Multi-layer perceptron-based data-driven multiscale modelling of granular materials with a novel Frobenius norm-based internal variable

One objective of developing machine learning(ML)-based material models is to integrate them with well-established numerical methods to solve boundary value problems(BVPs).In the family of ML models,recurrent neural networks(RNNs)have been extensively applied to capture history-dependent constitutive responses of granular materials,but these multiple-step-based neural networks are neither sufficiently efficient nor aligned with the standard finite element method(FEM).Single-step-based neural networks like the multi-layer perceptron(MLP)are an alternative to bypass the above issues but have to introduce some internal variables to encode complex loading histories.In this work,one novel Frobenius norm-based internal variable,together with the Fourier layer and residual architectureenhanced MLP model,is crafted to replicate the history-dependent constitutive features of representative volume element(RVE)for granular materials.The obtained ML models are then seamlessly embedded into the FEM to solve the BVP of a biaxial compression case and a rigid strip footing case.The obtained solutions are comparable to results from the FEM-DEM multiscale modelling but achieve significantly improved efficiency.The results demonstrate the applicability of the proposed internal variable in enabling MLP to capture highly nonlinear constitutive responses of granular materials.

A Well Productivity Model for Multi-Layered Marine and Continental Transitional Reservoirs with Complex Fracture Networks

Using the typical characteristics of multi-layered marine and continental transitional gas reservoirs as a basis,a model is developed to predict the related well production rate.This model relies on the fractal theory of tortuous capillary bundles and can take into account multiple gas flow mechanisms at the micrometer and nanometer scales,as well as the flow characteristics in different types of thin layers(tight sandstone gas,shale gas,and coalbed gas).Moreover,a source-sink function concept and a pressure drop superposition principle are utilized to introduce a coupled flow model in the reservoir.A semi-analytical solution for the production rate is obtained using a matrix iteration method.A specific well is selected for fitting dynamic production data,and the calculation results show that the tight sandstone has the highest gas production per unit thickness compared with the other types of reservoirs.Moreover,desorption and diffusion of coalbed gas and shale gas can significantly contribute to gas production,and the daily production of these two gases decreases rapidly with decreasing reservoir pressure.Interestingly,the gas production from fractures exhibits an approximately U-shaped distribution,indicating the need to optimize the spacing between clusters during hydraulic fracturing to reduce the area of overlapping fracture control.The coal matrix water saturation significantly affects the coalbed gas production,with higher water saturation leading to lower production.

A flexible ultra-broadband multi-layered absorber working at 2 GHz-40 GHz printed by resistive ink

A flexible extra broadband metamaterial absorber(MMA)stacked with five layers working at 2 GHz–40 GHz is investigated.Each layer is composed of polyvinyl chloride(PVC),polyimide(PI),and a frequency selective surface(FSS),which is printed on PI using conductive ink.To investigate this absorber,both one-dimensional analogous circuit analysis and three-dimensional full-wave simulation based on a physical model are provided.Various crucial electromagnetic properties,such as absorption,effective impedance,complex permittivity and permeability,electric current distribution and magnetic field distribution at resonant peak points,are studied in detail.Analysis shows that the working frequency of this absorber covers entire S,C,X,Ku,K and Ka bands with a minimum thickness of 0.098λ_(max)(λ_(max) is the maximum wavelength in the absorption band),and the fractional bandwidth(FBW)reaches 181.1%.Moreover,the reflection coefficient is less than-10 dB at 1.998 GHz–40.056 GHz at normal incidence,and the absorptivity of the plane wave is greater than 80%when the incident angle is smaller than 50°.Furthermore,the proposed absorber is experimentally validated,and the experimental results show good agreement with the simulation results,which demonstrates the potential applicability of this absorber at 2 GHz–40 GHz.

