Automatic identification of rock discontinuity and stability analysis of tunnel rock blocks using terrestrial laser scanning

Local geometric information and discontinuity features are key aspects of the analysis of the evolution and failure mechanisms of unstable rock blocks in rock tunnels.This study demonstrates the integration of terrestrial laser scanning(TLS)with distinct element method for rock mass characterization and stability analysis in tunnels.TLS records detailed geometric information of the surrounding rock mass by scanning and collecting the positions of millions of rock surface points without contact.By conducting a fuzzy K-means method,a discontinuity automatic identification algorithm was developed,and a method for obtaining the geometric parameters of discontinuities was proposed.This method permits the user to visually identify each discontinuity and acquire its spatial distribution features(e.g.occurrences,spac-ings,trace lengths)in great detail.Compared with hand mapping in conventional geotechnical surveys,the geometric information of discontinuities obtained by this approach is more accurate and the iden-tification is more efficient.Then,a discrete fracture network with the same statistical characteristics as the actual discontinuities was generated with the distinct element method,and a representative nu-merical model of the jointed surrounding rock mass was established.By means of numerical simulation,potential unstable rock blocks were assessed,and failure mechanisms were analyzed.This method was applied to detection and assessment of unstable rock blocks in the spillway and sand flushing tunnel of the Hongshiyan hydropower project after a collapse.The results show that the noncontact detection of blocks was more labor-saving with lower safety risks compared with manual surveys,and the stability assessment was more reliable since the numerical model built by this method was more consistent with the distribution characteristics of actual joints.This study can provide a reference for geological survey and unstable rock block hazard mitigation in tunnels subjected to complex geology and active rockfalls.

THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS

Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the spacetime meshes. Basic error estimates in L-infinity (L-2) norm, that is maximum-norm in time, L-2-norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.

THE QUASI-BOUNDARY VALUE METHOD FOR IDENTIFYING THE INITIAL VALUE OF THE SPACE-TIME FRACTIONAL DIFFUSION EQUATION

In this article,we consider to solve the inverse initial value problem for an inhomogeneous space-time fractional diffusion equation.This problem is ill-posed and the quasi-boundary value method is proposed to deal with this inverse problem and obtain the series expression of the regularized solution for the inverse initial value problem.We prove the error estimates between the regularization solution and the exact solution by using an a priori regularization parameter and an a posteriori regularization parameter choice rule.Some numerical results in one-dimensional case and two-dimensional case show that our method is efficient and stable.

Fault Diagnosis and Separation for a Distributed Rotary-laser Scanning System

The wMPS is a laser-based measurement system used for large scale metrology.However,it is susceptible to external factors such as vibrations,which can lead to unreliable measurements.This paper presents a fault diagnosis and separation method which can counter this problem.To begin with,the paper uses simple models to explain the fault diagnosis and separation methods.These methods are then mathematically derived using statistical analysis and the principles of the wMPS.A comprehensive solution for fault diagnosis and separation is proposed,considering the characteristics of the wMPS.The effectiveness of this solution is verified through experimental observations.It can be concluded that this approach can detect and separate false observations,thereby enhancing the reliability of the wMPS.

Mixed time discontinuous space-time finite element method for convection diffusion equations

A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.

Reformatted method for two-dimensional detector arrays measurement data in proton pencil beam scanning

The spatial resolution of a commercial two-dimensional(2D)ionization chamber(IC)array is limited by the size of the individual detector and the center-to-center distance between sensors.For dose distributions with areas of steep dose gradients,inter-detector dose values are derived by the interpolation of nearby detector readings in the conventional mathematical interpolation of 2D IC array measurements.This may introduce significant errors,particularly in proton spot scanning radiotherapy.In this study,by combining logfile-based reconstructed dose values and detector measurements with the Laplacian pyramid image blending method,a novel method is proposed to obtain a reformatted dose distribution that provides an improved estimation of the delivered dose distribution with high spatial resolution.Meanwhile,the similarity between the measured original data and the downsampled logfilebased reconstructed dose is regarded as the confidence of the reformatted dose distribution.Furthermore,we quantify the performance benefits of this new approach by directly comparing the reformatted dose distributions with 2D IC array detector mathematically interpolated measurements and original low-resolution measurements.The result shows that this new method is better than the mathematical interpolation and achieves gamma pass rates similar to those of the original low-resolution measurements.The reformatted dose distributions generally yield a confidence exceeding 95%.

Optimized air-ground data fusion method for mine slope modeling

Refined 3D modeling of mine slopes is pivotal for precise prediction of geological hazards.Aiming at the inadequacy of existing single modeling methods in comprehensively representing the overall and localized characteristics of mining slopes,this study introduces a new method that fuses model data from Unmanned aerial vehicles(UAV)tilt photogrammetry and 3D laser scanning through a data alignment algorithm based on control points.First,the mini batch K-Medoids algorithm is utilized to cluster the point cloud data from ground 3D laser scanning.Then,the elbow rule is applied to determine the optimal cluster number(K0),and the feature points are extracted.Next,the nearest neighbor point algorithm is employed to match the feature points obtained from UAV tilt photogrammetry,and the internal point coordinates are adjusted through the distanceweighted average to construct a 3D model.Finally,by integrating an engineering case study,the K0 value is determined to be 8,with a matching accuracy between the two model datasets ranging from 0.0669 to 1.0373 mm.Therefore,compared with the modeling method utilizing K-medoids clustering algorithm,the new modeling method significantly enhances the computational efficiency,the accuracy of selecting the optimal number of feature points in 3D laser scanning,and the precision of the 3D model derived from UAV tilt photogrammetry.This method provides a research foundation for constructing mine slope model.

