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American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

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Label_Title

Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
American Journal of Microbiological Research
Biomedical Science and Engineering

We are pleased to announce that submissions are now being accepted for peer review for all the journals across all our subject areas in SciEP.

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Development of Artificial Neural Network Models for Predicting Weld Output Parameters in Advanced Fusion Welding of a Magnesium Alloy

K.M. Oluwasegun*, O.A Ojo, O.T Ola, A. Birur, J. Cuddy, K. Chan

Department of Mechanical Engineering, University of Manitoba, Winnipeg, Manitoba, Canada

Abstract: This paper describes the development of artificial neural network (ANN) models and multi-response optimization technique to predict and select the best welding parameters during Hybrid Laser Arc Welding (HLAW), Hot Wire Cladding (HWC) and Cold Metal Transfer (CMT) of ZE41-T5 alloy. To predict the performance characteristics, namely; weld depth, underfill, percentage defect and total accumulated pore length, artificial neural network models were developed using Levenberg-Marquardt algorithm. ZE41-T5 was selected as the material to be welded with AZ61 alloy as filler material. Experiments were planned using a 3-factor central composite design and were performed under different welding conditions of laser power, travel speed, wire feed rate, current and frequency. The responses were optimized concurrently using ANN Levenberg-Marquardt algorithm. Finally, experimental confirmations were carried out to identify the effectiveness of ANN. A good agreement was obtained between the experimental output data and ANN predicted results.

Keywords: hybrid laser arc welding, hot wire cladding, cold metal transfer, artificial neural network, optimisation

Received August 17, 2018; Revised October 03, 2018; Accepted October 19, 2018

Citation: K.M. Oluwasegun, O.A Ojo, O.T Ola, A. Birur, J. Cuddy, K. Chan, Development of Artificial Neural Network Models for Predicting Weld Output Parameters in Advanced Fusion Welding of a Magnesium Alloy. American Journal of Modeling and Optimization, 6 (1). 18-34. January 2018. doi:10.12691/ajmo-6-1-2

1. Introduction

In recent years, one of the efficient methodologies in improving fuel economy and limiting environment-damaging emissions is the reduction of weight in ground vehicles and aircrafts [1,2,3,4]. Due to their light weight and good mechanical properties, the use of magnesium alloys as structural materials has been on the increase in the automotive and aerospace industries [1,5,6,7,8]. Welding of Magnesium alloys in structural applications is an inevitable important manufacturing process. Pertinent processing problems and welding defects such as cracks, oxide films and porosities could easily be triggered by the physical properties of Mg, such as its high thermal conductivity, strong propensity to oxidize, low melting and boiling temperatures, high solidiﬁcation shrinkage, and tendency to form low melting point constituents, among other limiting properties [7,8,9]. In their work performed on CO₂ laser welding of diﬀerent Mg alloys, Weisheit et al [10] revealed that most Mg alloys can be easily welded with less defects, except AZ series and AM series, which displayed extremely high levels of porosity. Zhao and Debroy [11] studied the formation of porosity in an AM60 Mg alloy during laser welding and suggested that hydrogen in the parent material was the main origin of porosity in the welds. TIG, CO₂, and pulsed Nd:YAG laser welded joints of AZ31 sheet were worked on by Sun et al [12] and they reported that TIG welding could be used to achieve welds without defects, but noted that coarser grain sizes in TIG welds could reduce the mechanical properties.

The continuous drive in improving the weldability of difficult to weld alloys led to the development and use of hybrid laser beam technology, a combination of a laser beam source with an additional secondary beam source or another joining technique as schematically shown in Figure 1. High-power laser and hybrid laser-arc welding have been reported to offer faster welding speeds, lower heat inputs, deeper penetration, less deformation and good bridging ability for relatively large gap over traditional arc welding processes in a range of different construction and fabrication industries [13,14,15,16]. However, these processes have also been reported to be susceptible to unique defects associated with their high aspect ratio and deep penetration. Most common of these defects include porosity from keyhole instability in partial-penetration weld [17,18,19] and complete joint-penetration welding root defects. The latter has been referred to as chain of pearls [20], dropping [21] and root humping [22], and is categorized by the formation of weld metal spheroids at the bottom surface of a complete-joint-penetration weld. The development of root defect has been reported to be linked to the competition between the surface tension and the weight of the liquid metal in the weld pool, and can also be orchestrated by the presence of oxide scale on the plates to be welded [23].

