## 1 Introduction  
Additive manufacturing (AM) is the process of depositing materials layer-by-layer to produce a part, as against subtractive manufacturing, which starts from a block of raw material, removing small parts to obtain the final product. The drawbacks of the subtractive method are its material waste and geometric limitations in creating complex geometries [1]. Laser Wire Additive Manufacturing (LWAM), also referred to as Laser Wire-Feed Metal Additive Manufacturing (LWMAM), is a variant of the Direct Energy Deposition (DED) method. DED creates parts by melting the material into a molten metal pool [2]. LWAM uses a wire-metal feed-stock and a laser source to create the molten pool, as shown in Figure 1. It usually requires a shroud of shielding gas to protect the deposition from contamination. Metal wires offer an environmentally friendly process by being cleaner, more cost-competitive, cheaper, and more abundant than metal powders. In addition to being identical to the wire used in welding applications, a standardized and qualified product can be obtained. Additionally, the wire-feed approach, in comparison with the arc-welding approach affords a larger build volume at high productivity [3, 4]. There is a growing interest in the aeronautical sector to find methods to create complex large parts that lead to the improvement of the buy-to-fly ratio [5]. Therefore, it becomes essential to improve process planning and deposition strategies to get an optimal combination of parameters involved in the LWAM process. One of them is layer geometry. When it is well defined, layer height and width improve the part's geometric accuracy and the surface quality of the product [6]. Figure 2 illustrates the flow path of process planning for LWAM. The importance of the prediction model for the whole LWAM process should be noted; this model can influence, for example, the method by which process parameters are chosen and optimized, improving the surface quality of the final product. Furthermore, the tool's path can be adjusted based on the obtained model and can be utilized when generating the robot code. Thus, if a predictive model can be implemented properly, it will lead to products of higher quality and productivity increases [7]. Methodologies for solving the issue of predicting layer geometry during the deposition process are divided into two approaches. The first approach uses numerical or mathematical models, wherein the layer deposition is predicted from experimental processes. The second approach uses sensing devices to develop control algorithms that  
Figure 1: Schematic diagram of the LWAM PRECITEC laser head with the optical path of the laser beam and injection of the filler metal. Figure 2: Flowchart diagram of the proposed approach for the LWAM system. regulate process parameters, such as laser power, the wire feed rate, travel speed and others during the printing process. The feedback control approach is commonly used in industry and employs sensors such as pyrometers or camera vision systems to monitor the melt-pool characteristics and temperature of the deposition [8; 9; 10]. Much research [11; 12; 13; 14; 15; 16] has been reported on the use of the control approach to monitor the deposition parameters to minimize observed fluctuation and keep a controlled deposition environment. However, such an approach is not always feasible, due to process uncertainties and variations occurring during the deposition process that augment the system's complexity. Also, sensing devices face some delay in acquiring information from the system and further delay is observed when transferring data between devices and analyzing the information before the control action. Another constraint occurs in the melt pool when laser reflection and conducted heat add complexity to the information acquisition [17]. A literature survey has confirmed this, (e.g., [6; 7]) since the majority of validation using this approach is performed for simply shaped structures, focusing on only one parameter.