Deciphering Double-Walled Corrugated Board Geometry Using Image Analysis and Genetic Algorithms.

Corrugated board, widely used in the packing industry, is a recyclable and durable material. Its strength and cushioning, influenced by geometry, environmental conditions like humidity and temperature, and paper quality, make it versatile. Double-walled (or five-ply) corrugated board, comprising two flutes and three liners, enhances these properties. This study introduces a novel approach to analyze five-layered corrugated board, extending a previously published algorithm for single-walled boards. Our method focuses on measuring the layer and overall board thickness, flute height, and center lines of each layer. Through the integration of image processing and genetic algorithms, the research successfully developed an algorithm for precise geometric feature identification of double-walled boards. Images were recorded using a special device with a sophisticated camera and image sensor for detailed corrugated board cross-sections. Demonstrating high accuracy, the method only faced limitations with very deformed or damaged samples. This research contributes significantly to quality control in the packaging industry and paves the way for further automated material analysis using advanced machine learning and image sensors. It emphasizes the importance of sample quality and suggests areas for algorithm refinement in order to enhance robustness and accuracy.

The Study of Humic Substances' Impact on Anion Exchangers.

Humic substances (HSs) present in water and wastewater cause fouling of anion exchange resins (AERs), which mainly results in reducing the ion exchange capacity (IEC). In this paper, an attempt was made to investigate fouling of two polystyrene and one polyacrylic AER using water from the Oder River, treated wastewater after the ultrafiltration process (UFTW) and digester reject water from sludge dewatering at the Janówek Wastewater Treatment Plant (WWTP) in Wroclaw. HSs contained in digester reject water were characterised by the lowest aromaticity and molecular weights (MWs), the highest proportion of hydrophilic fraction and the highest amount of oxygenated functional groups. The Fourier-transform infrared (FTIR) analyses made it possible to identify chemical bonds characteristic of HSs and determine the mechanism of their retention on the surface of AER beads. The conducted experiments brought unexpected results, as the IEC increased with the amount of organic matter in the feed. Presumably, the humic substances accumulated on the beads and in the porosity of the anion exchangers themselves participated in the ion exchange process.

In-Situ Classification of Highly Deformed Corrugated Board Using Convolution Neural Networks.

The extensive use of corrugated board in the packaging industry is attributed to its excellent cushioning, mechanical properties, and environmental benefits like recyclability and biodegradability. The integrity of corrugated board depends on various factors, including its geometric design, paper quality, the number of layers, and environmental conditions such as humidity and temperature. This study introduces an innovative application of convolutional neural networks (CNNs) for analyzing and classifying images of corrugated boards, particularly those with deformations. For this purpose, a special device with advanced imaging capabilities, including a high-resolution camera and image sensor, was developed and used to acquire detailed cross-section images of the corrugated boards. The samples of seven types of corrugated board were studied. The proposed approach involves optimizing CNNs to enhance their classification performance. Despite challenges posed by deformed samples, the methodology demonstrates high accuracy in most cases, though a few samples posed recognition difficulties. The findings of this research are significant for the packaging industry, offering a sophisticated method for quality control and defect detection in corrugated board production. The best classification accuracy obtained achieved more than 99%. This could lead to improved product quality and reduced waste. Additionally, this study paves the way for future research on applying machine learning for material quality assessment, which could have broader implications beyond the packaging sector.

Computer-Aided Structural Diagnosis of Bridges Using Combinations of Static and Dynamic Tests: A Preliminary Investigation.

Reinforced concrete bridges deteriorate over time, therefore displaying a regular need for structural assessment and diagnosis. The reasons for their deterioration are often the following: (a) intensive use, (b) very dynamic loads acting for long periods of time, (c) and sometimes chemical processes that damage the concrete or lead to corrosion of the reinforcement. Assuming the hypothesis that both the stiffness of the material and its density change over time, these parameters shall be identified, preferably in a non-destructive way, in different locations of the investigated structure. Such task is expected to be possibly exerted by means of one or more tests, which must not be laborious or cause the bridge to be out of service for a long time. In this paper, an attempt is made to prepare a procedure based on dynamic tests supplemented with several static measurements, in order to identify the largest number of parameters in the shortest possible time, within an inverse analysis methodology. The proposed procedure employs a popular algorithm for minimizing the objective function, i.e., trust region in the least square framework, as part of the inverse analysis, where the difference between measurements made in situ and those calculated numerically is minimized. As a result of the work performed, optimal sets of measurements and test configurations are proposed, allowing the searched parameters to be found in a reliable manner, with the greatest possible precision.

