The aim of this study was to investigate the spall propagation mechanism in ball bearing raceways using physics-based models. Spalling is one of the most common types of bearing failures that can lead to catastrophic failure. This research takes a step forward toward developing a prognostic tool for ball bearings. It is first necessary to understand the spall progression process in order to formulate a constitutive law of spall deterioration and to estimate the amount of remaining useful life. Fragment formation in the vicinity of the spall edge was found to consist of surface and sub-surface cracks that eventually coalesce, and a fragment is released from the raceway, based on naturally-developed spalls. Here, we describe a physics-based model, integrating a dynamic model with a finite element one to simulate this process. A continuum damage mechanics (CDM) approach and fracture mechanics tools were embedded into the finite element model to simulate the damage propagation. The formation of cracks in the vicinity of the spall (surface and sub-surface cracks) were studied using this effective stress CDM model, and the propagation of the cracks was examined using two approaches: a fracture mechanics approach and an accumulated inelastic hysteresis energy CDM approach. The latter also predicts the overall process of a single fragment release. The simulation results of the spall propagation models are supported by experimental results of spalls from both laboratory experimental bearings and an in-service Sikorsky CH-53 helicopter swashplate bearing. The results obtained show that the impact of the ball on the spall edge affects the crack propagation and the appearance of the surface and sub-surface cracks. Both release the residual stresses and cause crack propagation until a fragment is released. Understanding the driving mechanism of spall propagation is a step toward performing physics-based bearing prognostics for condition-based maintenance (CBM). These prognostics intend to enable the prediction of remaining useful life (RUL), and thereby improve safety and reduce costs and the probability of fault development. Spall evolution in raceways can be divided into three stages: (i) spall initiation by a rolling contact fatigue (RCF) mechanism, (ii) steady spall propagation, and (iii) accelerated spall propagation until final failure. As the spall initiation process has been studied both empirically ,2,3 and Understanding spall propagation involves three branches of knowledge: the dynamics of the impact by the rolling elements, the resultant mechanical fields in the race material, and the evolution of damage and cracks. Different damage models enable the different stages of spall propagation to be analyzed. Two damage mechanics models were embedded separately into the finite element (FE) model to simulate initiation and propagation of cracks. An alternative approach to the crack propagation stage was done in the framework of fracture mechanics. It required examination of the stress state at the crack tips in the vicinity of the spall edge. The proposed spall propagation mechanism may have the ability to predict the number of cycles until the fragment disconnects from the raceway and may eventually lead to development of a RUL model. The simulation results were supported and validated by experimental observations of several spalls by scanning electron microscopy (SEM), optical microscopy (OM), and micro-computerized tomography (CT) .This article is organized as follows: The particle release mechanism from the spall edge was analyzed in this work by a model for crack initiation and propagation in front of the spall and beneath its surface, until a particle is released. This section presents different physics-based models and tools that examine the mechanism governing spall propagation. These include: (a) a FE model that simulates the impact between a single rolling element (RE) and the spall edge, (b) the impact location between the RE and the spall edge and the contact force, taken from the dynamic model (used as boundary conditions for the FE model); (c) a damage model embedded into the FE model in order to examine crack initiation and propagation at the spall edge, and activated after the creation of plastic deformation and residual stresses within the spall edge; and (d) fracture mechanics applied to describe the crack propagation.A validated dynamic model  was utilfound in ,17.In order to understand the mechanics governing the fragment release from the spall edge, a FE model was developed based on the model in . The modrding to  and are rding to .Continuum damage mechanics (CDM) refers to various damaging processes in materials and structures at a macroscopic continuum level ,20. The nsor. In , the fatAs can be seen from Equations (1) and (2), the damage affects the stiffness of the material. The damage variable, When damage at some point reaches its critical value, The step-by-step description of the fragment release mechanism within the spall edge is modeled using CDM models. The description of crack initiation is based on an effective stress CDM model, and the crack propagation and overall process of fragment release are based on accumulated inelastic hysteresis energy.The CDM model, based on effective stress ,22,23,24found in ,25. The The proposed model, which simulates a single fragment formation, uses a CDM model that is based on the accumulation of plastic strain. In this model, the material damage initiation and evolution criteria depend on the stabilized accumulated inelastic hysteresis energy per cycle, Δw, ,27,28.The damage initiation criterion assumes a number of cycles, In order to avoid extensive computational time, a low-cycle fatigue analysis is accelerated, and each increment extrapolates the current damaged variable in the bulk material forward over many cycles to a new damaged variable after the current loading cycle is stabilized. The material constants Once the initial cracks started to evolve in the simulation, using CDM models, real cracks were implemented at the same location using tools for fracture mechanics in ABAQUS. Fracture mechanics was used to select the path of the propagating cracks. At each step, the stress distribution, especially at the crack tip, was calculated. The crack propagation direction (CPD) was predicted by examining three different built-in criteria: (a) maximum tangential stress, (b) maximum energy release rate, and (c) Two types of bearings were tested: the Sikorsky CH-53 helicopter swashplate bearing and an6206 ETN9. For the latter, a 0.75 mm bore diameter was initially seeded on the outer race in order to accelerate the bearing deterioration.The experimental setup is illustrated in TM micro-CT.After each experiment, the bearings were inspected by stereomicroscope. They were sectioned, and the bearing surfaces were inspected with a scanning electron microscope (SEM). Selected areas were then sectioned, mounted, polished up to a 0.3 μm level, and inspected with an optical microscope. Some bearings were inspected by RX SolutionSEM images of a spall are illustrated in Based on the experimental observations, the spall propagation process can be described as schematically presented in In order to better understand the mechanics governing crack initiation at the spall edge (surface and sub-surface cracks), two models were developed based on the tools and physics-based models presented in Using an effective stress CDM model, Equation (4) enables the investigation of the initiation of both surface and sub-surface cracks, as presented in he spall a, and tehe spall b. SimilaThe effective stress CDM model was also used to study the propagation of the surface cracks. For these cracks, pall see a, and whIn this section, we study the propagation of the two types of cracks initiated in the previous section. The propagation is controlled by the stresses generated by the impact of the REs. The RE–spall edge interaction has two characteristics: (a) after the first collision of the RE on the spall’s edge, the RE rattles on the raceways several times until it is locked back between the raceways ,33,34, a tension a, but usThe initial damage locations were chosen according to the damage simulation results presented in In CDM Model–Accumulated Inelastic Hysteresis Energy”, respectively. The boundary condition for the simulation is the normal impact force and location obtained from the dynamic model. Then, the simulation is composed of two steps, which are repeated until the damage propagates and forms the contour of a fragment. Step (1) consists of pre-loading, and solves by FEM the contact problem in which the RE is pressed against the spall edge. Then, the normal pressure distribution on the spall edge  and (6) in Section “A comparison between simulation and experimental results is presented in The details of the fragment release from the raceway may vary according to the different directions and locations of the impact, affecting the path of the crack propagation.The simulation results satisfactorily predicted the size and shape of the fragments well. The fragment size and aspect ratio (shape) from the simulation (presented in A dynamic model was used to determine the stresses due to RE impact events. The impact location of the RE on the spall edge has great influence on the crack behavior in terms of their appearance timing and location. Different fragment shapes and sizes results.The residual stresses caused by the RE–spall edge impact are tensile in front of the spall, and underneath it, the stresses are compressive, which prevent crack propagation. The appearance of surface and sub-surface cracks releases the residual stresses and changes areas of compression stresses into tension, causing crack propagation until a fragment is released.Integrating a dynamic model that can simulate different spall sizes in the FE spall propagation model establishes a constitutive law of spall deterioration.Previous work dealt with spall initiation during rolling contact fatigue and stress analysis in the vicinity of defects near the surface ,11,12,37Future work will study the material parameters for the proposed overall spall propagation model. This model will serve as a foundation for developing a physics-based prognostic tool for ball bearings.


