A simple approach to the multiscale analysis of a plain weave reinforced composite made of basalt fabrics bonded to a high performance epoxy resin L285 Havel is presented. This requires a thorough experimental program to be performed at the level of individual constituents as well as formulation of an efficient and reliable computational scheme. The rate-dependent behavior of the polymer matrix is examined first providing sufficient data needed in the calibration step of the generalized Leonov model, which in turn is adopted in numerical simulations. Missing elastic properties of basalt fibers are derived next using nanoindentation. A series of numerical tests is carried out at the level of yarns to promote the ability of a suitably modified Mori–Tanaka micromechanical model to accurately describe the nonlinear viscoelastic response of unidirectional fibrous composites. The efficiency of the Mori–Tanaka method is then exploited in the formulation of a coupled two scale computational scheme, while at the level of textile ply the finite element computational homogenization is assumed, the two-point averaging format of the Mori–Tanaka method is applied at the level of yarn to serve as a stress updater in place of another finite element model representing the yarn microstructure as typical of FE Ever-increasing special demands on structural components employ researchers in material engineering in search for material systems with exceptional properties. In particular, their mechanical and physical properties must be continuously improved to compete with the related technological progress. This also includes economical as well as ecological aspects. Textile composites appear as a suitable candidate to meet these requirements in a variety of engineering areas. Plain weave textile composites, where fibers are located in two perpendicular directions, guarantee high stiffness, strength and durability  togetherAn appropriate choice of individual components opens the door for creating products with entirely unique characteristics. This calls for considerable activity in both experimental and computational research as finding an optimal material composition is not an easy task . Carbon Basalt fibers as reinforcing material of composites have recently been exploited in the production of composites. The mechanical properties of such a composite are similar to the properties of composites reinforced with S-glass fibers and appear better than those with E-glass fiber reinforcement. Experimental results presented in  showed bAlthough the strength and stiffness of the composite are merely driven by the reinforcement, the overall behavior of a structural product including its durability might significantly be influenced by the choice of the matrix phase. The most common matrix material used in the production of composites is epoxy resin for its specific properties, such as hydrophobic properties, temperature, UV, and ozone resistance, and resistance to oxidation by atmospheric oxygen. Furthermore, it is inert with respect to other materials, biologically inert, non corrosive and has good electric-insulating properties . The marIn general, the mechanical response of various epoxy resins may considerably vary. Apart from common viscoelastic or nonlinear viscoelastic behavior, one may observe a transition to brittle-viscous or even brittle response with no viscose effects . Obviousapproach . With reapproach  is carriapproach . Howeverapproach . The Morapproach ,17 in paapproach ,19,20 foapproach  to incorIdentifying and calibrating a suitable constitutive model of the matrix phase.Providing a remedy of the Mori–Tanaka (MT) micromechanical model to yield the yarn response comparable to that delivered by the finite element method (FEM). In this regard, the finite element (FE) predictions are taken as a sufficiently accurate representation of the composite response substituting the actual measurements in the framework of virtual experiments.Developing an efficient computational scheme based on a two-scale modeling strategy where the Mori–Tanaka method is adopted as a stress updater at the level of macroscopically homogeneous yarns.These opening paragraphs motivated the content of the paper. The current interest in basalt fibers influenced the choice of textile reinforcements. Their potential exploitation in advanced structural elements such as wind turbine blade  called fThe last two items are described in detail in The present section introduces the basic properties of individual phases including their elastic parameters, geometrical details of the basalt fabric, and computational models taken from the authors’ previous work, see, e.g., ,23 for dAs pointed out in the introductory part, the L285 epoxy resin  suppliedAll tested specimens, see m stands for the matrix and The matrix phase is assumed isotropic and its properties were estimated from the results of the calibration process outlined in detail in The actual image analysis device used for structural image acquisition and analysis to arrive at A number of approaches are available in the literature to incorporate the random nature of geometrical details on both the mesoscale (level of textile ply) and microscale (level of yarn) into the formulation of a suitable computational model typically in terms of a statistically uniform periodic unit cell (SEPUC), see e.g., ,26,27,28On mesoscale, a single-ply periodic unit cell (PUC) of a plain weave textile composite evident in The binary image in E of the fiber phase were estimated from nanoindentation. The load-controlled quasi-static indentation was performed with the load function consisting of “loading” and “unloading” segments lasting 5 s each with an in-between 300 s segment of “holding” time. The maximum applied force of 2500 E = 1140 GPa and L and T stand for the longitudinal and transverse directions, respectively.The elastic Young moduli d bodies  assumingThe present section summarizes the theoretical background needed for a nonlinear viscoelastic modeling of plain weave textile reinforced polymer matrix composites. We begin with the formulation and calibration of the L285 epoxy resin. Essential steps to perform two-step homogenization are outlined next.It has been experimentally observed that polymers show, in general, a negligible volumetric strain during plastic flow. This is supported in  where thThe stepping stone in the formulation of the Leonov model is the Eyring flow equation representing the plastic component of the shear strain rate in the forms is the deviatoric stress vector. The viscosity of the The total shear strain rate combining the elastic and plastic strain rates then becomesve model  with thededt=deedK is the material bulk modulus, Admitting material isotropy, small strain theory, and the bulk response to be linearly elastic we arrive at the complete set of constitutive equations defining the compressible generalized Leonov modelThe most straightforward calibration of the stress shift factor ing plot ,36 assumWith reference to Equation  and realEquation  thus sugThe specimens in We open this section by assuming that the creep compliance function eries asJ(t)=∑μ=1(1)t is the time in [s] and K is calculated from the elastic modulus E estimated from the elastic part of the stress–strain curve when preloading the specimen to the desired stress level. The Poisson ratio Transform (2)Transform the (3a)t-axis using the corresponding shift factor Shift the (3b)fminbnd.Alternatively, as will yet be proven useful, the Eyring flow model parameter Equation  amounts The required data are provided by standard creep tests performed at different stress levels thus exploiting the time—stress superposition principle consistent with the Eyring flow model. In the present study, the MTS Mini Bionix 858.02 testing system equipped with 1000 N load cell was used, see As already mentioned the search for the compliances Equation . To arriEquation  is validApplication of Equation (9) calls for the transformation of creep compliance function  to relaxTypically, the Laplace transformation is employed to obtain the relaxation times e, e.g., .i-th time increment. In light of Equation  in time. For simplicity, the most simple, those only conditionally stable, fully explicit forward Euler scheme is employed. Provided that the total strain rate is constant during the integration of a new state of stress in the matrix phase at the end of the current time step, Equation  the instFurther details can be found, e.g., in .To introduce the subject we consider a representative volume element (RVE) of a single-ply balanced plain weave composite plotted in Analysis in the framework of FEThe FEWhen limiting attention