Even though the laser-arc hybrid welding technique offers an innovative way of joining materials by combining the benefits of laser welding and arc welding, many studies have revealed that some alloys of magnesium and aluminium usually exhibit weldability problems during welding [24,25,26]. According to Ola and Doern [27], keyhole-induced macro-porosity that developed from the collapse of the keyhole formed by the reaction forces of metal vapors is a major problem limiting laser and laser-arc hybrid weldability of age-hardenable aluminum alloys, such as AA2024-T3. A major challenge during keyhole mode laser and laser-arc hybrid welding of the alloys is their vulnerability to macro-porosity in the weld metal. Instability of the keyhole formed by intense evaporation of materials during laser-material interaction has been linked to the formation of macro-porosity during laser welding [18,28]. Keyhole-induced porosity has ben reported to be different from hydrogen-induced porosity [29,30], which is more microscopic in nature, and interdendritic porosity [31]. Porosity during welding of materials can lead to loss of mechanical strength and creep, fatigue, and corrosion failures [32,33]. The principle of porosity formation as illustrated by Ola and Doern [27] suggests that the weld metal solidifies more rapidly than the possible rise velocity of the gas bubbles that formed during key-hole collapse, resulting in severe porosity.

Liu et al. [34] reported that a hybrid laser-TIG welding (LATIG) of AZ31 alloy, achieved higher welding speed than in exclusively laser or TIG welding. Similar combination of laser beam and TIG was employed to weld AZ31B magnesium alloy with a mild steel, using a nickel interlayer [35]. This resulted in the achievement of semi-metallurgical bonding. Mg₂Ni phase with solid solution of Ni in Fe was formed along the Mg-Ni interlayer. However, at the interface of molten pool and steel, the fusion zone did not interact with solid solution, suggesting mechanical bonding. Thus, optimization process in this welding technique is now the paramount approach for structural integrity of the weld.

Recent works on joining techniques have also illustrated that the use of hot wire is a meaningfully means to improving the weld quality and efficiency of tungsten inert gas cladding process of joining difficult to weld magnesium alloys [36,37]. This involves the use of resistance heating induced by passing current to pre-preheat the filler wire. Nevertheless, the preheating approach can only be carried on filler metals with high resistance, e.g. steels, but is limited to alloys having low resistances like magnesium alloys. In order to overcome this challenge, Ly et al [37] developed an arc heating hot wire assisted TIG cladding process. Different methods like electroslag cladding, submerged arc cladding, explosive cladding and laser cladding have been used to join a base metal with a dissimilar metal [37,38,39,40].

Another welding process that offers many benefits over traditional clad/hard face welding processes is laser hot wire cladding (LHWC), which combines a preheated wire with a laser beam [39]. It’s applicable for a situation where there is a need for a metallurgical bond capable of handling strain that will not result in spallation of the coating [39]. It offers high volume deposition rates with high travel speed and minimal heat input and has lower dilution rate compared to other arc welding processes in addition to its potential application for the repair/refurbishment of damaged or worn, high-value parts [39].

Further search on welding methods that can overcome the challenges of large heat affected zone (HAZ), low welding speeds, distortion, high shrinkage, and high residual stresses associated with arc welding has led to the use of cold metal transfer (CMT) welding technique, a relatively new welding technique that offers the ability to produce low heat input welds with low dilution of the base alloy with the filler alloy, low residual stresses and low structural distortion [27,41,42]. Pickin and Young [42] reported the basic operating principles of CMT process.

