data with high dimensionality where visualization is not possible.