to elasticity, a simple bottom-up fully uncoupled homogenization can be used to predict the macroscopic effective properties of a single-ply textile composite. This, however, is no longer possible when loading the composite beyond the elastic limits as the material anisotropy precludes derivation of the homogenized nonlinear constitute law at the level of yarn. A two-step, fully coupled homogenization, is therefore needed. Two options are typically available:Both homogenization approaches, FE and MT method based, will be now briefly reviewed. Only the most relevant formulations will be outlined. Thus, for more details, the interested reader is referred to ,15.Y, representing all the geometrical and material details of the whole composite, is loaded on its outer boundary by the prescribed displacements or tractions that produce the macroscopically uniform strains E or stresses r and The presented first-order homogenization grounds on the formulation developed in . To thisely, see  for furthen readΔΣ=LhomΔEEquation  follows Because in the displacement-based finite element method the primary unknowns are the nodal displacements, we continue by decomposing the local displacements, while taking into account the periodicity of the unit cell, into a homogeneous parts asΔu(x)=ΔE·parts asΔu(x)=ΔE·Equation  and realBecause the variations Equation  can be sEquations  and (31)approach . HoweverEquation  simplifiu will be considered as the primary unknowns. Standard finite element discretization then readsr is the vector of unknown nodal degrees of freedom. Introducing the fluctuation strains from Equation (Y. It is worth mentioning that the fluctuation displacements In the framework of FEM the fluctuation displacements en readsΔu*(x)=NP=00The homogenized stiffness matrix, the overall stress and eigenstress vectors associated with a lower scale, here being represented by the level of yarn , are finally provided by substituting the local stress increments from Equation  into Equelations  togetherComparing Equation  with EquThe literature offers solid evidence regarding the inability of the original format of the Mori–Tanaka method  to provide results comparable to detailed numerical simulations using FEM for loading conditions exceeding the elastic limit, see ,43,44 Following the general structure of the previous section, we begin with the results concerning the calibration process of the matrix phase. The results of numerical simulations starting from the level of yarns and followed by the level of textile ply are summarized next.At the initial stage of our experimental program the attention was accorded to the L285 epoxy resin cured with the H508 hardener. Six specimens in particular were examined. Expecting the lack of H508 hardener on the Czech market we performed this particular set of experiments using the same L285 epoxy resin but cured with H500 hardener as a recommended substitute. Fourteen specimens were examined. Each test, except for tests at 40 and 45 MPa, was run twice. As seen in When deriving the Master curve the procedure described in To partially reconcile the discrepancy in the material response of the two material systems we carried out an additional set of measurements of the L285/H500 system in tension at the same strain–strain rate as originally used for the L285/H508 matrix. These results are shown in Equation , and theEquation . For ninEquation  closely To support the applicability of the adopted generalized Leonov model we performed the creep tests numerically. The results are available in For illustration, we also reproduced the tensile test numerically. The analysis was performed in the plane stress regime using 4-node quadrilateral elements. Similarly to experimental measurements, the analysis was carried out in the displacement control regime. The geometry of the computational model was selected such as to represent the part of the specimen covered by the extensometer. The resulting finite element meshes together with boundary and loading conditions is available in The first set of experiments aims at verifying the implementation of the generalized Leonov model and the Mori–Tanaka method in our in-house finite element code. Considering the strain control regime, Equation , we firsA remedy is offered in The evolution of local phase stresses is evident in It is fair to mention that here we accepted the prediction provided by FEM as sufficiently accurate to play the role of a virtual experiment, therefore replacing the actual laboratory measurements. These, however, are still needed to validate both computational strategies. However, this goes beyond the present scope. Furthermore, as the model is generally isotropic it remains to check whether a single set of parameters will still be sufficient to account for other, more general, loading scenarios. In this regard, a recently proposed modeling strategy, see , might pA suitably tuned new version of the MT method now opens the door to the desired multiscale modeling of a single plain weave textile ply. Such an approach should prove efficient making possible to perform an extensive parametric study for a variety of loading conditions and types of reinforcements. This would certainly be appreciated particularly at the initial stage of design of a given structural element. Nevertheless, the validity of such simulations should be checked. At this point, however, no experimental measurements performed directly on a textile ply under study are available. Therefore, we propose two simple loading scenarios enabling us to evaluate the performance of the basalt fabric reinforced polymer matrix at least qualitatively.In particular, we compare the macroscopic response of the composite to in-plane tension and in-plane and out-of-plane shear by loading the unit cell in Henceforth, the macroscopic stress–strain curve, the response at the level of textile ply, is denoted as X direction. Point out that this is the case of a unidirectional strain where With the above specification, we first address the tensile loading along the The piece-wise uniform evolution of these quantities in individual phases is displayed in As expected, the effect of the applied strain rate is more pronounced for shear loading conditions which is evident in Since gaining notable popularity, the basalt fabric/polymer matrix based composites should be thoroughly studied both experimentally and computationally, for only then new improved designs would be broadly accepted in structural applications. The present study partially contributes to this subject by offering an efficient fully coupled two-scale computational procedure to address both the geometrical complexity of basalt reinforcement and nonlinear behavior of the matrix.The proposed approach advocates the use of the Mori–Tanaka micromechanical model to substitute a computationally expensive finite element method when estimating local stresses and strains on the yarn scale. The fact that only the overall macroscopic response is usually of an engineering interest supports this approach as the MT method generally obviates the local details by considering the piece-wise uniform stress and strain averages only. However, even such a simplification should be reliable and generally comparable to more accurate FE predictions. This is why we introduced a certain reformulation of the original format of the MT method to closely match the mesoscopic response generated by FEM. In this context, the presented results seem promising so to accept the MT method for the stress update on the microscale  within the multiscale analysis. In this regard, some specific features of the macroscopic response of a textile ply with reference to the adopted local constitutive laws have successfully been illustrated.While this study is only computational and should be experimentally validated, the analysis concerning the material behavior of individual phases, the basalt fibers and L285 polymer matrix, integrated both experimental and computational components of research. A complex experimental program was executed to provide data for the calibration of the generalized Leonov model chosen to represent the nonlinear viscoelastic response of the matrix phase. Within this step, a calibration procedure for tuning the model parameters of the Eyring flow was developed solely on the basis of creep tests. The calibrated model was validated computationally by reproducing the laboratory measurements numerically. The reported results highlight the importance of properly addressing the whole system resin/hardener as the results derived for one particular hardener can hardly be transplanted to another one albeit using the same epoxy resin.


