A cognitive approach for quality assessment in laser welding

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51st CIRP Conference on Manufacturing Systems

A cognitive approach for qualityMay assessment inFrance laser welding 28th CIRP Design Conference, 2018, Nantes, a, John Stavridisa , Alexios Papacharalampopoulos Stavropoulos * A new methodology to analyze the functionala, Panagiotis and physical architecture of Laboratory for Manufacturing Systems and Department of Mechanical Engineering and Aeronautics, University of Patras, Patras 26504, Greece existing products forAutomation, an assembly oriented product family identification

a

* Corresponding author. Tel.: +30-2610910160; fax: +30-2610997744. E-mail address: [email protected]

Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat

École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France

Abstract

* Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]

Quality assessment in laser welding is of outmost importance. A plethora of in-line inspection techniques have been developed identifying melt pool geometry and weld defects for quality evaluation. This paper aims to introduce a cognitive assessment method for the prediction of weld quality and classification into different quality categories. The study corresponds to camera-based monitoring approaches utilizing thermal images Abstract obtained from process simulation models where artificial defects were inserted. A dimensionality reduction technique is deployed, and an image processing technique is afterwards implemented to identify weld defects based on specific melt pool features. A classification algorithm has also In today’s business been developed andenvironment, validated. the trend towards more product variety and customization is unbroken. Due to this development, the need of agile and reconfigurable production systems emerged to cope with various products and product families. To design and optimize production systems as to choose theby optimal product © 2018 as Thewell Authors. Published Elsevier B.V. matches, product analysis methods are needed. Indeed, most of the known methods aim to analyze a product or one product family on the physical level.ofDifferent families, however, may differSystems. largely in terms of the number and Peer-review under responsibility of the scientific committee the 51stproduct CIRP Conference on Manufacturing nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production system. A new methodology proposed to analyze products view of their functional and physical architecture. The aim is to cluster Keywords: Quality assessment; is Cognitive control; Defectsexisting recognition; Laser in processing; these products in new assembly oriented product families for the optimization of existing assembly lines and the creation of future reconfigurable assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the similarity between product families by providing design support to both,Furthermore, production system planners and product designers. Anduring illustrative 1. Introduction the ability to detect defects that occur LW example of a nail-clipper is used to explain the proposed methodology. Anand industrial case study on two families of steering columns of the valid change ofproduct the process parameters play an thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. Laser processing has been an increasingly indispensable part important role in assuring the pre-defined quality standards. © 2017 The Authors. Published by Elsevier B.V. of competitive manufacturing throughout the word [1]. Among Monitoring of the process, and consequently quality assessment Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.

the processes of laser-based manufacturing, Laser Welding (LW) hasAssembly; evolvedDesign significantly through the last years and has Keywords: method; Family identification been widely used in the automotive, aerospace, electronics and heavy manufacturing industries to join a variety of materials [2]. LW presents higher productivity, flexibility, effectiveness 1.and Introduction numerous more advantages such as deeper penetration, lower distortions and higher welding speeds [3] when compared Due to the welding fast development in thelaser domain with conventional methods. However, weldingof is communication and an that ongoing trend recognizable) of digitization and such a complex process the (visually quality digitalization, enterprises arevariables facing important of the weld ismanufacturing affected by several process [4]. The challenges in today’s environments: continuing potential defects can market significantly affect thea mechanical tendency reduction of product development times and propertiestowards of the weld and thus the risks of fatigue failure, are shortened product lifecycles. In addition, there is for an increasing significantly increased. Therefore, it’s important industry to demand of customization, at theseams sameintime in a global ensure adequate quality ofbeing the weld a product. ISO competition with by competitors all over the world. 9000 and other law-enforced regulations haveThis led trend, to the which is inducing development to micro understanding that the monitoring and from qualitymacro control is an markets, in diminished lot sizessystems due toand augmenting essential results tool in modern manufacturing necessary product (high-volume low-volume production) to keepvarieties production results intodeterministic boundaries [1]. [5]. To cope with this augmenting variety as well as to be able to identify possible optimization potentials in the existing 2212-8271 © system, 2018 The it Authors. Publishedtobyhave Elsevier B.V. production is important a precise knowledge