Figure 1. A schematic diagram showing the principle of the laser-TIG hybrid welding process [34]

The controlled method of material deposition and higher melting coefficient when compared to conventional arc welding processes highlighted the suitability of CMT for welding thin aluminium and magnesium alloy sheets [41,42]. However, to date, only limited work has been conducted on the cold metal transfer and repair of cast magnesium alloys using cold metal transfer.

Agudo et al. [43] and Zhang et al. [13] have reported the potential of the process to join steel to aluminium due to the reduced heat input which results in control over the formation of brittle intermetallics. However, it is notable that these studies have generally focused upon the properties of the deposited weld bead based upon the process operating principles as defined by the system manufacturer. No exhaustive works examining the characteristics of the process across the available parameter range have yet been reported. Picking et al. [44] concluded in a research on cold metal transfer process and its application for low dilution cladding that the technology can be used as a cladding process due to precise control of weld bead dilution. A lower dilution ratio was reported to be possible than that realized with pulsed MIG welding. They also reported that for cladding ternary aluminium systems using a binary filler wire, a layer of weld can be deposited exhibiting a quasi-binary composition. This composition was stated to be potentially less susceptible to solidification cracking due to control of the terminal ternary eutectic reactions [44].

Process design and optimization to increase process efficiency and to reduce heat input during welding processes is the focus of recent research on welding [45]. Modeling welding processes gives an alternative to reduce the experimental effort and enhances process optimization of which artificial neural network could be a versatile tool.

Artificial Neural Networks (ANN) are made of highly interconnected, simple processing units which are inspired by neural process observed in human brain [46]. Neural networks have been found applicable in areas not only limited to process engineering, process control and estimation, but also to pattern recognition, fault detection and image analysis. The peculiarity of these applications is the capability of ANN to learn complex input-output relationships. They require no clearly defined algorithm or theory, rather they have property of acquiring knowledge through the presentation of examples [46].

Artificial Neural Networks (ANN) are biologically stimulated, meaning that, they are composed of elements that perform in a manner that is similar to the most elementary functions of the biological neurons. It consists of a parallel distributed architecture with a large number of neurons and connections, which from one node to another and is associated with a weight [47]. Artificial neural networks are categorized by their topology, weight vectors and activation function that are used in the hidden layers and output layer. In the present paper, multilayer perceptrons, with each layer consisting of a number of computing neurons was adopted. A perceptron is nothing but a computing unit or neuron. A multilayer perceptron trained with the back-propagation algorithm may be viewed as a practical way of performing a non-linear input-output mapping of a general nature [47].

In ANN hidden and output layers, non-linear function has been adopted as the activation function, however, no activation function is used for the input layer, since no computation is involved in the input layer. Full and appropriate connections are ensured between the neurons in a layer and the neurons in its adjacent layers. Information flows from one layer to other layer in a feed-forward manner. The architecture with feed-forward-back propagation network has gained popularity among different types of neural networks and finds applications in several areas of Engineering [48].

To improve the generalization in neural networks, methods such as Bayesian regularization, Levenberg-Marquardt, and Scaled Conjugate Gradient are commonly used [49,50]. Levenberg-Marquardt algorithm was used in this work because the algorithm typically requires more memory but less time. Similarly, training using this algorithm automatically stops when generalization stops improving, as indicated by an increase in the mean square error of the validation samples [49,50]. To avoid over fitting problems, which hinders the generalization capability of neural network, the number of neurons to be used in the hidden layer of a neural network is critical.

Appropriate number of neurons was used for excellent optimization and prediction in this work.

In the current application, the objective is to use the network to learn mapping between input and output patterns and to predict an optimized outcome. The components of the input pattern consisted of the control variables during three welding types, whereas the output pattern components represented the measured weld characteristics (e.g. Weld depth, underfill, total accumulated pores and percentage defects) from the weld build-up.