Capacitive micromachined ultrasonic transducers (CMUT) are MEMS-based transducers with advantages over conventional ultrasonic transducers, such as their small size, the ease of integration with semiconductor electronics, and batch fabrication. In this study, the effect of different membrane topologies on the displacement, resonant frequency, and output pressure of the CMUT membrane is investigated in the transmission mode in an air environment. A novel structural-support feature, the rocker stem, is introduced, where the membrane is weakly held to the substrate in order to minimize mechanical constraints. Four different CMUT topologies are designed and assessed to analyze the impacts of topological variations. A new CMUT array configuration is also designed to provide an approach for maximizing CMUT density. This study aims to contribute to efficient CMUT design and the determination of optimum structural parameters for portable applications in air. Capacitive micromachined ultrasonic transducers (CMUTs) are an attractive alternative to the traditional piezoelectric film-based transducers because of several advantages they may offer, such as larger bandwidth, increased sensitivity, efficient performance, IC-compatible fabrication and a variety of possible array configurations . RelyingIn order to integrate CMUTs in systems for portable ultrasonic applications, it is critical for the device to operate efficiently at a small bias voltage. Since the power transfer efficiency of a CMUT is maximal when the DC bias is as close as possible to the electrostatic collapse voltage, it would be desirable to work with a structure exhibiting a collapse voltage as low as possible above the desired bias . The reqIn this work, a novel CMUT structure is introduced which exploits spring softening phenomena to increase frequency tunability at low bias voltages. This is made possible by the introduction of a spring arm structure holding the vibrating membrane through novel rocker support stems, as illustrated in The operation of the CMUT is explained in t) is given byA is the membrane area, ε is the permittivity of free space, g is the initial gap size between the two electrodes, x(t) is the vertical displacement of the membrane due to the electrostatic force, and CMUT devices have two modes of operation: ultrasound generation and ultrasound detection. For ultrasound generation, the CMUT transmits an acoustic wave caused by the membrane vibrating in response to the alternating electrostatic force generated by AC potential applied across the top electrode (vibrating membrane) and the bottom electrode (fixed). The generated electrostatic force x(t), is determined by the equilibrium of the electrostatic and restorative forces. However, above a certain DC bias voltage, the electrostatic force overwhelms the mechanical restoring force, rendering the system unstable, and the membrane collapses onto the bottom electrode. This voltage is known as the pull-in or collapse voltage.When applying a voltage across the electrodes, the electrostatic force pulls the membrane toward the bottom electrode. This force is balanced by the mechanical restoring force exerted by the CMUT membrane structure, defined asx at 0: the solution of the latter states that collapse always occurs when the displacement exceeds one third of the initial gap g:The collapse voltage can be calculated by solving the first derivative of g) of the system needs to be decreased. To lower the resonance frequency for a smaller CMUT structure, the stiffness of the system should be lowered, as perEquation  shows thg) is set by the thickness of the sacrificial layers in the PolyMUMPs process, it is important to minimize the stiffness of the vibrating CMUT membrane for improved sensitivity and lower resonance frequency for applications in portable devices. One of the most important parameters for a CMUT is its operating resonance frequency, as it determines the types of applications for which the device will be suitable. The acoustic energy loss of the ultrasonic wave is dependent on the type of medium, temperature, the distance of propagation and the frequency of the ultrasonic wave. For example, the amplitude of a sound wave is attenuated as some of the energy it carries is lost to friction and relaxation processes. Therefore, low-frequency sound waves are often preferred for longer ranges. However, a higher frequency ultrasonic wave may provide finer imaging resolution depth. As a result, an optimal resonant frequency range must often be selected [m is the equivalent membrane mass, R is the radiation impedance.Since the initial gap size  comparevoltages ,18.The deflection of the quarter-circular beam at the free end is given by (11)δ=π4Four alternate CMUT topologies were designed in this study to assess and compare the impact of the spring-arm geometry and anchoring method, as detailed in The CMUT and the array were designed according to PolyMUMPs guidelines and were taped out for implementation. 2) layer is deposited and DIMPLES are lithographically patterned to define the stems of the CMUT membrane, as shown in (B). Poly-1 is then deposited over Oxide-1 and forms a 2 μm thick structural layer for the CMUT membrane. Patterning using RIE creates the novel structure of the CMUT as illustrated in (C). A second oxide layer (Oxide-2) of 0.75 μm is deposited as shown in (D). Next, to anchor the enclosure to the substrate, Oxide-1 and Oxide-2 layers are etched through in (E). Then, the second PolySi is deposited and patterned to form the enclosures to contain the stem supports, as shown in (F). Since the stem supports are not affixed to the layer below, the CMUT is free to slide on the horizontal plane of the substrate. The enclosure is designed to contain the stem support and restrict large motion of the structure across the plane, potentially allowing only for small sliding of the stem base. Finally, the entire substrate is placed in hydrofluoric acid in order to dissolve the sacrificial oxide layers, releasing the finished product as shown in (G). PolyMUMPs’ layer thicknesses are given in The process begins with a silicon wafer substrate covered by a 600 nm silicon nitride (SiN) layer. A 500 nm layer of polysilicon (PolySi) is deposited and patterned with reactive ion etching (RIE) on the SiN layer and will serve as the lower electrode layer. Patterning divides the Poly-0 layer in three separate electrodes as visible in (A). The middle part serves as the fixed electrode, whereas the two surrounding electrodes serve to contact and electrically connect with the stems of the CMUT membrane. Next, a first 2 μm sacrificial silicon dioxide  reaction force 2 as per . Since t reduced ,22, leavIn this study, the behaviour of CMUTs with different arm shapes and support types was investigated in terms of displacement and output pressure under DC and AC actuation. Simulations were performed in the air domain. The behaviour and performance of CMUTs were assessed using finite-element methods (FEM) models by means of the COMSOL Multiphysics software. Collapse voltage varied greatly between device types; therefore, the value of DC bias voltage was selected in accordance with the device having the lowest collapse voltage.Collapse voltage was determined by plotting the displacement of a membrane with respect to DC biasing voltage for the devices, as shown in CMUTs have several damping loss mechanisms such as squeeze film damping, support losses and thermoelastic damping (TED). Air squeeze-film damping is produced when a DC voltage is combined with an AC signal across the electrodes of the CMUT, which leads to the membrane (piston) vibrating at the frequency of the AC excitation . SqueezeIn order to simulate a rocker support boundary condition for CMUT A and C, the inner edge of the bottom of the stem was constrained to a zero prescribed displacement in the direction perpendicular to the substrate. A fixed anchoring boundary condition for CMUT B and D was achieved by selecting the full bottom surface of the stem as a fixed constraint. A point at the center of the vibrating membrane was selected to plot in time the various displacement profiles. The bias voltage was applied to the device using a progressive ramp function at time t equal to zero in order to avoid potential instabilities that could be caused by a very fast step. After the transient displacement due to bias voltage settled down to its final position, the AC signal was applied with a smoothly increasing amplitude.The DC bias of each CMUT was increased until collapse to measure the decrease in the resonance frequency due to spring softening phenomena. A sharp drop in resonant frequency vs. DC bias can be seen near collapse voltage in Displacement vs. time graphs are shown for CMUTs A, B, C, and D in P is pressure, Z is the acoustic impedance of the medium through which the sound wave travels, and V is the vibrating membrane velocity. The output pressure P is proportional to the displacement based on acoustic wave theory [Far field pressure was measured 6 mm away from the CMUT surface using exterior field calculation in COMSOL. Pressure generated by an array of 50 × 50 CMUTs was also calculated by linearly adding pressure from each CMUT, assuming in-phase operation, with the results shown in e theory . InstantDisplacement efficiency is calculated as the peak–peak displacement per AC signal volt. The maximum displacement efficiency for the four designed CMUTs is 49.6 nm/V, 25.9 nm/V, 5.6 nm/V, and 2.96 nm/V for CMUT A, B, C and D, respectively. In comparison, CMUTs designed by ,28 showetotalE = elecE + mechE. This coefficient is an important parameter in ultrasonic transducer design because it measures the degree of energy coupling (efficiency) between the electrical and mechanical domains. The coupling coefficient of a CMUT is derived by calculating free and fixed capacitance in [In general, transducers convert energy from one domain to another. For acoustic transducers, the conversion is between the electrical and mechanical domains. The electromechanical coupling coefficient tance in  and is dg/3), the coupling coefficient approaches unity, indicating that all the energy in one domain is converted to the other domain. Electromechanical coupling coefficient as function of voltage normalized to collapse voltage is shown in The above result is important because near the collapse point  when operated at low bias voltage such as high tunability and use in portable applications. This work demonstrated the potential utility of the novel rocker stem support, which could eventually be applied to various MEMS device types. Physical devices have been taped out for fabrication and will be characterized experimentally to confirm this work’s conclusions.


