On the calibration and verification of Voronoi-based discontinuous deformation analysis for modeling rock fracture

Since its introduction,discontinuous deformation analysis(DDA)has been widely used in different areas of rock mechanics.By dividing large blocks into subblocks and introducing artificial joints,DDA can be applied to rock fracture simulation.However,parameter calibration,a fundamental issue in discontinuum methods,has not received enough attention in DDA.In this study,the parameter calibration of DDA for intact rock is carefully studied.To this end,a subblock DDA with Voronoi tessellation is presented first.Then,a modified contact constitutive law is introduced,in which the tensile and shear meso-strengths are modified to be independent of the bond lengths.This improvement can prevent the unjustified preferential failure of short edges.A method for imposing confining pressure is also introduced.Thereafter,sensitivity analysis is performed to investigate the influence of the calculated parameters and meso-parameters on the mechanical properties of modeled rock.Based on the sensitivity analysis,a unified calibration procedure is suggested for both cases with and without confining pressure.Finally,the calibration procedure is applied to two examples,including a biaxial compression test.The results show that the proposed Voronoi-based DDA can simulate rock fracture with and without confining pressure very well after careful parameter calibration.

A Survey of Error Analysis and Calibration Methods for MEMS Triaxial Accelerometers

MEMS accelerometers are widely used in various fields due to their small size and low cost,and have good application prospects.However,the low accuracy limits its range of applications.To ensure data accuracy and safety we need to calibrate MEMS accelerometers.Many authors have improved accelerometer accuracy by calculating calibration parameters,and a large number of published calibration methods have been confusing.In this context,this paper introduces these techniques and methods,analyzes and summarizes the main error models and calibration procedures,and provides useful suggestions.Finally,the content of the accelerometer calibration method needs to be overcome.

Sensitivity Analysis and Calibration of Hydrological Modeling of the Watershed Northeast Brazil

Mathematical models of the quantity and quality of water in hydrographic basins enable simulation of a wide variety of processes, including the production of water and sediments, and the dynamics of point and nonpoint sources of pollution. These models have become increasingly complex, requiring large amounts of input data, which can increase the uncertainty of the results of simulations. For this reason, it is essential to perform calibration and validation procedures. The objective of this work was to conduct sensitivity analysis and calibration of a distributed hydrological model (SWAT) applied to the flows of water in the watershed of the Poxim River. Satisfactory performance of the model was indicated by the values obtained for the Nash-Sutcliffe efficiency coefficient (0.77), the percent bias (5.05), the root mean square error (0.48), and the ratio of the RMSE to the standard deviation of the observations (RSR) (0.49). The set of parameters identified here could be used for the simulation and evaluation of other scenarios.

Application of SWAT Model to the Olifants Basin: Calibration, Validation and Uncertainty Analysis

The application of the Soil and Water Assessment Tool (SWAT) to the Olifants Basin in South Africa was the focus of our study with emphasis on calibration, validation and uncertainty analysis. The Basin was discretized into 23 sub-basins and 226 Hydrologic Response Units (HRUs) using 3 arc second (90 m × 90 m) pixel resolution SRTM DEM with stream gauge B7H015 as the Basin outlet. Observed stream flow data at B7H015 were used for model calibration (1988-2001) and validation (2002-2013) using the split sample approach. Relative global sensitivity analysis using SUFI-2 algorithm was used to determine sensitive parameters to stream flow for calibration of the model. Performance efficiency of the Olifants SWAT model was assessed using Nash-Sutcliffe (NSE), coefficient of determination (R2), Percent Bias (PBIAS) and Root Mean Square Error-Observation Standard deviation Ratio (RSR). Sensitivity analysis revealed in decreasing order of significance, runoff curve number (CN2), alpha bank factor (ALPHA_BNK), soil evaporation compensation factor (ESCO), soil available water capacity (SOIL_AWC, mm H2O/mm soil), groundwater delay (GW_ DELAY, days) and groundwater “revap” coefficient (GW_REVAP) to be the most sensitive parameters to stream flow. Analysis of the model during the calibration period gave the following statistics;NSE = 0.88;R2 = 0.89;PBIAS = -11.49%;RSR = 0.34. On the other hand, statistics during the validation period were NSE = 0.67;R2 = 0.79;PBIAS = -20.69%;RSR = 0.57. The observed statistics indicate the applicability of the SWAT model in simulating the hydrology of the Olifants Basin and therefore can be used as a Decision Support Tool (DST) by water managers and other relevant decisions making bodies to influence policy directions on the management of watershed processes especially water resources.

