Parameter calibration of the tensile-shear interactive damage constitutive model for sandstone failure

The tensile-shear interactive damage(TSID)model is a novel and powerful constitutive model for rock-like materials.This study proposes a methodology to calibrate the TSID model parameters to simulate sandstone.The basic parameters of sandstone are determined through a series of static and dynamic tests,including uniaxial compression,Brazilian disc,triaxial compression under varying confining pressures,hydrostatic compression,and dynamic compression and tensile tests with a split Hopkinson pressure bar.Based on the sandstone test results from this study and previous research,a step-by-step procedure for parameter calibration is outlined,which accounts for the categories of the strength surface,equation of state(EOS),strain rate effect,and damage.The calibrated parameters are verified through numerical tests that correspond to the experimental loading conditions.Consistency between numerical results and experimental data indicates the precision and reliability of the calibrated parameters.The methodology presented in this study is scientifically sound,straightforward,and essential for improving the TSID model.Furthermore,it has the potential to contribute to other rock constitutive models,particularly new user-defined models.

Parameter Calibration of SWMM Model Based on Optimization Algorithm

For the challenge of parameter calibration in the process of SWMM(storm water management model)model application,we use particle Swarm Optimization(PSO)and Sequence Quadratic Programming(SQP)in combination to calibrate the parameters and get the optimal parameter combination in this research.Then,we compare and analyze the simulation result with the other two respectively using initial parameters and parameters obtained by PSO algorithm calibration alone.The result shows that the calibration result of PSO-SQP combined algorithm has the highest accuracy and shows highly consistent with the actual situation,which provides a scientific and effective new idea for parameter calibration of SWMM model,moreover,has practical guidance for flood control and disaster mitigation.

Discrete element modeling and parameter calibration of safflower biomechanical properties

Understanding the biomechanical properties of safflowers is essential for appropriately designing harvesting machinery and optimizing the harvesting process.Safflower is a flexible crop that lacks a basis for relevant simulation parameters,which causes difficulties in designing harvesting machinery.In this study,a calibration method for safflowers was proposed.First,a discrete element model was established by measuring the intrinsic parameters of a safflower,such as its geometric parameters,density,Poisson’s ratio,and modulus of elasticity.Second,the contact and bonding parameters were calibrated using a combination of physical and simulation tests.In the contact parameter tests,the Hertz-Mindlin(no-slip)model was implemented for the stacking angle tests conducted regarding the safflower filament.A regular two-level factorial design was used to determine the important factors and perform the steepest climb test.Moreover,the Box-Behnken design was adopted to obtain the optimal contact parameters.In the bonding parameter tests,the Hertz-Mindlin model with bonding contact was applied for the safflower shear simulation tests;moreover,the optimum bonding parameters were obtained through the central composite design test.The results demonstrated that the relative errors between the simulated and measured stacking angles and maximum shear were 3.19%and 5.29%,respectively.As a result,the safflower simulation parameters were accurately calibrated,providing a reference for appropriately setting the simulation parameters and designing key mechanical components.

Parameter calibration of discrete element model for alfalfa seeds based on EDEM simulation experiments

In order to establish an accurate discrete element model of alfalfa seeds,real physical experiments were combined with simulation experiments,and the contact parameters of alfalfa seeds were calibrated using the repose angle of alfalfa seeds as the response value.Some intrinsic parameters(thousand grain weight,triaxial size,density)and contact parameters(static friction coefficient,rolling friction coefficient)of alfalfa seeds were obtained through physical experiments,and a spherical particle model was established.Through the Plackett Burman experiment,the static friction coefficient between alfalfa seeds,the rolling friction coefficient between alfalfa seeds,and the static friction coefficient between alfalfa seeds and ABS plastic were determined to have a significant impact on the experiment.The steepest climb test is used to narrow down the selection range of the optimal parameters,and the box Behnken test is used to obtain the quadratic regression equation of the repose angle.The optimal parameter combination was obtained with the objective of minimizing the repose angle error:the static friction coefficient between alfalfa seeds and alfalfa seeds was 0.418,the rolling friction coefficient between alfalfa seeds and alfalfa seeds was 0.086,and the static friction coefficient between alfalfa seeds and ABS plastic was 0.471.The repose angle and mass flow rate experiments show that the model is effective and reliable.

