# Application of Artificial Neural Network (ANN) in Predicting Box Compression Strength (BCS)
## 1 Introduction  
Corrugated fiberboard packages provide temporary protection for products against damaging forces throughout the distribution process. Among their structural properties, top-to-bottom box compression strength (BCS) is especially critical to the safe distribution and marketing of nearly all consumer goods. Since the invention of corrugated board, BCS has been a central focus of research, with extensive studies exploring the material's structural behavior during failure. Over the past 140 years, various methods have been developed to evaluate and improve BCS [1]. Methods for evaluating BCS generally fall into three main categories: analytical modeling, numerical analysis, and mechanical testing [2]. However, each approach has its limitations. The most common formula in analytical modeling is the approach presented by [PERSON], [PERSON], and [PERSON] in 1963 [3]. The McKee equation is still widely used in the industry due to its simplicity, which makes it very easy and fast to apply in real-world scenarios without the need for additional experiments [4]. However, it has been shown to be inaccurate in many cases, particularly for non-RSC boxes or RSC boxes modified with holes, cutouts, and other design changes [5]. Its limited accuracy is largely due to the wide range of factors influencing BCS, while the [PERSON] equation is a simplified model based on basic corrugated board parameters and empirically derived correction factors [3]. Numerical analysis, most commonly in the form of finite element analysis (FEA), has become the preferred method for predicting BCS, apart from analytical modeling, thanks to its efficiency and robust simulation capabilities, producing reasonable agreement between the model and the limited number of physical samples evaluated [2]. [PERSON], [PERSON] et al. applied FEM to estimate the static top-to-bottom compressive strength of simple corrugated packaging by including the torsional and shear stiffness of corrugated cardboard and the panel depth-to-width ratio [6]. [PERSON], [PERSON] predicted corrugated compression strength using FEM by inputting the data of the stress-strain curve obtained by the edge crush test of the corrugated fiberboard [7]. [PERSON], [PERSON] et al. investigated the edgewise compression behavior (load vs. displacement plot, ECT, and failure mechanism) of corrugated paperboard based on different types of testing standards and flute types using finite element analysis (FEA) [8], and [PERSON], [PERSON] et al. applied FEM to simulate box compression test for paperboard packages at different moisture levels based on an orthotropic linear elastic material model [9]. However, FEM faces challenges in accurately capturing the anisotropic, nonlinear mechanical behavior of paper-based materials. FEA requires a detailed set of input parameters to simulate stress and displacement, many of which are not regularly measured in the paper-making or box-making process [2]. The additional characteristics such as the humidity dependence of the mechanical properties, creep and hygroexpansion, and the dependency of paper material on time and temperature also makes the material characterization to obtain the input parameters for the FEA even more difficult [10]. Mechanical testing remains the most traditional and reliable method for evaluating BCS. However, it is time-consuming, costly, and destructive--particularly when multiple samples are needed to account for variations in material properties, packaging dimensions, and structural designs--making large-scale evaluations impractical. Furthermore, mechanical testing is constrained by laboratory conditions and equipment limitations, making it challenging to accurately replicate real-world storage and distribution environments. Therefore, more efficient and cost-effective methods are needed to improve the BCS evaluation process. In recent years, the application of machine learning (ML) in the packaging industry has demonstrated its transformative potential in optimizing operations and enhancing process efficiency.