Calibration and uniqueness analysis of microparameters for DEM cohesive granular material

The differential evolution(DE)algorithm was deployed to calibrate microparameters of the DEM cohesive granular material.4 macroparameters,namely,uniaxial compressive strength,direct tensile strength,Young’s modulus and Poisson’s ratio,can be calibrated to high accuracy.The best calibration accuracy could reach the sum of relative errors RE_(sum)<0.1%.Most calibrations can be achieved with RE_(sum)<5%within hours or RE_(sum)<1%within 2 days.Based on the calibrated results,microparameters uniqueness analysis was carried out to reveal the correlation between microparameters and the macroscopic mechanical behaviour of material:(1)microparameters effective modulus,tensile strength and normal-to-shear stiffness ratio control the elastic behaviour and stable crack growth,(2)microparameters cohesion and friction angles present a negative linear correlation that controls the axial strain and lateral strain prior to the peak stress,and(3)microparameters friction coefficient controls shear crack friction and slip mainly refers to the unstable crack behaviour.Consideration of more macroparameters to regulate the material mechanical behaviour that is dominated by shear crack and slip motion is highlighted for future study.The DE calibration method is expected to serve as an alternative method to calibrate the DEM cohesive granular material to its peak strength.

Analysis of sp Pillar Stability Experiment: Continuous thermo-mechanical model development and calibration

The paper describes an analysis of thermo-mechanical （TM） processes appearing during the Aspo Pillar Stability Experiment （APSE）. This analysis is based on finite elements with elasticity, plasticity and dam- age mechanics models of rock behaviour and some least squares calibration techniques. The main aim is to examine the capability of continuous mechanics models to predict brittle damage behaviour of gran- ite rocks. The performed simulations use an in-house finite element software GEM and self-developed experimental continuum damage MATLAB code. The main contributions are twofold. First, it is an inverse analysis, which is used for （1） verification of an initial stress measurement by back analysis of conver- gence measurement during construction of the access tunnel and （2） identification of heat transfer rock mass properties by an inverse method based on the known heat sources and temperature measurements. Second, three different hierarchically built models are used to estimate the pillar damage zones, i.e. elas- tic model with Drucker-Prager strength criterion, elasto-plastic model with the same yield limit and a combination of elasto-plasticity with continuum damage mechanics. The damage mechanics model is also used to simulate uniaxial and triaxial compressive strength tests on the ,Aspo granite.

Calibration chain design based on integrating sphere transfer radiometer for SI-traceable on-orbit spectral radiometric calibration and its uncertainty analysis

In order to satisfy the requirement of SI-traceable on-orbit absolute radiation calibration transfer with high accuracy for satellite remote sensors,a transfer chain consisting of a fiber coupling monochromator（FBM） and an integrating sphere transfer radiometer（ISTR） was designed in this paper.Depending on the Sun,this chain based on detectors provides precise spectral radiometric calibration and measurement to spectrometers in the reflective solar band（RSB） covering 300–2500 nm with a spectral bandwidth of 0.5–6 nm.It shortens the traditional chain based on lamp source and reduces the calibration uncertainty from 5% to 0.5% by using the cryogenic radiometer in space as a radiometric benchmark and trap detectors as secondary standard.This paper also gives a detailed uncertainty budget with reasonable distribution of each impact factor,including the weak spectral signal measurement with uncertainty of 0.28%.According to the peculiar design and comprehensive uncertainty analysis,it illustrates that the spectral radiance measurement uncertainty of the ISTR system can reach to 0.48%.The result satisfies the requirements of SI-traceable on-orbit calibration and has wider significance for expanding the application of the remote sensing data with high-quality.