Parameter calibration and experimental verification of discrete element simulation model for Protaetia brevitarsis larvae bioconversion mixture

To improve the survival rate of larvae during material separation after biotransformation of existing residual film mixtures of Protaetia brevitarsis larvae,this paper adopts the method of combining physical test and EDEM simulation test,and selects Hertz Mindlin with JKR contact model to calibrate the discrete element simulation contact parameters of the Protaetia brevitarsis larvae and the frass mixture.First,the cylinder lifting method was used to determine the actual repose angle of the mixture of larvae and frass.The collision recovery coefficients between larvae-frass and steel,static friction coefficient,kinetic friction coefficient and the collision recovery coefficient between larvae were measured through physical tests such as the inclined plane method.The Plackett-Burman test was then used to screen out the factors that have a significant impact on the repose angle:Poisson’s ratio of frass,frass-frass rolling friction coefficient,frass JKR surface energy,frass-larvae JKR surface energy.The optimal value intervals of four significant factors were determined based on the steepest climb test,Based on the Box-Behnken response surface analysis test,the second-order regression model between the repose angle and four significant factors was determined,and variance and interaction effects were analyzed.And with the actual repose angle as the goal,the significant factors were optimized and the optimal parameter combination of the four significant factors was determined.The simulation test of material repose angle and screening was carried out with the optimal parameter combination,and compared with the physical test.It was found that the maximum relative errors of the two tests were 1.48%and 3.79%respectively,indicating that the calibrated parameter values are true and reliable,It can provide a reference for the discrete element simulation of the transportation and separation of the Protaetia brevitarsis larvae-frass mixture.

Comparison of Parallel Genetic Algorithm and Particle Swarm Optimization for Parameter Calibration in Hydrological Simulation

Parameter calibration is an important part of hydrological simulation and affects the final simulation results.In this paper,we introduce heuristic optimization algorithms,genetic algorithm(GA)to cope with the complexity of the parameter calibration problem,and use particle swarm optimization algorithm(PsO)as a comparison.For large-scale hydrological simulations,we use a multilevel parallel parameter calibration framework to make full use of processor resources,and accelerate the process of solving high-dimensional parameter calibration.Further,we test and apply the experiments on domestic supercomputers.The results of parameter calibration with GA and PSO can basically reach the ideal value of 0.65 and above,with PSO achieving a speedup of 58.52 on TianHe-2 supercomputer.The experimental results indicate that using a parallel implementation on multicore CPUs makes high-dimensional parameter calibration in large-scale hydrological simulation possible.Moreover,our comparison of the two algorithms shows that the GA obtains better calibration results,and the PSO has a more pronounced acceleration effect.

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.

Parameter calibration of American ginseng seeds for discrete element simulation

The accurate contact parameters of American ginseng seed particles are the basis for establishing the discrete element simulation model of American ginseng seeds.The parameters of American ginseng seeds were calibrated by combining the physical tests and simulation tests together.The basic physical parameters,contact parameters and repose angle of sprouted American ginseng seeds were determined by physical tests.The simulation parameters were significantly screened by conducting the Plackett-Burman test.Meanwhile,it was determined that the collision recovery coefficient,static friction coefficient and rolling friction coefficient of interspecific contact parameters have significant influences on the repose angle of the simulation test.By the steepest climb test,the optimal interval for the value of the significance parameter was determined.Subsequently,the second-order regression equation between contact parameters and the repose angle was established,the regression equation was optimized and solved,and the best combination of simulation parameters was determined.The collision recovery coefficient between sprouted American ginseng seeds was 0.346,the static friction coefficient was 0.769,and the rolling friction coefficient was 0.490.By the calibrated seed group of American ginseng for discrete element simulation test,the average repose value angle was 38.80°,and the relative error with the measured repose angle was 0.733%.The results revealed that the simulation parameters of American ginseng seeds were reliable,which can provide a basis for the design and performance optimization of American ginseng seed-metering device in the later stage.

