Modeling constitutive relationship of 6013 aluminum alloy during hot plane strain compression based on Kriging method

Hot plane strain compression tests of 6013 aluminum alloy were conducted within the temperature range of 613?773 K and the strain rate range of 0.001?10 s?1. Based on the corrected experimental data with temperature compensation, Kriging method is selected to model the constitutive relationship among flow stress, temperature, strain rate and strain. The predictability and reliability of the constructed Kriging model are evaluated by statistical measures, comparative analysis and leave-one-out cross-validation (LOO-CV). The accuracy of Kriging model is validated by the R-value of 0.999 and the AARE of 0.478%. Meanwhile, its superiority has been demonstrated while comparing with the improved Arrhenius-type model. Furthermore, the generalization capability of Kriging model is identified by LOO-CV with 25 times of testing. It is indicated that Kriging method is competent to develop accurate model for describing the hot deformation behavior and predicting the flow stress even beyond the experimental conditions in hot compression tests.

Reliability Analysis of Flexure Hinge Based on Kriging Method

The uncertainty widely exists in the engineering practice.Therefore,it is necessary to research the effect of uncertainty on the structural system. In this paper,the reliability and sensitivity of the flexure hinge, which is the key component of the compliant mechanisms,are investigated. The results of the reliability analysis can effectively guide the engineer to design and optimize the flexure hinge. In order to improve the calculating efficiency,the kriging method is introduced to estimate the failure probability and reliability sensitivity.

A moving Kriging interpolation-based boundary node method for two-dimensional potential problems

In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.

A Size-Dependent Functionally Graded Higher Order Plate Analysis Based on Modified Couple Stress Theory and Moving Kriging Meshfree Method

A size-dependent computational approach for bending,free vibration and buckling analyses of isotropic and sandwich functionally graded(FG)microplates is in this study presented.We consider both shear deformation and small scale effects through the generalized higher order shear deformation theory and modified couple stress theory(MCST).The present model only retains a single material length scale parameter for capturing properly size effects.A rule of mixture is used to model material properties varying through the thickness of plates.The principle of virtual work is used to derive the discrete system equations which are approximated by moving Kriging interpolation(MKI)meshfree method.Numerical examples consider the inclusions of geometrical parameters,volume fraction,boundary conditions and material length scale parameter.Reliability and effectiveness of the present method are confirmed through numerical results.

Comparison analysis of sampling methods to estimate regional precipitation based on the Kriging interpolation methods： A case of northwestern China

The accuracy of spatial interpolation of precipitation data is determined by the actual spatial variability of the precipitation, the interpolation method, and the distribution of observatories whose selections are particularly important. In this paper, three spatial sampling programs, including spatial random sampling, spatial stratified sampling, and spatial sandwich sampling, are used to analyze the data from meteorological stations of northwestern China. We compared the accuracy of ordinary Kriging interpolation methods on the basis of the sampling results. The error values of the regional annual pre-cipitation interpolation based on spatial sandwich sampling, including ME （0.1513）, RMSE （95.91）, ASE （101.84）, MSE （？0.0036）, and RMSSE （1.0397）, were optimal under the premise of abundant prior knowledge. The result of spatial stratified sampling was poor, and spatial random sampling was even worse. Spatial sandwich sampling was the best sampling method, which minimized the error of regional precipitation estimation. It had a higher degree of accuracy compared with the other two methods and a wider scope of application.

Multi-objective optimisation of a vehicle energy absorption structure based on surrogate model

In order to optimize the crashworthy characteristic of energy-absorbing structures, the surrogate models of specific energy absorption （SEA） and ratio of SEA to initial peak force （REAF） with respect to the design parameters were respectively constructed based on surrogate model optimization methods （polynomial response surface method （PRSM） and Kriging method （KM））. Firstly, the sample data were prepared through the design of experiment （DOE）. Then, the test data models were set up based on the theory of surrogate model, and the data samples were trained to obtain the response relationship between the SEA ＆amp; REAF and design parameters. At last, the structure optimal parameters were obtained by visual analysis and genetic algorithm （GA）. The results indicate that the KM, where the local interpolation method is used in Gauss correlation function, has the highest fitting accuracy and the structure optimal parameters are obtained as： the SEA of 29.8558 kJ/kg （corresponding toa=70 mm andt= 3.5 mm） and REAF of 0.2896 （corresponding toa=70 mm andt=1.9615 mm）. The basis function of the quartic PRSM with higher order than that of the quadratic PRSM, and the mutual influence of the design variables are considered, so the fitting accuracy of the quartic PRSM is higher than that of the quadratic PRSM.