As the application of bone scaffolds becomes more and more widespread, the requirements for the high performance of bone scaffolds are also increasing. The stiffness and porosity of porous structures can be adjusted as needed, making them good candidates for repairing damaged bone tissues. However, the development of porous bone structures is limited by traditional manufacturing methods. Today, the development of additive manufacturing technology has made it very convenient to manufacture bionic porous bone structures as needed. In the present paper, the current state-of-the-art optimization techniques for designing the scaffolds and the settings of different optimization methods are introduced. Additionally, various design methods for bone scaffolds are reviewed. Furthermore, the challenges in designing high performance bone scaffolds and the future developments of bone scaffolds are also presented. Bone defects are one of the major challenges in orthopedics, with approximately 2.2 million bone graft procedures performed worldwide each year and the annual cost of these procedures approaching $2.5 billion ,2. TissuTissue engineering is a new discipline that has emerged in recent years with the development of modern biomaterials technology and cellular biotechnology and other emerging technologies to develop biological substitutes for repairing and maintaining or promoting functional and morphological recovery of tissues or organs after injury. Tissue engineering research consists of four main elements: signaling molecules, target cells that respond to the regulation of the signaling molecules, scaffold materials, and recipient beds with good blood supplies . Bone tiBone tissue engineering has benefited from the development of additive manufacturing technologies in the past few years. Scaffold geometric parameters such as porosity, pore size, shape, and interconnectivity can be precisely controlled by additive manufacturing techniques. Tissue scaffold structures can be fabricated to meet functional requirements. The additive manufacturing techniques that can produce tissue scaffolds include selective laser sintering (SLS), selective laser melting (SLM), electron beam melting (EBM), and binder jetting (BJ) .With the increasing maturity of additive manufacturing technology and computer-aided design (CAD) technology, it has become possible to achieve the design and fabrication of complex controllable porous scaffolds. To better mimic the function of natural bone structures, various methods have been proposed for the design of bone tissue scaffolds. However, in the investigations of bone tissue scaffolds, most review articles focus on the design and manufacturing methods of tissue scaffolds, while only a few of them systematically introduce the optimal design methods of tissue scaffolds ,16. The Bone is a three-dimensional non-homogeneous structure with complex characteristics ranging from macroscopic to the nanoscale. A sound design approach is needed that combines structural stiffness with fluid permeability so that the scaffold is both permeable enough to transport nutrients and rigid enough to resist physical loading. Completely solid metals are not compatible because they are impermeable, and the Young’s modulus of solid metals is much higher than the bone modulus of the human body. Because of the mismatch in stiffness, a stress shielding phenomenon will occur, resulting in scaffold failure. Recently, porous structures have been introduced into orthopedic surgery to replace damaged bone tissues. If the structure of porous metals can be digitally designed and fabricated with advanced manufacturing techniques, they can be designed to replicate the properties of bones .It is almost impossible to analyze quantitatively the properties of conventional porous scaffolds because they are composed of a large number of randomly shaped pores. In order to obtain a simplified model, researchers assume that the scaffold is composed of periodically repeating unit cells. CAD, image-based design, and implied surfaces are the conventional design strategies for typical cyclical scaffolds. The CAD-based approach is the most commonly used method in scaffold design, mainly using various CAD tools such as Unigraphics NX (UG),Computer Aided Tri-Dimensional Interface Application (CATIA), and Pro/ENGINEER (Pro/E) ,19. To sCurrently, there are numerous types of topology optimization methods. In the case of the SIMP method, it is a material interpolation model that allows for the existence of intermediate relative densities (between 0 and 1), penalizes the material density, and filters low-density cells to obtain accurate topological results. This method, which is of great power, can design complex structures with multiscale features . A cell The SIMP method was used to design the porous structure using the customized morphology and mechanical properties of trabecular bone to design a three-dimensional structure with gradient porosity similar to the pore structure . In ordeVoronoi tessellation method (VTM) is a way of modeling irregular open-hole structures that can be used to delineate spatial regions .In previous studies, a method that allows for the design of interconnected porous lattices was proposed, which can mimic specific tissue characteristics to achieve bone regeneration scaffolds . The metZ, strut density d, and strut thickness t during the design phase. The relative density, stiffness, and ultimate strength of the structure can also be predicted based on the parameters [A parametric design method for lattice porous structures was proposed based on the design characteristics of Voronoi structures . Deviatirameters . The desThe relationship between porosity or apparent elastic modulus and compressive strength of irregular porous structures cannot be simply generalized, as an increase in one parameter leads to a decrease in the other parameter. A more complex relationship may exist based on the complex irregular porous structure of VTM and needs to be further investigated .Machine learning (ML) has proven to be a valuable method for research in various fields. It is used to discern patterns from complex data sets and is a branch of artificial intelligence. ML algorithms are used in areas such as image and speech recognition, spam detection, and drug discovery . The proMachine learning techniques (MLTs) were combined with parametric finite element analysis (FEA) to further optimize the geometry of the short-stemmed hip scaffold to reduce proximal femoral stress shielding . The minHowever, as the number of parameters increases, the time required for MLT increases exponentially. As a data-driven model, IH-GAN cannot generate the shape and properties of cells outside of a given training data distribution. This may limit the performance of the optimized cell structure .Genetic algorithms are widely used in many structural optimization designs due to their high efficiency . TherefoAlthough the genetic algorithm is a very powerful tool, the need to evaluate the constraint and fitness functions for each generation in the process of scaffold optimization by the genetic algorithm is time-consuming, especially in the calculation of scaffolds with complex structures.A comparison of the advantages and disadvantages of the above-mentioned four methods is shown in The overall layout structure of the scaffold should be consistent with the homologous anatomy. Different material distribution but the same mass or volume of the metallic material will result in different biomechanical properties. Most studies have two main goals for the overall layout structure of the topology optimization design. The scaffold is described as a structural support framework that provides a temporary, artificial extracellular matrix for the growth of new tissue, preferably with properties similar to those of the host bone ,55. TherThe second goal is usually to reduce the weight of the bone scaffold. Solid metal devices may be too heavy to maintain body balance. Many studies have demonstrated that the reduction in mass or volume allows for more scaffold material and more room for tissue to grow inward. Specially tailored structures are more conducive to bone surface adaptation and weight reduction than modular scaffolds ,62. Withn) contained in the scaffold envelope box and the scale factors Sf and Sv are chosen as design variables [n and the beam radius r in the structural parameter lattice cell as design parameters [R, the seed number N and the scaling factor F are chosen as design variables [ρ of the structure, using it to evaluate the number of nodes required makes the design more reasonable. The performance of the irregular porous bracket can be adjusted by the three design parameters  [After the objective function is selected, the desired objective can be easily reached by adjusting different design variables . In a ceariables . By mainrameters . The ranariables . Kechagiariables  chose tharity i) .The geometric parameters of the scaffold are often selected as design variables to optimize its mechanical properties. Machine learning and genetic algorithms used to optimize bone scaffolds usually select geometric dimensions related to the scaffold geometry as design variables ,38,47. TOne of the important features of 3D-printed scaffolds for bone regeneration is the pore size . The porIn the design domain, the pore volume as a percentage of the total volume is the porosity. Having a scaffold with porosity allows cells to migrate smoothly and can improve the surface area for interaction with surrounding tissues. Theoretically, the higher the porosity, the more space is available for cell growth and migration, and the more cells are delivered for tissue repair, the more it can help new bone growth. TPMS structures with 80–95% porosity and moduli in the range of 0.12–1.25 GPa, which converge to the modulus of trabecular bone, were fabricated by the SLM technique. The effects of porosity and pore size on mechanical properties and permeability were investigated by experimental and simulation methods . ResearcDifferent pore shapes have different effects on the mechanical and biological properties of scaffolds. The 3D printed scaffolds with different pore geometries are shown in Although additive manufacturing techniques can theoretically allow for structures of any shape, the quality of the structure is highly dependent on the design parameters .Overhead Structural ConstraintsAdditive manufacturing is a “bottom-up” material layer-by-layer manufacturing method, which makes it possible to process overhanging structures with only powder as support  or no support at all in fused deposition modeling (FDM) ,81,82. PUsing a large number of SLM printing experiments and statistical analyses of variance experimental results, the design rules for optimizing the support structure of the commonly used metal printing materials 316L stainless steel and Ti6Al4V in SLM were summarized . A shapeThe Accuracy ConstraintsParts can be classified as consisting of basic structural features, such as planes, surfaces, columns, spheres, holes, angles, thin walls, gaps, etc. These structural features carry