THE LINEAR SAMPLING METHOD FOR RECONSTRUCTING A PENETRABLE CAVITY WITH UNKNOWN EXTERNAL OBSTACLES

We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the first part,we obtain the well-posedness of the direct scattering problem by the variational method.In the second part,we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity,and the shape of the external obstacle,however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.

Sampling Methods and Countermeasures for Food Enterprises

In this paper,by combining sampling methods for food statistics with years of sample sampling experience,various sampling points and corresponding sampling methods are summarized.It hopes to discover food safety risks and improve the level of food safety.

Importance Sampling Method in V-Space

Based on the observation of importance sampling and second order information about the failure surface of a structure, an importance sampling region is defined in V-space which is obtained by rotating a U-space at the point of maximum likelihood. The sampling region is a hyper-ellipsoid that consists of the sampling ellipse on each plane of main curvature in V-space. Thus, the sampling probability density function can be constructed by the sampling region center and ellipsoid axes. Several examples have shown the efficiency and generality of this method.

Sampling Methods for Efficient Training of Graph Convolutional Networks:A Survey

Graph convolutional networks(GCNs)have received significant attention from various research fields due to the excellent performance in learning graph representations.Although GCN performs well compared with other methods,it still faces challenges.Training a GCN model for large-scale graphs in a conventional way requires high computation and storage costs.Therefore,motivated by an urgent need in terms of efficiency and scalability in training GCN,sampling methods have been proposed and achieved a significant effect.In this paper,we categorize sampling methods based on the sampling mechanisms and provide a comprehensive survey of sampling methods for efficient training of GCN.To highlight the characteristics and differences of sampling methods,we present a detailed comparison within each category and further give an overall comparative analysis for the sampling methods in all categories.Finally,we discuss some challenges and future research directions of the sampling methods.

Analysis of the Linear Sampling Method for Boundary Reconstruction of Chiral Obstacle in Electromagnetic Scattering Problems

In this paper, we consider the inverse scattering by chiral obstacle in electromagnetic fields, and prove that the linear sampling method is also effective to determine the support of a chiral obstacle from the noisy far field data.

Interval sampling methods in Zagros forests using GIS

In this study, for accuracy and cost an optimal inventory method was examined and introduced to obtain information about Zagros forests, Iran. For this purpose,three distance sampling methods(compound, order distance and random-pairs) in 5 inventory networks(100 m × 100 m, 100 m × 150 m, 100 m × 200 m,150 m × 150 m, 200 m × 200 m) were implemented in GIS environment, and the related statistical analyses were carried out. Average tree density and canopy cover in hectare with 100% inventory were compared to each other.All the studied methods were implemented in 30 inventory points, and the implementation time of each was recorded.According to the results, the best inventory methods for estimating density and canopy cover were compound150 m × 150 m and 100 m × 100 m methods, respectively. The minimum amount of product inventory time per second(T), and(E%)2 square percent of inventory error of sampling for the compound 150 m × 150 m method regarding density in hectare was 691.8, and for the compound 100 m × 100 m method regarding canopy of 12,089 ha. It can be concluded that compound method is the best for estimating density and canopy features of the forests area.

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.

Research of matrix converter based on asymmetric regular sampling method SPWM control strategy

Based on the topological analysis of three-phase matrix AC to AC conversion circuit, an AC to AC nine-switch matrix isequivalent to rectification part and conversion part. The Matrix converter can be viewed as AC-DC-AC converter, the asymmetricregular sampling method SPWM(Sine Pulse Width Modulation) is studied and applied in the three-phase matrix AC to AC converter,Based on Matlab/simulink the simulation of the matrix converter with such strategy is carried out. Inductive load simulation is carriedout on the matrix converter prototype. The simulation results verify the workability of the asymmetric regular sampling method SPWMstrategy for matrix converter.

Underdetermined direction of arrival estimation with nonuniform linear motion sampling based on a small unmanned aerial vehicle platform

Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.

Reliability Sensitivity Algorithm Based on Stratified Importance Sampling Method for Multiple Failure Modes Systems

Combining the advantages of the stratified sampling and the importance sampling, a stratified importance sampling method （SISM） is presented to analyze the reliability sensitivity for structure with multiple failure modes. In the presented method, the variable space is divided into several disjoint subspace by n-dimensional coordinate planes at the mean point of the random vec- tor, and the importance sampling functions in the subspaces are constructed by keeping the sampling center at the mean point and augmenting the standard deviation by a factor of 2. The sample size generated from the importance sampling function in each subspace is determined by the contribution of the subspace to the reliability sensitivity, which can be estimated by iterative simulation in the sampling process. The formulae of the reliability sensitivity estimation, the variance and the coefficient of variation are derived for the presented SISM. Comparing with the Monte Carlo method, the stratified sampling method and the importance sampling method, the presented SISM has wider applicability and higher calculation efficiency, which is demonstrated by numerical examples. Finally, the reliability sensitivity analysis of flap structure is illustrated that the SISM can be applied to engineering structure.