Calibration of Discrete Element Heat Transfer Parameters by Central Composite Design

The efficiency and precision of parameter calibration in discrete element method （DEM） are not satisfactory, and parameter calibration for granular heat transfer is rarely involved. Accordingly, parameter calibration for granular heat transfer with the DEM is studied. The heat transfer in granular assemblies is simulated with DEM, and the effective thermal conductivity （ETC） of these granular assemblies is measured with the transient method in simulations. The measurement testbed is designed to test the ETC of the granular assemblies under normal pressure and a vacuum based on the steady method. Central composite design （CCD） is used to simulate the impact of the DEM parameters on the ETC of granular assemblies, and the heat transfer parameters are calibrated and compared with experimental data. The results show that, within the scope of the considered parameters, the ETC of the granular assemblies increases with an increasing particle thermal conductivity and decreases with an increasing particle shear modulus and particle diameter. The particle thermal conductivity has the greatest impact on the ETC of granular assemblies followed by the particle shear modulus and then the particle diameter. The calibration results show good agreement with the experimental results. The error is less than 4%, which is within a reasonable range for the scope of the CCD parameters. The proposed research provides high efficiency and high accuracy parameter calibration for granular heat transfer in DEM.

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.

Modeling of flexible wheat straw by discrete element method and its parameter calibration

To simulate the bending behavior of wheat straw,a flexible straw model was developed based on the Hertz-Mindlin with bonding model using discrete element method.The proposed model was constructed by bonding straw units(filled by multi-spherical method)through parallel bonding keys.By means of a three-point bending test,single-factor sensitivity analysis and calibration of bonding parameters were performed.Results showed that elastic modulus of the flexible straw enhanced with the increase of bonded disk radius,normal stiffness per unit area and shear stiffness per unit area.The three bonding parameters were respectively calibrated to be 2.11 mm,9.48×10^(9)N/m^(3)and 4.67×10^(9)N/m^(3) by solving the regression equation developed from Box-Behnken design.The simulated elastic modulus(in terms of those three calibrated parameters)exhibited 4.20%difference with the measured one.It proved that the flexible straw could accurately demonstrate bending property of the wheat straw.This would not only help to improve accuracy in simulating wheat straw,but also provide references for flexible straw modeling and parameters calibration of other crops.

STRUCTURAL PARAMETERS CALIBRATION BY POSTURE MEASUREMENT ON PARALLEL 6-DOF PLATFORM

Some approaches to measure parallel 6-degree of freedom platform's posturestatically and to calibrate the platform's actual structural parameters by measuring a series of theplatform's varying postures are studied. In the case where high posture accuracy is requiredrelatively, to obtain the platform's actual structural parameters is very important. Threedimensions measurement with 2 theodolites are used to obtain the platform's postures statically andNewton iterative method is adopted to calibrate structural parameters. Some measures taken in themeasurement and the calibration are discussed in detail. And the experiment results of theplatform's posture control before and after the calibration are given. The results show that theplatform's posture control accuracy after the calibration is improved notably.

Calibration and experimental verification of discrete element parameters of Panax notoginseng root

Existing discrete element method-based simulation analysis of Panax notoginseng root soil separation still has the challenge to get the accurate and reliable basic parameters,which are necessary for discrete element simulation.In this paper,the P.notoginseng roots suitable for harvesting period were taken as the experimental object.Then using 3D scanning reverse modeling technology and EDEM software to establish the discrete element model of P.notoginseng,based on which,the physical and virtual tests were carried out to calibrate the simulation parameters.First,the basic physical parameters(density,triaxial geometric size,moisture content,shear modulus,and elastic modulus)and contact coefficients(static friction coefficient,rolling friction coefficient,and crash recovery coefficient between P.notoginseng roots and 65Mn steel)were measured by physical tests.Furthermore,treating the contact coefficients of P.notoginseng roots as the influence factor,the steepest uphill test,and four factors combing five levels of rotational virtual simulation are conducted.The measured relative error accumulation angle and simulation accumulation angle are set as the performance indices.The results show that the static friction coefficient,rolling friction coefficient,crash recovery coefficient,and surface energy coefficient of P.notoginseng roots are 0.55,0.35,0.16,and 19.5 J/m2,respectively.Using calibration results as parameters of the vibration separation simulation test of P.notoginseng soil,the Box-Behnken vibration separation simulation tests were carried out,in which the vibration frequency,inclination angle,and vibration amplitude of separation device as factors,screening rate and damage rate of P.notoginseng soil complex are regarded as indices.The results show that the optimal operating parameters of the separation device are the vibration frequency of 10 Hz,the inclination angle of 5°,and the amplitude of 6 cm.Based on the optimal operation parameters,the discrete element simulation experiment and field experiment of P.notoginseng roots soil separation are also performed to compare the soil three-dimensional trajectory space coordinates of P.notoginseng roots.From the results,three axis coordinate error is less than 15%.This proves that the calibration results are reliable.It can also provide the theoretical basis and technical support for the further study of the P.notoginseng root soil separation platform.