the functional characteristics of the part, and their forming quality becomes the key to determining the performance of the part. Since additive manufacturing technology is not all-powerful, its ability to form structural features is limited by a variety of factors, such as the negative impact of processing equipment accuracy, and process parameter errors on forming accuracy are common in additive manufacturing. Moreover, these factors can cause differences in additive manufacturing molding accuracy due to differences in materials and printing processes. The problem of molding accuracy constraints has been a factor limiting the development of additive manufacturing technology . For exaConnectivity ConstraintsAdditive manufacturing requires the removal of residual uncured resin, unmelted powder, and auxiliary support depending on the process. For structures with internal closed cavities, the residual material cannot be removed, so secondary modifications or partitioning of the structure is often required, which greatly increases the manufacturing process’s difficulty and cost . In ordeThe real bone trabecular structure is a complex and irregular porous structure, which can only be designed using the irregular porous structure design method and needs to achieve a close approximation to the real bone trabecular in terms of morphology, characteristic parameters, mechanical properties, and biological properties to achieve replacement, which is eventually used to treat bone defects, comminuted fractures, and other orthopedic diseases. The bionic structure of porous scaffolds is characterized by SEM and micro-CT . Random Optimization is based on digital models simulating the real situation, which cannot summarize all the information of the sample, and there must be many simplifications and assumptions, such as most of the models do not introduce muscles and ligaments, or they replace them with simplifications, thus affecting the accuracy of the results . The optConsidering multi-material and multi-scale optimization models in bone scaffold optimization, using different optimization methods in performing model optimization, and joint optimization of bone scaffolds based on macroscopic and microscopic scales are essential for the lightweight and mechanical properties of bone scaffolds . With thConsidering the capability of current additive manufacturing technology, the optimized bone scaffold structure may have a local structure that is not suitable for additive manufacturing, the initial structure needs to be modified for manufacturability, and the modified structure may have the problem of destroying the optimized optimal configuration and affecting the optimal design . TherefoIt is worth mentioning that most optimization methods do not consider the degradation of the scaffold, as it usually occurs at a later stage of bone remodeling . What ne(1)Currently, the research and application of digital twin technology are still in their infancy. There are various possibilities for its combined application with additive manufacturing and topology optimization, such as modeling techniques using digital twins and the application of additive manufacturing technology. The integration of these new technologies with different optimization methods will lead to breakthroughs in the field of optimization of the bone scaffold.(2)The manufacturing and clinical application of personalized implants are still in their early stages, owing to the process of developing the medical 3D printing materials required for implant manufacturing. The current bone implants are mostly based on metal materials. More high-performance materials that conform to the elastic modulus of human bones need to be investigated and developed.(3)Optimization techniques based on finite element analysis have been used to simulate the mechanical interaction between bones and implants outside the human body. However, there is a lack of evidence to support in vivo studies. Therefore, biomechanical research work in the human body is needed in the future to make the optimization method more clinically relevant.In conclusion, various numerical methods for designing bone scaffolds are presented in the present study. In the past few years, various methods have been developed to design bone scaffolds with complex internal structures. In the design setup of bone scaffolds, special attention should be paid to the pore shape, the pore size, etc. The current challenge is to design bionic bone scaffolds with better performance and longevity. Optimization of bone scaffolds is a dynamic and promising research area. The future developments in the design of bone scaffolds are as follows:The optimization of the bone scaffold is a dynamic and prospective research area. In the future, many new techniques and methods will be emerged to solve the current challenges. For example, in terms of the method, one of the most prospective design methods might be the machine learning-based method.


Conventional hollow fiber hemodialyzers have a cylindrical shell-and-tube design. Due to their circular cross-section and radial flow distribution and collection in the headers, the flow of blood in the header as well as in the hollow fiber membranes is non-uniform. The creation of high shear stress and high shear rate zones or stagnation zones could result in problems, such as cell lysis and blood clotting. In this paper, a novel cuboid hemodialyzer design is proposed as an alternative to the conventional cylindrical hemodialyzer. The primary motivation behind the proposed design is to create uniform flow conditions and thereby minimize some of the above-mentioned adverse effects. The most salient feature of the proposed design is a cuboid shell within which the hollow fiber membrane bundle is potted. The lumen of the fibers is fed from one side using a flow distributor consisting of embedded primary and secondary channels, while the fibers are drained from the other side using a flow collector, which also has embedded primary and secondary channels. The flow characteristics of the lumen side of the cuboid hemodialyzer were compared with those of a conventional hemodialyzer based on computational fluid dynamics (CFD) simulations. The results of CFD simulations clearly indicated that the flow of liquid within the cuboid dialyzer was significantly more uniform. Consequently, the shear rate and shear stress were also more uniform. By adopting this new design, some of the problems associated with the conventional hemodialyzer design could potentially be addressed. End-stage renal disease (ESRD), which leads to loss of kidney function, affected more than 500,000 people in the US in 2021 ,4,5,6. AHemodialyzers are being used with great clinical outcomes. However, as with anything, there is always room for improvement ,8, and tFlow maldistribution in shell-and-tube configuration hollow fiber modules has been extensively examined ,15,16,17−1) would lead to problems, such as cell lysis, life-threatening hemorrhage or arterial occlusion [Shear rate and the resultant shear stress are key factors in hemodialysis, as they not only affect membrane performance but impact the stability and viability of the blood cells being processed . High shcclusion .In addition to improvements in membrane material, hemodialyzer performance could also be improved by addressing the following factors: design of the hemodialyzer device, proper selection of potting material and proper selection of operating conditions . The pac2 flow distribution and collection system, which has successfully been used in resin and membrane-based chromatography, addresses the problem of flow maldistribution by reformatting the separation media (resin or membrane) into a cuboid shape [In this paper, we propose a radically different design for a hollow fiber membrane based hemodialyzer. This new design is based on the cuboid chromatography devices, which were developed in our research group as alternatives to conventional cylindrical chromatography columns ,43,44,45id shape ,47. The id shape ,43,44,45The above explanation for flow maldistribution in a wide column could be extended to explain flow maldistribution in a conventional cylindrical hemodialyzer, i.e., blood traveling down a fiber located along the axis of a cylindrical hemodialyzer not only travels a shorter distance than blood traveling down a fiber located close to the wall, but it also travels at a significantly higher average velocity than in the latter. Therefore, it is tempting to think that by reformatting the cylindrical hollow fiber membrane bundle to one with a cuboid shape and by employing primary and secondary channels similar to those in the cuboid chromatography devices, better flow uniformity could be achieved in a hemodialyzer. In this paper, we explore this idea based on computational fluid dynamics (CFD), which is a powerful tool that allows preliminary feasibility testing of design ideas and concepts before embarking on the long path of real physical design development. CFD also makes it possible to determine the expected values for flow velocity, pressure, shear rate, shear stress in the different sections of the flow path, based on which physical prototype devices could be designed.In this study, two cuboid hemodialyzers (cuboid 1 and cuboid 2) are compared with a conventional cylindrical hemodialyzer  by CFD simulations. The comparison is made based on the flow velocity, shear rate and shear stress in the flow field and the tracer flow through these devices. The inlet radius for all these devices was 2 mm  . The dimCOMSOL Multiphysics 6.0  was used to carry out the computational fluid dynamic simulations for this study. Two physics packages were used: Laminar Flow for steady-state simulation and Transport of Diluted Species for time-dependent tracer studies. The finite element method (FEM) was applied, physics-controlled mesh was used, and the element sizes were coarse in all the models.(1)Blood is a viscous and incompressible fluid ,48. Bloo(2)The lumen of the membranes is always filled with liquid.(3)There is no clotting in the bloodstream.(4)Fully developed laminar flow is assumed within the lumen .(5)Since this work focuses on fluid flow characteristics in the headers and within the membrane lumen, the transport of species through the membrane wall is not considered. The hollow fiber is considered to be a cylindrical tube with impermeable wall. Blood is transported along the length of the hollow fiber without any change in composition .(6)No slip conditions exist at the wall .