Ice thickness distribution and volume estimation of Burqin Glacier No.18 in the Chinese Altay Mountains

Information on the thickness distribution and volume of glacier ice is highly important for glaciological applications;however,detailed measurements of the ice thickness of many glaciers in the Chinese Altay Mountains remain lacking.Burqin Glacier No.18 is a northeast-orientated cirque glacier located on the southern side of the Altay Mountains.This study used PulseEKKO®PRO 100A enhancement ground-penetrating radar(GPR)to survey the ice thickness and volume of Burqin Glacier No.18 in summer 2018.Together with GPR surveying,spatial distributed profiles of the GPR measurements were concurrently surveyed using the real-time kinematic(RTK)global navigation satellite system(GNSS,Unistrong E650).Besides,we used QuickBird,WorldView-2,and Landsat TM to delineate accurate boundary of the glacier for undertaking estimation of glacier ice volume.GPR measurements revealed that the basal topography of profile B1-B2 was flat,the basal topography of profile C1-C2 presented a V-type form,and the basal topography of profile D1-D2 had a typical U-type topographic feature because the bedrock near the central elevation of the glacier was relatively flat.The longitudinal profile A1-A2 showed a ladder-like distribution.Glacier ice was thin at the terminus and its thickness increased gradually from the elevation of approximately 2620 m a.s.l.along the main axis of the glacier tongue with an average value of 80(±1)m.The average ice thickness of the glacier was determined as 27(±2)m and its total ice volume was estimated at 0.031(±0.002)km3.Interpretation of remote sensing images indicated that during 1989–2016,the glacier area reduced from 1.30 to 1.17 km2(reduction of 0.37%/a)and the glacier terminus retreated at the rate of 8.48 m/a.The mean ice thickness of Burqin Glacier No.18 was less than that of the majority of other observed glaciers in China,especially those in the Qilian Mountains and Central Chinese Tianshan Mountains;this is probably attributable to differences in glacier type and climatic setting.

Distribution of Extracellular Polymeric Substances in Pilot-Scale Membrane Bioreactor

The spatial distribution of extracellular polymeric substances （EPS） in a pilot-scale membrane bioreactor （MBR） was studied. The sampling points on top of and inside the membrane module were measured and analyzed by the experimental variant function. The content of EPS was spatially interpolated by ordinary Kriging method, and il- lustrated with SURFER software. A case study was carried out in an MBR with membrane aperture of 0.4 ~tm and handling capacity of 120 ma/d in Jizhuangzi sewage treatment plant, Tianjin. From the visualization of EPS distribu- tion, it is seen that on the horizontal plane, the content of EPS was the lowest at the center; and on the vertical plane, the content of EPS decreased with the increase of depth. The shearing force caused by aeration of perforated pipe and the influent mode are the main influencing factors for this distribution.

Using Remote Sensing Data to Delineate the Lineaments for Hydrothermal Mineral Prediction in Heqing Area, Northwest Yunnan Province, China

Lineament extraction and analysis is one of the routine work in mapping medium and large areas using remote sensing data, most of which are satellite images. Landsat Enhanced Thematic Mapper （ETM） of 945×1 232 pixels subscene acquired on 21 March 2000 covering the northwestern part of Yunnan Province has been digitally processed using ER Mapper software. This article aims to produce lineament density map that predicts favorable zones for hydrothermal mineral occurrences and quantify spatial associations between the known hydrothermal mineral deposits. In the process of lineament extraction a number of image processing techniques were applied. The extracted lineaments were imported into MapGIS software and a suitable grid of 100 m×100 m was chosen. The Kriging method was used to create the lineament density map of the area. The results show that remote sensing data could be useful to extract the lineaments in the area. These lineaments are closely correlated with the faults obtained through other geological investigation methods. On comparing with field data the lineament-density map identifies two important high prospective zones, where large-scale deposits are already existing. In addition the map highlights unrecognized target areas that require follow up investigation.

Prediction of Aircraft＇s Longitudinal Motion Based on Aerodynamic Coefficients and Derivatives by Surrogate Model Approach

The accuracy of a flight simulation is highly dependent on the quality of the aerodynamic database and prediction accuracies of the aerodynamic coefficients and derivatives. A surrogate model is an approximation method that is used to predict unknown functions based on the sampling data obtained by the design of experiments. This model can also be used to predict aerodynamic coefficients/derivatives using several measured points. The objective of this paper is to develop an efficient digital flight simulation by solving the equation of motion to predict the aerodynamics data using a surrogate model. Accordingly, there is a need to construct and investigate aerodynamic databases and compare the accuracy of the surrogate model with the exact solution, and hence solve the equation of motion for the flight simulation analysis. In this study, sample datas for models are acquired from the USAF Stability and Control DATCOM, and a database is constructed for two input variables （the angle of attack and Mach number）, along with two derivatives of the X-force axis and three derivatives for the Z-force axis and pitching moment. Furthermore, a comparison of the value predicted by the Kriging model and the exact solution shows that its flight analysis prediction ability makes it possible to use the surrogate model in future analyses.

A Novel Twist Deformation Model of Soft Tissue in Surgery Simulation

Real-time performance and accuracy are two most challenging requirements in virtual surgery training.These difficulties limit the promotion of advanced models in virtual surgery,including many geometric and physical models.This paper proposes a physical model of virtual soft tissue,which is a twist model based on the Kriging interpolation and membrane analogy.The proposed model can quickly locate spatial position through Kriging interpolation method and accurately compute the force change on the soft tissue through membrane analogy method.The virtual surgery simulation system is built with a PHANTOM OMNI haptic interaction device to simulate the torsion of virtual stomach and arm,and further verifies the real-time performance and simulation accuracy of the proposed model.The experimental results show that the proposed soft tissue model has high speed and accuracy,realistic deformation,and reliable haptic feedback.