are mainly categorized in three stages (pre-process, in-process and post-process) based on the time accomplished. As far as it concerns the in-process quality inspection techniques, optical (UV, VIS, IR) and acoustic sensors are often used to identify weld defects and monitor the penetration depth’s evolution [6]. of the product range andsolutions characteristics manufactured and/or However, camera-based have been lately integrated in assembled in this system. this context, the main challenge in LW operations for theIn same purposes offering critical modelling is nowmonitoring not only to cope with single advantagesand overanalysis the traditional systems. Vision and products, a limited rangetemperature or existinginformation product families, IR cameras provideproduct spatial and about but be able to analyze andLW to compare to define the also heattoaffected zone during processproducts and further data new productcan families. can be observed that classical existing elaboration lead toItreliable quality evaluation of the welds product families are regrouped in function of clients or features. [6]. However, are given hardly to In thisassembly regard, oriented lately, product focus families has been to find. the On the product family assessment level, products differ with mainly in two development of quality systems cognitive main characteristics: (i) themachine number of components and (ii) the capabilities integrating learning techniques for type of components (e.g. mechanical, electrical, electronical). classification and prediction of the welding quality [7]. In [8], methodologies consideringarchitecture mainly single an Classical integrated machine intelligence toproducts address or solitary, control alreadydifficulties existing product analyze the significant of laser families welding is presented. product structure on a physical level (components level) which causes difficulties regarding an efficient definition and comparison of different product families. Addressing this

Peer-review under responsibility of the scientific committee of the 51st CIRP Conference on Manufacturing Systems.

2212-8271©©2017 2018The The Authors. Published by Elsevier 2212-8271 Authors. Published by Elsevier B.V. B.V. Peer-review under responsibility of scientific the scientific committee theCIRP 51stDesign CIRP Conference Conference2018. on Manufacturing Systems. Peer-review under responsibility of the committee of the of 28th 10.1016/j.procir.2018.03.119

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This architecture combines three contemporary machine learning techniques to allow a laser welding controller to learn and improve in a self-directed manner. A deep auto-encoding neural network was developed to extract low-dimensional features form real data while these features were used as input to a temporal-difference learning algorithm acquiring important real-time information about the process. Temporally extended predictions were utilized in combination with deep learning to directly map sensor data to the final quality of a weld seam. The authors in [9], developed a cognitive system for autonomous robotic welding, verified also for laser beam welding. This system was based on a Support Vector Machines algorithm. In order to improve and verify the approach, an extensive experimental setup had been described and realized, with the details given in respect to the sensors used, the data recorded, and the pre-processing analysis of the data. In contrast to previous efforts, this system is capable of autonomously adapting the welding process to changes in the workpiece properties. On the other hand, work-piece thickness and welding gap were used as inputs in the Neural Network (NN) developed in [10], while the output parameters ‘responses’ were optimal focus position, acceptable welding parameters of laser power, welding speed and weld quality, including weldwidth, undercut and distortion. In [11], authors focused on the prediction of keyhole size and inclination angle by creating a static NN model for the correlation of process parameters with the investigated measures. In addition, a dynamic NN was also trained based on the transient welding conditions predicted by a numerical model and then used to estimate the time-varying keyhole geometry. This paper aims to introduce a quality assessment method for the classification of the welds into different quality classes. The study corresponds to camera-based monitoring approaches, taking as input artificial defected simulation images of the thermal field for the design of the method and the algorithm. At the first stage, an image processing technique for the identification of weld defect’s location and size was deployed. Moreover, machine learning techniques were also tested for the classification model development and the prediction of the quality status. Real experimental datasets were used for the retraining of the classification algorithm and the prediction of the quality status. Finally, the requirements and specifications of a unified quality diagnosis platform for laser processing based on dimensionality reduction, machine learning and statistical techniques for the overall stitch quality status were discussed and presented. 2. Quality Assessment Method The design of the method developed herein is based on thermal simulations performed in ANSYS software. Since it is difficult to capture the formation of a defect during laser welding with thermal based numerical simulations, the investigated defects were prior designed within the specimen while a heat flux was simulated and applied on the surface area above the weld. This offered the opportunity to examine the variations in the thermal field for the identification of the existence, size and position of different weld defects. Based on a literature review [5], [6] and on industrial applications of laser welded products [12], the main defects and