(7)Although the neighboring fibers in a real hemodialyzer are randomly spaced due to the nature of the manufacturing process, the fibers in the simulated devices are considered to be equally spaced according to a specific pattern.The following assumptions were made to simplify the model:At each “mesh node” in the CFD models, the mass balance, i.e., the continuity Equation (1), and momentum balance, i.e., the Navier–Stokes Equation (2), were established and solved to determine the nature of fluid flow in the conventional and cuboid hemodialyzer.For fully developed laminar, incompressible and viscous flow with no-slip conditions, the Navier–Stokes equations can be simplified to Equation (3) (time-dependent) and Equation (4) (steady-state):As the density of an incompressible fluid would not change with time, the continuity equation can be simplified to Equation (5) below:The parameters used in the CFD simulations are summarized in In addition to steady-state simulations for velocity, shear rate and shear stress, dynamic tracer tests were performed using the Transport of Diluted Species physics package to compare solute dispersion in the hemodialyzers. Sodium chloride solution (0.8 mol/L) was introduced at the device inlet as a pulse function. The volume of the tracer used in these simulations was 5% of the total internal volume of the flow path.In CFD simulations, there is a trade-off between the precision of the model and the computational cost  ,53. In tFlow velocity, shear rate and shear stress data for the three devices  were obtained through steady-state simulations, while a time variant study was used to simulate the tracer experiments.The results discussed in the preceding paragraphs clearly showed that the flow non-uniformity in the conventional cylindrical hemodialyzer was primarily due to the dependence on radial flow in the header for flow distribution. In particular, the very high radial velocity close to the central region of the header on the inlet side would likely manifest itself in terms of high shear rate and shear stress in this region. 3 sodium chloride in water. The volume of sodium chloride solution injected was 5% of the total internal volume of the flow path, and the flow rate was the same as the operational flow rate used in the previous experiments. CFD allows visualization of the transit of a tracer pulse through a device. Such visualization, which is based on a color coding for concentration of the tracer within the device, is useful, as it provides information, such as the location of dead zones and reasons for flow maldistribution, based on which, a device could be redesigned for better performance. It also allows qualitative comparison of the flow characteristics of different devices. Tracer studies are useful for determining residence time distribution in flow through devices. A pulse of the tracer is introduced along with the flowing feed, and the extent to which the solute in the pulse is dispersed during its transit through the device is determined by measuring its concentration at the outlet as a function of time (or effluent volume), i.e., the sharper the solute peak, the narrower the residence time distribution. The residence time distribution is a useful tool for measuring flow uniformity (or non-uniformity). The tracer flow simulations were carried out using the conventional cylindrical hemodialyzer and cuboid 2, which was the better of the two cuboid devices. The tracer solution used was 800 mol/mThe simulation results discussed in the paper indicate that the cuboid hemodialyzer could potentially solve some of the problems associated with the conventional cylindrical hemodialyzer. The flow in a cuboid device is expected to be more uniform, and the high shear rate and shear stress zones seen in the conventional hemodialyzer could potentially be eliminated. However, the “proof of the pudding is in the eating”, and therefore, any definitive claims could only be made based on real experiments carried out using physical devices. The prototype cuboid hemodialyzer device is currently being fabricated, and we hope to carry out the comparison experiments soon. The cuboid hemodialyzer design proposed in this paper could also be adapted and adopted for designing other types of hollow fiber membrane devices, such as those used for industrial dialysis , hollow The cuboid hemodialyzer design proposed in this paper could potentially solve some of the problems associated with the conventional cylindrical hemodialyzer. Simulation studies showed that there is significant back mixing in the header of the conventional hemodialyzer, particularly close to the inlet. This resulted in regions of high shear rate and high shear stress, which could be detrimental to the blood cells. It was shown based on computational simulations that the overall flow of blood in the cuboid hemodialyzer was significantly more uniform. The flow of blood in and out of the proposed cuboid hemodialyzer is based on complimentary sets of primary and secondary channels. Due to such flow arrangement, jetting of blood from the device inlet into the header was minimized. Consequently, the flow in the fiber bundle of the cuboid hemodialyzer was more uniform, with no observable back mixing. Additionally, the high shear rate and shear stress zones could be avoided. While the simulations do seem to suggest that the proposed cuboid hemodialyzer would be better than the conventional hemodialyzer in several respects, real experiments carried out using physical cuboid hemodialyzers fabricated based on the proposed design would be necessary before firm claims could be made.


After high-intensity exercise, athletes have a greatly increased possibility of pneumonia infection due to the immune function of athletes decreasing. Diseases caused by pulmonary bacterial or viral infections can have serious consequences on the health of athletes in a short period of time, and can even lead to their early retirement. Therefore, early diagnosis is the key to athletes’ early recovery from pneumonia. Existing identification methods rely too much on professional medical knowledge, which leads to inefficient diagnosis due to the shortage of medical staff. To solve this problem, this paper presents an optimized convolutional neural network recognition method based on an attention mechanism after image enhancement. For the collected images of athlete pneumonia, we first use contrast boost to adjust the coefficient distribution. Then, the edge coefficient is extracted and enhanced to highlight the edge information, and enhanced images of the athlete lungs are obtained by using the inverse curvelet transformation. Finally, an optimized convolutional neural network with an attention mechanism is used to identify the athlete lung images. A series of experimental results show that, compared with the typical image recognition methods based on DecisionTree and RandomForest, the proposed method has higher recognition accuracy for lung images. Pneumonia is one of the most common infectious diseases in clinics. Because of its short onset and complex causes, the early identification of pneumonia plays an important role in the diagnosis and treatment of pneumonia. X-ray examination has been widely used in image examination because of its advantages such as low radiation, low cost and high practicability. However, X-ray chest radiography also has some deficiencies , such asIn order to quickly and accurately identify athlete pneumonia, researchers have invested significant energy and put forward many ideas. In summary, the current research works can be divided into three categories: the first is the pneumonia image recognition method based on DecisionTree. Wendy Webber Chapman et al. applied the DecisionTree algorithm to pneumonia image recognition. They used Quinlan’s SEE5.0 DecisionTree Software  to learn DecisionTree from data and use the DecisionTree algorithm to identify pneumonia. The accuracy of this method for pneumonia image recognition is 78% . The secTo solve the problem, this paper presents an optimized convolutional neural networks based on an attention mechanism for lung image recognition after image enhancement. Firstly, for the low frequency coefficient matrix after curvelet transformation, an adaptive contrast boost method is proposed, which makes the coefficient distribution in the matrix more uniform, enhances the contrast of the image, improves the value of the image and is easier to process by the machine. Second, the edge coefficient method is used to enhance the extracted edge coefficient to improve the image contrast and enhance the edge factor. Then, the enhanced image is obtained by inverse curvelet transformation, which is more conducive to image edge recognition. Finally, an optimized convolutional neural network incorporating an attention mechanism is used to identify the images. It was found that the enhanced image has a higher recognition rate and can be effectively used in the field of image recognition of athlete lungs to improve the accuracy of recognition of athlete pneumonia.The rest of this paper is arranged as follows. This section will optimize image enhancement from three perspectives: contrast, edge coefficient and overall enhancement contrast , so as ti and column j. Here, we use contrast boosting to process the low-frequency coefficient matrix. The specific process is shown in Algorithm 1.Algorithm 1: Contrast improvementInput: Coefficient matrix Output: Transformed coefficient matrix  1:Normalize the coefficient values in  2:n original intervals, then count the number of coefficients in interval;Set  3:Calculate the frequency of each interval  4:n intervals are expressed as:Use  5:b,Use Equation  to trans 6:Perform anti-normalization to obtain the transformed coefficient matrix.The contrast of the image reflects the difficulty of image recognition. That means that the greater the contrast, the easier it is to recognize for people and machines. Thereby, increasing the contrast of the image can reduce the difficulty of image recognition. The image contour and contrast mainly come from the low-frequency coefficient matrix after curvelet transformation. Therefore, the low-frequency coefficient matrix needs to be processed accordingly to achieve the image enhancement effect . GeneralExample 1: Comparing the two matrices, it can be seen that the coefficients in It can be concluded from the above that after Algorithm 1, the coefficient matrix achieves the effect of improving image contrast, and finally achieves the goal of easy image recognition.d, and position M represents the maximum coefficient satisfying condition m represents the minimum coefficient satisfying condition In order to recognize the athlete lung images more accurately, this paper uses the edge coefficient extraction and enhancement operation to further enhance the image. Curvelet transformation is a multifaceted transformation, which includes scale, direction and resolution. After the curvelet transform, edge coefficients are enhanced, which can achieve the purpose of enhancing the image. The enhancement equation of the edge coefficient is as follows,Algorithm 2: Edge coefficient extraction and enhancementInput: Edge coefficient extraction and enhancement;Output: Enhanced image after inverse transformation; 1:Based on the mapping characteristics of curvelet coefficients, the mapping coefficient matrices  2:Calculate the sum of the absolute values of the coefficients within the matrix; 3:n original intervals; then, count the number of coefficients in the interval;Set  4:Set a threshold value  5:Perform inverse curvelet transform on The specific steps of edge coefficient extraction and enhancement are shown in Algorithm 2.Through Algorithm 2, the athlete pneumonia image is further