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.

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.

Application of response surface method for optimal transfer conditions of multi-layer ceramic capacitor alignment system

The multi-layer ceramic capacitor (MLCC) alignment system aims at the inter-process automation between the first and the second plastic processes.As a result of testing performance verification of MLCC alignment system,the average alignment rates are 95% for 3216 chip,88.5% for 2012 chip and 90.8% for 3818 chip.The MLCC alignment system can be accepted for practical use because the average manual alignment is just 80%.In other words,the developed MLCC alignment system has been upgraded to a great extent,compared with manual alignment.Based on the successfully developed MLCC alignment system,the optimal transfer conditions have been explored by using RSM.The simulations using ADAMS has been performed according to the cube model of CCD.By using MiniTAB,the model of response surface has been established based on the simulation results.The optimal conditions resulted from the response optimization tool of MiniTAB has been verified by being assigned to the prototype of MLCC alignment system.

Seismogram Synthesis in Multi-layered Half-space Part Ⅰ. Theoretical Formulations

In the past two decades numerous studies were made to develop and improve the theory and practical computation techniques of synthesizing theoretical seismograms for the model of multi-layered half-space. Today, synthesizing theoretical seismograms in multi-layered half-space is an important tool for understanding the structure of the Earth’s interior as well as the seismic source process from well-recorded seismograms data. As part of a review of the state-of-the-art, in this article I shall present a systematic and self-contained theory of elastic waves in multi-layered half-space media based on the developments in the past two decades.

In-plane dynamic Green's functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic half-space

The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green’s functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic（TI）half-space.The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces,which are then applied to the total system with the opposite sign.By adding solutions restricted in the loaded layer to solutions from the reaction forces,the global solutions in the wavenumber domain are obtained,and the dynamic Green’s functions in the space domain are recovered by the inverse Fourier transform.The presented formulations can be reduced to the isotropic case developed by Wolf（1985）,and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI halfspace subjected to horizontally distributed loads which are special cases of the more general problem addressed.The deduced Green’s functions,in conjunction with boundary element methods,will lead to significant advances in the investigation of a variety of wave scattering,wave radiation and soil-structure interaction problems in a layered TI site.Selected numerical results are given to investigate the influence of material anisotropy,frequency of excitation,inclination angle and layered on the responses of displacement and stress,and some conclusions are drawn.

A Reverse Numerical Approach to Determine Elastic-plastic Properties of Multi-layer Material Systems with Flat Cylindrical Indenters

In the present study, the indentation testing with a flat cylindrical indenter on typical multi-layer material systems was simulated successfully by finite element method. The emphasis was put on the methods of extracting the yield stresses and strain-hardening modulus of upper and middle-layers of three-layer material systems from the indentation testing. The slope of the indentation depth to the applied indentation stress curve was found to have a turning point, which can be used to determine the yield stress of the upper-layer. Then, a different method was also presented to determine the yield stress of the middle-layer. This method was based on a set of assumed applied indentation stresses which were to be intersected by the experimental results in order to meet the requirement of having the experimental indentation depth. At last, a reverse numerical algorithm was explored to determine the yield stresses of upper and middle-layers simultaneously by using the indentation testing with two different size indenters. This method assumed two ranges of yield stresses to simulate the indentation behavior. The experimental depth behavior was used to intersect the simulated indentation behavior. And the intersection corresponded to the values of yield stresses of upper and middle-layers. This method was also used further to determine the strain-hardening modulus of upper and middle-layers simultaneously.

Lattice Boltzmann simulation of phase change and heat transfer characteristics in the multi-layer deposition

The metal droplets deposition method(MDDM)is a rapid prototyping technology,implemented via metallurgy bonding within droplets.The anisotropy of heat transfer and re-melting is caused by an asymmetric deposition process.A lattice Boltzmann method(LBM)model is established to predict the heat transfer and phase change in the multi-layer deposition.The prediction model is verified by the experimental temperature profiles in existing literature.The monitoring points are set to compare the temperature profiles,and decoupling analyze the heat transfer mechanism in different positions.The negative relationships between the re-molten volume of the temperature difference,as well as the influence of the dispositive position and the relative position of the adjacent component are observed and analyzed under the heat conduction.This work is helpful to choose the appropriate temperature conditions and the optimal dispositive method.