A Spacecra Equipment Layout Optimization Method for Diverse and Competitive Design

The spacecraequipment layout optimization design(SELOD)problems with complicated performance con-straints and diversity are studied in this paper.The previous literature uses the gradient-based algorithm to obtain optimized non-overlap layout schemes from randomly initialized cases eectively.However,these local optimal solutions are too dicult to jump out of their current relative geometry relationships,signi􀀀cantly limiting their further improvement in performance indicators.Therefore,considering the geometric diversity of layout schemes is put forward to alleviate this limitation.First,similarity measures,including modi􀀀ed cosine similarity and gaussian kernel function similarity,are introduced into the layout optimization process.Then the optimization produces a set of feasible layout candidates with the most remarkable dierence in geometric distribution and the most representative schemes are sampled.Finally,these feasible geometric solutions are used as initial solutions to optimize the physical performance indicators of the spacecra,and diversi􀀀ed layout schemes of spacecraequipment are generated for the engineering practice.The validity and eectiveness of the proposed methodology are demonstrated by two SELOD applications.

Upgraded Analytical Protocols in Bauxite Refining Industry Using Composite Sampling Approach to Minimize Laboratory Analysis Load

The laboratories in the bauxite processing industry are always under a heavy workload of sample collection, analysis, and compilation of the results. After size reduction from grinding mills, the samples of bauxite are collected after intervals of 3 to 4 hours. Large bauxite processing industries producing 1 million tons of pure aluminium can have three grinding mills. Thus, the total number of samples to be tested in one day reaches a figure of 18 to 24. The sample of bauxite ore coming from the grinding mill is tested for its particle size and composition. For testing the composition, the bauxite ore sample is first prepared by fusing it with X-ray flux. Then the sample is sent for X-ray fluorescence analysis. Afterwards, the crucibles are washed in ultrasonic baths to be used for the next testing. The whole procedure takes about 2 - 3 hours. With a large number of samples reaching the laboratory, the chances of error in composition analysis increase. In this study, we have used a composite sampling methodology to reduce the number of samples reaching the laboratory without compromising their validity. The results of the average composition of fifteen samples were measured against composite samples. The mean of difference was calculated. The standard deviation and paired t-test values were evaluated against predetermined critical values obtained using a two-tailed test. It was found from the results that paired test-t values were much lower than the critical values thus validating the composition attained through composite sampling. The composite sampling approach not only reduced the number of samples but also the chemicals used in the laboratory. The objective of improved analytical protocol to reduce the number of samples reaching the laboratory was successfully achieved without compromising the quality of analytical results.

Determination of the full-field stress and displacement using photoelasticity and sampling moirémethod in a 3D-printed model

The quantitative characterization of the full-field stress and displacement is significant for analyzing the failure and instability of engineering materials.Various optical measurement techniques such as photoelasticity,moiréand digital image correlation methods have been developed to achieve this goal.However,these methods are difficult to incorporate to determine the stress and displacement fields simultaneously because the tested models must contain particles and grating for displacement measurement;however,these elements will disturb the light passing through the tested models using photoelasticity.In this study,by combining photoelasticity and the sampling moirémethod,we developed a method to determine the stress and displacement fields simultaneously in a three-dimensional(3D)-printed photoelastic model with orthogonal grating.Then,the full-field stress was determined by analyzing 10 photoelastic patterns,and the displacement fields were calculated using the sampling moirémethod.The results indicate that the developed method can simultaneously determine the stress and displacement fields.

Land use and cover change and influencing factor analysis in the Shiyang River Basin,China

Land use and cover change(LUCC)is the most direct manifestation of the interaction between anthropological activities and the natural environment on Earth's surface,with significant impacts on the environment and social economy.Rapid economic development and climate change have resulted in significant changes in land use and cover.The Shiyang River Basin,located in the eastern part of the Hexi Corridor in China,has undergone significant climate change and LUCC over the past few decades.In this study,we used the random forest classification to obtain the land use and cover datasets of the Shiyang River Basin in 1991,1995,2000,2005,2010,2015,and 2020 based on Landsat images.We validated the land use and cover data in 2015 from the random forest classification results(this study),the high-resolution dataset of annual global land cover from 2000 to 2015(AGLC-2000-2015),the global 30 m land cover classification with a fine classification system(GLC_FCS30),and the first Landsat-derived annual China Land Cover Dataset(CLCD)against ground-truth classification results to evaluate the accuracy of the classification results in this study.Furthermore,we explored and compared the spatiotemporal patterns of LUCC in the upper,middle,and lower reaches of the Shiyang River Basin over the past 30 years,and employed the random forest importance ranking method to analyze the influencing factors of LUCC based on natural(evapotranspiration,precipitation,temperature,and surface soil moisture)and anthropogenic(nighttime light,gross domestic product(GDP),and population)factors.The results indicated that the random forest classification results for land use and cover in the Shiyang River Basin in 2015 outperformed the AGLC-2000-2015,GLC_FCS30,and CLCD datasets in both overall and partial validations.Moreover,the classification results in this study exhibited a high level of agreement with the ground truth features.From 1991 to 2020,the area of bare land exhibited a decreasing trend,with changes primarily occurring in the middle and lower reaches of the basin.The area of grassland initially decreased and then increased,with changes occurring mainly in the upper and middle reaches of the basin.In contrast,the area of cropland initially increased and then decreased,with changes occurring in the middle and lower reaches.The LUCC was influenced by both natural and anthropogenic factors.Climatic factors and population contributed significantly to LUCC,and the importance values of evapotranspiration,precipitation,temperature,and population were 22.12%,32.41%,21.89%,and 19.65%,respectively.Moreover,policy interventions also played an important role.Land use and cover in the Shiyang River Basin exhibited fluctuating changes over the past 30 years,with the ecological environment improving in the last 10 years.This suggests that governance efforts in the study area have had some effects,and the government can continue to move in this direction in the future.The findings can provide crucial insights for related research and regional sustainable development in the Shiyang River Basin and other similar arid and semi-arid areas.