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Figure 1: Quality assessment method schematic

melt-pool geometry characteristics that were examined in this study were porosity, cracks, penetration depth and melt pool width. Weld penetration depth and melt pool width are the two main characteristics that are normally monitored in in-line quality inspection systems. In the case of lap welding the weld strength is strongly correlated with the interface width, while in the case of butt welding with the depth of penetration. In both cases, the association with thermal measurements has been done through these simulations. On the other hand, hot cracking is one of the major challenges in laser welding especially in aluminium welding applications. Cracking phenomena are initiated during the solidification phase of the weld and are formulated mainly due to stresses on the surface of the material tending to close the keyhole created during the process [13]. Cracking can be critical for the welds’ strength and for this reason several ISO and empirical standards have been documented indicating the acceptable dimensions of a crack especially on the surface of the part. Finally, weld porosity was also considered herein. Porosity is normally created from trapped gasses within the melt-pool due to increased welding speed or high values of laser power [6]. Therefore, porous defects were the last category examined for the development of the proposed image processing technique with target the defect identification as well as their size and position. The addition of dimensionality reduction and machine learning techniques for extracting image features and predicting welds’ quality can lead to a complete quality diagnosis and control system for industrial environments. It worth to be mentioned that the developed classification algorithm was trained with real experimental data and was able to predict quality classes when was fed with new ones. In Figure 1, the steps of the proposed method for the development of a unified quality diagnosis platform are presented. 3. Artificial defects and process modeling Laser welding process modeling can be divided into three phases, namely the heating, the melting and the vaporization phase. Regarding the heating phase, the governing equation that describes thermal problems is the heat equation [14].

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a 2  

T 0 t

(1)

where T is the temperature, t is the time, ∇2 is the Laplacian operator, with (x, y) being spatial coordinates, and a being the thermal diffusivity. On the other hand, melting phase is slightly more complicated, as solid and liquid phases coexist and interchange heat. The temperature should be a continuous function at the interface between the two phases [15]. Melting phenomena are known to be able to be described with Stefan Problem [15], also known as moving Boundary Value Problem (BVP) for the heat equation. Below, the equations regarding the melting phenomenon are shown, denoting solid (s) and liquid (l) phases, diffusion equation is satisfied (eq.2), where phase change itself is described from a relevant boundary condition known as Stefan condition (eq.3).

a s  2Ts 

Ts T  0 / al  2Tl  l  0 t t

 kl Tl  ksTs  L f u

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Figure 2: Surface artificial defects (left) - Melt-pool modeling (right) Table 1: Simulations set up Defects Porosity Cracking

(2) (3)

Where u is the velocity of the moving boundary, Lf is the amount of energy required to cause phase change, known as latent heat of fusion. Stefan condition describes the energy conservation at the phase change phenomenon. Similarly, in the case of evaporation, a boundary velocity can be set. Throughout the study, the geometry that is under investigation for the preparations of defected specimens is a simple rectangular one, as given in Figure 2. Symmetry conditions are used to reduce the computational effort, while the laser radius is a realistic portion of the dimensions of the specimen. Also, several simplifying assumptions have been taken into account: • Thermal conductivity, density and heat capacity were assumed to be constant in both solid and liquid phase of the material • The direction of the influx produced by the laser beam was assumed to remain vertical. • Reflectivity of the metal has been ignored, as well as defocusing • The laser profile has been assumed to be uniform. • The interaction between the laser and the specimen has been considered in terms of heat flux, while the rest of the part boundary has been considered to be convective. • A non-uniform mesh has been adapted for easier convergence. The link between the characteristics of the melt-pool (measurable vs quality related), as well as the utilization of voids in geometry as cracks models have been utilized to compute the thermal images if the case under investigation. The set-up conditions for the simulation of porosity, cracking and penetration- melt pool width relation extraction is summarized and presented in Table 1.