Blast wave characteristics of multi-layer composite charge:Theoretical analysis,numerical simulation,and experimental validation

This article investigates the characteristics of shock wave overpressure generated by multi-layer composite charge under different detonation modes.Combining dimensional analysis and the explosion mechanism of the charge,a peak overpressure prediction model for the composite charge under singlepoint detonation and simultaneous detonation was established.The effects of the charge structure and initiation method on the overpressure field characteristics were investigated in AUTODYN simulation.The accuracy of the prediction model and the reliability of the numerical simulation method were subsequently verified in a series of static explosion experiments.The results reveal that the mass of the inner charge was the key factor determining the peak overpressure of the composite charge under single-point detonation.The peak overpressure in the radial direction improved apparently with an increase in the aspect ratio of the charge.The overpressure curves in the axial direction exhibited a multi-peak phenomenon,and the secondary peak overpressure even exceeded the primary peak at distances of 30D and 40D(where D is the charge diameter).The difference in peak overpressure among azimuth angles of 0-90°gradually decreased with an increase in the propagation distance of the shock wave.The coupled effect of the detonation energy of the inner and outer charge under simultaneous detonation improved the overpressure in both radial and axial directions.The difference in peak overpressure obtained from model prediction and experimental measurements was less than 16.4%.

Three-Dimensional Modelling of a Multi-Layer Sandstone Reservoir： the Sebei Gas Field, China

Multi-layer sandstone reservoirs occur globally and are currently in international production. The 3D characteristics of these reservoirs are too complicated to be accurately delineated by general structural-facies-reservoir modelling. In view of the special geological features, such as the vertical architecture of sandstone and mudstone interbeds, the lateral stable sedimentation and the strong heterogeneity of reservoir poroperm and fluid distribution, we developed a new three-stage and six-phase procedure for 3D characterization of multi-layer sandstone reservoirs. The procedure comprises two-phase structural modelling, two-phase facies modelling and modelling of two types of reservoir properties. Using this procedure, we established models of the formation structure, sand body structure and microfacies, reservoir facies and properties including porosity, permeability and gas saturation and provided a 3D fine-scale, systematic characterization of the Sebei multi-layer sandstone gas field, China. This new procedure, validated by the Sebei gas field, can be applied to characterize similar multi-layer sandstone reservoirs.

Prediction of flyrock distance induced by mine blasting using a novel Harris Hawks optimization-based multi-layer perceptron neural network

In mining or construction projects,for exploitation of hard rock with high strength properties,blasting is frequently applied to breaking or moving them using high explosive energy.However,use of explosives may lead to the flyrock phenomenon.Flyrock can damage structures or nearby equipment in the surrounding areas and inflict harm to humans,especially workers in the working sites.Thus,prediction of flyrock is of high importance.In this investigation,examination and estimation/forecast of flyrock distance induced by blasting through the application of five artificial intelligent algorithms were carried out.One hundred and fifty-two blasting events in three open-pit granite mines in Johor,Malaysia,were monitored to collect field data.The collected data include blasting parameters and rock mass properties.Site-specific weathering index(WI),geological strength index(GSI) and rock quality designation(RQD)are rock mass properties.Multi-layer perceptron(MLP),random forest(RF),support vector machine(SVM),and hybrid models including Harris Hawks optimization-based MLP(known as HHO-MLP) and whale optimization algorithm-based MLP(known as WOA-MLP) were developed.The performance of various models was assessed through various performance indices,including a10-index,coefficient of determination(R^(2)),root mean squared error(RMSE),mean absolute percentage error(MAPE),variance accounted for(VAF),and root squared error(RSE).The a10-index values for MLP,RF,SVM,HHO-MLP and WOA-MLP are 0.953,0.933,0.937,0.991 and 0.972,respectively.R^(2) of HHO-MLP is 0.998,which achieved the best performance among all five machine learning(ML) models.

Explosive synchronization of multi-layer complex networks based on star connection between layers with delay

Explosive synchronization(ES)is a kind of first-order jump phenomenon that exists in physical and biological systems.In recent years,researchers have focused on ES between single-layer and multi-layer networks.Most research on complex networks with delay has focused on single-layer or double-layer networks,multi-layer networks are seldom explored.In this paper,we propose a Kuramoto model of frequency weights in multi-layer complex networks with delay and star connections between layers.Through theoretical analysis and numerical verification,the factors affecting the backward critical coupling strength are analyzed.The results show that the interaction between layers and the average node degree has a direct effect on the backward critical coupling strength of each layer network.The location of the delay,the size of the delay,the number of network layers,the number of nodes,and the network topology are revealed to have no direct impact on the backward critical coupling strength of the network.Delay is introduced to explore the influence of delay and other related parameters on ES.