Variations of suction and suction stress of unsaturated loess due to changes in lignin content and sample preparation method

Unsaturated loess in natural sites loses stability as the overburden load continuously increases.Traditional soil modifiers such as cement and fly ash affect the surrounding environment.A new type of material,i.e.,lignin,is environmentally friendly and able to increase the strength of loess.However,the engineering characteristics of the improved loess under unsaturated conditions are not yet clear.In this study,the soil-water characteristic curves(SWCCs)of lignin-improved loess samples were determined from 0 kPa to 700 kPa using a pressure plate instrument,and then,they were fitted using the van Genuchten(VG)model and the Fredlund and Xing(FX)model.In addition,the effects of the lignin content and sample preparation methods on the SWCCs were investigated to determine the optimal lignin content and a suitable sample preparation method for loess foundations.As the lignin content increases,the matric suction and residual water content of the improved loess increase.The suction stress increases with the increasing lignin contents of 1%–2%.At lignin contents of 3%–4%,the suction stress begins to decrease and the samples prepared using the slurry method has a lower suction stress than that prepared using the wet mixing method.The air entry value(AEV)increases with increasing lignin content.In addition,scanning electron microscopy(SEM)was used to investigate the microstructural variations.It was found that after the addition of lignin,the entrapment of the loess particles by the lignin fibers created some larger particles and smaller pore diameters,which in turn led to poor connectivity of the loess pores.These changes cause the matric suction of the modified loess to increase.

Efficient sampling for decision making in materials discovery

Accelerating materials discovery crucially relies on strategies that efficiently sample the search space to label a pool of unlabeled data.This is important if the available labeled data sets are relatively small compared to the unlabeled data pool.Active learning with efficient sampling methods provides the means to guide the decision making to minimize the number of experiments or iterations required to find targeted properties.We review here different sampling strategies and show how they are utilized within an active learning loop in materials science.

A New Curve Fitting Method for Forming Limit Experimental Data

The forming limit curve （FLC） can be obtained by means of curve fitting the limit strain points of different strain paths. The theory of percent regression analysis is applied to the curve fitting of forming limit experimental data.Forecast intervals of FLC percentiles can be calculated. Thus reliability and confidence level can be considered. The theoretical method to get the limits of limit strain points distributing region is presented, and the FLC position can be adjusted according to practical requirement. Method for establishing FLC with high reliability using small samples is presented at the same time. This method can make full use of the current experimental data and the previous data.Compared with the traditional method that can only use current experimental data, fewer specimens are required in the present method to obtain the same precision and the result is more accurate with the same number of specimens.

The determination of 52 elements in marine geological samples by an inductively coupled plasma optical emission spectrometry and an inductively coupled plasma mass spectrometry with a high-pressure closed digestion method

An improved analytical method to determine the content of 52 major, minor and trace elements in marine geological samples, using a HF-HCl-HNO_3 acid system with a high-pressure closed digestion method（HPCD）, is studied by an inductively coupled plasma optical emission spectrometry（ICP-OES） and an inductively coupled plasma mass spectrometry（ICP-MS）. The operating parameters of the instruments are optimized, and the optimal analytical parameters are determined. The influences of optical spectrum and mass spectrum interferences, digestion methods and acid systems on the analytical results are investigated. The optimal spectral lines and isotopes are chosen, and internal standard element of rhodium is selected to compensate for matrix effects and analytical signals drifting. Compared with the methods of an electric heating plate digestion and a microwave digestion, a high-pressure closed digestion method is optimized with less acid, complete digestion,less damage for digestion process. The marine geological samples are dissolved completely by a HF-HCl-HNO_3 system, the relative error（RE） for the analytical results are all less than 6.0%. The method detection limits are 2–40μg/g by the ICP-OES, and 6–80 ng/g by ICP-MS. The methods are used to determine the marine sediment reference materials（GBW07309, GBW07311, GBW07313）, rock reference materials（GBW07103, GBW07104,GBW07105）, and cobalt-rich crust reference materials（GBW07337, GBW07338, GBW07339）, the obtained analytical results are in agreement with the certified values, and both of the relative standard deviation（RSD） and the relative error（RE） are less than 6.0%. The analytical method meets the requirements for determining 52 elements contents of bulk marine geological samples.