Fluid–structure interaction (FSI) gained a huge attention of scientists and researchers due to its applications in biomedical and mechanical engineering. One of the most important applications of FSI is to study the elastic wall behavior of stenotic arteries. Blood is the suspension of various cells characterized by shear thinning, yield stress, and viscoelastic qualities that can be assessed by using non-Newtonian models. In this study we explored non-Newtonian, incompressible Casson fluid flow in a bifurcated artery with a stenosis. The two-dimensional Casson model is used to study the hemodynamics of the flow. The walls of the artery are supposed to be elastic and the stenosis region is constructed in both walls. Suitable scales are used to transform the nonlinear differential equations into a dimensionless form. The problem is formulated and discretized using Arbitrary Lagrangian–Eulerian (ALE) approach. The finite element method (FEM) technique is used to solve the system of equations, together with appropriate boundary conditions. The analysis is carried out for the Bingham number, Hartmann number, and Reynolds number. The graphical results of pressure field, velocity profile, and load on the walls are assessed and used to study the influence of hemodynamic effects on stenotic arteries, bifurcation region, and elastic walls. This study shows that there is an increase in wall shear stresses (WSS) with increasing values of Bingham number and Hartmann number. Also, for different values of the Bingham number, the load on the upper wall is computed against the Hartmann number. The result indicate that load at the walls increases as the values of Bingham number and Hartmann number increase. Blood flow's is complex rheological dynamics that cannot be predicted by any structural mode. Therefore to analyze blood hemodynamics, researchers formulate new methods2. Blood is a mixture of cells suspended in a fluid4. Red blood cells round the greater volume of blood5. According to Hunter6, the blood was assumed to be incompressible, homogeneous, and Newtonian fluid. Due to the elasticity of the vessel wall, blood flow was unsteady in this model. A finite difference method was used to calculate the blood flow. Also, a one-dimensional heat equation was used. Computed results were estimated by assuming that there was no heat loss around the artery.Featuring the human circulatory system, the bio-fluid dynamic has grown rapidly in recent decades, particularly concerning atherosclerosis diagnosis and etiology. Due to a buildup of fatty deposits like calcium, arterial stenosis occurs. Atherosclerotic plaque is determined by the geometry of the arteries. The most common places for stenosis to develop are the curvatures, crossings, and forks of the medium and large arteries. The study of atherosclerosis and the patterns of blood flow in stenotic or bifurcated arteries has witnessed a substantial increase in interest in recent years. Blood composition, cell concentrations, and artery geometry all have a direct impact on the arterial system's flow characteristics. Several research has sought to better predict a flow of blood in a bifurcated artery by implementing Newtonian and non-Newtonian fluids. According to vein geometries and blood rheological behavior in the circulation, theoretical and empirical research of blood flow through arterioles are complex task with numerous challenges7. Shear stress and strain are nonlinearly related in the Casson model. This model is used to study the blood flow, paints industry, manufacturing of medicine, and synthetic lubricants. Misra and Pandey8 used CF model to study the peristaltic blood transport in small vessels. The CF model is also used to describe the core region of the blood flow in mathematical model of small vessels in their mathematical model. It is worth noting that human blood flow is essentially pulsed and irregular due to its cyclic nature, and this poses a unique challenge to both computational and experimental science. To date this CF model is the best formulation for predicting a flow of blood11. Khair et al.12 studied the pulsatile blood flow in a constricted channel. Chakravarty and Mandal13 studied the blood flow in a stenosis of tapered artery. For further study on CF model and its application the readers are referred to16 and references therein.There are many non-Newtonian fluid models, but one of the most well-known is the Casson Fluid (CF) model17. Sharma et al.18 reported that MHD can be controlling parameter for blood velocity. Considering the micropolar fluid non-linear model19, Shit and Roy found that enhancing the effects of induced magnetic field on blood flow via a confined channel the blood flow velocity at the centerline is reduced and raised the pressure gradient. Diviya et al.20 studied the hemodynamics of the MHD peristaltic process of non-Newtonian fluid with mass and heat transfer. Their studies show that an increase in variable viscosity parameters accelerates the flow hence bolus size increases. Pulsatile flow analysis has gained a lot of attention because of its applications in respiratory system, circulatory systems, microelectromechanical system, reciprocal pumps, vascular diseases, and internal combustion engines25. Malathy and Srinivas26 used perturbation method to investigate the MHD pulsating flow between two permeable beds. A perturbation technique was used by Srinivas et al.27 to study the non-Newtonian pulsative flow in a porous channel. Recent studies by Bilgi and Atalik28 have explored the elastic properties of blood for pulsative arterial hemodynamics and risk indicators for aneurysm rift to their impact on velocity, stress fields, and vorticity.Magnetohydrodynamics (MHD) is a part of fluid dynamics that does incorporate the fluid’s magnetization or polarization while studying fluid dynamics in the magnetic field. MHD has a wide range of potential applications in bioengineering and medicine29 proposed employing a unified continuum and an interdisciplinary variant formula. A quasi-direct approach was used to solve the FSI problem to assess velocity and pressure. To compute the solid displacement and mesh motion a segregated algorithm is used. Using biological approaches, Foong et al.30 studied the numerical similarity of blood flow within the artery under continuous heat flux. The study shows that non-Newtonian blood flow changes into Newtonian blood flow properties by replenishing fluid and electrolytes in the bodily arteries, which promotes the heat transfer in blood flow and causes blood flow temperature to be reduced. Heat transmission through oscillatory blood circulation in an incised permeable artery was studied by Ogulu and Abbey31. Khaled and Vafaei32 studied the concept of transport in biological tissue and proposed new model incorporating heat transfer and thermic biology equation. Recently, Shahzad et al.33 used power-law fluid to study the hemodynamics of blood flow in a stenotic artery with elastic walls by using ALE approach to couple equations. The results show that there is an increase in load on the walls for the shear thickening case.Many physiological processes in the body are influenced by the FSI. For example, pulmonary airway reopening and closure, flow-rate limitation and wheezing during forced expiration, snoring and phonation, pulse wave propagation in arteries, flow-induced deformation, and ultimate rupture of arterial cerebral aneurysms, etc. To represent the FSI in the pulmonary arteries, Liu et al.Casson model widely used over a long ranges of shear rates for the study of blood rheology was not implemented in fluid solid interaction in an artery. In the presented study, a Casson model is considered to investigate the hemodynamic effects of the blood flow flowing through a bifurcated artery having elastic walls. The scope of the study involves testing impact the Bingham number, Reynolds number, and Hartmann number on the hemodynamics of the artery, stenotic region, and elastic walls. In the next section governing equations are modeled and converted into dimensionless form. In problem setup section the geometry of the problem and solution approach is explained. In the final section, a conclusion is drawn based on the results.34We studied the flow of two-dimensional, non-Newtonian incompressible fluid through the double stenosis bifurcated artery. The artery walls are considered to be linearly elastic. A magnetic field is applied toward the axial direction of the flow. Considering, motions of solid and fluids described by Lagrangian and Eulerian approaches, one can state that ALE is a more general method mixing fluid and solid domains (FSI). Governing equations for FSI case are written as35, an improved continuous version36 can be used37 was established that when The discontinuous nature of the Casson model makes it challenging to implement in numerical simulation. Using a strategy that was previously utilized to overcome a Bingham plastic fluid singularityEquations for the elastic structure domain areAs elastic walls are exposed to a stress tensor (caused by fluid pressure) the walls are deformed,To make the analysis more general, the governing equations are converted into dimensionless form by non-dimensional variables mentclass2pt{minimion Eqs.  takes thThe dimensionless equation for elastic structure domain is defined asA parabolic inflow velocity with 33.In Fig. The inner diameter of the artery