## 1 Introduction  
Electrical steel, renowned for its exceptional soft magnetic properties, comprises specific steel grades utilized in electrical motors and transformers [1]. These grades primarily consist of iron-silicon (Fe-Si) and iron-silicon-aluminium (Fe-Si-Al) alloys, which are often available in the form of thin plates with thicknesses ranging from 0.35 mm to 0.5 mm [1]. These steel materials find diverse applications in transformer cores, generators, and motors, falling into two primary categories: grain-oriented electrical steel (GOES) and non-oriented electrical steel (NOES). GOES is cold-rolled steel containing 3% silicon, exhibiting grain orientations aligned in the rolling direction, and imparting excellent magnetic properties in that orientation. It is extensively used in transformer cores [2]. On the other hand, NOES is more common in drives and generators, featuring a cubic texture with specific planes aligned parallel to the layer and a uniformly scattered direction [100]. When examining how texture influences the magnetic characteristics of electrical steel, it becomes essential to have reliable quantitative parameters that can effectively define both the magnetic properties, which are the dependent variables, and the texture, which serves as the independent variable. Concerning the magnetic attributes, typical quantitative measures can be utilized, including core losses, permeability, coercive field values, remnant induction, and other features associated with the hysteresis curve. As for texture, it is important to consider the physical fact that the preferred magnetization directions within a Fe-singlecrystal are the [100] directions [3]. Analysing the magnetization curves of Fe-single crystals reveals that optimal soft magnetic properties emerge when the external field is applied along the [100] direction. Consequently, the most desirable texture for a soft iron core is one that maximizes the density of [100] crystal directions aligning with the magnetic induction's flux lines. Since, in rotating applications, the flux lines are nearly evenly distributed across the laminated sheets, the optimal texture is that which enhances the prevalence of [100] directions within the sheet's plane. This does not refer to the well-known Goss component ([110][001]), often observed in grain-oriented steels [4], but rather pertains to the orientations of the cube fibre, where [001] planes align parallel to the rolling plane. The latter texture components feature two coplanar [100] directions within the sheet's plane, whereas the former component only presents one [100] direction within the lamellar plane. Under alternating current (AC) magnetization, electrical steel generates heat and sound, leading to power losses through hysteresis, eddy currents, and hysteresis anomalous losses [5]. Transformers play a crucial role in efficient power delivery by stepping up or stepping down the voltage from high transmission levels (e.g., 400 kV) to lower voltages (e.g., 220-240 V) for residential and industrial use, thereby minimizing power losses during transmission [6]. However, magnetostriction, a change in a material's length due to a magnetic field, can lead to cyclic magnetization and demagnetization, causing transformer hum noise that may inconvenience residents. While noise-isolating enclosures can mitigate this noise, they can be costly. Alternatively, modifying material properties, such as using coatings to eliminate surface closure domains, offers a potential solution to controlling magnetostriction and reducing transformer hum noise [7]. A growing trend in electrical steel production involves increasing the silicon (Si) and/or aluminium (Al) concentration beyond the traditional 3% weight composition. This trend is driven by the advantageous properties of these alloy compositions, such as their lower magnetic friction and magnetic contrast (K) values, coupled with higher electrical resistance.