Improved calibration method for displacement transformation coefficient in optical and visual measurements

Optical and visual measurement technology is used widely in fields that involve geometric measurements,and among such technology are laser and vision-based displacement measuring modules(LVDMMs).The displacement transformation coefficient(DTC)of an LVDMM changes with the coordinates in the camera image coordinate system during the displacement measuring process,and these changes affect the displacement measurement accuracy of LVDMMs in the full field of view(FFOV).To give LVDMMs higher accuracy in the FFOV and make them adaptable to widely varying measurement demands,a new calibration method is proposed to improve the displacement measurement accuracy of LVDMMs in the FFOV.First,an image coordinate system,a pixel measurement coordinate system,and a displacement measurement coordinate system are established on the laser receiving screen of the LVDMM.In addition,marker spots in the FFOV are selected,and the DTCs at the marker spots are obtained from calibration experiments.Also,a fitting method based on locally weighted scatterplot smoothing(LOWESS)is selected,and with this fitting method the distribution functions of the DTCs in the FFOV are obtained based on the DTCs at the marker spots.Finally,the calibrated distribution functions of the DTCs are applied to the LVDMM,and experiments conducted to verify the displacement measurement accuracies are reported.The results show that the FFOV measurement accuracies for horizontal and vertical displacements are better than±15μm and±19μm,respectively,and that for oblique displacement is better than±24μm.Compared with the traditional calibration method,the displacement measurement error in the FFOV is now 90%smaller.This research on an improved calibration method has certain significance for improving the measurement accuracy of LVDMMs in the FFOV,and it provides a new method and idea for other vision-based fields in which camera parameters must be calibrated.

CALCULATION METHOD FOR EARTH PRESSURE CONSIDERING DISPLACEMENT

The calculation of earth pressure is a difficult problem in the pit foundation design. Aiming at the problem, the earth pressure calculation formulas considering the displacement are proposed. A method for determining the limit displacement is given and it is convenient for use. The result indicates that the earth pressure calculated by the formulas is between the earth pressure at rest and the Rankine earth pressure, the formulas can reflect the change rules of active and passive earth pressures along with the displacement. Moreover, the calculation result using the formulas is approximate to the monitoring result. It confirms the validity of the formula deduction and the rationality of the calculation results. As for the passive earth pressure, the calculation method is theoretically feasible.

Analysis of the Wenchuan Ms8.0 Earthquake's Co-seismic Stress and Displacement Change by Using the Finite Element Method

The variation of in situ stress before and after earthquakes is an issue studied by geologists. In this paper, on the basis of the fault slip dislocation model of Wenchuan Ms8.0 earthquake, the changes of co-seismic displacement and the distribution functions of stress tensor around the Longmen Shan fault zone are calculated. The results show that the co-seismic maximum surface displacement is 4.9 m in the horizontal direction and 6.5 m in the vertical direction, which is almost consistent with the on-site survey and GPS observations. The co-seismic maximum horizontal stress in the hanging wall and footwall decreased sharply as the distance from the Longmen Shan fault zone increased. However, the vertical stress and minimum horizontal stress increased in the footwall and in some areas of the hanging wall. The study of the co-seismic displacement and stress was mainly focused on the long and narrow region along the Longmen Shan fault zone, which coincides with the distribution of the earthquake aftershocks. Therefore, the co-seismic stress only affects the aftershocks, and does not affect distant faults and seismic activities. The results are almost consistent with in situ stress measurements at the two sites before and after Wenchuan Ms8.0 earthquake. Along the fault plane, the co-seismic shear stress in the dip direction is larger than that in the strike direction, which indicates that the faulting mechanism of the Longmen Shan fault zone is a dominant thrust with minor strike-slipping. The results can be used as a reference value for future studies of earthquake mechanisms.

Mechanical mechanism analysis of tension type anchor based on shear displacement method

Based on the fact that the shear stress along anchorage segment is neither linearly nor uniformly distributed, the load transfer mechanism of the tension type anchor was studied and the mechanical characteristic of anchorage segment was analyzed. Shear stress?strain relationship of soil surrounding anchorage body was simplified into three-folding-lines model consisting of elastic phase, elasto-plastic phase and residual phase considering its softening characteristic. Meanwhile, shear displacement method that has been extensively used in the analysis of pile foundation was introduced. Based on elasto-plastic theory, the distributions of displacement, shear stress and axial force along the anchorage segment of tension type anchor were obtained, and the formula for calculating the elastic limit load was also developed accordingly. Finally, an example was given to discuss the variation of stress and displacement in the anchorage segment with the loads exerted on the anchor, and a program was worked out to calculate the anchor maximum bearing capacity. The influence of some parameters on the anchor bearing capacity was discussed, and effective anchorage length was obtained simultaneously. The results show that the shear stress first increases and then decreases and finally trends to the residual strength with increase of distance from bottom of the anchorage body, the displacement increases all the time with the increase of distance from bottom of the anchorage body, and the increase of velocity gradually becomes greater.