Discussion of Muskingum method parameter X

The parameter X of the Muskingum method is a physical parameter that reflects the flood peak attenuation and hydrograph shape flattening of a diffusion wave in motion. In this paper, the historic process that hydrologists have undergone to find a physical explanation of this parameter is briefly discussed. Based on the fact that the Muskingum method is the second-order accuracy difference solution to the diffusion wave equation, its numerical stability condition is analyzed, and a conclusion is drawn： X ≤ 0.5 is the uniform condition satisfying the demands for its physical meaning and numerical stability. It is also pointed out that the methods that regard the sum of squares of differences between the calculated and observed discharges or stages as the objective function and the routing coefficients C0, C1 and C2 of the Muskingum method as the optimization parameters cannot guarantee the physical meaning of X.

Friction Coefficient Calibration of Sunflower Seeds for Discrete Element Modeling Simulation

Sunflower(Helianthus annuus L.)is one of the four major oil crops in the world and has high economic value.However,the lack of discrete element method(DEM)models and parameters for sunflower seeds hinders the application of DEM for computer simulation in the key working processes of sunflower seed sowing and harvesting.The present study was conducted on two varieties of sunflower,and the DEM model of sunflower seeds was established by using 3D scanning technology based on the distribution of triaxial dimensions and volumes of the geometric model of sunflower seeds.Similarly,the physical characteristics parameters of sunflower seeds were determined by physical tests and the simulation parameters were screened for significance based on the Plackett-Burman test.Our results show that the coefficient of static friction between sunflower seeds and the coefficient of rolling friction have significant effects on the repose angle of the simulation test.Furthermore,the optimal range of the significance parameters was further determined by the steepest climb test,and the second-order regression model of the significance parameters and the repose angle was obtained according to the Box-Behnken design test and Response Surface Methodology(RSM),with the repose angle measured by the physical test as the optimized target value to obtain the optimal parameter combination.Finally,a two-sample t-test for the repose angle of the physical test and the repose angle of the simulation test yielded P>0.05.Our results confirms that the repose angle obtained from simulation is not significantly different from the physical test value,and the relative errors between the repose angle of the simulation test and the physical test are 1.43%and 0.40%,respectively,for the optimal combination of parameters.Based on these results it can be concluded that the optimal parameters obtained from the calibration can be used for DEM simulation experiments related to the sunflower seed sowing and harvesting process.

Analysis of Hydrological Simulation Models Using the Parameter Combinatorial Diagram

The aim of this paper is to present graphically the behaviour of a simulation model to the varying parameters and to establish the suitability of this representation as a valid tool for the analysis of the same parameters. In this paper, we define parameter combinatorial diagram as the joint graphical representation of all box plots related to the adjustment between real and simulated data, by setting and/or changing the parameters of the simulation model. To do this, we start with a box plot representing the values of an objective adjustment function, achieving these results when varying all the parameters of the simulation model, Then we draw the box plot when setting all the parameters of the model, for example, using the median or average. Later, we get all the box plots when carrying out simulations combining fixed or variable values of the model parameters. Finally, all box plots obtained are represented neatly in a single graph. It is intended that the new parameter combinatorial diagram is used to examine and analyze simulation models useful in practice. This paper presents combinatorial diagrams of different examples of application as in the case of hydrologic models of one, two, three, and five parameters.

Complex granular flows of sticky-wet material on flip-flow screens:Calibration of discrete element simulations

Discrete element method(DEM)is an effective approach for studying the screening process of flip-flow screens.However,there have been few studies focusing on the thick layer of sticky-wet particles on flip-flow screens.To achieve accurate simulations of the thick layer of sticky-wet particles on a flip-flow screen,firstly,the movement law of particle flow was studied,and a multi-regime combination cali-bration method based on characteristics of particle flow regimes was proposed.Based on the Plackett-Burman experiment,the curse of dimensionality caused by multi-state and multi-contact parameters was overcome.Subsequently,the lifting cylinder,rotating drum,and trampoline tests were carried out to obtain macroscopic reference values under various granular flow regimes.The calibration results were then determined using the response surface method and climbing algorithm.Finally,the calibration results were tested at both macroscopic and mesoscopic scales and compared with a commonly used calibration method.The results demonstrate that the calibration method,which considers the multi-state characteristics,improves simulation accuracy by 2%-10%and reduces the simulation error to less than 10%,thus meeting the requirements for engineering optimization of flip-flow screens.