2. Materials and Method

2.1. Process Design and Welding

ZE41-T5 coupons (see Table 1 for composition) having 0.5 inches groove was welded using three advanced welding technologies; hybrid laser arc welding, hot wire cladding and cold metal transfer, with 0.06 inches diameter AZ61 being the filler wire. The welding parameters and the range of values used for the welding are presented in Tables 2a-c. Twenty experiments were initially designed for each welding technique from the values in Tables 2a-c using a 3-factor central composite design as shown in Tables 2d-f. The corresponding output parameters in the weld for each set of the input variables were experimentally determined.

Table 1. ZE41-T5 and AZ61Alloys’ Nominal Composition (wt. %)

Table 2a. Process variables and levels for Hybrid Laser Arc Welding of ZE41-T5 with AZ61 filler

Table 2b. Process variables and levels for Hot Wire Cladding of ZE41-T5 with AZ61 filler

Table 2c. Process variables and levels for Cold Metal Transfer of ZE41-T5 with AZ61 filler

Table 2d. The design table for the 3-factor central composite design for Hybrid Laser Arc Welding of ZE41-T5 with AZ61 filler

Table 2e. The design table for the 3-factor central composite design for Hot Wire Cladding of ZE41-T5 with AZ61 filler

Table 2f. The design table for the 3-factor central composite design for Cold Metal Transfer of ZE41-T5 with AZ61 filler

2.2. Sample Preparation

The welded coupons were sectioned transversely from three locations along the weld bead using a Hansvedt DS-2 Travelling Wire Electrical Discharge Machine (EDM). A distance of 6 mm from both ends of the weld beads were excluded before selecting the sectioned regions. The sectioned samples were carefully prepared by using standard metallography procedures. MasterPrep™ Alumina Suspension, a sol-gel product with an average particle size of 0.05 μm was used as the final polishing solution. The as-polished samples were cleaned in acetone and subsequently examined, using an Axionvert 25 optical microscopy equipped with Clemex Vision TM 3.0 image analyzer.

Image J software was used for defect analysis in the weld. It’s worth mentioning that the defects within the crowns of all welds were disregarded because they would be machined down in a real application.

2.3. Matlab

Matrix lab (MATLAB) version 7.0, a software package used for high performance numerical computations and visualization was used in this work. It provides an interactive environment with hundreds of built-in functions for technical computations, graphics and animations. The built-in functions provide excellent tools for linear algebra computation data analysis, signal processing, optimization and other scientific computations. In this work, ANN module (a Matlab built-in function) was utilized for predicting weld properties from different input welding parameters for the welding techniques understudy.

2.4. Training

Artificial neural network consists of a number of layers (generally three) each with a number of nodes. These nodes process the data and pass it to the next layer. The input is given to the input layer and the network, after processing it, gives the result via the output layer. It has been found that they have the capacity of learning a complex polynomial equation of any degree. Since the working of the network is based on simple mathematical equations, they have a low response time which is extremely useful in controlling dynamic processes.

The welding parameters were designed by the use of a 3-factor central composite design platform (Tables 2d-f) and the measured weld properties were fed to the artificial neural network program as training set of data. These experiments are referred to as the training set of experiments. Training of the ANN was performed with an allowable error of 0.001.

Once the network was trained such that the maximum error for any of the training data was less than allowable error, the weights and the threshold values were automatically saved by the program.

2.5. ANN Architecture

There are different types of architecture for ANN model. For creating a model, neural network requires different experimental data with regard to different welding input parameters and quantifiable weld output parameters.

Twenty sets of experimental data generated by a 3-factor central composite design and experimental/quantifiable output parameters for each welding technique were taken for training the artificial neural network. Normalized input data were fed to the system, which in turn gave the optimized output. The ANN architecture model used for the prediction of weld optimized output parameters has the following layers: (i) input layer (ii) hidden layer and (iii) output layer. Prediction and optimization were made with a feed-forward back propagation multi-layer neural network. An example of the multi-layer neural network structure used in this work is shown in Figure 2.

Figure 2. Function fitting neural network structure used in the optimization of the welds build-up

Different statistical plots (regression, performance, histogram, and training state) describing the ANN training and optimization process were obtained at the end of the process.