H^1 space-time discontinuous finite element method for convection-diffusion equations

An H1 space-time discontinuous Galerkin （STDG） scheme for convection- diffusion equations in one spatial dimension is constructed and analyzed. This method is formulated by combining the H1 Galerkin method and the space-time discontinuous finite element method that is discontinuous in time and continuous in space. The existence and the uniqueness of the approximate solution are proved. The convergence of the scheme is analyzed by using the techniques in the finite difference and finite element methods. An optimal a-priori error estimate in the L∞ （H1） norm is derived. The numerical exper- iments are presented to verify the theoretical results.

An Eigenspace Method for Detecting Space-Time Disease Clusters with Unknown Population-Data

Space-time disease cluster detection assists in conducting disease surveillance and implementing control strategies.The state-of-the-art method for this kind of problem is the Space-time Scan Statistics(SaTScan)which has limitations for non-traditional/non-clinical data sources due to its parametric model assumptions such as Poisson orGaussian counts.Addressing this problem,an Eigenspace-based method called Multi-EigenSpot has recently been proposed as a nonparametric solution.However,it is based on the population counts data which are not always available in the least developed countries.In addition,the population counts are difficult to approximate for some surveillance data such as emergency department visits and over-the-counter drug sales,where the catchment area for each hospital/pharmacy is undefined.We extend the population-based Multi-EigenSpot method to approximate the potential disease clusters from the observed/reported disease counts only with no need for the population counts.The proposed adaptation uses an estimator of expected disease count that does not depend on the population counts.The proposed method was evaluated on the real-world dataset and the results were compared with the population-based methods:Multi-EigenSpot and SaTScan.The result shows that the proposed adaptation is effective in approximating the important outputs of the population-based methods.

SPACE-TIME FINITE ELEMENT METHOD FOR SCHRDINGER EQUATION AND ITS CONSERVATION

Energy conservation of nonlinear Schrodinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory.

SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR MAXWELL EQUATIONS IN DISPERSIVE MEDIA

In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the un-derlying problem. Unconditional L2-stability and error estimate of order O？τr＋1＋hk＋1/2？ are obtained when polynomials of degree at most r and k are used for the temporal dis-cretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r＋1 in temporal variable t.

A Space-Time Interior Penalty Discontinuous Galerkin Method for the Wave Equation

A new higher-order accurate space-time discontinuous Galerkin(DG)method using the interior penalty flux and discontinuous basis functions,both in space and in time,is pre-sented and fully analyzed for the second-order scalar wave equation.Special attention is given to the definition of the numerical fluxes since they are crucial for the stability and accuracy of the space-time DG method.The theoretical analysis shows that the DG discre-tization is stable and converges in a DG-norm on general unstructured and locally refined meshes,including local refinement in time.The space-time interior penalty DG discre-tization does not have a CFL-type restriction for stability.Optimal order of accuracy is obtained in the DG-norm if the mesh size h and the time stepΔt satisfy h≅CΔt,with C a positive constant.The optimal order of accuracy of the space-time DG discretization in the DG-norm is confirmed by calculations on several model problems.These calculations also show that for pth-order tensor product basis functions the convergence rate in the L∞and L2-norms is order p+1 for polynomial orders p=1 and p=3 and order p for polynomial order p=2.

Identification of key residues in protein functional movements by using molecular dynamics simulations combined with a perturbation-response scanning method

The realization of protein functional movement is usually accompanied by specific conformational changes,and there exist some key residues that mediate and control the functional motions of proteins in the allosteric process.In the present work,the perturbation-response scanning method developed by our group was combined with the molecular dynamics(MD)simulation to identify the key residues controlling the functional movement of proteins.In our method,a physical quantity that is directly related to protein specific function was introduced,and then based on the MD simulation trajectories,the perturbation-response scanning method was used to identify the key residues for functional motions,in which the residues that highly correlated with the fluctuation of the function-related quantity were identified as the key residues controlling the specific functional motions of the protein.Two protein systems,i.e.,the heat shock protein 70 and glutamine binding protein,were selected as case studies to validate the effectiveness of our method.Our calculated results are in good agreement with the experimental results.The location of the key residues in the two proteins are similar,indicating the similar mechanisms behind the performance of their biological functions.