Evalution of Application of p-y Curve Method in Offshore Engineering Foundation

Based on the Mohr-Coulomb failure principle and Rankine's theory, the laterally loaded pile ultimate resistance formulas of sand and soft clay proposed by Reese and Matlock respectively are discussed in this paper. The authors put forward the modified ultimate resistance formulas on the basis of which the ultimate resistance formula is developed for horizontally loaded pile in multi-layer soil in consideration of the effect of the overburden soil pressure on the calculation of soil layer. It is significant to the correct application of the ultimate resistance formulas in API and ZCS Rules into offshore engineering.

A novel specimen preparation method for TJ-1 lunar soil simulant in hollow cylinder apparatus

Conventional methods for hollow cylinder apparatus （HCA） specimen preparation are not applicable for T J-1 lunar soil simulant due to its wide particle size distribution. A novel method to prepare uniform T J-1 specimen for HCA tests is put forward. The method is a combination of the multi-layering dry-rodding method and a new under-compaction criterion in the multi-layer with under-compaction method （UCM）. In the novel method, the specimen is prepared with 5 layers by dry-rodding and the UCM is used to determine the height after each layer is compacted. The density uniformity of specimen is evaluated by the freezing method to find out the best under-compaction criterion. Two HCA specimens with the same target density are prepared by the novel method and examined in the tests of pure rotation of the principal stresses. Their conformable mechanical behaviors ascertain the effectiveness of the method to produce uniform and reproducible HCA specimens. Four groups of HCA tests are carried out to investigate the anisotropic and non-coaxial behaviors of TJ-I lunar soil simulant. The results indicate that the principal stress direction, the deviator stress ratio, the stress level and the coefficient of the intermediate principal stress significantly influence the strength and deformation properties of T J-1 lunar soil simulant.

Numerical Study on an Applicable Underground Mining Method for Soft Extra-Thick Coal Seams in Thailand

The EGAT Mae Moh Mine is the largest open pit lignite mine in Thailand and it produces lignite about 16 million tons annually. In the near future, the pit limit of the mine will be reached and underground mine will then be developed through the open pit in the depth of 400 - 600 m from the surface. However, due to the challenges for underground mining such as poor geological conditions, extra thickness (20 - 30 m) of coal seams, and weak mechanical properties of coal seams and the surrounding rock, the success possibility of underground mining and an applicable underground mining method is being investigated at the present. The paper discusses the applicability of multi-slice bord-and-pillar method for the soft extra thick coal seams in the Mae Moh mine by means of numerical analyses using the 3D finite difference code “FLAC3D”.

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.

Aerodynamic optimization of rotor airfoil based on multi-layer hierarchical constraint method

Rotor airfoil design is investigated in this paper. There are many difficulties for this highdimensional multi-objective problem when traditional multi-objective optimization methods are used. Therefore, a multi-layer hierarchical constraint method is proposed by coupling principal component analysis(PCA) dimensionality reduction and e-constraint method to translate the original high-dimensional problem into a bi-objective problem. This paper selects the main design objectives by conducting PCA to the preliminary solution of original problem with consideration of the priority of design objectives. According to the e-constraint method, the design model is established by treating the two top-ranking design goals as objective and others as variable constraints. A series of bi-objective Pareto curves will be obtained by changing the variable constraints, and the favorable solution can be obtained by analyzing Pareto curve spectrum. This method is applied to the rotor airfoil design and makes great improvement in aerodynamic performance. It is shown that the method is convenient and efficient, beyond which, it facilitates decision-making of the highdimensional multi-objective engineering problem.

The wave absorption efficiency of multi-layer vertical perforated thin plates

This paper analyzes the wave absorption efficiency of multi-layer perforated plates in an ideal fluid, based on the linear potential flow theory. The influence of the thickness, the porosity and the layout form of the plates on the wave absorptivity is studied on the assumption that all perforated plates are composed of the same materials and have the same thickness and porosity. The calculation results indicate that the larger the number of layers of the perforated plate set, the better the wave absorption efficiency, however, when the layer number exceeds a certain value, the efficiency of the plates is not significantly increased. For the case of porosity ？= 0.2, thickness b= 0.07 m and 4 layers of perforated plates with a distance l= 1.0 m between the layers, 90% of the energy of the wave within the incident wave period between 1.6 s and 4.4 s can be absorbed.