enhanced.Convolutional neural networks can distinguish medical images and the video data. Using the optimized convolution neural network with an attention mechanism, the enhanced image is recognized. According to the different importance of features, different weights are given to features on different channels to highlight important features and suppress secondary features , so as tThe hierarchy of a convolutional neural network includes the convolutional layer, excitation layer, pooling layer and full connection layer, which are shown in In the convolution layer, data exists in 3D. For example, if a region in a gray image is in the input layer, one feature will be obtained by computing. Similarly, a region in a color image will have three features. The features of the previous layer are convoluted with the corresponding convolution kernel, which outputs new features. The convolutional layer equation is as follows,Convolutional kernels are also known as filters; each convolutional kernel has three dimensions: length, width and depth. In each convolutional layer, the length and width of the convolution kernels are specified artificially. Because the depth of the convolutional kernel is the same as the current image (the number of feather maps), it is not necessary to specify. This paper decides to use In order to improve the expression ability of linear models, an activation function is added after the convolution layer when the convolutional neural network is built. The function of LeakyReLU (Leaky Rectified Linear Unit) has the advantages of no gradient dissipation, fast convergence, increasing network sparsity and less computation. Therefore, the LeakyReLU function is selected as the activation function in this paper. The analytic equation of the LeakyReLU function is as follows,The purpose of the pooling layer is to reduce the characteristic graph and improve the robustness of the model. Among many pooling operations, maximum pooling is the most widely used and has the best effect. The maximum pooling is as follows,Thus, in this paper, maximum pooling is adopted as a pooling operation in the convolutional neural network. Here, the weight of each cell used is There are some inherent problems with the recognition process in the traditional convolutional neural network that will reduce the recognition accuracy of the convolutional neural network, such as high learning rate, overfitting and large oscillation at the optimal point. Therefore, it is necessary to optimize the convolutional neural network.The exponential decay learning rate strategy, dropout method, and Adam algorithm can all optimize the convolutional neural network model to improve its generalization ability and prevent overfitting.Generally, the method of gradient descent is used to adjust the learning rate of the model to ensure that the machine learning model finds the optimal solution  in the ldecayed_learning is the exponential decay learning rate, learning_rate is the initial learning rate, decay_rate is the decay coefficient, global_step is the round iteration number, decay_steps is the control decay rate.In this paper, the exponential decay learning rate strategy is used to update the model learning rate. When the learning rate is large, the network parameters update quickly and the local convergence is fast at the initial stage of model training. As the number of iterations increases, the model will reverberate to the global optimal point. At this time, a smaller learning rate can make the model converge. Learning rate is a super parameter that guides us as to how to adjust the weight of the network through the gradient of the loss function. By setting the learning rate, the speed of parameter updating is controlled. The equation is as follows,In the process of machine learning, if the model parameters are too many and the number of samples used for training is too small, overfitting of the trained model will occur. Adding dropout to network training can effectively mitigate the occurrence of overfitting .Dropout is a regularization method. In training, the hidden layer of neurons are suppressed with probability P and part of the hidden layer neurons are discarded, while the parameter values of the discarded nodes are retained. Only the parameter values of the activated neurons are updated during error backpropagation. The process will be repeated in the next training and each training will obtain a different neural network, which will finally be integrated.Dropout can learn the corresponding features in different subsets of hidden layers to reduce the dependence between features and prevent overfitting. The standard neural network and the neural network diagram with dropout applied are shown in In machine learning, the Adam algorithm is a method to optimize the loss function with a one-step degree . The algt is timestep after initialization, t, where In order to make the optimized convolutional neural network ignore the irrelevant information and pay more attention to the key information, this paper adds an attention mechanism module to the optimized convolutional neural network. It is an attentional module called Convolutional Block Attention Module (CBAM) that combines spatial and channel dimensions.CBAM is an end-to-end, simple and effective computer visual attention module. In a convolutional neural network, CBAM can input any intermediate feature map along two independent dimensions: spatial and channel . Then, tMLP is a multi-layer perceptron and AvgPool is the averaging pooling operation, MaxPool is the maximum pooling operation and F is the feature map of the input.The calculation method of the channel attention model in CBAM is shown in Equation ,(11)McMsF′=After several experiments, this paper adds a CBAM attention mechanism module after each excitation layer of the optimized convolutional neural network. The specific adding method is shown in Due to the limitation of medical image imaging conditions, the contrast of the image is low. Details are often high-frequency signals, but they are often embedded in a large number of low-frequency background signals, which reduces the visibility of the image . TherefoImage edge is one of the most basic characteristics of an image, which often carries most of the information. The edge exists on the irregular and unstable structure of the image, that is, at the mutation point of the signal. These points give the position of the image contour, which often contains important features required for image edge detection. Therefore, it is necessary to extract and enhance the edge coefficient of the image to further improve the accuracy of image recognition.For enhanced athlete lung images, this paper adopts an optimized convolutional neural network based on an attention mechanism to recognize the image.The optimized convolutional neural network based on image enhancement and an attention mechanism (CIEA) recognizes the athlete pneumonia image in three steps: image acquisition, image enhancement and image recognition. First, the images of the athlete lungs are collected. Then, contrast enhancement and edge coefficient enhancement are performed on the collected images of athlete lungs to improve the image recognition accuracy. Finally, the optimized convolutional neural network based on an attention mechanism can recognize the optimized lung images of athletes, which improves the efficiency of diagnosis and treatment to help athletes to resume training as soon as possible. The image enhancement parts uses the method of contrast enhancement and edge enhancement of the second part of this paper. In the image recognition part, the optimized convolutional neural network based on an attention mechanism in Part 3 of this paper is adopted.Algorithm 3: CIEA method for identifying athlete pneumoniaInput: Preprocessed gray images;Output: P; 1:Input the preprocessed gray images; 2:Calculate the sum of the absolute values of the coefficients within the matrices; 3:Carry out curvelet forward transformation on the images to obtain the transformed coefficient matrices  4: 5:Based on the mapping characteristics of curvelet coefficients, the mapping coefficient matrices  6:The edge coefficients are judged according to Algorithm 2; then, the enhanced edge coefficient matrices are calculated according to Equation . An attention mechanism module is added in each down sampling layer.Adam is used as the optimizer, the batch size is set to 16, the number of training cycles epochs is set to 300 and the initial learning rate is set to In order to test the effectiveness of image enhancement methods, this paper uses the methods of contrast enhancement and edge coefficient enhancement to enhance the athlete lung medical images. Five medical images were taken as examples  and image enhancement was performed on these five images. The original images, the images with enhanced contrast, the images with enhanced edge information, and the images with integrated enhancement are shown in The comparison results of the optimized convolutional neural network recognition algorithm based on an attention mechanism before and after image enhancement are shown in As can be seen from The optimized convolutional neural network with an attention mechanism is used trained on the datasets before and after enhancement; the results are shown in In In In order to compare the method proposed in this paper with the traditional DecisionTree pneumonia recognition algorithm in machine learning and the RandomForest pneumonia recognition algorithm, we conducted the following comparative experiments.Wendy Webber Chapman et al. applied DecisionTree algorithm to pneumonia image recognition . SpecifiAkgundogdu Abdurrahim proposed a RandomForest algorithm based on chest X-ray images to classify the diagnosis of pediatric pneumonia . The algPranav Rajpurkar et al proposed a chest X-ray pneumonia recognition algorithm (ChexNet), which is a 121-layer convolutional neural network that inputs a chest X-ray image and outputs the probability of pneumonia along with a heatmap localizing the areas of the image most indicative of pneumonia .Based on the athlete lung images, the comparison results using the DecisionTree, Random- Forest, ChexNet and CIEA recognition algorithms are shown in From In this paper, an optimized convolutional neural network recognition method based on image enhancement and an attention mechanism is proposed to recognize athlete pneumonia. First, we collected medical images of athlete lungs. Then, image enhancement methods, such as enhancing contrast and enhancing edge coefficients, were used to enhance the lung image of athletes. Finally, this paper used the optimized convolutional neural network recognition method based on an attention mechanism to recognize images; the results show that the accuracy of the method proposed in this paper was improved by 11.96% on the test set, indicating that this method can help to improve the generalization ability of the model and make the model more accurate. At the same time, the recognition rate of athlete pneumonia by the optimized convolutional neural network based on an attention mechanism is as high as 97.31%.