mentclass2pt{minim38, Donea and Huerta39, Kuhl et al.40, and Mazumder41 provide more information on the ALE approach implementation. The accuracy of the solution can be improved by using a hybrid mesh of triangular and rectangular components. A Galerkin finite element technique is used to convert the FSI problem into a weak form and discretized. The element pair P2-P1 is chosen to approximate the pressure, velocity, and elastic walls behavior. The Newton’s method is used to solve the nonlinear algebraic system of equations. The nonlinear iteration convergence criteria are defined as:1 and P2 to approximate the domain's elements. A quadrilateral and triangular grid are used to create the mesh. To ensure that results are independent of the number of mesh elements. A grid independence study was carried out by computing WSS for the upper elastic wall. The numerical values of WSS from coarser (level 1) to extremely fine (level 6) were computed at The Eqs. –14 are n42 for contour plots and velocity magnitude and are shown in Fig. Once grid independence is established, the validation of code is presented against the results of Anwar et al.To study the hemodynamics of the flow the numerical study of non-Newtonian biomagnetic blood flow flowing through a bifurcated channel is carried out by using the two-dimensional CF model. The walls of the artery are assumed to be elastic and the stenosis region is constructed in both walls. Suitable scales are used to transform the nonlinear differential equations into a dimensionless form. The problem is formulated and discretized using the ALE approach. The system of equations is solved using the FEM technique along with appropriate boundary conditions. To get a better view of the problem, the numerical solution is derived for various values of parameters involved. The ranges of the parameters used in the study are In Figs. Mechanical features of the bifurcated channel are critical since they are directly related to flow pattern, recirculation area, and WSS. The distribution of WSS along the upper wall for the variation of Reynolds number and Hartmann number are shown in Table Figure mentclasspt{minimaThe WSS is higher for rigid wall scenarios than elastic wall cases.As the Reynolds number increases, the viscous forces inside the fluid increase which retards the fluid velocity inside the artery.The WSS decreases for increasing values of Reynolds number.WSS is minimum for the Newtonian case (As the values of This study presents results of FSI study aimed to model interaction between double stenosis bifurcated channel and blood flow implemented as non-Newtonian incompressible fluid described by two-dimensional CF model. The channel’s walls are assumed to be elastic. The magnetic field is applied along the axial direction of the flow. The system of differential equations is transformed into a dimensionless form by utilizing suitable scales. ALE-based FEM is used to discretize the system of governing equations. The study’s primary findings are noted as follows:


Infrared thermography techniques with thermographic data analysis have been widely applied to non-destructive tests and evaluations of subsurface defects in practical composite materials. However, the performance of these methods is still restricted by limited informative images and difficulties in feature extraction caused by inhomogeneous backgrounds and noise. In this work, a novel generative manifold learning thermography (GMLT) is proposed for defect detection and the evaluation of composites. Specifically, the spectral normalized generative adversarial networks serve as an image augmentation strategy to learn the thermal image distribution, thereby generating virtual images to enrich the dataset. Subsequently, the manifold learning method is employed for the unsupervised dimensionality reduction in all images. Finally, the partial least squares regression is presented to extract the explicit mapping of manifold learning for defect visualization. Moreover, probability density maps and quantitative metrics are proposed to evaluate and explain the obtained defect detection performance. Experimental results on carbon fiber-reinforced polymers demonstrate the superiorities of GMLT, compared with other methods. As one of the advanced composite materials, the demand for carbon fiber-reinforced polymer (CFRP) in new energy, equipment manufacturing, and other fields is growing rapidly . ResearcMachine learning methods have been widely utilized in various fields over the last two decades ,9,10, inObtaining informative data is one feasible way to improve the performance of machine learning algorithms, especially in tasks where short or small data problems exist . In caseA generative manifold learning thermography (GMLT) method is proposed for defect detection and the evaluation of polymer composites.The spectral normalization generative adversarial network (SNGAN) is designed as a thermogram augmenter which enlarges the dataset; the isometric feature mapping (ISOMAP) manifold learning is adopted to learn the intrinsic geometric structure of the nonlinear thermographic data; and the partial least squares regression (PLSR) latent variable method is proposed for visualizing defects.A quantified defect–background separation index is developed for the performance evaluation of different methods. Experiments on CFRP specimens demonstrate the advantages of the proposed GMLT method. The probability density plot is used for model interpretation.The aim of this work is to facilitate the success of thermography-based defect detection through data augmentation and analysis, achieving an accurate inspection of the geometric properties of subsurface defects in the specimen. The main contributions can be summarized as follows:In IRT defect detection, the experimental system is an indispensable experiment foundation, which provides the thermal images directly for subsequent thermographic data analysis methods. Here, the main components and functions of the IRT system are briefly introduced so that the readers can better understand its working principle and refer to it in practice. tN sampling instants. Each thermogram is tN-th time instant. Moreover, as shown in The operation process of each component of the IRT system is described briefly. First, the flash lamp is used as the heat source to emit thermal pulses for heating the specimen. Then, an infrared camera is used to record the surface temperature pattern of the test specimen during the cooling stage. Finally, the captured thermal images are stored on a computer for subsequent analysis. As shown in In this section, a deep learning-based GMLT framework is established to facilitate IRT defect assessment. As shown in Data augmentation has become one primary method of saving data collection costs to solve small data problems ,29,30. FL2 matrix norm of The SNGAN contains two deep neural networks, one is a generator and the other is a discriminator. Compared with the GAN, the other structures of SNGAN remain unchanged, but the weight matrix of the discriminator is spectrally normalized . This stiminator :(1)W^i=Weral GAN .G contains one fully connected layer and four deconvolutional layers, and the discriminator D contains one fully connected layer and three convolutional layers. All the convolution kernels are set to 3 × 3. All the convolution steps of the whole model are 2, except for the last deconvolution layer of G where the convolution step is 1. G network, while the leaky ReLU activation function is used in the D network. More importantly, compared to the G network, the D network performs spectral normalization at each layer in addition to the use of batch normalization.The SNGAN-based thermography augmentation architecture is shown in As a manifold learning algorithm, the ISOMAP  has beentN frames of gN simulated thermal images are obtained. Similar to the original data, they are viewed as a In this work, the GMLT approach is proposed to address the challenge of insufficient thermographic data. X. Each column of X is a one-dimension expansion of a single thermal image, and each row is the temperature response at a single pixel location. To reduce the computational effort and efficiently extract features, a normalization procedure is performed on the matrix X.Then, the original IRT data and the SNGAN-generated data are merged and preprocessed. Specifically, the Y of X. Let each column xi of X be a sample. The k-nearest neighborhood algorithm is used to construct the neighborhood graph H. After this, the Euclidean distance xi and xj are linked by an edge; otherwise, r = 1, 2, ∞, H.Next, the ISOMAP method is implemented to solve the low-dimensional embedding manifold ,20. SpecY. Let the squared distances matrix H be calculated as follows:I are an identity matrix. Then, multidimensional scaling is applied to the matrix of distances τ as follows:Define the operator d eigenvalues (in descending order) d eigenvectors Y of the input data X, is calculated, and After the eigenvalue decomposition of the matrix The main drawback of the manifold learning approach is that there is no explicit mapping from the input data manifold to the output embedding. When the ISOMAP method is used for IRT data analysis, the low-dimensional embedding results do not provide direct visual convenience for defect detection. Previously, the MLT method employed ordinary least squares regression (OLSR) in finding the explicit