Method for array gain and phase uncertainties calibration based on ISM and ESPRIT

A new method for array calibration of array gain and phase uncertainties, which severely degrade the performance of spatial spectrum estimation, is presented. The method is based on the idea of the instrumental sensors method （ISM）, two well-calibrated sensors are added into the original array. By applying the principle of estimation of signal parameters via rotational invariance techniques （ESPRIT）, the direction-of-arrivals （DOAs） and uncertainties can be estimated simultaneously through eigen-decomposition. Compared with the conventional ones, this new method has less computational complexity while has higher estimation precision, what＇s more, it can overcome the problem of ambiguity. Both theoretical analysis and computer simulations show the effectiveness of the proposed method.

An extended displacement discontinuity method for analysis of stress wave propagation in viscoelastic rock mass

An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as 'macro-joints',while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as 'micro-defects'.The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass (ERM) from the conventional displacement discontinuity method (CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored.

Calibration of Soil Electromagnetic Conductivity in Inverted Salinity Profiles with an Integration Method

Various calibration methods have been propounded to determine profiles of apparent bulk soil electrical conductivity (ECa) and soil electrical conductivity of a saturated soil paste extract (ECe) or a 1:5 soil water extract (EC1:5) using an electromagnetic induction instrument (EM38). The modeled coefficients, one of the successful and classical methods hitherto, were chosen to calibrate the EM38 measurements of the inverted salinity profiles of characteristic coastal saline soils at selected sites of Xincao Farm, Jiangsu Province, China. However, this method required three parameters for each depth layer. An integration approach, based on an exponential decay profile model, was proposed and the model was fitted to all the calibration sites. The obtained model can then be used to predict EC1:5 at a certain depth from electromagnetic measurements made using the EM38 device positioned in horizontal and vertical positions at the soil surface. This exponential decay model predicted the EC1:5 well according to the results of a one-way analysis of variance, and the further comparison indicated that the modeled coefficients appeared to be slightly superior to, but not statistically different from, this exponential decay model. Nevertheless, this exponential decay model was more significant and practical because it depended on less empirical parameters and could be used to perform point predictions of EC1:5 continuously with depth.

Propagation simulation and dilatancy analysis of rock joint using displacement discontinuity method

A revised displacement discontinuity method(DDM) program is developed for the simulation of rock joint propagation and dilatancy analysis. The non-linear joint model used in the program adopts Barton-Bandis normal deformation model, Kulhaway shear deformation model and Mohr-Coulomb criterion. The joint propagation criterion is based on the equivalent stress intensity factor which can be obtained by regression analysis. The simulated rock joint propagation accords well with the existing knowledge. The closure and opening of joint is investigated by DDM, and it is shown that if the opening volume of propagated joint is larger than closure volume of the old joint, the joint dilatancy occurs. The dilatancy condition is mainly controlled by the normal stiffness of the rock joint. When the normal stiffness is larger than the critical value, joint dilatancy occurs. The critical normal stiffness of rock joint changes with the joint-load angle, and joint dilatancy is most possible to occur at 30°.

APPROXIMATION OF THE CONCENTRATION BY A VISCOSITY SPLITTING METHOD FOR TWO-PHASE MISCIBLE DISPLACEMENT PROBLEM

The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation within each lime step. The pressure and Us velocity field is computed by a mixed finite element method. Optimal order estimates are derived for the no diffusion case and the diffusion case.

On the accuracy of higher order displacement discontinuity method(HODDM) in the solution of linear elastic fracture mechanics problems

The higher order displacement discontinuity method(HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics(LEFM) problems. The paper has selected several example problems from the fracture mechanics literature(with available analytical solutions) including center slant crack in an infinite and finite body, single and double edge cracks, cracks emanating from a circular hole. The numerical values of Mode Ⅰ and Mode Ⅱ SIFs for these problems using HODDM are in excellent agreement with analytical results(reaching up to 0.001% deviation from their analytical results). The HODDM is also compared with the XFEM and a modified XFEM results. The results show that the HODDM needs a considerably lower computational effort(with less than 400 nodes) than the XFEM and the modified XFEM(which needs more than 10000 nodes) to reach a much higher accuracy. The proposed HODDM offers higher accuracy and lower computation effort for a wide range of problems in LEFM.