Multi-layer Tectonic Model for Intraplate Deformation and Plastic-Flow Network in the Asian Continental Lithosphere

In a large area of the east—central Asian continent there is a unified seismic network system composed of two families of large—seismic belts that intersect conjugately. Such a seismic network in the middle—upper crust is actually a response to the plastic flow network in the lower lithosphere including the lower crust and lithospheric mantle. The existence of the unified plastic flow system confirms that the driving force for intraplate tectonic deformation results mainly from the compression of the India plate, while the long-range transmission of the force is carried out chiefly by means of plastic flow. The plastic flow network has a control over the intraplate tectonic deformation.

Prediction of Logistics Demand via Least Square Method and Multi-Layer Perceptron

To implement the prediction of the logistics demand capacity of a certain region,a comprehensive index system is constructed,which is composed of freight volume and other eight relevant economic indices,such as gross domestic product(GDP),consumer price index(CPI),total import and export volume,port's cargo throughput,total retail sales of consumer goods,total fixed asset investment,highway mileage,and resident population,to form the foundation for the model calculation.Based on the least square method(LSM)to fit the parameters,the study obtains an accurate mathematical model and predicts the changes of each index in the next five years.Using artificial intelligence software,the research establishes the logistics demand model of multi-layer perceptron(MLP)neural network,makes an empirical analysis on the logistics demand of Quanzhou City,and predicts its logistics demand in the next five years,which provides some references for formulating logistics planning and development strategy.

Recommendation System Based on Perceptron and Graph Convolution Network

The relationship between users and items,which cannot be recovered by traditional techniques,can be extracted by the recommendation algorithm based on the graph convolution network.The current simple linear combination of these algorithms may not be sufficient to extract the complex structure of user interaction data.This paper presents a new approach to address such issues,utilizing the graph convolution network to extract association relations.The proposed approach mainly includes three modules:Embedding layer,forward propagation layer,and score prediction layer.The embedding layer models users and items according to their interaction information and generates initial feature vectors as input for the forward propagation layer.The forward propagation layer designs two parallel graph convolution networks with self-connections,which extract higher-order association relevance from users and items separately by multi-layer graph convolution.Furthermore,the forward propagation layer integrates the attention factor to assign different weights among the hop neighbors of the graph convolution network fusion,capturing more comprehensive association relevance between users and items as input for the score prediction layer.The score prediction layer introduces MLP(multi-layer perceptron)to conduct non-linear feature interaction between users and items,respectively.Finally,the prediction score of users to items is obtained.The recall rate and normalized discounted cumulative gain were used as evaluation indexes.The proposed approach effectively integrates higher-order information in user entries,and experimental analysis demonstrates its superiority over the existing algorithms.

Digital modulation classification using multi-layer perceptron and time-frequency features

Considering that real communication signals corrupted by noise are generally nonstationary, and timefrequency distributions are especially suitable for the analysis of nonstationary signals, time-frequency distributions are introduced for the modulation classification of communication signals： The extracted time-frequency features have good classification information, and they are insensitive to signal to noise ratio （SNR） variation. According to good classification by the correct rate of a neural network classifier, a multilayer perceptron （MLP） classifier with better generalization, as well as, addition of time-frequency features set for classifying six different modulation types has been proposed. Computer simulations show that the MLP classifier outperforms the decision-theoretic classifier at low SNRs, and the classification experiments for real MPSK signals verify engineering significance of the MLP classifier.

Identification of low-resistivity-low-contrast pay zones in the feature space with a multi-layer perceptron based on conventional well log data

In the early exploration of many oilfields,low-resistivity-low-contrast(LRLC)pay zones are easily overlooked due to the resistivity similarity to the water zones.Existing identification methods are model-driven and cannot yield satisfactory results when the causes of LRLC pay zones are complicated.In this study,after analyzing a large number of core samples,main causes of LRLC pay zones in the study area are discerned,which include complex distribution of formation water salinity,high irreducible water saturation due to micropores,and high shale volume.Moreover,different oil testing layers may have different causes of LRLC pay zones.As a result,in addition to the well log data of oil testing layers,well log data of adjacent shale layers are also added to the original dataset as reference data.The densitybased spatial clustering algorithm with noise(DBSCAN)is used to cluster the original dataset into 49 clusters.A new dataset is ultimately projected into a feature space with 49 dimensions.The new dataset and oil testing results are respectively treated as input and output to train the multi-layer perceptron(MLP).A total of 3192 samples are used for stratified 8-fold cross-validation,and the accuracy of the MLP is found to be 85.53%.