mappings . HoweverX and Y as samples and each row as a dimension. The column vectors of matrix Y are normalized before the analysis. The multivariate model of PLSR is as follows:X is the Y is the V and U are the score matrices obtained after applying principal component analysis (PCA) for X and Y, respectively; P and Q are the load matrices obtained after applying PCA for X and Y, respectively; and the matrices E and F are the corresponding error terms.Here, PLSR is used to solve the explicit mapping and give the procedure for defect visualization . One maiX and Y cannot be established by directly using (4) or (5). Regression analysis is performed on the score matrices V and U based on the correlation of the column vectors to obtain the transformation matrix B:The relationship between B describes how matrix X is mapped by ISOMAP to the embedding matrix Y, which can be used as a display mapping for ISOMAP dimensionality reduction. To visually defect defects, each column vector  of matrix B is reconstructed into a two-dimensional matrix of size d IV images   is a popHowever, when the backgrounds are inhomogeneous, the SNR indicator often provides results against human experiences. The reason is that this index reflects the global signal-to-noise ratio, while human beings identify defects based on the local contracts between the defect regions and their surroundings. To solve this, this work proposes a defect-background separation (DBS) indicator as a complement to SNR. It is calculated as follows:The DBS index evaluates the thermogram analysis methods from the perspective of signal separation. Specifically, the DBS index quantifies the degree of separation of information between defects and intact areas in the extracted features, which is related to the ease of identifying defects with the naked eye and helps determine the shape and location of defects. A larger DBS value indicates a larger inter-class distance and a smaller intra-class distance, which means the defect is more separable from the intact area. Therefore, a larger DBS indicates better defect identification results.2 and were inserted into the carbon fiber sheets prior to the injection of thermosetting resin into the fiber preforms that had been placed in a closed mold. The deepest defect, which is diamond-shaped, is located under three layers of carbon fiber sheets, the circular defect is located under two layers of fiber sheets, and the trapezoidal defect is located under a single layer. A diagram of the CFRP specimen with defects is shown in The shapes of defects in real industrial products composed of composite materials are usually irregular and diverse. It is difficult to evaluate these products because the unknown nature of its defects makes it impossible to judge the accuracy of the evaluation results. In this experiment, a CFRP specimen was fabricated using the resin transfer molding process . The 20 After the specimen is prepared, pulse thermography (PT) is used to detect internal defects. PT ,20 is onIn this case, TSR, PCT, and MLT methods were performed to evaluate the subsurface defects of CFRP specimens for comparison with GMLT. TSR, as a signal reconstruction method, improves the spatiotemporal resolution of thermographic data by filtering the data in the time direction. As a representative data dimensionality reduction method, PCA and its extended algorithm have been applied in thermography because of its ability to reduce noise and simple implementation . As showOn a computer with 16 G of RAM, an Intel Core i7 CPU, and a Windows 7 operating system based on the TensorFlow framework, the GMLT method is calculated and implemented. The batch size is set to 5, the loss function is optimized using the Adam optimizer, and the learning rate is set at 0.002 during the SNGAN training. The training parameters of ISOMAP are: the number of neighbors is also 5 and the target dimension is 6.It is inevitable to consider how much thermogram generation is appropriate in the GMLT method. Too few generations are not conducive to the learning of the model, whereas too many generations will not endlessly improve the model’s performance. In this work, considering that there were 90 raw thermal images, 80 simulated thermal images were generated. This is not guaranteed to be optimal, but after several tests, it was found that the performance of the GMLT method is relatively robust when varying around this quantity. Eventually, the whole dataset contains 170 thermal images. As shown in The analysis results of the GMLT method are shown in The DBS values of several methods are listed in The results in the previous section demonstrate that the GMLT method outperforms the MLT method in terms of defect identification, while the only difference between the two is the fused thermogram augmentation strategy or not. To explore the impact or benefit of data augmentation, the pixel distribution plots and probability density plots of MLT and GMLT in the directions of IVs are plotted, respectively.Taking As shown in In summary, the proposed GMLT method works well in the task of defect identification. It demonstrates that thermogram augmentation is an effective way to improve the performance of thermography analysis methods. A reasonable interpretation is that larger datasets allow the GMLT model to build a neighborhood graph that reflects the inherent structure of the data, and to obtain embedded components that retain its manifold after dimensionality reduction.Many NDE applications of IRT require machine learning-based data analysis models to obtain faster and more accurate inspection results. The performance of existing thermographic data processing methods is often constrained by the limited thermogram dataset. In this work, an image augmentation strategy was considered to solve the problem of data shortage. A GMLT method was developed to promote the effectiveness of the IRT-based defect detection and assessment. This method employed a SNGAN-based augmentation strategy and PLSR to address the challenges of limited data and large display mapping solution errors in the manifold thermography method, respectively. The feasibility and superiority of the proposed method for detecting subsurface defects in CFRP specimens were experimentally illustrated. The t-SNE visualizations and the DBS index denote that the proposed method finds a better projection direction for compressing nonlinear thermographic data and obtains the intrinsic data structure. The limitation of this study is that the time series properties of the thermograms were not considered during image augmentation. Therefore, there is still room for improvement in thermogram augmentation for further enhancing detection accuracy. In the future, the problem of how to find generated images in a more efficient and effective manner, such as using 3D GAN, will be further investigated.


Water distribution systems (WDSs) are used to transmit and distribute water resources in cities. Water distribution networks (WDNs) are partitioned into district metered areas (DMAs) by water network partitioning (WNP), which can be used for leak control, pollution monitoring, and pressure optimization in WDS management. In order to overcome the limitations of optimal search range and the decrease of recovery ability caused by two-step WNP and fixed DMAs in previous studies, this study developed a new method combining a graph neural network to realize integrated WNP and dynamic DMAs to optimize WDS management and respond to emergencies. The proposed method was tested in a practical case study; the results showed that good hydraulic performance of the WDN was maintained and that dynamic DMAs demonstrated excellent stability in emergency situations, which proves the effectiveness of the method in WNP. The British Water Industry Association proposed the concept of water network partitioning (WNP), which divides a WDN into several district metered areas (DMAs) to more effectively manage the WDS2, an approach which has proven to be of great benefit to the control of water leakage8.A water distribution network (WDN) is composed of demand nodes and supply pipelines and provides water to domestic and nondomestic users. WDN is managed by water distribution companies. Owing to pipe bursts, connection leakages, water theft, and other factors, WDNs are susceptible to significant unexpected water consumption14, optimising pressure management17 and helping to repair the water pipe network in emergencies18. However, WNP has some drawbacks, primarily the associated economic cost, deterioration of water quality20 and reduced capacity to respond to abnormal situations22. Further, research has shown that the disadvantages of WNP can be overcome by using methods such as dynamic DMAs management and other technologies21.Dividing a WDN into several DMAs has many benefits, including but are not limited to reducing leakage, reducing the flow of contaminants31, community structure34, modularity-based algorithms35, multi-level partitioning37, spectral graph algorithms40 and multi-agent approaches42. The methods applied in the dividing phase include single-objective programming43, multiple-objective programming48, iterative methods32 and heuristic algorithms49. The above methods can perform WNP, simplify management, monitor sudden leakage, and control the flow rate of contaminants, but the following two limitations need to be addressed:Using two phases and different