Optimal Design of Bubble Deck Concrete Slabs: Serviceability Limit State.

In engineering practice, one can often encounter issues related to optimization, where the goal is to minimize material consumption and minimize stresses or deflections of the structure. In most cases, these issues are addressed with finite element analysis software and simple optimization algorithms. However, in the case of optimization of certain structures, it is not so straightforward. An example of such constructions are bubble deck ceilings, where, in order to reduce the dead weight, air cavities are used, which are regularly arranged over the entire surface of the ceiling. In the case of these slabs, the flexural stiffness is not constant in all its cross-sections, which means that the use of structural finite elements (plate or shell) for static calculations is not possible, and therefore, the optimization process becomes more difficult. This paper presents a minimization procedure of the weight of bubble deck slabs using numerical homogenization and sequential quadratic programming with constraints. Homogenization allows for determining the effective stiffnesses of the floor, which in the next step are sequentially corrected by changing the geometrical parameters of the floor and voids in order to achieve the assumed deflection. The presented procedure allows for minimizing the use of material in a quick and effective way by automatically determining the optimal parameters describing the geometry of the bubble deck floor cross-section. For the optimal solution, the concrete weight of the bubble deck slab was reduced by about 23% in reference to the initial design, and the serviceability limit state was met.

A Simplified Dynamic Strength Analysis of Cardboard Packaging Subjected to Transport Loads.

The article presents a simplified method for determining the strength of corrugated board packaging subjected to dynamic transport loads. The proposed algorithm consists of several calculation steps: (1) a static analysis of the compressive strength of the package, (2) an analysis of random vibrations in the frequency domain used to determine the resonance frequencies and (3) a dynamic analysis of the package loaded with computed resonant frequencies. For this purpose, numerical models of the static compression test of the packaging before and after the dynamic analysis of the package subjected to general transport loads were developed. In order to validate the model, laboratory packaging compression tests were also performed for samples of boxes using three-layer cardboard. Due to this, it was possible to verify the numerical simulation results of the compression tests for several box geometries. This, in turn, allowed for the development of a method based on dynamic and post-dynamic (static) numerical analyses, permitting a high-accuracy determination of the resistance of the selected packaging to vibrations and dynamic loads. The results of the (experimentally validated) numerical analysis proved the usefulness of the simplified method presented herein for precise estimation of the load capacity of various packages dynamically loaded during transport.

Identification of Geometric Features of the Corrugated Board Using Images and Genetic Algorithm.

The corrugated board is a versatile and durable material that is widely used in the packaging industry. Its unique structure provides strength and cushioning, while its recyclability and bio-degradability make it an environmentally friendly option. The strength of the corrugated board depends on many factors, including the type of individual papers on flat and corrugated layers, the geometry of the flute, temperature, humidity, etc. This paper presents a new approach to the analysis of the geometric features of corrugated boards. The experimental set used in the work and the created software are characterized by high reliability and precision of measurement thanks to the use of an identification procedure based on image analysis and a genetic algorithm. In the applied procedure, the thickness of each layer, corrugated cardboard thickness, flute height and center line are calculated. In most cases, the proposed algorithm successfully approximated these parameters.

Optimal Design of Bubble Deck Concrete Slabs: Sensitivity Analysis and Numerical Homogenization.

The use of layered or hollow floors in the construction of buildings obviously reduces the self-weight of the slab, and their design requires some expertise. In the present work, a sensitivity analysis and numerical homogenization were used to select the most important characteristics of bubble deck floors that have a direct or indirect impact on their load capacity. From the extensive case study, conclusions were drawn regarding the optimal selection of geometry, materials, and the arrangement and size of air voids in such a way as to ensure high stiffness of the cross-section and at the same time maximally reduce the self-weight of the slabs. The conducted analyses showed that the height of the slab and the geometry of the voids had the greatest impact on the load-bearing capacity. The concrete class and reinforcement used are of secondary importance in the context of changes in load-bearing capacity. Both the type of steel and the amount of reinforcement has a rather small or negligible influence on the bubble deck stab stiffness. Of course, the geometry of the voids and their arrangement and shape have the greatest influence on the drop in the self-weight of the floor slabs. Based on the presented results of the sensitivity analysis combined with numerical homogenization, a set of the most important design parameters was ordered and selected for use in the optimization procedure.