The paper industry is closely related to forestry resources, which constitute an essential part of achieving sustainable development. Green credit can provide financial support to assist the paper industry in achieving carbon neutrality. To develop a method for performing green credit risk assessments in the paper industry, first, an initial index system was established on the basis of two dimensions: financial risk and socio-environmental risk. Then, the KMV model was applied to measure credit risk. The combined results of this model, along with the environmental penalties of an enterprise, formed the basis for the classification of green credit risk. Third, the Gini index was used to filter out, one by one, the indexes with the least influence among the factors, and then random forest iterations were performed until the prediction accuracy reached the optimum, thus establishing a green credit risk prediction model for the paper industry. The results show that the accuracy of the sample classification reached 93.75%, and the accuracy of the sample classification for high-risk enterprises reached 100%. The established index system offers good guidance for the assessment of green credit risk in the paper industry, in which the interest coverage ratio, current ratio, asset-liability ratio, and green emissions are the main factors affecting green credit risk. Nowadays, much more attention is paid to environmental issues in the pursuit of economic growth ,2. To spThe management of credit risk in banks involves two main aspects: on the one hand, the systemic risk faced by the bank in the course of its own operation, and on the other hand, the credit risk generated by the bank in the course of its operation as a credit business. There are many different methods for measuring systemic risk. Marginal expected shortfall (MES) is often used as an index for measuring systemic risk, and this index has been used to establish a model for risk prediction ,4. The SGreen finance integrates environmental protection and economic interests . In ChinAccording to previous studies, scholars have conducted deep research on credit risk assessments, using artificial intelligence, big data, and other methods to perfect them. Later, the credit risk assessment method was applied to the field of green credit, where green factors have not been really considered. The green credit research fields are mostly in low-polluting and low-energy-consuming sectors, such as the new-energy industry, and there is no research on high-polluting and high-energy-consuming sectors, such as the paper industry. Therefore, the characteristics and contributions of this paper are: Firstly, the index system not only takes the green factors into account, but also has paper industry specificity. Considering the paper industry’s financial and socio-environmental responsibility, a set of green credit risk evaluation index systems are established. Secondly, compared to other models, the random forest model has a higher accuracy in data mining. This paper combines the random forest with the KMV model, which is widely used in credit risk assessments, to establish the assessment model.This study was divided into four steps see . The firA reasonable evaluation index system is the basis of the green credit risk assessment, whereas a practical and professional evaluation index system can improve the accuracy and validity of the evaluation results. The green credit implementation regulations of major Chinese commercial banks and the Green Credit Guidelines issued by the China Banking Regulatory Commission (CBRC) in 2012 indicate that the green credit risk assessment index system should not only involve the financial status of enterprises, but also take social and environmental risks into account. Moreover, profitability is related to environmental performance , and theThis paper selected solvency, profitability, operating capacity, and growth ability as the primary indexes to measure the financial credit risk of listed enterprises ,37. EachHexun.com. The Hexun Social Responsibility Score for listed companies is the score that Hexun calculates by systematically evaluating corporate social responsibility undertakings through a system of relevant indicators, with scores published on Hexun.com. There is a strong correlation between enterprise environmental disclosure and environmental pollution [We measured the socio-environmental index from two perspectives: social responsibility and environmental performance. Enterprise social responsibility was measured by the social responsibility score published by ollution . Therefoollution , which iThe granting of green credit also needs to be based on the evaluation of the environmental protection situation of polluting industries, such as resource consumption, pollution emissions, and environmental disclosure, in their daily production and business activities. The better the environmental credentials of the enterprise, the higher the degree of pollution treatment. Therefore, this paper used the major pollution emissions of the industry as a proxy for environmental performance . The maiAccording to the above process, the final green credit risk assessment index system was obtained under two dimensions of the financial and social environment see , totalinThis paper comprehensively considered credit risk and environmental risk to measure whether paper-making enterprises had a high potential for green credit risk.In terms of credit risk, the KMV model was used to calculate the credit risk of enterprises in different years. We must select a standard as the main basis for classifying enterprise credit risk. That is, the paper-making enterprise did not have a high credit risk and was deemed qualified if the default distance (DD) was not lower than a certain number, whereas the paper-making enterprise had a high credit risk and was deemed unqualified if the DD was lower than a certain number. The focus of green credit origination also includes environmental risks. This paper decided whether there was an environmental pollution incident as the basis for “green” judgment. Reviewing the environmental penalty information of each paper-making enterprise from 2017 to 2021, if there were major environmental pollution incidents or fines, that means that the company lacks environmental protection and should be set as unqualified. If there were no major environmental pollution incidents or fines, that means that the company works well with regard to environmental protection and should be set as qualified. We used the combined results of the DD and environmental penalties to classify green credit risk for paper-making enterprises. The output value is 0 or 1. That is, the random forest output value is 1 if one of the paper-making company’s credit risk assessment and environmental risk assessment fails, and the random forest output value is 0 if the paper-making company passes both.The KMV model has wide applicability and is often used in credit risk assessment. The model evaluates the credit risk of listed companies by calculating the expected default frequency (EDF) from the asset volatility and asset value. The discriminatory accuracy of EDF in China is inferior to that of DD ; therefoThe first step is to figure out the asset value and the annual volatility of asset values. The key to the KMV model is to figure out each enterprise’s asset value and annual volatility of asset value through the enterprise equity value and annual volatility of equity value. The simultaneous equations are as Equation (1) shows:, D is the enterprise book value, T is the repayment term, all of which can be acquired from publicly available market data. The equity value volatility in Equation (1) is calculated using the historical volatility method, and the formula is as follows:The daily standard deviation of the stock is The second step is to figure out the default point (DP). By studying historical default data, KMV found that the default condition is only partially valid when the enterprise asset value is lower than the debt value due to long-term debt (LTD). Enterprises choose to default when the value of assets is less than half of the value of short-term debt (STD) plus the value of long-term debt. The formula is as follows:The third step is to figure out the value of the DD. The value of the DD represents the distance of the enterprise market asset value from the DP. Enterprises are less likely to default if the value of the DD is long, and enterprises are more likely to default if the value of the DD is short. Apply In this paper, we used the random forest model for green credit risk prediction in the paper industry. The initial evaluation index value was used as the input value of the random forest, and the conclusion of green credit risk classification was used as the output value of the random forest.Random forest is a classification model that combines random sampling and decision trees. The indexes of all samples are entered into the random forest. After that, the sample size and indexes are randomly selected by the bootstrap sampling method to construct the decision tree models. Each decision tree model obtains a different classification result, and thus, the decision tree classifier produces a judgment with the principle of the minority obeying the majority to improve the prediction accuracy. The principle of the random forest algorithm is shown in As a machine learning algorithm, the prediction accuracy of random forest can be further improved by iterative computation on the underlying model. The Gini index applied to the random forest model can discern the importance of the input indexes . The indEquation (6) shows the importance of the index Suppose Suppose there are The normalized processing of We selected 26 A-share listed paper-making enterprises based on the research period between 2017 and 2021 for the study. The total number of A-share listed paper-making enterprises in China is 40. There was no mandatory requirement for enterprises to publish pollution emission data until 2022, and therefore, the published data were not comprehensive. This paper screened out the paper-making enterprises that were missing serious environmental information disclosures, and the remaining enterprises numbered 26. This paper selected 2017–2021 as the measurement interval because of the incomplete disclosure of corporate environment-related data before 2017. December 31 of each of the five years was used as the base date for the measurements. If there were paper-making companies listed after 2017, the year after listing was taken as the empirical interval.The paper-making industry is a highly polluting industry, and its main pollutant emissions contain chemical oxygen demand (VC) and ammonia nitrogen (VN) in wastewater, and sulfur dioxide (VS) and nitrogen oxides (VO) in exhaust gases. As a result, we took the pollutants mentioned above as the influencing factors of green emissions. The annual reports and CSRs of each company from 2017 to 2021 were reviewed to obtain the emissions of chemical oxygen demand (VC), ammonia nitrogen (VN), sulfur dioxide (VS), and nitrogen oxides (VO). Then, we screened out the years with incomplete environmental information disclosures of 26 paper companies. Finally, we obtained 104 samples for the study. All financial data of listed enterprises came from the CSMAR, and pollution emission data came from corporate annual reports or CSRs.The green emission score of each enterprise was calculated with the help of MATLAB see . On the (1)Parameter setting for the risk-free rate  to make up for the gap in China’s official risk-free rate data. If an interest rate adjustment was encountered during the year, the calculation formula would be (2)Parameter setting for the repayment term Parameter setting for the equity value , and 32 samples into the test set (n_test).Secondly, we determined the sampling times (n_tree). The accuracy of the random forest improves to be stable with the increase in sampling times. Therefore, the sampling times were set to 3000 in this paper (n_tree = 3000).Finally, the number of indexes (m_features) needed to be adjusted, which is one of the most important parameters of the random forest. As the number of indexes increases, the accuracy of the random forest will also improve. However, if the number of indexes continues to rise, the correlation between decision trees will also increase. In other words, the accuracy of the random forest model will decrease as the number of indexes increases. Generally, the random forest complexity is moderate when We used Python to construct the initial random forest algorithm based on the parameters set above. To figure out the optimal parameters given by printing the gradient optimization, we input 0.2, 0.3, and 0.4 into the random forest, which was carried out to find the initial value of m_features and its proximal minima. It can be seen that when m_features=0.4, the random forest model error rate of the test set was the smallest (12.5%), and the model accuracy was the highest see .The importance of the 19 indexes in the random forest was measured by the Gini index see .X18 had the least influence on the model and was removed according to the importance ranking, and then, the remaining 18 indexes were used to train the random forest again until the misclassification rate was minimized. After the above steps, we can find that the error rate of the model was the lowest when the number of indexes decreased to 11, and at this point, m_features = 0.2 see .In the end, the minimum misclassification rate of the random forest was 6.25%, which meant that the prediction accuracy reached 93.75%. The model covered 11 indexes see , which aWe set the socio-environmental indexes from the perspective of the degree of corporate social responsibility , environmental awareness (green culture), and actual environmental protection actions (green emissions). After the random forest iteration, green emissions was the only one left, which meant that enterprises’ actual environmental protection actions played a more important role in the classification of green credit risk.This paper had assumed that a DD less than 1 or enterprises subjected to environmental penalties had potential green credit risks. This assumption was adjusted to test the model’s robustness further. That is, a DD less than 0.5 or the enterprises subjected to environmental penalties had potential credit risks. Firstly, the variable parameter involved in the above assumption was set as i. Secondly, the green credit risk classification result obtained as i = 0.5 was substituted into the random forest model. Finally, the above model construction and iteration process was repeated. The results show that when the misclassification rate of the random forest drops to a low level, the final indexes of the model include the interest coverage ratio, current ratio, asset-liability ratio, green emissions, inventory turnover, current assets turnover, revenue growth ratio, quick ratio, net profit growth ratio, total assets turnover, EPS growth ratio, and other indicators, but the order of importance was slightly adjusted. It can be concluded that the above indicators were exactly the main factors which affected the green credit risk see , and the(1)The DD calculated by the KMV model showed the credit difference between paper enterprises, which can distinguish the credit risk status faced by other paper enterprises. Even the DD of the same paper enterprise in different years could fluctuate sharply; thus, enterprises should strengthen the stability of their risk management.(2)The random forest model had a high prediction accuracy for the green credit risk assessment of the paper industry, as shown in (3)Commercial banks will decide whether to extend green credit based on the forecast results. Generally speaking, commercial banks will suffer a greater loss when they extend credit to enterprises with a high credit risk and normal prediction results, compared with enterprises with a normal credit risk and high prediction results. It can be seen from (4)(5)Based on the Gini index, the interest coverage ratio (X04), current ratio (X02), asset-liability ratio (X01), and green emissions (X19) had been ranked relatively high in terms of their impact on the green credit risk of the paper industry. They can be considered as the main factors affecting the green credit risk of the paper industry.This paper extended the application of the random forest model to the field of green credit research. The empirical analysis used 104 samples from 26 paper-making enterprises and established a green credit risk assessment model for the paper industry based on the random forest. The conclusions are as follows: Environment and finance, two main parts of the green credit risk evaluation index system, had a significant impact on assessing the credit risk of the enterprise. On one hand, it was reflected that the green credit risk index system of the paper industry established in this paper had a good reference for green credit risk assessment. Among them, the interest coverage ratio, current ratio, asset-liability ratio, and green emissions had a greater impact on green credit risk in the paper industry. Therefore, commercial banks need to focus on solvency and environmental performance when assessing the green credit risk in the paper industry. On the other hand, the random forest had an excellent performance in green credit risk assessment. The accuracy of sample classification for high-risk enterprises reached 100%. This means that the random forest had an excellent evaluation effect and a high practical value in green credit risk assessment, and can effectively reduce the influence of subjective factors.The innovation point of this paper mainly involved two aspects. Firstly, the green credit risk index system of the paper industry was constructed with strong industry pertinence, considering both financial and socio-environmental aspects. In particular, the secondary index of green emissions was designed to identify pollution discharge in the paper industry. Secondly, the research method combined the random forest and KMV model. We used the Gini index to continuously select indexes and conducted random forest iterations to establish the model with the best prediction effect. The green credit risk prediction model of the paper industry established in this paper had a high accuracy, which provided some reference for domestic and foreign commercial banks to issue green credit. The development of green credit is an irreversible trend, and thus, we should promote the implementation of green credit to achieve the goal of carbon neutrality as early as possible.Due to the limited number of Chinese paper enterprises and the polluting emission data of each enterprise not being fully disclosed, the advantages of machine learning with large random forest samples was not the best due to the limitation of sample size. In the future, the model can be adjusted to improve the prediction accuracy by continuously expanding the sample size. Moreover, the green index system in China has not been standardized. If China publishes a complete set of green index systems in the future, the selection of socio-environmental indexes in this paper can be further strengthened.