A Calibration Method of Robot Base Frame with Procrustes Analysis

In order to realize high precision industrial operations,based on the POE formula,an effective approach to calibrate the robot's actual base frame(ABF) is proposed. Due to the existence of manufacturing errors,the ABF deviates slightly from nominal base frame( NBF). Using external precision measurement,the ABF can be established only through the three dimension(3D) position of the robot's end-effector.To ensure the orthonormal constraints of rotation matrix as well as the precise solutions,Procrustes Analysis is introduced,where an optimal orthogonal matrix is solved out by the Lagrange Multiplier method and Singular Value Decomposition(SVD). Furthermore,calibration experiment on a serial 6-DOF robot is performed,where a FARO laser tracker is utilized to measure the 3D position. Finally, calibration result indicates that the positioning accuracy has been significantly improved after calibration. The calibration method is also applicable to other similar problems,such as multi-robot coordination and robot hand-eye system calibration.

Pharmacokinetic Analysis of Four Bioactive Iridoid and Secoiridoid Glycoside Components of Radix Gentianae Macrophyllae and Their Synergistic Excretion by HPLC-DAD Combined with Second-Order Calibration

An HPLC-DAD method combined with second-order calibration based on the alternating trilinear decomposition(ATLD)algorithm with the aid of region selection was developed to simultaneously and quantitatively characterize the synergistic relationships and cumulative excretion of the four bioactive ingredients of Radix Gentianae Macrophyllae in vivo.Although the analytes spectra substantially overlapped with that of the biological matrix,the overlapping profiles between analytes and co-eluting interferences can be successfully separated and accurately quantified by the ATLD method on the basis of the strength of region selection.The proposed approach not only determined the content change but also revealed the synergistic relationships and the cumulative excretion in vivo of the four ingredients in urine and feces samples collected at different excretion time intervals.In addition,several statistical parameters were employed to evaluate the accuracy and precision of the method.Quantitative results were confirmed by HPLC-mass spectrometry.Satisfactory results indicated that the proposed approach can be utilized to investigate the pharmacokinetics of Radix Gentianae Macrophyllae excretion in vivo.

NOVEL METHOD FOR ERROR ANALYSIS AND SELF-CALIBRATION OF LASER TRACKING MIRROR MECHANISM

Laser tracking system （LTS） is an advanced device for large size 3D coordinates measuring with the advantages of broad range, high speed and high accuracy. However, its measuring accuracy is highly dominated by the geometric errors of the tracking mirror mechanism. Proper calibration of LTS is essential prior to the use of it for metrology. A kinematics model that describes not only the motion but also the geometric variations of LTS is developed. Through error analysis of the proposed model, it is claimed that gimbals axis misalignments and tracking mirror center off-set are the key contributors to measuring errors of LTS. A self-calibration method is presented of calibrating LTS with planar constraints. Various calibration strategies utilizing single-plane and multiple-plane constraints are proposed for different situations. For each calibration strategy, issues about the error parameter estimation of LTS are exploded to find out in which conditions these parameters can be uniquely estimated. Moreover, these conditions reveal the applicability of the planar constraints to LTS self-calibration. Intensive studies have been made to check validity of the theoretical results. The results show that the measuring accuracy of LTS has increased by 5 times since this technique for calibration is used.

A calibration method of Argo floats based on multiple regression analysis

Argo floats are free-moving floats that report vertical profiles of salinity, temperature and pressure at regular time intervals. These floats give good measurements of temperature and pressure, but salinity measurements may show significant sensor drifting with time. It is found that sensor drifting with time is not purely linear as presupposed by Wong (2003). A new method is developed to calibrate con- ductivity data measured by Argo floats. In this method, Wong’s objective analysis method was adopted to estimate the background climatological salinity field on potential temperature surfaces from nearby his- torical data in WOD01. Furthermore, temperature and time factors are taken into account, and stepwise regression was used for a time-varying or temperature-varying slope in potential conductivity space to correct the drifting in these profiling float salinity data. The result shows salinity errors using this method are smaller than that of Wong’s method, the quantitative and qualitative analysis of the conductivity sen- sor can be carried out with our method.