Estimation of the Edge Crush Resistance of Corrugated Board Using Artificial Intelligence.

Recently, AI has been used in industry for very precise quality control of various products or in the automation of production processes through the use of trained artificial neural networks (ANNs) which allow us to completely replace a human in often tedious work or in hard-to-reach locations. Although the search for analytical formulas is often desirable and leads to accurate descriptions of various phenomena, when the problem is very complex or when it is impossible to obtain a complete set of data, methods based on artificial intelligence perfectly complement the engineering and scientific workshop. In this article, different AI algorithms were used to build a relationship between the mechanical parameters of papers used for the production of corrugated board, its geometry and the resistance of a cardboard sample to edge crushing. There are many analytical, empirical or advanced numerical models in the literature that are used to estimate the compression resistance of cardboard across the flute. The approach presented here is not only much less demanding in terms of implementation from other models, but is as accurate and precise. In addition, the methodology and example presented in this article show the great potential of using machine learning algorithms in such practical applications.

Modified Compression Test of Corrugated Board Fruit Tray: Numerical Modeling and Global Sensitivity Analysis.

This article presents a modified configuration of the box compression test (BCT), which reflects the actual behavior of the vegetable or fruit trays during transport and storage. In traditional load capacity tests, trays are treated as classic transport boxes, i.e., they are compressed between two rigid plates, which does not take into account the specific geometry of this type of packaging. Both the boundary conditions and the loads acting on the tray were modified. The paper presents the concept of a new test, as well as numerical models and a sensitivity analysis of the modified BCT to the basic geometrical dimensions of the tray. The conducted research clearly shows that the proposed configuration of the load-bearing capacity test of a tray is closer to the actual operation of the packaging. As a result, most of the parameters that are not active under the conditions of the classical BCT become more important in the new configuration, which corresponds to the observations on the real performance of the packaging.

Influence of Imperfections on the Effective Stiffness of Multilayer Corrugated Board.

There are many possible sources of potential geometrical inaccuracies in each layer of corrugated board during its manufacture. These include, among others, the processes of wetting the corrugated layers during profiling, the process of accelerated drying, the gluing process, and any mechanical impact of the pressure rollers on the cardboard. Work taking into account all the above effects in numerical modeling is not well described in the literature. Therefore, this article presents a simple and practical procedure that allows us to easily account for geometric imperfections in the calculation of the effective stiffness of corrugated board. As a main tool, the numerical homogenization based on the finite element method (FE) was used here. In the proposed procedure, a 3D model of a representative volumetric element (RVE) of a corrugated board is first built. The numerical model can include all kinds of geometrical imperfections and is used to calculate the equivalent tensile and bending stiffnesses. These imperfections were included in the 3D numerical model by appropriate modeling of individual layers, taking into account their distorted shape, which was obtained on the basis of a priori buckling analysis. This paper analyzes different types of buckling in order to find the most representative one. The proposed procedure is easy to implement and fully scalable.

An Analysis of Hydromorphological Index for Rivers (HIR) Model Components, Based on a Hydromorphological Assessment of Watercourses in the Central European Plain.

Assessing the hydromorphological conditions of watercourses is a requirement of the Water Framework Directive (WFD) and national river status monitors (e.g., in Poland,the State Environmental Monitoring, and Water Monitoring coordinated by Chief Inspectorate of Environmental Protection). This paper evaluates the hydromorphological status of 10 watercourses (30 measurement sections) in Poland based on the multimetric Hydromorphological Index for Rivers (HIR). A new approach to the delineation of the river valley (small watercourses) is proposed. An analysis of the influence of river valley management on the value of HIR and its components was carried out using statistical methods (basic statistics, Mann-Whitney U Test and Ward's cluster analysis). In addition, the relationship between the components of the HDS (Hydromorphological Diversity Score) and HMS (Hydromorphological Modification Score) was analyzed (Spearman's Rank Correlation Coefficient). HIR values for the watercourse sections ranged from 0.553 to 0.825. HDS values ranged from 27.5 to 75.5 and HMS from 2.0 to 17.5. The results of the basic statistical analyses showed slight differences between the two river valley delineation methods. The Mann-Whitney U Test showed a significant difference in the test significance level of the HDS, HMS and HIR for the river valley delineation methods. Spearman's rank correlation analysis showed that most of the HDS and HMS parameters components had a low degree of correlation. The juxtaposition of the two methods for delineating a river valley and its influence on the HIR allows for a better understanding of the interdependence between its parameters.