This work presents an in-depth numerical investigation into a hypothesized two-layer central pattern generator (CPG) that controls mammalian walking and how different parameter choices might affect the stepping of a simulated neuromechanical model. Particular attention is paid to the functional role of features that have not received a great deal of attention in previous work: the weak cross-excitatory connectivity within the rhythm generator and the synapse strength between the two layers. Sensitivity evaluations of deafferented CPG models and the combined neuromechanical model are performed. Locomotion frequency is increased in two different ways for both models to investigate whether the model’s stability can be predicted by trends in the CPG’s phase response curves (PRCs). Our results show that the weak cross-excitatory connection can make the CPG more sensitive to perturbations and that increasing the synaptic strength between the two layers results in a trade-off between forced phase locking and the amount of phase delay that can exist between the two layers. Additionally, although the models exhibit these differences in behavior when disconnected from the biomechanical model, these differences seem to disappear with the full neuromechanical model and result in similar behavior despite a variety of parameter combinations. This indicates that the neural variables do not have to be fixed precisely for stable walking; the biomechanical entrainment and sensory feedback may cancel out the strengths of excitatory connectivity in the neural circuit and play a critical role in shaping locomotor behavior. Our results support the importance of including biomechanical models in the development of computational neuroscience models that control mammalian locomotion. Mammals can swiftly react to terrain changes during locomotion by dynamically adapting their limb movements. Although the strategies and neural systems that legged animals use to produce stepping motions are still not fully understood, many experiments suggest that the spinal cord and associated peripheral nervous system contribute to the generation and adaptation of gaits ,2,3. It Many earlier models of rhythm-generating spinal circuitry assumed a half-center organization for the network, in which two neuronal groups mutually inhibit each other ,8,9. TheTo enable separate control of CPG timing and MN patterning, Rybak and colleagues introduced a two-layer CPG model . It is cThe two-layer CPG model has continued to evolve and has been further refined to capture a range of experimental observations through the inclusion of additional structural elements and modeling parameters. For example, recent modeling work has included weak mutual excitation between oscillators in the rhythm generator level of the classic half-center CPG model ,22. ThisIn the present study, we investigate how variations in these connection strengths affect the overall CPG network function. We use a perturbation analysis, evaluating how the phase changes in response to perturbations under different modeling conditions applied at different times in the gait cycle. We employ a similar approach to the phase response analyses used previously to characterize oscillators’ performance in experimental ,28 and mWe examine several aspects of the performance of this two-layer CPG. We first examine the influence of the hypothesized cross-excitatory connection on the rhythm-generating behavior. Specifically, we analyze how changes in this connection affect the locomotor frequency and phase adjustments in response to perturbations. After that, we vary the synapse strength between the two layers and evaluate the rhythm generator’s ability to phase lock with the pattern formation network at different intrinsic frequencies. The two-layer CPG is then connected to motoneuron pools and used to actuate a simulated biomechanical rat hindlimb, which provides the CPG with sensory feedback. The movement speed is increased through two methods: (1) adding an external drive to stimulate the rhythm generator, as from a direct connection between the midbrain locomotor region (MLR) and the rhythm generator; and (2) increasing the conductance of the mutually excitatory connections between the rhythm generator oscillators, as if neuromodulation were used to increase the synaptic strength. Our results show that, despite trends in differences between the two models during deafferented and air walking, no discernible difference in locomotor behavior is found during ground walking experiments.The development of the rat hindlimb model was completed in Animatlab , a simulTo inspect how the simulated models’ reactions to perturbation are influenced by different two-layer CPG designs, the hip joint control network from the previous synthetic nervous system (SNS) was isolated, as shown in V is the membrane potential, mC is the membrane capacitance, t is the time variable, rE is the resting potential of the neuron, and mG is the leak conductance. appI is an externally applied current. sE is the reversal potential of the thi synapse, loE and hiE are the lower and the upper thresholds of the synapse, respectively. preV is the presynaptic neuron voltage. z represents either All neurons in the SNS are non-spiking neurons, where each neuron represents the mean activity of a population of spiking neurons ,37. EachloE is the synaptic threshold it must cross to begin inhibiting the other half. When Szczecinski et al. used a bifurcation parameter, ter CPGs . The bif’s study  explaineThe present study expands the analysis from Szczecinski’s work with two additional variables as shown in The equilibrium potential loE is set to equal the resting potential of the neuron, rE. Hence, the bifurcation parameter rE subtracted from it:When modeling the CPG circuit, usually the synaptic threshold All analysis of the two-layer CPG in this work is performed through MATLAB .Hz. The 1 Hz frequency is close to a slow stride frequency of a rat, making comparisons to in vivo data easier. The intrinsic frequency of the pattern formation layer was varied between 0.5 Hz and 2.3 Hz by adjusting the mutual inhibition strength. Different connection strengths were then tested for phase locking and phase shift between the two layers.First, the experiment in Szczecinski et al.’s study was replicated, with nA or 0.5 nA with a duration of 5 percent of the oscillation period, which is consistent with the stimulus in Szczecinski et al.’s study; keeping the same duration here allowed us to compare our results to those described in that previous study. After that, for a two-layer CPG, external stimuli were applied to different layers of the CPG, and the corresponding PRCs were analyzed and compared.Phase response analysis was performed on the deafferented two-layer CPG neural model and used to predict the behavior of the mechanical model when integrated, i.e., the neural model generates muscle contractions and receives sensory feedback from the resulting motion. In the deafferented neural model, the rhythm generator’s response to changes in the external drive and the synaptic conductance between the rhythm generators was studied. Then, phase response curves (PRCs) of two rhythm generators, one driven entirely by the external drive and one driven entirely by mutual excitation, were numerically calculated by applying a square pulse stimulus to the RG flexor interneuron. The advancement or delay of the cycle was measured and normalized to the entire cycle. The perturbation current was either −0.5 Hz through (1) adding an external drive to stimulate the rhythm generator; and (2) increasing the conductance of the mutual excitatory connections between the rhythm generator oscillators. PRCs and the phase shift between the two layers were calculated and compared. The faster frequency (2 Hz) was chosen to compare how a baseline CPG responds to two different types of stimulation, as though the animal is modulating its speed. In addition, 2 Hz is closer to the locomotion frequency of rats observed in previous X-ray treadmill experiments performed by our collaborators [Frequencies of the two-layer CPGs were then increased to 2 borators . A similborators .Finally, each configuration of the network model was incorporated with the biomechanical model. The response of each model to perturbations was tested, and the implications with respect to future and past modeling work are discussed.In Szczecinski’s study , the halHz can be obtained by a rhythm generator with no mutual excitation  and no external drive. However, the shape of each neural burst underlying these oscillations with similar frequencies is substantially different. As seen in In the present study, we expanded Szczecinski’s results by exploring two additional variables: (1) the weak excitatory conductance Hz  to the same intrinsic frequencies as the rhythm generators.In the previous section, it was shown that the synaptic conductances , the system is less likely to phase lock, and therefore, the range of phase differences is also reduced.When an excitatory synapse Gc in  connectse system B. For excG = 0.1 uS) and an inhibitory perturbation current sI is applied at the RG or the PF layer, the phase shift difference between the layers is effectively zero  also becomes smaller as the connections strengthen. One could surmise that increasing the magnitude of the perturbation in relation to cG could produce similar phase responses as reducing the coupling strength cG. To examine this, the PRCs of the same ratio sI/cG were also calculated for different cG  have been reported to be responsible for changing gait and posture while an animal is in motion . Our anarbations A. The madulation B. This dIn previous sections, the experiments were performed by simulating a deafferented two-layer CPG without a simulated mechanical model or sensory feedback. However, feedback plays an important role throughout locomotion, and it is unclear if the inclusion of feedback would give different results in response to perturbations. Therefore, a single joint (hip) model actuated by pairs of antagonistic muscles A was creHz. The torque perturbation is applied at 0.5 s and ends at 1 s. When the external torque is small  and the weak excitatory strength between oscillators influence the oscillation frequency. Increasing the excitatory strength proportionally alters the bifurcation parameter, δ, similar to previous work that demonstrated increases in δ due to increases in direct stimulus . HoweverThe connection strength between the two layers determines whether the two layers will lock phases and if so, the phase delay between the layers. A high connection strength forces the pattern formation network to replicate all phase shifts and phase resetting that occur in the rhythm generator. This replicates the type of connection that has been observed at the hip joint, where the joint position is closely related to the swing-stance transition ,34,35. HIncreasing the frequency of the two-layer CPG generally decreases the system’s sensitivity to external inputs. This holds true for both the deafferented neural circuit, as well as for the neuromechanical model performing air walking. When connecting the CPG with a physical body and type II feedback, trends in the PRCs analyzed in the deafferented model are directly reflected in the behavior of the neuromechanical model. The simulated hip joint driven by the direct stimulus is less disturbed during a small torque perturbation and recovers faster when a step cycle is totally deleted during air walking.In contrast, when either model is implemented in a neuromechanical model of two hindlimbs walking on the ground, most of these differences disappear. Both neural models exhibit powerful stability against the disturbance and there is no functional difference in step timing for these two mechanisms. These results suggest that the precise behavior of the deafferented neural circuit may be of little importance to how the whole system performs in the real world. This finding is consistent with observations based on sea slug feeding behaviors , where tMoreover, biomechanics plays a significant role in stabilization. A study from Matrangola et al.  suggestsWhat causes the air-walking and ground-walking models to behave differently? There are two changes made from air walking to ground walking: the ground contact and Ib feedback from the ankle extensor, which is the load sensory feedback. We tried to build a ground walking model without Ib afferent. However, as the inclusion of Ib feedback makes ground walking more stable, we still do not know the answer. More attention should be paid to investigating the influence of load feedback in the future. Would the system become more sensitive to perturbations if the feedback strengths were reduced? Or is it the shape of the load feedback or the ground contact timing that stabilizes the phase transition from swing to stance? Further experiments exploring a range of perturbations to investigate time-torque relationships and the strength of sensory feedback might help resolve some of these issues.There is another limitation in this study that may be important. We only implemented II and Ib feedback into the CPG. As joint motion profiles are used to tune the neural parameters, presumably, the strong velocity sensitivity afferent would be similar for air-walking and ground-walking models. However, the Ia feedback might also strongly affect CPG phase relations. Hence, the air-walking and ground-walking models might be expected to perform differently. Therefore, further inspection of how Ia feedback influences CPG phase relations is also necessary for future studies.The results of this study suggest that the strengths of excitatory connectivity do not have to be fixed precisely for stable walking. This suggests focusing on more detailed biomechanical models to investigate whether additional muscles or muscle groups provide benefits to the stability of the model as suggested by some previous work with biarticular muscles . Biartic