Development and Calibration of a Hyperstatic Six-component Force/Torque Sensor

The six-component force/torque sensor has become one kind of the most important sensors with the ability of measuring all the external forces and torques. A novel hyperstatic six-component force/torque sensor based on the Stewart platform structure, which can be used for the force measurement of the robot wrist, is proposed, and its structural optimal design, finite element analysis and calibration experimentation is presented. The characteristic of the sensor structure is analyzed in comparison with the traditional Stewart platform-based sensor. The mathematical expression of the sensor＇s force mapping matrix is introduced. The condition number and generalized amplifying coefficient defined by singular values of force Jacobian matrix are used to evaluate the performances of isotropy and sensitivity of the sensor respectively. The optimal design of the sensor structure is performed with the objective of achieving high measurement sensitivity and good isotropy. The sensor prototype is fabricated, and the static and dynamic characteristics of the sensor are analyzed with finite element analysis software package ANSYS. The calibration device is manufactured, and the data acquisition and processing system is developed. The theoretical and experimental study of the static calibration of the sensor prototype is carried out. The results of simulation analysis and calibration experimentation prove the feasibility of the hyperstatic sensor structure, and the contents of this paper possess theoretical significance and engineering value for the further research and practical application of the six-component force sensor.

Research on Calibration Transfer across Infrared Spectrometric Instruments for Fast Evaluation of Crude Oils

The spectral analysis method is suitable for the process control and the process analysis such as the fast evaluation of crude oils. In this study, model transfer between the same type of spectrometer and different type of spectrometers was discussed respectively, and the results have shown that the transfer of calibration model can satisfy the demand of rapid analysis.

Study of sedimentary sequence cycles by well-seismic calibration

In order to solve the problems of the fine division of sedimentary sequence cycles and their change in two-dimensional space as well as lateral extension contrast, we developed a method of wavelet depth-frequency analysis. The single signal and composite signal of different Milankovitch cycles are obtained by numerical simulation. The simulated composite signal can be separated into single signals of a single frequency cycle. We also develop a well-seismic calibration insertion technology which helps to realize the calibration from the spectrum characteristics of a single well to the seismic profile. And then we determine the change and distribution characteristics of spectrum cycles in the two-dimensional space. It points out the direction in determining the variations of the regional sedimentary sequence cycles, underground strata structure and the contact relationship.

Relative flux calibration for the Guoshoujing Telescope (LAMOST)

This paper presents a relative flux calibration method for the Guoshoujing Telescope （LAMOST）, which may be applied to connect a blue spectrum to a red spectrum to build the whole spectrum across the total wavelength range （3700 ～ 9000 A）. In each spectrograph, we estimate the effective temperatures of selected stars using a grid of spectral line indices in the blue spectral range and a comparison with stellar atmosphere models. For each spectrograph, stars of types A and F are selected as pseudo-standard stars, and the theoretical spectra are used to calibrate both the blue （3700 ～ 5900 A） and red spectrograph arms （5700 ～ 9000 A）. Then the spectral response function for these pseudo-standard stars could be used to correct the raw spectra provided by the other fibers of the spectrograph, after a fiber efficiency function has been derived from twilight flat-field exposures. A key problem in this method is the fitting of a pseudo stellar continuum, so we also give a detailed description of this step. The method is tested by comparing a small sample of LAMOST spectra calibrated in this way on stars also observed by the Sloan Digital Sky Survey. The result shows that the T eff estimation and relative flux calibration method are adequate.