PenetrationMelt pool width

Specimen dimensions 25x5x0,5 mm 25x5x0,5 mm 25x5x0,5 mm

Pore radius N/A

Crack dimensions N/A

Laser Power / Frequency 100 W / 2 kHz

Material

0.15 mm N/A

0,2x0,01 mm N/A

100 W / 1 kHz

Steel

100 W / 1 kHz

Steel

Steel

4. Dimensionality reduction and defects recognition Within the paper two different approaches were followed for the features extraction procedure of the image data obtained from the simulations. In the first one a self-developed image processing algorithm was created aiming to extract features from the images which would provide feedback on the differences of the temperature field. However due to the high dimensionality problem another algorithm was also created. This algorithm was based on PCA [16] technique which is also presented below. Algorithm for retrieving geometrical characteristics of the defect: The results of the thermal simulations in ANSYS were exported in an excel file. The temperature values were inserted in a matrix of 20x20 and afterwards the excel file was loaded from the developed MATLAB code constructing an image. Considering the current resolution of commercial available IR cameras (32x32 pixels) [17] as the worst-case scenario, the authors obtained the particular resolution as the minimum threshold with which the detection algorithm could identify the variations produced by the existence of the defects. Based on the images acquired for each of the defected specimens, an image processing algorithm was developed and implemented in the MATLAB software. The steps of the algorithm are described below. 1) Extract images (20x20) from simulations, 2) Insert images matrix through excel in MATLAB, 3) Read the values and construct the images, 4) Apply a filter on the image derivatizing in space (this can be optional, but offers good visualization of several metrics among others), 5) Identify center of melt pool, 6) Extract moments of low order of the image, 7) Compare with values retrieved from ideal case, 8) Identify defects position from the melt-pool center with moments (1st & 2nd order were used for the calculation of defects’ position and size), 9) Repeat for bigger defects and different location within the field Several techniques were tested for the filtering of the image at the beginning and afterwards for the calculation of the mean

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Figure 3: Pores position detection (left) - Crack size identification (right)

value of matrix’s temperature. The variation of moments of low order between the different set-up of porosity cracking or lack of penetration and the ideal specimen (without porosity) can indeed indicate successfully the existence, the size and the position of the defect. As far as it concerns the filtering method followed for the purposes of this work, the equation (4) was first implemented while a notch filter [18] was applied afterwards. This discrete version of differentiation in space would allow to identify the variance of the temperature field leading to indications on the existence of the defect and the mean filtered temperature field which will provide information on the relevant size of the detected defects. Below, the difference equation that was used is provided, a spatial filter of finite response (P is the original thermal image and P2 the outcome).

P2 (n, k) = 4 * P(n, k) - P(n + 1, k) - P(n - 1, k) P(n, k + 1) - P(n, k - 1) - P(n, k) * 0

(4)

It is worth to be mentioned that in order to examine the sensitivity of the proposed image processing techniques, besides the placement of the defect inside the specimen different depths were tested and different pores diameters. The method worked satisfactory up to 2 mm depth which is more than adequate. In addition, the method with some alterations

successfully detected the smallest observed pores based on experiments found in literature[6]; however, the filters applied would lead to increased noise in the signal and thus more calculating time. As it can be observed in Figure 3, all the defects could be identified, and imprinted differences compared to the ideal thermal field. The method had some implications when it regards the vertical (coaxial to the potential camera) cracks appearing in the specimens. However, this is dependent from the size of the crack. The bigger one can be identified with the same success as the rest of the cracks. On the other hand, Figure 3(right) demonstrates the fact that the technique can predict and visualize the difference in the size of the cracks while the numerical value can be a future threshold for accepting or rejecting the monitored weld. As far as it concerns the results on the porosity, the image processing technique can successfully identify the existence of pores in the images through comparing them to the ideal temperature field. Furthermore, it can be noticed that the position of the defects in relation to the center of laser beam can be also detected (Figure 3). Finally, the size identification capability was also tested leading to satisfactory conclusions. The pores in center, left, right, and far right positions had been modified and were designed with different diameters during the simulation phase. Furthermore, in many problems, the measured data vectors are high-dimensional but there are reasons to believe that the data lie near a lower-dimensional manifold. In other words, it

Figure 4: Identification of defects through PCA (left) – Importance of each component (right)