NEW MODEL OF GAS FLOW PROBLEM IN MULTI-LAYERED GAS RESERVOIR AND APPLICATION

In this paper, the new model of the real gas filtration problem has been presented multi-layered gas reservoir, when a gas well output and wellbore storage may be variable, and have obtained the exact solutions of pressure distribution for each reservoir bed under three kinds of typical out-boundary conditions. As a special case, according to the new model have also obtained the qxact solutions of presssure distribution in homogeneous reservoir and is given important application in gas reservoir development.

Multi-layer Evacuation Model: A solution of Emergency Evacuation

The large-scale population accumulation in modem cities has become one of their important characteristics. With the development of urbanization in the world, the large-scale gathering activities are increasing, and the accidents caused by them are also rising. At the same time, the evacuation of visitors is faced with severe challenges in the event of an emergency such as terrorist attacks. The main problem for tourists is how to evacuate quickly and safely in an emergency. The Louvre is one of the largest and most visited art museums in the world.Visitors are large and come from all over the world, the volume of passengers varies greatly, and the interior architecture design is complicated, etc. These characteristics challenge the design of evacuation paths. Based on the consideration of these factors, we should develop the optimal evacuation scheme and minimize the accident risk and evacuation cost.

Energy Absorption Diagrams of Multi-layer Corrugated Boards

Based on the static compression experiments, the compressive stress-strain curve of multi-layer corrugated boards is simplified into three sections of linear elasticity, sub-buckling going with local collapse and densification. By considering the structure factors of multi-layer corrugated boards, the energy absorption model is obtained and characterized by the structure factors of corrugated cell-wall. The model is standardized by the solid modulus and it is universal for corrugated structures of different basis material. In the liner-elastic section, with the increase of the load, the energy absorption per unit volume of multi-layer corrugated boards gradually increases; in the sub-buckling section going with local collapse, the compression resistance of multi-layer corrugated boards goes on under a nearly constant load, but the energy absorption per unit volume rapidly increases with the increase of the compression strain. It is shown as an ascending curve in the energy absorption diagram. In the densification section, the corrugated sandwich core has no energy absorption capability. A good consistency is achieved between theoretical and experimental energy absorption curves. In designing the cushioning package, the cushioning properties can be evaluated by the theoretical model without more experiments. The suggested method to develop the energy absorption diagram for corrugated boards can be used to characterize the cushioning properties and optimize the structures of corrugated sandwich structures.

Design of multi-layered porous fibrous metals for optimal sound absorption in the low frequency range

We present a design method for calculating and optimizing sound absorption coefficient of multi-layered porous fibrous metals （PFM） in the low frequency range. PFM is simplified as an equivalent idealized sheet with all metallic fibers aligned in one direction and distributed in periodic hexagonal patterns. We use a phenomenological model in the literature to investigate the effects of pore geometrical parameters （fiber diameter and gap） on sound absorption performance. The sound absorption coefficient of multi- layered PFMs is calculated using impedance translation theorem, To demonstrate the validity of the present model, we compare the predicted results with the experimental data. With the average sound absorption （low frequency range） as the objective function and the fiber gaps as the design variables, an optimization method for multi-layered fibrous metals is proposed. A new fibrous layout with given porosity of multi-layered fibrous metals is suggested to achieve optimal low frequency sound absorption. The sound absorption coefficient of the optimal multi-layered fibrous metal is higher than the single- layered fibrous metal, and a significant effect of the fibrous material on sound absorption is found due to the surface Dorosity of the multi-layered fibrous.