2.6. Neural Network Algorithm Used for the Prediction in HLAW of ZE41-T5 with AZ61 Filler

function [y1] = myNeuralNetworkFunction(x1)

%MYNEURALNETWORKFUNCTION neural network simulation function.

%

% Generated by Neural Network Toolbox function genFunction, 05-Jul-2017 08:02:01.

%

% [y1] = myNeuralNetworkFunction(x1) takes these arguments:

% x = Qx3 matrix, input #1

% and returns:

% y = Qx2 matrix, output #1

% where Q is the number of samples.

%#ok<*RPMT0>

% ===== NEURAL NETWORK CONSTANTS =====

% Input 1

x1_step1_xoffset = [2;12;6];

x1_step1_gain=[1.33333333333333;0.111111111111111;0.8];

x1_step1_ymin = -1;

% Layer 1

b1 = [-2.927564122348834; 2.140686388458823;

-1.228745504273046;0.15786626753757294;

-0.91728736031910918;1.4391294629490912;

2.7659368632453449];

IW1_1 = [0.8043022344421582; 1.7635327474638858; 1.8089961335960016; -1.620210653647721;

0.98434098983287532;1.4947818814316554; 2.1785911160596916;-0.32958212650247876; 1.1938385683345523;1.2486306330041952;

-1.0738671702805089;2.2234346910881118;

-1.8313706303221431; 0.69814245255994445;

-1.8056117131369986;0.5972875966546457;

-2.594394008946368;0.03295904951749748; 2.2973960847547774;-1.0016926866014884; 0.76193885876268497];

% Layer 2

b2 = [0.6874304194903591;0.52656729269184677];

LW2_1 = [0.82254670915030403;

-1.1224180699498967; 0.27518510048195677;

-0.50706686429710945; -0.69715907612787809;

-0.14255569782209787;0.55622674765334756; 0.32570790979211839;-0.69637402358741007 0.079213170835870872;0.16635102425366588; 0.14397413305052731;-0.11880087619259146;

-0.29779985729735908];

% Output 1

y1_step1_ymin = -1;

y1_step1_gain=[0.503778337531486;1.78571428571429;

y1_step1_xoffset = [1.96;0];

% ===== SIMULATION ========

% Dimensions

Q = size(x1,1); % samples

% Input 1

x1 = x1';

xp1 = mapminmax_apply (x1, x1_step1_gain, x1_step1_xoffset, x1_step1_ymin);

% 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_gain, y1_step1_xoffset, y1_step1_ymin);

y1 = y1';

end

% ===== MODULE FUNCTIONS ========

% Map Minimum and Maximum Input Processing Function

functiony=mapminmax_apply(x,settings_gain,settings_xoffset,settings_ymin)

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_gain, settings_xoffset, settings_ymin)

x = bsxfun(@minus,y,settings_ymin);

x = bsxfun(@rdivide,x,settings_gain);

x = bsxfun(@plus,x,settings_xoffset);

end

2.7. Neural Network Algorithm Used for the Prediction in HWC of ZE41-T5 with AZ61 Filler

function [y1] = myNeuralNetworkFunction(x1)

%MYNEURALNETWORKFUNCTION neural network simulation function.

%

% Generated by Neural Network Toolbox function genFunction, 28-Jun-2017 08:32:32.

%

% [y1] = myNeuralNetworkFunction(x1) takes these arguments:

% x = Qx3 matrix, input #1

% and returns:

% y = Qx2 matrix, output #1

% where Q is the number of samples.