Sensitivity Analysis of Open-Top Cartons in Terms of Compressive Strength Capacity.

Trays in which fruit and vegetables are transported over vast distances are not only stored in extreme climatic conditions but are also subjected to long-term loads. Therefore, it is very important to design them correctly and select the optimal raw material for their production. Geometric parameters that define the shape of the packaging may also be optimized in the design process. In this work, in order to select the most important parameters that affect the load capacity of a tray, sensitivity analysis was used. A sensitivity analysis is often the first step in the process of building artificial-intelligence-based surrogates. In the present work, using the example of a specific tray's geometry, the selection of starting parameters was carried out in the first step, based on the Latin hypercube sampling method. In the next step, local sensitivity analyses were performed at twenty selected starting points of the seventeen-dimensional space of the selected parameters. Based on the obtained results, it was possible to select the parameters that have a significant impact on the load capacity of the tray in the box compression test and whose influence is negligible or insignificant.

Simplified Modelling of the Edge Crush Resistance of Multi-Layered Corrugated Board: Experimental and Computational Study.

The edge crush test is the most popular laboratory test in the corrugated packaging industry. It measures the edge crush resistance of a sample in the cross-fiber direction (CD), also known as the ECT index. This parameter is widely used for the specification of the board by its producers. It is also utilized in most analytical formulas describing the load capacity of the packaging. On the other hand, the ECT value can be estimated from both analytical and numerical models based on the basic parameters of each constituent paper. Knowing the compressive strength in CD (commonly known as SCT) and the elastic properties of the individual layers, the sample geometry (i.e., the period and height of the corrugated layer), as well as the boundary conditions, the ECT value can be calculated. This is very useful as new boards can be virtually analyzed before being manufactured. In this work, both detailed numerical models based on finite elements (FE) methods and very simple analytical (engineering) models were used for the ECT calculations. All presented models were validated with experimental data. The surprising consistency and high precision of the results obtained with the simplest approach was additionally analyzed in the study.

Effective Stiffness of Thin-Walled Beams with Local Imperfections.

Thin-walled beams are increasingly used in light engineering structures. They are economical, easy to manufacture and to install, and their load capacity-to-weight ratio is very favorable. However, their walls are prone to local buckling, which leads to a reduction of compressive, as well as flexural and torsional, stiffness. Such imperfections can be included in such components in various ways, e.g., by reducing the cross-sectional area. This article presents a method based on the numerical homogenization of a thin-walled beam model that includes geometric imperfections. The homogenization procedure uses a numerical 3D model of a selected piece of a thin-walled beam section, the so-called representative volume element (RVE). Although the model is based on the finite element method (FEM), no formal analysis is performed. The FE model is only used to build the full stiffness matrix of the model with geometric imperfections. The stiffness matrix is then condensed to the outer nodes of the RVE, and the effective stiffness of the cross-section is calculated by using the principle of the elastic equilibrium of the strain energy. It is clear from the conducted analyses that the introduced imperfections cause the decreases in the calculated stiffnesses in comparison to the model without imperfections.

Parametric Study of the Numerical Model of a Bolted Connection of Steel Structure for Photovoltaic Panels.

In the face of the reality that unexpectedly mobilized the governments of most central European countries (including Poland), the development of renewable energy sources (RES) seems to be an important direction. Therefore, both wind parks and solar farms will be constructed at double speed for energetic independence. This urgency makes the market of producers of structures for mounting solar panels also need to adapt quickly to the new situation. New constructions adapted to quick assembly with the use of nutless screw connections seem to be one of the best solutions. These structures must not only be easy and quick to install but also durable, which makes the connections resistant to cyclical loads. The speed of assembly of the substructure can be achieved precisely with the help of nutless connections, but their durability should be carefully analyzed. This article presents parametric analyses of the numerical model of this type of connection. The selection of appropriate numerical models for simulation is of key importance in the fatigue strength analysis of bolted connections. This article investigates two different models used in numerical fatigue analyses performed in the Abaqus FEA and FE-Safe program, namely, traditional bolt with nut and innovative self-tapping nutless bolt. Extended parametric analyses of both numerical models were carried out, which ultimately allowed optimization of the fatigue capacity of the connection.

Influence of Analog and Digital Crease Lines on Mechanical Parameters of Corrugated Board and Packaging.

