**4. Case study: "Prediction of the Vickers microhardness and ultimate tensile strength of AA5754 H111 friction stir welding butt joints using artificial neural network"**

Among the artificial neural networks applications to the production processes, this section describes the research of De Filippis et al. [74] in which a simulation model was developed for the monitoring, controlling and optimization of a particular solid-state welding process called friction stir welding (FSW). The approach based on the use of neural networks, using the FSW technique, has allowed identifying the relationships between the process parameters (input variable) and the mechanical properties (output responses) of the AA5754 H111 welded joints. The optimization of the technological parameters has been developed with the aim to produce a stable welding process that can provide welded joints with no defects. The experimental plans that were tested have been constructed by varying the following parameters:


case the algorithm allows to predict the output parameter on the basis of a set of known inputoutput pairs [69, 70]. Second algorithm is unsupervised learning, in this case the output is not given, the aim consisting of inferring a function in order to describe a hidden structure (e.g., clustering, anomaly detection, etc.). Therefore the output parameters are considered 'unlabelled' (the observations are not classified) and is not provided any evaluation about the prediction reliability ensured by the ANN [71]. Third algorithm is named reinforcement learning, in this case a continue interaction between the learning system and the environment allows to identify the input-output mapping minimizing the performance scalar index. The approach is very similar to unsupervised learning (also in this case there are not given input-output pairs), reward or punishment signals are adopted for the prediction of output parameters [72]. In most cases, the unsupervised learning allows to ensuring lower cost function. Three different methods, usually considered to be supervised learning methods, are described in this work: Quick Propagation (QP), Conjugate Gradient (CG) and Levenberg-Marquardt

QP is a heuristic modification of the standard back propagation, the output of the *m*th output

(∑ *k*=1 *K*

neuron and the *k*th hidden neuron. The value of *opk* depends by two parameters: the first is

All network weights are updated after presenting each pattern from the learning data set.

As far as concern CG method, the learning algorithm starts with a random weight vector that is iteratively updated according the direction of the greatest rate of decrease of the error

∆*ω*(*τ*) = −*η*∇*Eω*(*τ*) (3)

eter. For each step (*τ*) the gradient is re-evaluated in order to reduce *E.* The performance of the gradient descent algorithm is very sensitive to the proper setting of the learning rate, in case *η* is too high the algorithm can oscillate and become unstable, for *η* too small the algorithm takes too long to converge. In this case an adaptive learning rate allows to keep the learning step size as large as possible, ensuring, in this way, the learning rate stable. The LM algorithm allows to minimize the squares of the differences (*E*) between

(*t*), and the predicted output *yp*

given by the weight between *k*th hidden neuron and the *n*th input neuron (¯¯

*<sup>ω</sup>*¯¯ *km opk*) (1)

(1 <sup>+</sup> *<sup>e</sup>*<sup>−</sup>*<sup>x</sup>*) (2)

and *η* is the arbitrary learning rate param-

(*t*) [73]. '*E*' is given by

*<sup>ω</sup>km* is the weight between the *m*th output

*<sup>ω</sup>nk*). The second

algorithm (LM).

evaluated as *ω*(*τ*)

node for the *p*th input pattern is given by *opm* (Eq. (1)).

where *f* is the activation sigmoidal function (Eq. (2)), ¯¯

parameter is *xpn* given by *p*th input pattern of *n*th neuron.

*f*(*x*) = \_\_\_\_\_\_ <sup>1</sup>

in Eq. (3).

the desirable output, identified as *yd*

the follow equation:

where *E* is the error function evaluated at *ω*(*τ*)

*opm* = *f*

210 Advanced Applications for Artificial Neural Networks


The quality of welded joints was evaluated through the following destructive and nondestructive tests:


The simulation model was based on the adoption of artificial neural networks (ANNs) using a back-propagation learning algorithm. Different types of architecture were analysed, which were able to predict with good reliability the FSW process parameters for the welding of the AA5754 H111 in Butt-Joint configuration.

#### **4.1. About the friction stir welding process**

The process of friction stir welding (FSW) is a solid-state welding method based on frictional and stirring phenomena, which was discovered and patented by the Welding Institute of Cambridge in 1999. In this process, a rotating non-consumable tool that plunges into the work piece and moves forward produces the heat necessary to weld the parts together. Therefore, given the particular geometry of the tool used, as shown in **Figure 5**, the following actions are performed in the process:


The much lower temperatures compared with those achieved in traditional welding processes by melting, determine the main advantages of this process. In fact, there is minimal mechanical distortion, with minimal Heat Affected Zone (HAZ), and an excellent surface finish.

No crack formation and porosity right after welding thanks to the low input of total heat.

The main parameters of the friction stir welding process are the tool rotation speed (*n*) and the tool travel speed (*v*). The friction stir welding process enjoys major successful applications

**Figure 5.** Schematic diagram of the FSW process.

in many fields, such as aeronautics, aerospace, rail, automotive, computer science, marine, chemical and petrochemical industries. Important advantages are also documented in the application of FSW processes on dissimilar materials, Al alloys, Cu alloys, Ti alloys and steel. The main applications are on aluminium alloys because these materials, due to their high strength-to-weight ratio, low density, forming properties, low cost and recyclability, are the main metals used in automotive, marine and aerospace applications. An aluminium alloy of large aeronautical and automotive interest is the AA5754 H111; on this material, there are still few researches about the advantages to apply the FSW. It has been shown that the mechanical properties of the AA5xxx friction stir welded joints depend mainly on the grain size and the dislocation density, due to the phenomena of plastic deformation and recrystallization occurring during the FSW process. To study and optimize properly the friction stir welding process, it is necessary to know the influence of process parameters on the mechanical properties of the joints. In general, the traditional process control techniques cannot provide information about the performance of the process during welding and require lengthy testing times, making them feasible for the industrial field. Therefore, in the production engineering, the control and the optimization of the manufacturing processes is becoming increasingly important. For the FSW process is necessary to carry out a control of the significant variables, in addition to the use of thermographic techniques. This justifies the deepening and use of information technology for enhancing the quality of manufacturing systems. The implementation of numerical and analytical models can reduce time and cost for experiment and analysis through quantitative solutions.

The simulation model was based on the adoption of artificial neural networks (ANNs) using a back-propagation learning algorithm. Different types of architecture were analysed, which were able to predict with good reliability the FSW process parameters for the welding of the

The process of friction stir welding (FSW) is a solid-state welding method based on frictional and stirring phenomena, which was discovered and patented by the Welding Institute of Cambridge in 1999. In this process, a rotating non-consumable tool that plunges into the work piece and moves forward produces the heat necessary to weld the parts together. Therefore, given the particular geometry of the tool used, as shown in **Figure 5**, the following actions are

The much lower temperatures compared with those achieved in traditional welding processes by melting, determine the main advantages of this process. In fact, there is minimal mechanical distortion, with minimal Heat Affected Zone (HAZ), and an excellent surface finish. No crack formation and porosity right after welding thanks to the low input of total heat.

The main parameters of the friction stir welding process are the tool rotation speed (*n*) and the tool travel speed (*v*). The friction stir welding process enjoys major successful applications

AA5754 H111 in Butt-Joint configuration.

212 Advanced Applications for Artificial Neural Networks

performed in the process:

**Figure 5.** Schematic diagram of the FSW process.

**4.1. About the friction stir welding process**

• The tool shoulder generates heat with the base material,

• The tool pin generates plastic deformation and mixing of the material.