%#ok<*RPMT0>

% ===== NEURAL NETWORK CONSTANTS =====

% Input 1

x1_step1_xoffset = [8;1.4;20];

x1_step1_gain= [0.5;3.33333333333333;0.0333333333333333];

x1_step1_ymin = -1;

% Layer 1

b1=[2.8837772804640776;2.1772641480255892;0.99599448241231459;-0.071436571676796068;

0.83880388942978923;2.0478352497870871;2.9255358911889289];

IW1_1 = [0.84593804930533278; -1.9897939348418114; 1.2843663163187344;-2.3151009963021809; 0.46916213490894654;-0.70941522218057429;

-0.79487165479438648;-1.3510577540170312;

-1.9013174194526885;-0.4980023319377323; 2.6606879184407184;0.5287373509167993;

-1.929149674616224; -0.060283961169541156;

-1.7384924895931686;1.9533058439857762; 0.64085163234057607 1.6351485506972232;0.23783699935862995; 0.023503618901415294; -3.2823918591903776];

% Layer 2

b2 = [0.29257943985203666;-0.54494697985054685];

LW2_1= [-0.02262396084316189; 0.8939219227284767; -0.71416633987482081;-0.8175402897872045;

-0.40170596559822397; -0.66214080810780307;

-0.25380156287439792;0.22861345935914468;

-0.56696561546382562;-0.87049565012169972; 0.15667355856791959; -0.25913284513173818;

-0.39421885822067038; 1.6191302680424531];

% Output 1

y1_step1_ymin = -1;

y1_step1_gain = [1.2987012987013;2.8169014084507];

y1_step1_xoffset = [2.92;0];

% ===== SIMULATION ========

% Dimensions

Q = size(x1,1); % samples

% Input 1

x1 = x1';

xp1=mapminmax_apply(x1,x1_step1_gain,x1_step1_xoffset,x1_step1_ymin);

% 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_gain,y1_step1_xoffset,y1_step1_ymin);

y1 = y1';

end

% ===== MODULE FUNCTIONS ========

% Map Minimum and Maximum Input Processing Function

Functiony=mapminmax_apply(x,settings_gain,settings_xoffset,settings_ymin)

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

functionx=mapminmax_reverse(y,settings_gain,settings_xoffset,settings_ymin)

x = bsxfun(@minus,y,settings_ymin);

x = bsxfun(@rdivide,x,settings_gain);

x = bsxfun(@plus,x,settings_xoffset);

end

2.8. Neural Network Algorithm Used for the Prediction in CMT of ZE41-T5 with AZ61 Filler

function [y1] = myNeuralNetworkFunction(x1)

%MYNEURALNETWORKFUNCTION neural network simulation function.

%

% Generated by Neural Network Toolbox function genFunction, 27-Jun-2017 09:31:51.

%

% [y1] = myNeuralNetworkFunction(x1) takes these arguments:

% x = Qx3 matrix, input #1

% and returns:

% y = Qx2 matrix, output #1

% where Q is the number of samples.

%#ok<*RPMT0>

% ===== NEURAL NETWORK CONSTANTS =====

% Input 1

x1_step1_xoffset = [20;8;3];

x1_step1_gain = [0.133333333333333;0.363636363636364;0.666666666666667];

x1_step1_ymin = -1;

% Layer 1

b1 = [2.3416505313819571;

-1.2740928782474972;0.82963358843289703;0.0038614997021745173;1.0800821965696763;

-1.9335280944581741;-2.8321274629900488];

IW1_1 = [-0.15169469951932121; -1.83697258374909

-2.4161157478782691;0.9786984235836732 1.6439037040005724;-2.4601166899099622;

-2.0889114670772537; 1.2839241282702023;

-0.69295516248077127;1.5673512434121597 1.3003197769934292;1.7118971531199585;1.5094995678999361; -1.193159965610683; -1.8177222349167497;

-1.5521835352142808;1.77436047085499;

-0.49864879574296028;-2.5039547948599838;

-0.11771757237618742; 1.2261075814939959];

% Layer 2

b2 = [-0.47440532822471321;-0.60325390154423508];

LW2_1=[-0.060597788832621222; 0.55786576083722594;-0.13385902540764183; 0.11628993073541834;-0.0034728189116335767;

-0.13754420070429177;-0.21793000115199826;

-1.806313121199328;-0.50666207013222986; 0.73208195242823138; -0.54253247585363418;