sets of objectives reduces the search range of the global optimal solution.The use of a fixed boundary causes a water pressure drop owing to the reduction of inflow in the emergency.Normally, WNP is accomplished in two phases: clustering and dividing. The methods and concepts applied in the clustering phase include graph theoryGraph neural network used for the first time in water network partitioning.Dynamic district metered areas are used to optimise water network management.A simulation shows that this method is efficient and highly resilient to emergencies.Integrated WNP and dynamic DMAs are solutions to the above two problems. These approaches are used for the integrated establishment of DMAs and dynamic management of DMA boundaries, to achieve intelligent and flexible WDS management. In this study, an integrated WNP and dynamic DMAs method were developed, and simulating these methods in a network and proving the advantages of the method, which can maintain the normal operation of a network in an emergency. The contributions of this study are as follows:2. This method is quite straightforward, but it is difficult to apply to a large WDN. In addition, a WNP implemented by the trial-and-error method is usually unreasonable and negatively affects water quality. Tzatchkov et al. introduced graph theory into WNP and proposed a WNP method based on depth-first search (DFS) and breadth-first search (BFS)  Fig. a24, whic32, and finally formed DMAs with similar spatial locations. Giustolisi et al. found that the demand nodes’ altitude and consumption will also affect WNP. It is unreasonable to implement WNP based solely on spatial locations. Thus, they proposed implementing a community structure algorithm and proposed a modularity-based algorithm considering the hydraulic performance in WNP . Subsequently, Kip et al. proposed the use of graph convolutional networks (GCN)58 and Velickovic et al. proposed the use of graph attention networks (GAT)59, which greatly improved the effectiveness of GNN use. At present, GNNs have been effectively used in the fields of recommendation systems, financial risk control, molecular chemistry, traffic prediction, etc.63. They can also be used for the feature extraction, aggregation, and node classification of WNP. The process of using a GNN for WNP and dynamic boundary management is mainly composed of three logical steps: aggregate node information, integrated WNP, and dynamic boundary management.In recent years, some research has provided possibilities for new WNP methods. Inspired by word2vec “This section discusses the feasibility of integrated WNP and dynamic DMAs using a GNN. A WDN can be integrally partitioned through this method and can realize dynamic boundary management to cope with emergencies. The steps of this method for the WDN are shown in Fig. The WDN can be regarded as a graph The process of aggregate node information involves adding the attributes of the node itself and its neighbouring nodes, then using the sum of the addition as the attribute of the node in the next graph 64, When using the process of Build neural networksEstablish the evaluation indexTrain neural networksAccording to the results obtained from aggregate node information in Sect.  3.1, the following steps must be performed to classify nodes by using unsupervised learning and forming several DMAs.The proposed structure of the GNN and the training process are shown in Fig. The classification neural network of the WNP is composed of three parts: the input layer, hidden layer, and output layer. The input layer contains the information of the nodes, including information regarding the node characteristics and quantities. The hidden layer is composed of several layers, each of which is composed of several neurons, and the node parameters are iteratively optimized through training. The output layer is the WNP result under the ultimate network, and the evaluation index is used to evaluate the results of the classification. The neural network will use gradient descent to optimize the weights and bias of neurons, and then make the result of WNP as close as possible to the optimal score. After several iterations of optimization, the most reasonable result can be output.Resilience index Water quality index Aggregation index Balance index The evaluation index 51.The resilience index 45.The water quality index is used to evaluate the age of the water in the WDN. Water age affects the content of chlorine in WDNs and thus affects the quality of water. Further research shows that the installation of valves at the boundary pipes to close water will increase the water age at the boundary, but the impact on the overall water quality is not significantThe aggregation index Another indicator used to evaluate the reasonableness of WNP is the balance index In the neural network training stage, the model parameters are iteratively optimized until the expected result is obtained or Integrated WNP takes the 48; that is, multiple DMAs are combined into a large DMA, which overcomes the shortcomings caused by WNP.In the traditional WNP, boundary pipes no longer change state once the division is complete. This causes an overall water pressure drop in the DMAs when a sudden situation occurs that consumes a large amount of water. Giudicianni et al. proposed the creation of a dynamic WNP method that allows a fixed DMA boundary to be opened in emergenciesWhen a node in the DMAs bursts with a large amount of water, the optimal strategy is to open some boundary pipes near the node. In contrast opening a pipe that is far away from the abnormal node costs more energy and may not obtain good results. This means that each boundary pipe needs to be analysed and classified into three categories: normally open, normally closed, and dynamic.This paper proposes a dynamic method of managing the boundary pipes of DMAs. By calculating the influence factor 65. The Hanoi network is a part of the total Hanoi water distribution network, which includes 31 water demand nodes, and 50 pipes, as shown in Fig. This method was tested on a medium-sized WDN in Hanoi, C-town and E-townTo partition the water network of C-town to facilitate management and leakage control, the differences in the number of boundary pipes mentclass2pt{minim49 and community structure method (CS-WNP)32, DMAs based on GNN-WNP had fewer boundary pipes, which means that using this method to set up DMAs requires less cost; compared with the According to Fig. Next, the experiment focused on the influence of the aggregate node information process on WNP. The aggregate node information parameter In addition, the experiment focused on the influence of the number of DMAs on WNP. Using more DMAs is conducive to locating the leak location. However, in this case, more boundary pipelines were closed, which affected the hydraulic performance. Comparing the MAs Fig. , the hydThe main disadvantage of fixed DMAs is that the emergency capability of the WDN is reduced because of the closure of boundary pipes. When an emergency occurs (such as a large amount of water being used by fire-fighting equipment), regional water inflow restrictions lead to a decrease in overall water pressure and affect regional water use. Therefore, this study explores the possibility of using dynamic DMA boundary management to overcome the disadvantages of fixed WNP.Install flowmeters in boundary pipes with high Install fixed valves in boundary pipes with low Install dynamic valves in boundary pipes with medium The dynamic DMAs evaluate the daily status and emergency response status of the boundary pipes by calculating The WDN of C-town is simulated to determine the boundaries of DMAs and the opening or closing schemes of dynamic boundary pipes under different conditions. The The dynamic DMA configuration scheme for three emergencies  simulated in the WDS of C-town is shown in Table In the case of the medium fire, the dynamic WNP maintained normal operation and the fixed WNP fell into an abnormal situation. Compared with the unpartitioned water network, the In the case of the large fire, the resilience of the dynamic DMAs was much stronger than that of the fixed DMAs. Compared with the unpartitioned water network, the Thus, the dynamic DMAs were shown to have significantly stronger resilience under emergency conditions than fixed DMAs.The manuscript is conducted within the ethical manner advised by the journal.This paper presents a new method which can realize integrated WNP using dynamic DMAs. This method is based on graph neural network technology, which is often used for the classification of graph data; influence evaluation technology, which is often used for data importance ranking; and hydraulic simulation, which is often used for the rationality assessment of water network partitioning. A framework of integrated WNP and dynamic DMAs was developed based on PyTorch to apply the described method to a simulated medium-sized water distribution network called C-town, and used general indicators (such as Future work will focus on solving the problem of DMA interactivity. Specifically, when DMAs in the water network are connected in a loop. Therefore, a single boundary pipe does not only affect the two DMAs connected to it. Evaluating the hydraulic impact of the boundary pipes on the overall network will help to determine the optimal plan under emergency conditions and improve the efficiency of boundary dynamic operations.