A Novel Staggered Semi-implicit Space-Time Discontinuous Galerkin Method for the Incompressible Navier-Stokes Equations

A new high-order accurate staggered semi-implicit space-time discontinuous Galerkin(DG)method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions.The staggered DG scheme defines the discrete pressure on the primal triangular mesh,while the discrete velocity is defined on a staggered edge-based dual quadrilateral mesh.In this paper,a new pair of equal-order-interpolation velocity-pressure finite elements is proposed.On the primary triangular mesh(the pressure elements),the basis functions are piecewise polynomials of degree N and are allowed to jump on the boundaries of each triangle.On the dual mesh instead(the velocity elements),the basis functions consist in the union of piecewise polynomials of degree N on the two subtriangles that compose each quadrilateral and are allowed to jump only on the dual element boundaries,while they are continuous inside.In other words,the basis functions on the dual mesh arc built by continuous finite elements on the subtriangles.This choice allows the construction of an efficient,quadrature-free and memory saving algorithm.In our coupled space-time pressure correction formulation for the incompressible Navier-Stokes equations,the arbitrary high order of accuracy in time is achieved through tire use of time-dependent test and basis functions,in combination with simple and efficient Picard iterations.Several numerical tests on classical benchmarks confirm that the proposed method outperforms existing staggered semi-implicit space-time DG schemes,not only from a computer memory point of view,but also concerning the computational time.

ANALYSIS OF HUMAN PLACENTA BY ^(31)P NUCLEAR MAGNETIC RESONANCE AND THIN-LAYER CHROMATOGRAPHY SCANNING COMBINED WITH THE CORRECTIVE METHOD OF ABSORBANCE PROPORTIONAL COEFFICIENT

Five phospholipids in human placenta were determined by phosphorus 31 nuclear magnetic resonance(^(31)P NMR)spectroscopy and thin-layer chromatography(TLC) scanning combined with the corrective method of absorbance proportional coefficient. The NMR spectrometer used this investigation was a Bruker AM-500 spectrometer operating at 202.4 MHz for ^(31)P chemical shifts are relative to 85% phosphoric acid. TIC was carried out by silica gel H plate developed in chloroform-methanol-glacial acetic acid-ethanol-water(25:4:6:2:0.5),with Vaskovsky reagent as colour -developing agent of phospholipids.

Tip-Nanoparticle Near-Field Coupling in Scanning Near-Field Microscopy by Coupled Dipole Method

We use the couple dipole method to investigate the scanning near-field optical microscopy metallic tip-nanoparticle near-field interaction. Dependences of the local field intensity inside the nanoparticle on the nanosized tip shape,the tip open angle and the illumination angle are revealed. In combination with the previous results, we establish a complete model to understand the tip-nanoparticle near-field coupling mechanism.

Image reconstruction based on total-variation minimization and alternating direction method in linear scan computed tomography

Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.

Analytical approximate solution for nonlinear space-time fractional Klein Gordon equation

The fractional derivatives in the sense of Caputo and the homotopy analysis method are used to construct an approximate solution for the nonlinear space-time fractional derivatives Klein-Gordon equation. The numerical results show that the approaches are easy to implement and accurate when applied to the nonlinear space-time fractional derivatives Klein- Gordon equation. This method introduces a promising tool for solving many space-time fractional partial differential equations. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.

Numerical Investigation of Laser Surface Hardening of AISI 4340 Using 3D FEM Model for Thermal Analysis of Different Laser Scanning Patterns

Laser surface hardening is becoming one of the most successful heat treatment processes for improving wear and fatigue properties of steel parts. In this process, the heating system parameters and the material properties have important effects on the achieved hardened surface characteristics. The control of these variables using predictive modeling strategies leads to the desired surface properties without following the fastidious trial and error method. However, when the dimensions of the surface to be treated are larger than the cross section of the laser beam, various laser scanning patterns can be used. Due to their effects on the hardened surface properties, the attributes of the selected scanning patterns become significant variables in the process. This paper presents numerical and experimental investigations of four scanning patterns for laser surface hardening of AISI 4340 steel. The investigations are based on exhaustive modelling and simulation efforts carried out using a 3D finite element thermal analysis and structured experimental study according to Taguchi method. The temperature distribution and the hardness profile attributes are used to evaluate the effects of heating parameters and patterns design parameters on the hardened surface characteristics. This is very useful for integrating the scanning patterns’ features in an efficient predictive modeling approach. A structured experimental design combined to improved statistical analysis tools is used to assess the 3D model performance. The experiments are performed on a 3 kW Nd:Yag laser system. The modeling results exhibit a great agreement between the predicted and measured values for the hardened surface characteristics. The model evaluation reveals also its ability to provide not only accurate and robust predictions of the temperature distribution and the hardness profile as well an in-depth analysis of the effects of the process parameters.

高能激光光束质量β因子测量方法

高能激光光束质量β因子测量装置主要用于强激光系统状态调试和综合性能参数诊断,用于评价激光系统出光性能以及远场光斑可聚焦的能力。针对接近衍射极限光束质量β因子测量过程中被测光斑在面阵相机上所占的像素点太少等缺陷,研究了采用聚焦显微放大与高精度扫描狭缝相结合的光束质量β因子测量方法,并对相关方案进行了分析计算。此外还设计了采用固定像差元件及平行光管光源组合的激光光束质量β因子测量结果验证方案,对研制的高能激光光束质量β因子测量装置进行了不确定度分析,测量不确定度优于10%。