Analysis of Three-dimensional Crack Propagation by Using Displacement Discontinuity Method

A technique for modelling of three-dimensional(3D)quasi-statically propagating cracks in elastic bodies by the displacement discontinuity method(DDM)was described.When the crack is closed,the Mohr-coulomb rule on the two contacted surfaces of the crack must be satisfied.A simple iterative method was adopted in order to consider three different states of cracks.Under the assumption that the advance of the point on the crack front would occur only in the normal plane which is through this edge point,the maximum energy release rate criterion is modified to be used as the criterion for the crack growth.With discretization,the process of crack propagation can be seen as the advance of the vertices of the crack front.The program MCP3D was developed based on these theories to simulate the 3D quasi-static crack propagation.A numerical example of a penny-shaped crack subject to tension and compression in an infinite elastic media was analyzed with MCP3D,and the results in comparison with others' show that the present method for 3D crack propagation is effective.

Approximate analysis method for displacement responses of structures with active variable stiffness systems

The performance of structures with active variable stiffness (AVS) systems exhibits strong nonlinearity due to the variety with time of the stiffness of each storey unit,in which the AVS system is installed.Hence,the classical dynamic analysis method for linear structures,such as the mode-superposition method,is not applicable to structures with AVS systems.In this paper,an approximate analysis method is proposed for displacement responses of structures with AVS systems.Firstly,an equivalent relationship between single-degree-of-freedom (SDOF) structures equipped with AVS systems and so-called fictitious linear structures is established.Then,an approximate mode-superposition (AMS) method is presented for multi-degree-of-freedom (MDOF) structures equipped with AVS systems.The accuracy of this method is investigated through extensive parametrical study using different types of earthquake excitations,and some modification is made to the method. Numerical calculation results indicate that the modified AMS method is effective for estimating the maximum displacements relative to the ground and the maximum interstorey drifts of MDOF structures equipped with AVS systems.

Simulation of crack coalescence mechanism underneath single and double disc cutters by higher order displacement discontinuity method

The present research is focused on the numerical crack coalescence analysis of the micro-cracks and cracks produced during the cutting action of TBM disc cutters. The linear elastic fracture mechanics(LEFM) concepts and the maximum tangential stress criterion are used to investigate the micro crack propagation and its direction underneath the excavating discs. A higher order displacement discontinuity method with quadratic displacement discontinuity elements is used to estimate the stress intensity factors near the crack tips. Rock cutting mechanisms under single and double type discs are simulated by the proposed numerical method.The main purposes of the present modeling are to simulate the chip formation process of indented rocks by single and double discs.The effects of specific disc parameters(except speed) on the thrust force Ft, the rolling force Fr, and the specific energy ES are investigated. It has been shown that the specific energy(energy required to cut through a unit volume of rock) of the double disc is less than that of the single disc. Crack propagation in rocks under disc cutters is numerically modeled and the optimum ratio of disc spacing S to penetration depth Pd(i.e. S/Pd ratio) of about 10 is obtained, which is in good agreement with the theoretical and experimental results cited in the literature.

A method to calculate displacement factors using SVM

In order to improve the precision of mining subsidence prediction, a mathematical model using Support Vector Machine （SVM） was established to calculate the displacement factor. The study is based on a comprehensive analysis of factors affecting the displacement factor, such as mechanical properties of the cover rock, the ratio of mining depth to seam thickness, dip angle of the coal seam and the thickness of loose layer. Data of 63 typical observation stations were used as a training and testing sample set. A SVM regression model of the displacement factor and the factors affecting it was established with a kernel function, an insensitive loss factor and a properly selected penalty factor. Given an accurate calculation algorithm for testing and analysis, the results show that an SVM regression model can calcu- late displacement factor precisely and reliable precision can be obtained which meets engineering requirements. The experimental results show that the method to calculation of the displacement factor, based on the SVM method, is feasible. The many factors affecting the displacement factor can be consid- ered with this method. The research provides an efficient and accurate approach for the calculation of displacement in mining subsidence orediction.