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may be commonly accepted that high-dimensional data are multiple, indirect measurements of an underlying source, which typically cannot be directly measured. Learning a suitable low-dimensional manifold from high-dimensional data is essentially the same as learning this underlying source [16]. Therefore. the developed PCA algorithm is provided below. Towards an algorithm for blind classification of defects (PCA): 1) Insert 10 matrixes with temperatures of 10 different experiments, 2) Specify which data corresponds to which defect and ideal temperature field, 3) Determine the size of the data sets, 4) Calculate the sample mean vector and the sample standard deviation vector, 5) Standardize the data (centering and scaling of the data), 6) Calculate the coefficients of the principal components and their respective variances, 7) Extract the diagonal, 8) Multiply each observation by the sample standard deviation vector and add the mean vector, 9) Obtain information on the principal components, 10) Plot of the results and defects identification, 11) Feed classification and prediction algorithm. In the Figure 4, the results from the implementation of a PCA algorithm for the laser welding case of this paper are provided. The outcome of the simulations as these are described above were inserted as 20x20 matrices in the algorithm and the above steps were then executed. As it can be seen in Figure 4, the algorithm was capable to distinguish the different defected specimens. It is worth mentioned the fact that the defects with double size are also placed far away in x-axis from the normal ones. Furthermore, in Figure 4 the most important features identified through the PCA algorithm are depicted. It can be safely concluded that with just one feature the dimensionality reduction can be successfully performed. 5. Quality labeling, training and prediction In the paper, after the feature extraction (image processing technique & PCA), several machine learning algorithms were tested to classify the simulation data. The main target was to connect the defected specimens with quality labelled simulations trials and teach the algorithm how to predict welding defects. Thus, a supervised classification and prediction method had to be implemented. A plethora of welding simulation trials have been characterized in detail based on the included defect with quality labels (O.K., lack of fusion, Cracks, Porosity, no seam). This process as it

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Figure 6: Two different instances from real video measurements captured through MATLAB - IR images [20]

was described above, is called data labelling and has to be done very carefully in real experiments since the outcome of the classification process depends on it. Following the creation of training data sets with both feature data and the related quality labels, the classification algorithm had to be selected and developed. The supervised learning approach led to the testing of several classification algorithms such as Logistic Regression, Support Vector Machines (SVM), Random Forests and Neural Networks (NN) through a cross-validation technique. Additionally, based on certain criteria such as heterogeneity of data, redundancy in the data and presence of interactions and non-linearities it was decided that a SVM with linear kernel would operate and perform better for this application. “Support Vector Machine” (SVM) is a supervised machine learning algorithm which can be used for both classification or regression challenges [19]. However, it is mostly used in classification problems. In this technique, each data item is plotted as a point in n-dimensional space (where n is number of features you have) with the value of each feature being the value of a coordinate. Then, classification by finding the hyper-plane that differentiate the classes is performed. Support Vectors are simply the co-ordinates of individual observation. Support Vector Machine is a frontier which best segregates two or more classes (hyper-plane/ line). In conclusion, each SVM algorithm works as a large-margin classifier which identifies a hyper plane between two or more linear separable classes with the largest separation between the classes [19]. Following the principle component analysis performed above, the data set for the training of the classification algorithm was inserted and defined. The simulation data were used for the first run of SVM. SVM classifier was then enabled performing a first classification in “GOOD” and “NOT GOOD” classes. A re-training step followed based on new simulation data. The results of this algorithm’s section are provided in Figure 5. As it can be

Figure 5: "Good" & "Not Good" classification (left) - SVM prediction of real data - two classes (Good/Not Good) (Right)

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concluded the developed method successfully classified new simulation trials based on the training model. As far as it concerns the quality prediction of new experimental data, labelled images from one IR camera were acquired [20] (Figure 5) aiming to re-train the SVM classifier while new experimental datasets were used to predict the welding quality and validate the fact that the developed method can work with real measurements. In this regard, the linear SVM was trained with two welding data sets and the outcome of the prediction for a new trial can be achieved for each frame labelled by the algorithm. It was observed that by using ten (10) principle components based on the real image data as features, quality prediction accuracy of 92% on training and test data was achieved. Afterwards, the same processes referred previously have been applied to more experimental trials to predict the quality state for two classes (“Good” and “Not Good”). The results are shown in Figure 5. The algorithm was able to successfully predict this welding issue regarding the correct class and the error position. 6. Conclusions and Discussion The quality assessment method presented constitutes a significant solution for inline monitoring and control of laserbased processes including cognitive characteristics for the prediction of quality. In extend to that, the design of a possible web HMI which can facilitate the communication of process outcome to operators within the factory can combine process level with Industry 4.0 requirements and the need for digitization. Below the main remarks coming from the work are cited while an outlook on the field is also provided. Quality Assessment Method:  Implementation of cognitive characteristics to monitoring and control systems  Development and Implementation of features extraction and machine learning techniques  Interference with control systems either online or in-line  Dimensionality reduction and features extraction techniques can identify the most important information of the images reducing the volume of the data and the computational time of machine learning and other control algorithms.  Machine learning techniques can successfully classify data and predict quality Future Outlook:  Further elaboration can lead to more detailed classification considering more defects and welding condition.  Test performance of the method with bigger data volume  More image features may appear in real experiments / adjust PCA & image processing algorithms.  Implementation of statistical methods (Hidden Markov model) for predicting overall quality of a stitch  Development of a unified digital quality diagnosis platform. Acknowledgements This work is under the framework of EU Project MAShES. This project has received funding from the European Union’s