With the rise of biomass-based materials such as nanocellulose, there is a growing need to develop statistical methods capable of leveraging inter-dependent experimental data to improve material design, product development, and process optimisation. Statistical approaches are essential given the multifaceted nature of variability in lignocellulosic biomass, which includes a range of different biomass feedstock types, a combinative arrangement of different biomass processing routes, and an array of different product formats depending on the focal application. To account for this large degree of variability and to extract meaningful patterns from research studies, there is a requirement to generate larger datasets of biomass-derived material properties through well-designed experimental systems that enable statistical analysis. To drive this trend, this article proposes the cross-disciplinary utilisation of statistical modelling approaches commonly applied within the field of statistical genetics to evaluate data generated in the field of biomass-based material research and development. The concepts of variance partitioning, heritability, hierarchical clustering, and selection gradients have been explained in their native context of statistical genetics and subsequently applied across the disciplinary boundary to evaluate relationships within a model experimental study involving the production of sorghum-derived cellulose nanofibres and their subsequent fabrication into nanopaper material. Variance partitioning and heritability calculates the relative influence of biomass vs. processing factors on material performance, while hierarchical clustering highlights the obscured similarity between experimental samples or characterisation metrics, and selection gradients elucidate the relationships between characterisation metrics and material quality. Ultimately, these statistical modelling approaches provide more depth to the investigation of biomass-processing-structure-property-performance relationships through outlining a framework for product characterisation, quality evaluation, and data visualisation, not only applicable to nanocellulose production but for all biomass-based materials and products. Biomass-derived nanocellulose is a highly versatile material currently under investigation across a wide range of burgeoning material applications, including paper and packaging, adsorbents, cosmetics, catalysts, construction, biomedicine, and electronic devices . The bioExperimental system design and statistical modelling approaches that account for these sources of variability are a significantly underdeveloped aspect of the nanocellulose research field . StatistThis work utilizes data from an experimental system outlined in an existing research study, involving the generation of cellulose nanofibres (CNFs) from sorghum agricultural byproducts and the subsequent fabrication of nanopaper material . The facThe key characterisation metrics used in this study included the nanofibre-water interaction properties of sedimentation behavior and water retention value, and the mechanical properties of nanopaper material, specifically nanopaper tensile index. Sedimentation behavior was based on the sediment height of a series of diluted cellulose nanofibre samples after settling over a period of 48 h. The derivative of the sediment height trendline over the dilution series is used to calculate the estimated average nanofibre aspect ratio based on the Effective Medium Theory . The watIn statistics, variance partitioning (or partitioning of the sums of squared deviations) involves estimating the spread of observations from the mean value for different sources of variability (or “componentsˮ) within the data set. Interestingly, the development of this field of statistics was largely driven by its application in quantitative genetics. In quantitative genetics, this concept is used to partition the variance in a phenotypic trait based on the effect of genetic and environmental components, as well as the interaction between these components. In other words, variance partitioning in this field estimates the influence of genetic and environmental factors on the phenotypic outcome of interest, a concept that is also known as heritability. In common parlance, this is the technical aspect of the “nature vs. nurture” debate. Based on the variance partitioning results, heritability can be calculated as the proportion of phenotype variance attributed to genetic factors out of the total phenotype variance for a specific trait .In the context of the current biomass-based material study, the genetic component is attributed to the type of biomass feedstock utilised for CNF preparation. On the other hand, the environmental component is not attributed to the growth conditions of the biomass, as would typically be the case in heritability studies. In this case, the variance due to the growth conditions is assumed to be negligible, as the biomass was grown in the same geographical location over the same period of time. Instead, the environmental component is attributed to the laboratory processing conditions, which act as a pseudo-environment encompassing everything from biomass grinding, pulping, nanofibrillation, and nanopaper fabrication. Therefore, heritability in the context of biomass-based material engineering is a measure of the relative influence of biomass factors  compared to the influence of processing conditions on the phenotypic trait value. The phenotypic trait can be selected as any property measured for the CNF or nanopaper material samples, such as a metric of nanofibre morphology, or the nanopaper tensile strength or toughness. The methodology required to partition the variance of biomass and processing components within the experimental system initially involves application of a statistical model to fit the data. In this case, a linear mixed-effects model was developed to fit the data, with the sorghum variety, plant section, and processing energy level comprising the fixed effects and the nanopaper duplicate and nanopaper strip replicates comprising the random effects. The experimental factors included within this Biomass-to-Nanopaper model are outlined in The response variable of the model was initially selected as the nanopaper tensile index (TI), as this metric generally indicates the quality of CNF samples for nanocomposite reinforcement applications. Therefore, the mixed-effects model is required to determine which experimental factors significantly influence the value of nanopaper tensile index value  and allow the statistical ranking of samples based on this metric . However, determination of the variance attributed to the biomass factors in relation to the processing factors required the conversion of the mixed effects model into a purely random effects model. The structure of the random effects model that was implemented within the R software workspace is outlined in Subsequently, an analysis of variance (ANOVA) was performed on the random effects model, with the outcome yielding component variance values. The heritability scores for each component were calculated as a proportion of the overall variance, as outlined in The break down of results for the partitioning of variance analysis are presented in In a similar manner, the response variable for the random effects model, which in the case above was the nanopaper tensile index, can be changed to any other CNF or nanopaper characterisation metric within the experimental system. To demonstrate an example of this, the response variable was changed to each one of the fibre morphology metrics assessed on CNF suspension samples using an automated fibre analysis device . Refer to the In this sense, a higher heritability value indicates a fibre morphology parameter that is more influenced by biomass factors related to different sorghum varieties or plant sections, while a lower heritability value indicates a fibre morphology parameter that is more influenced by the processing factor related to the mechanical treatment energy level. In phylogenetics, hierarchical clustering is a statistical method used to evaluate the genetic similarity between a set of different genes, species, or other taxa, typically visualized in the form of a branching tree diagram. The data used to generate the relationship between samples in the form of phylogenetic trees  is typically measured phenotypic data, or more recently on the nucleotide sequence of genes. However, this statistical method of measuring similarity between samples can be applied to a wide variety of different data set types, including for CNF morphology generated in the experimental system visually outlined in the Supplementary Material . In thisInterestingly, the groupings generated for both the biomass sample and fibre morphology parameter clustering were highly intuitive and presented informative groups. For biomass sample clustering, this approach readily distinguishes the variability in fibre morphology for the leaf section of sorghum biomass  The ascending order of the mean value between the selection gradient values for the two quality definitions (represented as the middle line of each box plot) signifies how the fibre morphology parameter influences quality on average across the two contexts. For example, fibre coarseness (fibre_coarse) has a strong negative selection gradient  for both the Q1 and Q5 definitions, indicating that a high fibre coarseness generates a low quality material in both the fibre-fibre and fibre-water interaction strength situations. On the other hand, a high fibre content (fibre_cont) generates a high quality material for both of these situations; 2) The fibre morphology parameters that are situated in the middle of the diagram  exhibit a minimal impact on product quality for both situations; and 3) The spread of the box plot indicates how much the selection gradient value changes across the two quality definitions. For example, fibre length (fibre_L) has a very similar influence on product quality for both fibre-fibre and fibre-water interaction applications, whereas the fine content (fine_cont) has a divergent influence on product quality depending on the application, such that a high fine content sample generates a high quality material for the fibre-water interaction application but significantly less so for the nanopaper strength application.Overall, this quantitative genetics-inspired methodology provides a new approach to visualizing the effect of characterisation metrics on nanocellulose material quality across multiple focal applications. Utilizing the selection gradient values in concert with the metric variance and covariance values, as outlined in This article outlines a novel approach to experimental data analysis and visualisation for biomass-based material processing, utilizing a combination of statistical methods commonly applied in quantitative genetics. Variance partitioning and heritability estimation  presents the opportunity to uncover the relative influence of biomass or processing factors on the final material performance, given a well-structured experimental design. Furthermore, the relative influence of biomass or processing factors can be estimated for each CNF characterisation metric, which in this case was demonstrated for the fibre morphology parameters. The relationships between characterisation metrics can also be assessed through a phylogenetics approach, which estimated the relative similarity of samples or characterisation metrics within the data set and exhibited intuitive clustering of the fibre morphology parameters. Lastly, a statistical approach commonly employed for predictive evolution and selective breeding studies was utilised to generate selection gradient values outlining the relationship between each characterisation metric and the quality score of samples within the experimental population, which serves as a proxy for evolutionary fitness. This approach enables visualisation of the characterisation metric influence on sample quality, when quality can be defined in different ways depending on the product type or focal application. The importance of these statistical approaches resides in their versatility across different material types—these methods are not limited to nanocellulose materials but can be applied across different studies that involve the processing of biomass feedstock for the production of various bio-based materials or products. Overall, integration of statistical genetics concepts into the field of biomass-based material engineering has the potential to increase the depth of investigation into the factors that influence sample quality, the relationships between characterisation metrics, and creates the opportunity for incorporation of genetic data of biomass feedstock in sustainable material investigation, all of which are essential for the industrial scale-up of highly variable and difficult to quantify, and qualify, nanocellulose materials.