Convective transport of nanoparticles in multi-layer fluid flow

Technologically, multi-layer fluid models are important in understanding fluid-fluid or fluid-nanoparticle interactions and their effects on flow and heat transfer characteristics. However, to the best of the authors＇ knowledge, little attention has been paid to the study of three-layer fluid models with nanofluids. Therefore, a three-layer fluid flow model with nanofluids is formulated in this paper. The governing coupled nonlinear differential equations of the problem are non-dimensionalized by using appropriate fundamental quantities. The resulting multi-point boundary value problem is solved numerically by quasi-linearization and Richardson＇s extrapolation with modified boundary conditions. The effects of the model parameters on the flow and heat transfer are obtained and analyzed. The results show that an increase in the nanoparticle concentration in the base fluid can modify the fluid-velocity at the interface of the two fluids and reduce the shear not only at the surface of the clear fluid but also at the interface between them. That is, nanofluids play a vital role in modifying the flow phenomena. Therefore, one can use nanofluids to obtain the desired qualities for the multi-fluid flow and heat transfer characteristics.

Constitutive modelling of idealised granular materials using machine learning method

Predicting the constitutive response of granular soils is a fundamental goal in geomechanics.This paper presents a machine learning(ML)framework for the prediction of the stress-strain behaviour and shearinduced contact fabric evolution of an idealised granular material subject to triaxial shearing.The MLbased framework is comprised of a set of mini-triaxial tests which provide a benchmark for the setup and validation of the discrete element method(DEM)model of the granular materials,a parametric DEM simulation programme of virtual triaxial tests which provides datasets of micro-and macro-mechanical information,as well as a multi-layer perceptron(MLP)neural network which is trained and tested using the DEM-based datasets.The ML model only requires the initial void ratio of the granular sample as the input for predicting its constitutive response.The excellent agreement between the ML model prediction and experimental test and DEM simulation results indicates that the MLebased modelling approach is capable of capturing accurately the effects of initial void ratio on the constitutive behaviour of idealised granular materials,bypassing the need to incorporate the complex micromechanics underlying the macroscopic mechanical behaviour of granular materials.Lastly,a detailed comparison between the used MLP model and long short-term memory(LSTM)model was made from the perspective of technical algorithm,prediction accuracy,and computational efficiency.

Explosive synchronization of multi-layer complex networks based on inter-layer star network connection

Explosive synchronization(ES)is a first-order transition phenomenon that is ubiquitous in various physical and biological systems.In recent years,researchers have focused on explosive synchronization in a single-layer network,but few in multi-layer networks.This paper proposes a frequency-weighted Kuramoto model in multi-layer complex networks with star connection between layers and analyzes the factors affecting the backward critical coupling strength by both theoretical analysis and numerical validation.Our results show that the backward critical coupling strength of each layer network is influenced by the inter-layer interaction strength and the average degree.The number of network layers,the number of nodes,and the network topology can not directly affect the synchronization of the network.Enhancing the inter-layer interaction strength can prevent the emergence of explosive synchronization and increasing the average degree can promote the generation of explosive synchronization.

Multi-objective optimization of the cathode catalyst layer micro-composition of polymer electrolyte membrane fuel cells using a multi-scale,two-phase fuel cell model and data-driven surrogates

Polymer electrolyte membrane fuel cells(PEMFCs)are considered a promising alternative to internal combustion engines in the automotive sector.Their commercialization is mainly hindered due to the cost and effectiveness of using platinum(Pt)in them.The cathode catalyst layer(CL)is considered a core component in PEMFCs,and its composition often considerably affects the cell performance(V_(cell))also PEMFC fabrication and production(C_(stack))costs.In this study,a data-driven multi-objective optimization analysis is conducted to effectively evaluate the effects of various cathode CL compositions on Vcelland Cstack.Four essential cathode CL parameters,i.e.,platinum loading(L_(Pt)),weight ratio of ionomer to carbon(wt_(I/C)),weight ratio of Pt to carbon(wt_(Pt/c)),and porosity of cathode CL(ε_(cCL)),are considered as the design variables.The simulation results of a three-dimensional,multi-scale,two-phase comprehensive PEMFC model are used to train and test two famous surrogates:multi-layer perceptron(MLP)and response surface analysis(RSA).Their accuracies are verified using root mean square error and adjusted R^(2).MLP which outperforms RSA in terms of prediction capability is then linked to a multi-objective non-dominated sorting genetic algorithmⅡ.Compared to a typical PEMFC stack,the results of the optimal study show that the single-cell voltage,Vcellis improved by 28 m V for the same stack price and the stack cost evaluated through the U.S department of energy cost model is reduced by$5.86/k W for the same stack performance.