Quantitative Analysis of Fe Content in Iron Ore via External Calibration in Conjunction with Internal Standardization Method Coupled with LIBS

The external calibration in conjunction with internal standardization（ECIS） coupled with laser-induced breakdown spectroscopic（LIBS） technique was proposed to perform the quantitative analysis of Fe content in iron ore The plasma temperature and the electron number density were calculated to prove that the plasma was under local thermodynamic equilibrium（LTE） conditions and to ensure that the integral intensities of Fe I lines were reasonable. In addition, the result of the quantitative analysis shows a content of （20.26±0.59）% by mass of Fe in the iron ore. It was determined by four calibration curves, drawn for four emission lines of Fe I（373.48, 373.71,404.58 and 438.35 nm） normalized by Mn I line, base on the ECIS method which can eliminate the influence of matrix effect and improve the accuracy of quantitative analysis, compared with the standard addition method. Both the results of these two analytical methods were compared with that listed in the Standard Substance Certificate. The percentage content of Fe in the same sample of iron ore by the ECIS method was （20.17±0.08）% by mass, which shows a good performance to analyze the Fe content of iron ore in combination with LIBS.

Accurate determination of calibration factor for tidal gravity observation of a GWR-superconducting gravimeter

It is recognized widely nowadays that the superconducting gravimeter (SG) is a kind of best relative gravimeter with high observing precision, good continuity and stability. However, it is necessary to calibrate the direct output (change in voltage) by using scale value (calibration factor) before getting the change of the real gravity field. Studies show that the accuracy of the scale value will influence the late analysis and explanation of the observations. By using absolute gravity measurements of a FG5 absolute gravimeter (AG) at Wuhan international tidal gravity fundamental station (two campaigns each for 3 days) and by using known tidal parameters at the same station, the calibration factors of the SG and their precision are studied in detail in this paper.

Elemental and proximate analysis of coal by x-ray fluorescence assisted laser-induced breakdown spectroscopy

Although laser-induced breakdown spectroscopy(LIBS),as a fast on-line analysis technology,has great potential and competitiveness in the analysis of chemical composition and proximate analysis results of coal in thermal power plants,the measurement repeatability of LIBS needs to be further improved due to the difficulty in controlling the stability of the generated plasmas at present.In this paper,we propose a novel x-ray fluorescence(XRF) assisted LIBS method for high repeatability analysis of coal quality,which not only inherits the ability of LIBS to directly analyze organic elements such as C and H in coal,but also uses XRF to make up for the lack of stability of LIBS in determining other inorganic ash-forming elements.With the combination of elemental lines in LIBS and XRF spectra,the principal component analysis and the partial least squares are used to establish the prediction model and perform multi-elemental and proximate analysis of coal.Quantitative analysis results show that the relative standard deviation(RSD) of C is 0.15%,the RSDs of other elements are less than 4%,and the standard deviations of calorific value,ash content,sulfur content and volatile matter are 0.11 MJ kg,0.17%,0.79% and 0.41%respectively,indicating that the method has good repeatability in determination of coal quality.This work is helpful to accelerate the development of LIBS in the field of rapid measurement of coal entering the power plant and on-line monitoring of coal entering the furnace.

Error analysis and calibration for underwater sound intensity measuring system

Based on measuring the cross-spectrum density of sound pressure between two hydrophones, the facility for underwater sound intensity measurement is investigated and designed. According to the principle of two-hydrophone method for intensity measurement, the error analysis is carried out. Given the method of sound intensity measurement calibration for this underwater sound intensity measurement facility, the uncertainty of intensity measurement by this facility is evaluated. It is shown that the analysis and evaluation are agreeable to the experimental results.

Calibration of discrete element modeling: Scaling laws and dimensionless analysis

In this paper,dynamic similarity conditions are derived for discrete element simulations by non-dimensionalising the governing equations.These conditions must be satisfied so that the numerical model is a good representation of the physical phenomenon.For a pure mechanical system,if three independent ratios of the corresponding quantities between the two models are set,then the ratios of other quantities must be chosen according to the similarity principles.The scalability of linear and non-linear contact laws is also investigated.Numerical tests of 3D uni-axial compression are carried out to verify the theoretical results.Another example is presented to show how to calibrate the model according to laboratory data and similarity conditions.However,it is impossible to reduce computer time by scaling up or down certain parameters and continue to uphold the similarity conditions.The results in this paper provide guidelines to assist discrete element modelers in setting up the model parameters in a physically meaningful way.