MLP training in a self-organizing state space model using unscented Kalman particle filter

Many Bayesian learning approaches to the multi-layer perceptron （MLP） parameter optimization have been proposed such as the extended Kalman filter （EKF）. This paper uses the unscented Kalman particle filter （UPF） to train the MLP in a self- organizing state space （SOSS） model. This involves forming augmented state vectors consisting of all parameters （the weights of the MLP） and outputs. The UPF is used to sequentially update the true system states and high dimensional parameters that are inherent to the SOSS moder for the MLP simultaneously. Simulation results show that the new method performs better than traditional optimization methods.

Intra-layer synchronization in duplex networks

This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between, within, and across layers. Based on the Lyapunov stability method, we prove theoretically that the duplex network can achieve intra-layer synchronization under some appropriate conditions, and give the thresholds of coupling strength within layers for different types of inner coupling matrices across layers. Interestingly,for a certain class of coupling matrices across layers, it needs larger coupling strength within layers to ensure the intra-layer synchronization when the coupling strength across layers become larger, intuitively opposing the fact that the intra-layer synchronization is seemly independent of the coupling strength across layers. Finally, numerical simulations further verify the theoretical results.

Predictive defect detection for prototype additive manufacturing based on multi-layer susceptibility discrimination

This paper presents a predictive defect detection method for prototype additive manufacturing(AM)based on multilayer susceptibility discrimination(MSD).Most current methods are significantly limited by merely captured images,disregarding the differences between layer-by-layer manufacturing approaches,without combining transcendental knowledge.The visible parts,originating from the prototype of conceptual design,are determined based on spherical flipping and convex hull theory,on the basis of which theoretical template image(TTI)is rendered according to photorealistic technology.In addition,to jointly consider the differences in AM processes,the finite element method(FEM)of transient thermal-structure coupled analysis was conducted to probe susceptible regions where defects appeared with a higher possibility.Driven by prior knowledge acquired from the FEM analysis,the MSD with an adaptive threshold,which discriminated the sensitivity and susceptibility of each layer,was implemented to determine defects.The anomalous regions were detected and refined by superimposing multiple-layer anomalous regions and comparing the structural features extracted using the Chan-Vese(CV)model.A physical experiment was performed via digital light processing(DLP)with photosensitive resin of a non-faceted scaled V-shaped engine block prototype with cylindrical holes using a non-contact profilometer.This MSD method is practical for detecting defects and is valuable for a deeper exploration of barely visible impact damage(BVID),thereby reducing the defect of prototypical mechanical parts in engineering machinery or process equipment via intellectualized machinevision.

A simple model for approximate bandgap structure calculation of all-solid photonic bandgap fibre based on an array of rings

A simple model for approximate bandgap structure calculation of all-solid photonic bandgap fibre based on an array of rings is proposed. In this model calculated are only the potential modes of a unit cell, which is a high-index ring in the low-index background for this fibre, rather than the whole cladding periodic structure based on Bloch＇s theorem to find the bandgap. Its accuracy is proved by comparing its results with the results obtained by using the accurate full-vector plane-wave method. High speed in computation is its great advantage over the other exact methods, because it only needs to find the roots of one-dimensional analytical expressions. And the results of this model, mode plots, offer an ideal environment to explore the basic properties of photonie bandgap clearly.

Rounded Data Analysis Based on Multi-Layer Ranked Set Sampling

Observations of sampling are often subject to rounding, but are modeled as though they were unrounded. This paper examines the impact of rounding errors on parameter estimation with multi-layer ranked set sampling. It shows that the rounding errors seriously distort the behavior of covariance matrix estimate, and lead to inconsistent estimation. Taking this into account, we present a new approach to implement the estimation for this model, and further establish the strong consistency and asymptotic normality of the proposed estimators. Simulation experiments show that our estimates based on rounded multi-layer ranked set sampling are always more efficient than those based on rounded simple random sampling.