When producing packaging from corrugated board, material weakening often occurs both during the die-cutting process and during printing. While the analog lamination and/or printing processes that degrade material can be easily replaced with a digital approach, the die-cutting process remains overwhelmingly analog. Recently, new innovative technologies have emerged that have begun to replace or at least supplement old techniques. This paper presents the results of laboratory tests on corrugated board and packaging made using both analog and digital technologies. Cardboard samples with digital and analog creases are subject to various mechanical tests, which allows for an assessment of the impact of creases on the mechanical properties of the cardboard itself, as well as on the behavior of the packaging. It is proven that digital technology is not only more repeatable, but also weakens the structure of corrugated board to a much lesser extent than analog. An updated numerical model of boxes in compression tests is also discussed. The effect of the crushing of the material in the vicinity of the crease lines in the packaging arising during the analog and digital finishing processes is taken into account. The obtained enhanced computer simulation results closely reflect the experimental observations, which prove that the correct numerical analysis of corrugated cardboard packaging should be performed with the model taking into account the crushing.

Parametric Optimization of Thin-Walled 3D Beams with Perforation Based on Homogenization and Soft Computing.

The production of thin-walled beams with various cross-sections is increasingly automated and digitized. This allows producing complicated cross-section shapes with a very high precision. Thus, a new opportunity has appeared to optimize these types of products. The optimized parameters are not only the lengths of the individual sections of the cross section, but also the bending angles and openings along the beam length. The simultaneous maximization of the compressive, bending and shear stiffness as well as the minimization of the production cost or the weight of the element makes the problem a multi-criteria issue. The paper proposes a complete procedure for optimizing various open sections of thin-walled beam with different openings along its length. The procedure is based on the developed algorithms for traditional and soft computing optimization as well as the original numerical homogenization method. Although the work uses the finite element method (FEM), no computational stress analyses are required, i.e., solving the system of equations, except for building a full stiffness matrix of the optimized element. The shell-to-beam homogenization procedure used is based on equivalence strain energy between the full 3D representative volume element (RVE) and its beam representation. The proposed procedure allows for quick optimization of any open sections of thin-walled beams in a few simple steps. The procedure can be easily implemented in any development environment, for instance in MATLAB, as it was done in this paper.

Optimal Design of Double-Walled Corrugated Board Packaging.

Designing corrugated board packaging is a real challenge, especially when the packaging material comes from multiple recycling. Recycling itself is a pro-ecological and absolutely necessary process, but the mechanical properties of materials that are processed many times deteriorate with the number of cycles. Manufacturers are trying to use unprecedented design methods to preserve the load-bearing capacity of packaging, even when the material itself is of deteriorating quality. An additional obstacle in the process of designing the structure of paper packaging is the progressive systematic reduction of the grammage (the so-called lightweight process) of corrugated cardboard. Therefore, this research presents a critical look at the process of optimal selection of corrugated cardboard for packaging structures, depending on the paper used. The study utilizes analytical, simplified formulas to estimate the strength of cardboard itself as well as the strength of packaging, which are then analyzed to determine their sensitivity to changes in cardboard components, such as the types of paper of individual layers. In the performed sensitivity analysis, numerical homogenization was used, and the influence of initial imperfections on the packaging mechanics was determined. The paper presents a simple algorithm for the optimal selection of the composition of corrugated cardboard depending on the material used and the geometry of the packaging, which allows for a more conscious production of corrugated cardboard from materials derived, e.g., from multiple recycling.

Shell-to-Beam Numerical Homogenization of 3D Thin-Walled Perforated Beams.

Determining the geometric characteristics of even complex cross-sections of steel beams is not a major challenge nowadays. The problem arises when openings of various shapes and sizes appear at more or less regular intervals along the length of the beam. Such alternations cause the beam to have different stiffnesses along its length. It has different bending and shear stiffnesses at the opening point and in the full section. In this paper, we present a very convenient and easy-to-implement method of determining the equivalent stiffness of a beam with any cross-section (open or closed) and with any system of holes along its length. The presented method uses the principles of the finite element method (FEM), but does not require any formal analysis, i.e., solving the system of equations. All that is needed is a global stiffness matrix of the representative volumetric element (RVE) of the 3D representation of a beam modeled with shell finite elements. The proposed shell-to-beam homogenization procedure is based on the strain energy equivalence, and allows for precise and quick determination of all equivalent stiffnesses of a beam (flexural and shear). The results of the numerical homogenization procedure were compared with the existing analytical solution and experimental results of various sections. It has been shown that the results obtained are comparable with the reference results.