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Horizon 2020 research and innovation programme under grant agreement No 637081. The dissemination of results herein reflects only the authors’ view and the Commission is not responsible for any use that may be made of the information it contains. References [1] Chryssolouris, G. (2013). Manufacturing systems: theory and practice. Springer Science & Business Media.. [2] Tsoukantas, G., Salonitis, K., Stournaras, A., Stavropoulos, P., & Chryssolouris, G. (2007). On optical design limitations of generalized two-mirror remote beam delivery laser systems: the case of remote welding. The International Journal of Advanced Manufacturing Technology, 32(9-10), 932-941. [3] Iordachescu, D., Blasco, M., Lopez, R., Cuesta, A., Iordachescu, M., & Ocana, J. L. (2011). Recent achievements and trends in laser welding of thin plates. Journal of Optoelectronics and Advanced Materials, 13(7), 981. [4] Chryssolouris, G. (2013). Laser machining: theory and practice. Springer Science & Business Media. [5] Kaierle, S. (2008). Process monitoring and control of laser beam welding. Laser Technik Journal, 5(3), 41-43. [6] Stavridis, J., Papacharalampopoulos, A., & Stavropoulos, P. (2017). Quality assessment in laser welding: a critical review. The International Journal of Advanced Manufacturing Technology, 1-23. [7] Thombansen, U., & Ungersb, M. (2014, February). Cognition for robot scanner based remote welding. In Proc. of SPIE Vol(Vol. 8963, pp. 89630N-1). [8] Günther, J., Pilarski, P. M., Helfrich, G., Shen, H., & Diepold, K. (2016). Intelligent laser welding through representation, prediction, and control learning: An architecture with deep neural networks and reinforcement learning. Mechatronics, 34, 1-11. [9] Schroth, G., genannt Wersborg, I. S., & Diepold, K. (2009). A cognitive system for autonomous robotic welding. In Intelligent Robots and Systems, 2009. IROS 2009. IEEE/RSJ International Conference on (pp. 3148-3153). IEEE. [10] Jeng, J. Y., Mau, T. F., & Leu, S. M. (2000). Prediction of laser butt joint welding parameters using back propagation and learning vector quantization networks. Journal of Materials Processing Technology, 99(1), 207-218. [11] Luo, M., & Shin, Y. C. (2015). Estimation of keyhole geometry and prediction of welding defects during laser welding based on a vision system and a radial basis function neural network. The International Journal of Advanced Manufacturing Technology, 81(1-4), 263-276. [12] Beersiek, J. (2001). A CMOS camera as a tool for process analysis not only for laser beam welding ICALEO 2001. [13] Sheikhi, M., Malek Ghaini, F., & Assadi, H. (2014). Solidification crack initiation and propagation in pulsed laser welding of wrought heat treatable aluminium alloy. Science and Technology of Welding and Joining, 19(3), 250-255. [14] Lienhard, J. H. (2013). A heat transfer textbook. Courier Corporation. [15] Truex, M. (2010). Numerical simulation of liquid-solid, solid-liquid phase change using finite element method in h, p, k framework with space-time variationally consistent integral forms (Doctoral dissertation, University of Kansas). [16] Ghodsi, A. (2006). Dimensionality reduction a short tutorial. Department of Statistics and Actuarial Science, Univ. of Waterloo, Ontario, Canada, 37, 38. [17] Web link: http://www.niteurope.com/tachyon-1024/?lang=en [18] Web link: https://www.mathworks.com/help/dsp/ref/fdesign.notch.html?requested Domain=www.mathworks.com [19] Shalev-Shwartz, S., & Ben-David, S. (2014). Understanding machine learning: From theory to algorithms. Cambridge university press. [20] Zenodo MAShES community: https://zenodo.org/communities/mashes/?page=1&size=20