Performance prediction of magnetorheological fluid‐based liquid gating membrane by kriging machine learning method

Smart liquid gating membrane is a responsive structural material as a pressure-driven system that consists of solid membrane and dynamic liquid,responding to the external field.An accurate prediction of rheological and mechanical properties is important for the designs of liquid gating membranes for various applications.However,high predicted accuracy by the traditional sequential method requires a large amount of experimental data,which is not practical in some situations.To conquer these problems,artificial intelligence has promoted the rapid development of material science in recent years,bringing hope to solve these challenges.Here we propose a Kriging machine learning model with an active candidate region,which can be smartly updated by an expected improvement probability method to increase the local accuracy near the most sensitive search region,to predict the mechanical and rheolo-gical performance of liquid gating system with an active minimal size of ex-perimental data.Besides this,this new machine learning model can instruct our experiments with optimal size.The methods are then verified by liquid gating membrane with magnetorheological fluids,which would be of wide interest for the design of potential liquid gating applications in drug release,microfluidic logic,dynamic fluid control,and beyond.

Optimization of Shanghai marine environment monitoring sites by integrating spatial correlation and stratified heterogeneity

The water quality grades of phosphate（PO4-P） and dissolved inorganic nitrogen（DIN） are integrated by spatial partitioning to fit the global and local semi-variograms of these nutrients. Leave-one-out cross validation is used to determine the statistical inference method. To minimize absolute average errors and error mean squares,stratified Kriging（SK） interpolation is applied to DIN and ordinary Kriging（OK） interpolation is applied to PO4-P.Ten percent of the sites is adjusted by considering their impact on the change in deviations in DIN and PO4-P interpolation and the resultant effect on areas with different water quality grades. Thus, seven redundant historical sites are removed. Seven historical sites are distributed in areas with water quality poorer than Grade IV at the north and south branches of the Changjiang（Yangtze River） Estuary and at the coastal region north of the Hangzhou Bay. Numerous sites are installed in these regions. The contents of various elements in the waters are not remarkably changed, and the waters are mixed well. Seven sites that have been optimized and removed are set to water with quality Grades III and IV. Optimization and adjustment of unrestricted areas show that the optimized and adjusted sites are mainly distributed in regions where the water quality grade undergoes transition.Therefore, key sites for adjustment and optimization are located at the boundaries of areas with different water quality grades and seawater.

Mapping runoff based on hydro-stochastic approach for the Huaihe River Basin, China

Theoretical difficulties for mapping and for estimating river regime characteristics in a large-scale basin remain because of the nature of the variable under study： river flows are related to a specific area, i.e. the drainage basin, and are hierarchically organized in space through the river network with upstream-downstream dependencies. Another limitation is there are not enough gauge stations in developing countries. This presentation aims at developing the hydro-stochastic approach for producing choropleth maps of average annual runoff and computing mean discharge along the main river network for a large-scale basin. The approach applied to mean annual runoff is based on geostatistical interpolation proce- dures coupled with water balance and data uncertainty analyses. It is proved by an applica- tion in the upstream at Bengbu in the Huaihe River Basin, a typical large-scale basin in China. Hydro-stochasitic approach in a first step interpolates to a regular grid net and in a second step the grid values are integrated along rivers, The interpolation scheme includes a constraint to be able to account for the lateral water balance along the rivers. Grid runoff map with 10 km x 10 km resolution and the discharge map along the river with the 1 km basic length unit are the main results in this study. This kind of statistic approach can be widely used because it avoids the complexity of hydrological models and does not depend on the meteorological data.

Water content distribution in the surface layer of Maoping slope

The water content distribution in the surface layer of Maoping slope has been studied by testing the water content at 31 control sites.The water content profiles at these sites have also been determined.The water content distributions at different segments have been obtained by using the Kriging method of geostatistics.By comparing the water content distributions with the landform of the slope,it was shown that the water content is closely dependent on the landform of the slope.The water content distribution in the surface layer provided a fundamental basis for landslide predication and treatment.

Rotorcraft flight endurance estimation based on a new battery discharge model

To avoid the numerical complexities of the battery discharge law of electric-powered rotorcrafts,this study uses the Kriging method to model the discharge characteristics of Li-Po batteries under standard conditions.A linear current compensation term and an ambient temperature compensation term based on radial basis functions are then applied to the trained Kriging model,leading to the complete discharged capacity-terminal voltage model.Using an orthogonal experimental design and a sequential method,the coefficients of the current and ambient temperature compensation terms are determined through robust optimization.An endurance calculation model for electric-powered rotorcrafts is then established,based on the battery discharge model,through numerical integration.Laboratory tests show that the maximum relative error of the proposed discharged capacity-terminal voltage model at detection points is 0.0086,and that of the rotorcraft endurance calculation model is 0.0195,thus verifying their accuracy.A flight test further demonstrates the applicability of the proposed endurance model to general electric-powered rotorcrafts.