Fourth-Order Predictive Modelling: I. General-Purpose Closed-Form Fourth-Order Moments-Constrained MaxEnt Distribution

This work (in two parts) will present a novel predictive modeling methodology aimed at obtaining “best-estimate results with reduced uncertainties” for the first four moments (mean values, covariance, skewness and kurtosis) of the optimally predicted distribution of model results and calibrated model parameters, by combining fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters. Underlying the construction of this fourth-order predictive modeling methodology is the “maximum entropy principle” which is initially used to obtain a novel closed-form expression of the (moments-constrained) fourth-order Maximum Entropy (MaxEnt) probability distribution constructed from the first four moments (means, covariances, skewness, kurtosis), which are assumed to be known, of an otherwise unknown distribution of a high-dimensional multivariate uncertain quantity of interest. This fourth-order MaxEnt distribution provides optimal compatibility of the available information while simultaneously ensuring minimal spurious information content, yielding an estimate of a probability density with the highest uncertainty among all densities satisfying the known moment constraints. Since this novel generic fourth-order MaxEnt distribution is of interest in its own right for applications in addition to predictive modeling, its construction is presented separately, in this first part of a two-part work. The fourth-order predictive modeling methodology that will be constructed by particularizing this generic fourth-order MaxEnt distribution will be presented in the accompanying work (Part-2).

Triaxial elastoplastic damage constitutive model of unreinforced clay brick masonry wall

Due to differences in the properties of composition materials and construction techniques,unreinforced masonry is characterized by low strength,anisotropy,nonuniformity,and low ductility.In order to accurately simulate the mechanical behavior of unreinforced brick masonry walls under static and dynamic loads,a new elastoplastic damage constitutive model was proposed and the corresponding subroutine was developed based on the concrete material constitutive model.In the proposed constitutive model,the Rankine strength theory and the Drucker-Prager strength theory were used to define the tensile and compressive yield surface function of materials,respectively.Moreover,the stress updating algorithm was modified to consider the tensile plastic permanent deformation of masonry materials.To verify the accuracy of the proposed constitutive model,numerical simulations of the brick masonry under monotonic and cyclic uniaxial tension and compression loads were carried out.Comparisons among the numerical and theoretical and experimental results show that the proposed model can properly reflect the masonry material mechanical properties.Furthermore,the numerical models of four pieces of masonry walls with different mortar strengths were established.Low cyclic loadings were applied and the results show that the proposed constitutive model can properly simulate the wall shear failure characteristics,and the force-displacement hysteretic curves obtained by numerical simulation are in good agreement with the tests.Overall,the proposed elastic-plastic damage constitutive model can simulate the nonlinear behavior of unreinforced brick masonry walls very well,and can be used to predict the structural response of masonry walls.

Contact parameter analysis and calibration in discrete element simulation of rice straw

Discrete element method was used to study and analyze the interaction between rice straws and between rice straw and agricultural machinery parts,thereby providing a scientific basis for post-harvest paddy field processing.Calibrations of rice straw-rice straw,rice straw-agricultural machinery part contact parameters(collision recovery coefficient,static friction coefficient and rolling friction coefficient)constitute an important prerequisite for the discrete element research process.In this study,the collision recovery coefficients of rice straw-steel and rice straw-rice straw were 0.230 and 0.357,respectively,which were calibrated by the collision method.The static friction coefficient and rolling friction coefficient of rice straw-steel were 0.363 and 0.208 respectively,which were calibrated by the inclined plate method and the slope method.The static friction coefficient and rolling friction coefficient of rice straw-rice straw were 0.44 and 0.07,respectively,which were calibrated by the split cylinder method.The paired t-test showed insignificant differences between calibration parameter simulation results and the physical test values(p>0.05).Taking the angle of repose that reflecting rice straw flow and friction characteristics as the evaluation index,the verification tests of the above calibration values indicated that the simulated angle of repose has no significant difference from the physical test value(p>0.05).The side plate lifting test on rice straw of different lengths showed no significant difference between the simulated angle of repose and the physical test value(p>0.05).This study can provide a basis for contact parameters choice in discrete element simulation analysis with rice straw-rice straw and rice straw-agricultural machinery parts as the research object.The calibration method can provide a reference for the contact parameter calibration of other crop straws.