0.20544708676213919; -0.34734378588992193;

-0.8416781415811555];

% Output 1

y1_step1_ymin = -1;

y1_step1_gain= [1.38888888888889;0.869565217391304];

y1_step1_xoffset = [2.03;0];

% ===== SIMULATION ========

% Dimensions

Q = size(x1,1); % samples

% Input 1

x1 = x1';

xp1=mapminmax_apply(x1,x1_step1_gain,x1_step1_xoffset,x1_step1_ymin);

% 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_gain,y1_step1_xoffset,y1_step1_ymin);

y1 = y1';

end

% ===== MODULE FUNCTIONS ========

% Map Minimum and Maximum Input Processing Function

functiony=mapminmax_apply(x,settings_gain,settings_xoffset,settings_ymin)

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

functionx=mapminmax_reverse(y,settings_gain,settings_xoffset,settings_ymin)

x = bsxfun(@minus,y,settings_ymin);

x = bsxfun(@rdivide,x,settings_gain);

x = bsxfun(@plus,x,settings_xoffset);

end

3. Results and Discussion

3.1. Neural Network Predictions

Figure 3, Figure 7, and Figure 11 are some selected micrographs of samples used for the measurements of the weld output parameters required for the development of ANN models in HLAW, HWC and CMT welding techniques respectively. Tables 3a-c present the twenty-experimental input and output parameters in each of the welding types respectively.

A network structure of 3-7-2-2 (Figure 2) was chosen for the prediction of the weld outputs in the weld build-up of the three welding types. Figure 4 – Figure 6; Figure 8 -Figure 10 and Figure 12 – Figure 14 show the regression curves, performance curves and error histograms in the respective welding types for the prediction of the weld outputs in the weld build-up, using ANN. It can be seen in each of Figure 4, Figure 8 and Figure 12 that the correlation coefficient, R, which measures the strength and direction of a linear relationship between two variables on a scatter plot approaches +1, which suggests that the models explain considerable high percentage of variability of the response data around its mean, and thus, the models have very strong positive linear relationship within the variables analysed. The closeness of the mean square errors (MSE) to zero in the performance plots (Figure 5, Figure 9 and Figure 13) show that the ANN models were well trained at the end of the training phases. This suggests that the desired outputs and the ANN models’ outputs for the training sets have become very close to each other, which implies that the ANN models can essentially predict arbitrarily close to the target. The error histograms (Figure 6, Figure 10 and Figure 14) show normal distributions with residuals (errors), indicating that many of the residuals fall on or near zero. All of these suggest that the ANN models used for the prediction in this work are capable of excellent predictions. Tables 3d-f are the tables of optimization, showing the selected optimum parameters (highlighted green) for the HLAW, HWC and CMT processes respectively.

Depth, D was chosen as an output to be optimized in HLAW, HWC and CMT based on the fact that it correlates with heat input. High laser power and/or welding current will increase the heat input and results in more material being melted, which will consequently increase the weld depth or weld size. However, an optimized laser power or welding current that will minimise heat input and produce appropriate weld depth (a low value of D with complete fusion of the filler with the substrate) and size without jeopardising other weld output requirements is desired.

Total accumulated pore length (Po) was chosen as an output to be optimized in HLAW because of the tendency of hybrid laser-arc welding process to produce high amount of porosity. Minimizing or eliminating the amount of porosity in a weld is desired for maximum strength.

Underfill, U was chosen as an output to be optimized in HWC because its samples did not completely fill the machined groove. Many are acceptable based on standards (AWS D17.1) and therefore this property must be minimized or eliminated.

