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.

Glacial debris flow susceptibility mapping based on combined models in the Parlung Tsangpo Basin,China

Machine learning(ML)-based prediction models for mapping hazard(e.g.,landslide and debris flow)susceptibility have been widely developed in recent research.However,in some specific areas,ML models have limited application because of the uncertainties in identifying negative samples.The Parlung Tsangpo Basin exemplifies a region prone to recurrent glacial debris flows(GDFs)and is characterized by a prominent landform featuring deep gullies.Considering the limitations of the ML model,we developed and compared two combined statistical models(FA-WE and FA-IC)based on factor analysis(FA),weight of evidence(WE),and the information content(IC)method.The final GDF susceptibility maps were generated by selecting 8 most important static factors and considering the influence of precipitation.The results show that the FA-IC model has the best performance.The areas with a very high susceptibility to GDFs are primarily located in the narrow valley section upstream,on both sides of the valley in the middle and downstream of the Parlung Tsangpo River,and in the narrow valley section of each tributary.These areas encompass 86 gullies and are characterized as"narrow and steep".

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%.

Determining safe yield and mapping water level zoning in groundwater resources of the Neishabour Plain

Groundwater is a crucial sources of water supply,especially in arid and semi-arid areas around the world.With uncontrolled withdrawals and limited availability of these resources,it is essential to determine the safe yield of these valuable resources.The Hill method approach was used in this study to determine the safe yield the Neishabour aquifer in Khorasan Razvi province in Iran.The results showed that the safe yield in the Neishabour aquifer is 60%lower than the current pumping amounts during the study period,indicating that further overdrafts could result in the destruction of this aquifer.This highlights the importance of using the Hill method to estimate the permitted exploitation from other aquifers,thus preventing problems caused by over-extraction and maintaining stability of global groundwater levels.

An integrated method of selecting environmental covariates for predictive soil depth mapping

Environmental covariates are the basis of predictive soil mapping.Their selection determines the performance of soil mapping to a great extent,especially in cases where the number of soil samples is limited but soil spatial heterogeneity is high.In this study,we proposed an integrated method to select environmental covariates for predictive soil depth mapping.First,candidate variables that may influence the development of soil depth were selected based on pedogenetic knowledge.Second,three conventional methods(Pearson correlation analysis(PsCA),generalized additive models(GAMs),and Random Forest(RF))were used to generate optimal combinations of environmental covariates.Finally,three optimal combinations were integrated to produce a final combination based on the importance and occurrence frequency of each environmental covariate.We tested this method for soil depth mapping in the upper reaches of the Heihe River Basin in Northwest China.A total of 129 soil sampling sites were collected using a representative sampling strategy,and RF and support vector machine(SVM)models were used to map soil depth.The results showed that compared to the set of environmental covariates selected by the three conventional selection methods,the set of environmental covariates selected by the proposed method achieved higher mapping accuracy.The combination from the proposed method obtained a root mean square error(RMSE)of 11.88 cm,which was 2.25–7.64 cm lower than the other methods,and an R^2 value of 0.76,which was 0.08–0.26 higher than the other methods.The results suggest that our method can be used as an alternative to the conventional methods for soil depth mapping and may also be effective for mapping other soil properties.

A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM,FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS,AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].

VISCOSITY ITERATIVE METHODS FOR COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS WITHOUT COMMUTATIVITY ASSUMPTION IN HILBERT SPACES

In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without commutativity assumption, that the iterates converge to a common fixed point of the mappings which solves some variational inequality. The results presented extend the corresponding results of Shimizu and Takahashi IT. Shimizu, W. Takahashi, Strong convergence to common fixed point of families of nonexpansive mappings, J. Math. Anal. Appl. 211 （1997）, 71-83], and Yao and Chen [Y. Yao, R. Chert, Convergence to common fixed points of average mappings without commutativity assumption in Hilbert spaces, Nonlinear Analysis 67（2007）, 1758-1763].

Fatigue Topology Optimization Design Based on Distortion Energy Theory and Independent Continuous Mapping Method

Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.

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.

A Seismotectonic Zonation Map of Eastern Siberia: New Principles and Methods of Mapping

The paper reviews goals and objectives, stages and components of a seismotectonic study conducted in Eastern Siberia, Russia. Based on a comprehensive analysis of geological and geophysical data, our study establishes whether the local earthquakes are of tectonic origin and reveals relationships among earthquakes with recent geodynamic processes in the area under study. Seismic hazard assessment and evaluation of tectonic processes are the two major closely interrelated aspects of seismotectonic studies. A seismotectonic study is generally combined with a seismic study and conducted prior to the stage of detailed seismic zonation (DSZ) which is followed by seismic micro-zonation (SMZ). In three stages of the seismotectonic study, we analyze specific geological structures, reveal the regional dynamics of seismotectonic processes, clarify details of potential seismic hazard locations and identify sites of the potential instantaneous deformation of the crust which may take place due to active faulting. Based on results of our longterm studies, a seismotectonic zonation map of Eastern Siberia is compiled. The paper briefly reviews the methods of mapping and refers to data on active faults and neotectonic structures revealed in the area under study, which are closely related to regional earthquake sources.

Precise method to control elastic waves by conformal mapping

The transformation method to control waves has received widespread attention in electromagnetism and acoustics. However, this machinery is not directly applicable to the control of elastic waves, because it has been shown that the Navier＇s equation does not usually retain its form under coordinate transformation. In this letter, we prove the form invariance of the Navier＇s equation under the conformal mapping based on the Helmholtz decomposition method. The needed material parameters are provided to manipulate elastic waves. The validity of this approach is confirmed by an active stealth device which can disguise the signal source by changing its position. Experimental verifications and potential applications may be expected in nondestructive testing, structural seismic design and other fields.

Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings

Let K be a closed convex subset of a real reflexive Banach space E, T:K→K be a nonexpansive mapping, and f:K→K be a fixed weakly contractive (may not be contractive) mapping. Then for any t∈(0, 1), let xt∈K be the unique fixed point of the weak contraction x tf(x)+(1?t)Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E*, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the cor- responding results in (Xu, 2004).

Stochastic response analysis of noisy system with non-negative real-power restoring force by generalized cell mapping method

The stochastic response of a noisy system with non-negative restoring force is investigated. The generalized cell mapping （GCM） method compute the transient and stationary probability density functions （PDFs） real-power is used to Combined with the global properties of the noise-free system, the evolutionary process of the tran- sient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.

Hybrid Extragradient-Type Methods for Finding a Common Solution of an Equilibrium Problem and a Family of Strict Pseudo-Contraction Mappings

This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.

On the basis of the morphology of the T-wave alternans: A Poincare mapping method research

Presently T-wave alternans (TWA) has become a clinical index of non-invasive diagnosis for heart sudden death prediction, and detecting T-wave alternate accurately is particularly important. This paper introduces an algorithm for detecting TWA using Poincare mapping method which is a technique for nonlinear dynamic systems to display periodic behavior. Sample series of beat to beat cycles were selected to prepare Poincare mapping method. Vector Angle Index (VAI), which is the mean of the difference between θi (the angle between the line connecting the i point to the origin and the X axis) and 45 degrees was used to present the presence or absence of TWA. The value of 0.9 rad ≤ VAI ≤ 1.03 rad is accepted as a level determinative for presence of TWA. VAI via Poincare mapping method (PM) is used for correlation analysis with T-wave alternans voltage (Vtwa) by way of the spectral method (SM). The cross-correlation coefficient between Vtwa and VAI is γ = 0.8601. The algorithm can identify the absence and presence of TWA accurately and provide idea for further study of TWA-PM.

CQ Method for Strictly Pseudo-Contractive Mapping

This paper obtains a strong convergence theorem for k-strictly pseudo-contractive mapping under the framework of Hilbert spaces using CQ method. Due to the fact that non-expansive mapping is only O-strictly pseudo-contractive, the main result obtained in this paper extends the corresponding main result of Nakajo-Takahashi from non-expansive mapping to k-strictly pseudo-contractive one, where k∈ [0,1）.

Patchwise Mapping Method for Solving Elliptic Boundary Value Problems Containing Multiple Singularities

In the paper [1], the geometrical mapping techniques based on Non-Uniform Rational B-Spline (NURBS) were introduced to solve an elliptic boundary value problem containing a singularity. In the mapping techniques, the inverse function of the NURBS geometrical mapping generates singular functions as well as smooth functions by an unconventional choice of control points. It means that the push-forward of the NURBS geometrical mapping that generates singular functions, becomes a piecewise smooth function. However, the mapping method proposed is not able to catch singularities emerging at multiple locations in a domain. Thus, we design the geometrical mapping that generates singular functions for each singular zone in the physical domain. In the design of the geometrical mapping, we should consider the design of control points on the interface between/among patches so that global basis functions are in C0?space. Also, we modify the B-spline functions whose supports include the interface between/among them. We put the idea in practice by solving elliptic boundary value problems containing multiple singularities.

数字填图系统RGMAP在野外实测地质剖面中的应用与方法探索

数字填图系统(RGMAP)是中国地质调查局开发的数字地质调查系统(DGSS)的移动端系统,能够实现野外实测地质剖面数字化采集,由于手机(掌上机)GPS定位精度易受硬件和环境因素的影响,致使数据精度不足。笔者结合工作实际,简述RGMAP实测剖面操作流程和逻辑,分析与传统剖面测量的区别,并进行3种方法测试对比,总结出了一套实测剖面测量方法,实测剖面测量主要通过掌上机进行野外数据采集,融入RTK进行坐标测量,再配合测绳对分层、照片、产状等要素进行控制,辅助确认要素在导线间的位置,该套方法能切实有效地提高工作效率和数据精度。

A bottom-up method for module-based product platform development through mapping,clustering and matching analysis

Designing product platform could be an effective and efficient solution for manufacturing firms. Product platforms enable firms to provide increased product variety for the marketplace with as little variety between products as possible. Developed consumer products and modules within a firm can further be investigated to find out the possibility of product platform creation. A bottom-up method is proposed for module-based product platform through mapping, clustering and matching analysis. The framework and the parametric model of the method are presented, which consist of three steps:(1) mapping parameters from existing product families to functional modules,(2) clustering the modules within existing module families based on their parameters so as to generate module clusters, and selecting the satisfactory module clusters based on commonality, and(3) matching the parameters of the module clusters to the functional modules in order to capture platform elements. In addition, the parameter matching criterion and mismatching treatment are put forward to ensure the effectiveness of the platform process, while standardization and serialization of the platform element are presented. A design case of the belt conveyor is studied to demonstrate the feasibility of the proposed method.

Extended Mapping Transformation Method and Its Applications to Nonlinear Partial Differential Equation（s）

In this paper, we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method, many explicit and exact general solutions with arbitrary functions for some nonlinear partial differential equations, which contain solitary wave solutions, trigonometric function solutions, and rational solutions, are obtained.