Inverse displacement analysis of the general six degree-of-freedom serial robot based on optimization method

The paper presents a new solution of inverse displacement analysis of the general six degree-of-freedom serial robot.The inverse displacement analysis of the general serial robot is transformed into a minimization problem and then the optimization method is adopted to solve the nonlinear least squares problem with the analytic form of new Jacobian matrix.In this way,joint variables of the general serial robot can be searched out quickly under the desired precision when positions of the three non-collinear end effector points are given.Compared with the general Newton iterative method,the proposed algorithm can search out the solution when the robot is at the singular configuration and the initial configuration used in the optimization method may also be the singular configuration.So the convergence domain is bigger than that of the general Newton iterative method.Another advantage of the proposed algorithm is that positions of the three non-collinear end effector points are usually much easier to be measured than the orientation of the end effector.The inverse displacement analysis of the general 6R(six-revolute-joint) serial robot is illustrated as an example and the simulation results verify the efficiency of the proposed algorithm.Because the three non-collinear points can be selected at random,the method can be applied to any other types of serial robots.

Practical calibration method for instantaneous polarization radar systems utilizing a metal sphere

A practical calibration method is proposed for instantaneous polarization radar systems.The method only needs one measurement by using a metal sphere.The distortions of system and the actual polarization scattering matrix（PSM）of target can be obtained.First,an instantaneous polarization radar system is presented.The system can obtain PSM by a single pulse echo.The dual-polarization antenna can transmit and receive two orthogonal polarization waves.The multilayer micro-strip patch antenna is adopted for this kind of radar system.Second,based on the multi-port network theory,the operation and system errors of instantaneous polarization radar system are analyzed.By making assumption on the cross-talk factors of antenna,distortion matrices of R and Tare derived.Finally,the calibration method based on instantaneous polarization measurement is introduced.Simulation results show the performance of this calibration method.The values of calibrated PSM are in agreement with the actual ones after calibration.

Mixed Method for Compressible Miscible Displacement with Dispersion in Porous Media

Compressible miscible displacement of one fluid by another in porous media is modelled by a nonlinear parabolic system. A finite element procedure is introduced to approximate the concentration of one fluid and the pressure of the mixture. The concentration is treated by a Galerkin method while the pressure is treated by a parabolic mixed finite element method. The effect of dispersion, which is neglected in [1], is considered. Optimal order estimates in L2 are derived for the errors in the approximate solutions.

General displacement arch-cantilever element method for stress analysis of arch dam

Based on the general displacement method and the basic hypothesis of the trial load method, a new advanced trial load method, the general displacement arch-cantilever element method, was proposed to derive the transformation relation of displacements and loads between the surface nodes and middle plane nodes. This method considers the nodes on upstream and downstream surfaces of the arch dam to be exit nodes （master nodes）, and the middle plane nodes to be slave nodes. According to the derived displacement and load transformation matrices, the equilibrium equation treating the displacement of middle plane nodes as a basic unknown variable is transformed into one that treats the displacement of upstream and downstream nodes as a basic unknown variable. Because the surface nodes have only three degrees of freedom （DOF）, this method can be directly coupled with the finite element method （FEM）, which is used for foundation simulation to analyze the stress of the arch dam with consideration of dam-foundation interaction. Moreover, using the FEM, the nodal load of the arch dam can be easily obtained. Case studies of a typical cylindrical arch dam and the Wudongde arch dam demonstrate the robustness and feasibility of the proposed method.

Processes of the displacement field change of the 2009 April 6 M_W6.3 L'Aquila earthquake using persistent scatterer and small baseline methods

Using a time series method that combines both the persistent scatterer and small baseline approaches, we analyzed 9 scenes Envisat ASAR data over the L＇Aquila earthquake, and obtained a Shocke＇s displacement field and its evolution processes. The results show that： （1） Envisat ASAR clearly detected the whole processes of displacement field of the L＇Aquila earthquake, and distinct variations at different stages of the displacement field. （2） Preseismic creep displacement → displacement mutation when faulting → constantly slowed down after the earthquake. （3） The area of the strongest deformation and ground rupture was a low-lying oval depression region to the southeast. Surface faulting within a zone of about 22 km× 14 km, with an orientation of 135°, occurred along the NW-striking and SW-dipping Paganica-S. Demetrio normal fault. （4） In analyzing an area of about 54 km x 59 km, bounded by north-south axis to the epicenter, the displacement field has significant characteristics of a watershed： westward of the epicenter shows uplift with maximum of 130 mm in line-of-sight （LOS）, and east of the epicenter was a region with 220 mm of maximum subsidence in the LOS, concentrating on the rupture zone, the majority of which formed in the course of faulting and subsequence.

CHARACTERISTIC DIFFERENCE METHODS FOR TWO-PHASE DISPLACEMENT IN NATURALLY FRACTURED RESERVOIRS

In this paper we shall give the characteristic difference methods for two phase displace meat problem in naturally fractured reservoirs.We shall prove the existence,uniqueness of the ap proximate solution and a priori discrete L2-error estimates.