Figure 3. Optical Micrographs of a sections from weld 6 of HLAW, showing the weld geometry and defect

Figure 4. Regression plots for the optimization of HLAW of ZE41-T5 weld build-up with AZ61 filler wire

Figure 5. Performance curve for the optimization of HLAW of ZE41-T5 weld build-up with AZ61 filler wire

Figure 6. Error Histogram in the optimization of HLAW of ZE41-T5 weld build-up with AZ61 filler wire

Table 3a. Experimental weld input and output parameters for HLAW of ZE41-T5 with AZ61 filler

Table 3b. Experimental weld input and output parameters for HWC of ZE41-T5 with AZ61filler

Table 3c. Experimental weld input and output parameters for CMT of ZE41-T5 with AZ61 filler

Table 3d. Weld input and ANN predicted output parameters for HLAW of ZE41-T5 with AZ61 filler wire

Table 3e. Weld input and ANN predicted output parameters for HWC of ZE41-T5 with AZ61 filler wire

Table 3f. Weld input and ANN predicted output parameters for CMT of ZE41-T5 with AZ61 filler wire

Table 3g. Average output parameters from experimentally verified weld coupons for HLAW of ZE41-T5 with AZ61 filler wire

Table 3h. Average output parameters from experimentally verified weld coupons for HWC of ZE41-T5 with AZ61 filler wire

Table 3i. Average output parameters from experimentally verified weld coupons for CMT of ZE41-T5 with AZ61 filler wire

Figure 7. Optical Micrographs of a sections from weld 2 of HWC, showing the weld geometry and defects

Figure 8. Regression plots for the optimization of HWC of ZE41-T5 weld build-up with AZ61 filler wire

Figure 9. Performance curve for the optimization of HWC of ZE41-T5 weld build-up with AZ61 filler wire

Figure 10. Error histogram in the optimization of HWC of ZE41-T5 weld build-up with AZ61 filler wire

Figure 11. Optical Micrographs of a sections from weld 19 of CMT, showing the weld geometry and defect

Figure 12. Regression plots for the optimization of CMT of ZE41-T5 weld build-up with AZ61 filler wire

Figure 13. Performance curve for the optimization of CMT of ZE41-T5 weld build-up with AZ61 filler wire

Figure 14. Error histogram in the optimization of CMT of ZE41-T5 weld build-up with AZ61 filler wire

Figure 15. A representative optical micrograph of a section from the experimentally verified HLAW weld, showing the weld geometry (Solution 2 from Table 3g)

Figure 16. A representative optical micrograph of a section from the experimentally verified CMT weld, showing the weld geometry and zero weld defect (Solution 2 from Table 3i)

Percentage defects, Pd was chosen as an output to be optimized because CMT cross-sections show extensive amount of delamination and lack of fusion, which needs to be minimized or eliminated to produce acceptable welds. These desirabilities were achieved by the ANN models used in this work (Tables 3d-f) by predicting an excellent relationship among the welding input parameters and output responses.

3.2. Validation of Neural Network Model

To validate the accuracy of the 3-7-2-2 neural network models for predicting the weld outputs in each of the weld types, two experimental tests from HLAW and three experimental tests each from HWC and CMT were conducted within the window of the optimized welding parameters, and the corresponding experimental output were determined as shown in Table 3g-i. A comparison of the experimentally measured weld output and predicted values using Artificial Neural Network (ANN) shows that the verified experimental results agreed well with the ANN predictions. Figure 15 -Figure 16 are the typical representative optical micrographs of sections from the experimentally verified HLAW and CMT welds, showing the weld geometry.

4. Conclusion

A 3-7-2-2 feed-forward back propagation artificial neural network (ANN) models for predicting accurately, the weld output parameters in three advanced welding techniques for a conventionally difficult to weld magnesium alloy was successively developed. The weld input parameters and experimentally measured output parameters were utilized to train the neural network models. The trained neural network models were used in successively predicting the weld outputs for various operating conditions. The developed models were found to be capable of predicting the weld output parameters perfectly within the range it has been trained. This suggests that ANN is a versatile tool that can be adopted in the optimization of the welding processes of difficult to weld alloys.

Disclosure Statement

There is no potential conflict of interest reported by the author.

Acknowledgements

The authors gratefully acknowledge the financial support of Consortium for Aerospace Research and Innovation in Canada (CARIC) through [grant number CARIC DPHM-711]

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